US20160044195A1  Imaging Device and Method for Sensing Media Type  Google Patents
Imaging Device and Method for Sensing Media Type Download PDFInfo
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 US20160044195A1 US20160044195A1 US14/295,838 US201414295838A US2016044195A1 US 20160044195 A1 US20160044195 A1 US 20160044195A1 US 201414295838 A US201414295838 A US 201414295838A US 2016044195 A1 US2016044195 A1 US 2016044195A1
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 G—PHYSICS
 G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
 G03G—ELECTROGRAPHY; ELECTROPHOTOGRAPHY; MAGNETOGRAPHY
 G03G15/00—Apparatus for electrographic processes using a charge pattern
 G03G15/20—Apparatus for electrographic processes using a charge pattern for fixing, e.g. by using heat
 G03G15/2003—Apparatus for electrographic processes using a charge pattern for fixing, e.g. by using heat using heat
 G03G15/2014—Apparatus for electrographic processes using a charge pattern for fixing, e.g. by using heat using heat using contact heat
 G03G15/2039—Apparatus for electrographic processes using a charge pattern for fixing, e.g. by using heat using heat using contact heat with means for controlling the fixing temperature
 G03G15/205—Apparatus for electrographic processes using a charge pattern for fixing, e.g. by using heat using heat using contact heat with means for controlling the fixing temperature specially for the mode of operation, e.g. standby, warmingup, error

 H—ELECTRICITY
 H04—ELECTRIC COMMUNICATION TECHNIQUE
 H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
 H04N1/00—Scanning, transmission or reproduction of documents or the like, e.g. facsimile transmission; Details thereof
 H04N1/00681—Detecting the presence, position or size of a sheet or correcting its position before scanning
 H04N1/00684—Object of the detection
 H04N1/00724—Type of sheet, e.g. colour of paper or transparency

 G—PHYSICS
 G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
 G03G—ELECTROGRAPHY; ELECTROPHOTOGRAPHY; MAGNETOGRAPHY
 G03G15/00—Apparatus for electrographic processes using a charge pattern
 G03G15/50—Machine control of apparatus for electrographic processes using a charge pattern, e.g. regulating differents parts of the machine, multimode copiers, microprocessor control

 G—PHYSICS
 G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
 G03G—ELECTROGRAPHY; ELECTROPHOTOGRAPHY; MAGNETOGRAPHY
 G03G15/00—Apparatus for electrographic processes using a charge pattern
 G03G15/50—Machine control of apparatus for electrographic processes using a charge pattern, e.g. regulating differents parts of the machine, multimode copiers, microprocessor control
 G03G15/5029—Machine control of apparatus for electrographic processes using a charge pattern, e.g. regulating differents parts of the machine, multimode copiers, microprocessor control by measuring the copy material characteristics, e.g. weight, thickness

 G—PHYSICS
 G06—COMPUTING; CALCULATING OR COUNTING
 G06K—GRAPHICAL DATA READING; PRESENTATION OF DATA; RECORD CARRIERS; HANDLING RECORD CARRIERS
 G06K15/00—Arrangements for producing a permanent visual presentation of the output data, e.g. computer output printers
 G06K15/02—Arrangements for producing a permanent visual presentation of the output data, e.g. computer output printers using printers
 G06K15/021—Adaptations for printing on specific media

 G—PHYSICS
 G06—COMPUTING; CALCULATING OR COUNTING
 G06K—GRAPHICAL DATA READING; PRESENTATION OF DATA; RECORD CARRIERS; HANDLING RECORD CARRIERS
 G06K15/00—Arrangements for producing a permanent visual presentation of the output data, e.g. computer output printers
 G06K15/02—Arrangements for producing a permanent visual presentation of the output data, e.g. computer output printers using printers
 G06K15/10—Arrangements for producing a permanent visual presentation of the output data, e.g. computer output printers using printers by matrix printers
 G06K15/102—Arrangements for producing a permanent visual presentation of the output data, e.g. computer output printers using printers by matrix printers using ink jet print heads

 G—PHYSICS
 G06—COMPUTING; CALCULATING OR COUNTING
 G06K—GRAPHICAL DATA READING; PRESENTATION OF DATA; RECORD CARRIERS; HANDLING RECORD CARRIERS
 G06K15/00—Arrangements for producing a permanent visual presentation of the output data, e.g. computer output printers
 G06K15/02—Arrangements for producing a permanent visual presentation of the output data, e.g. computer output printers using printers
 G06K15/14—Arrangements for producing a permanent visual presentation of the output data, e.g. computer output printers using printers by electrographic printing, e.g. xerography; by magnetographic printing

 G—PHYSICS
 G06—COMPUTING; CALCULATING OR COUNTING
 G06K—GRAPHICAL DATA READING; PRESENTATION OF DATA; RECORD CARRIERS; HANDLING RECORD CARRIERS
 G06K15/00—Arrangements for producing a permanent visual presentation of the output data, e.g. computer output printers
 G06K15/40—Details not directly involved in printing, e.g. machine management, management of the arrangement as a whole or of its constitutive parts
 G06K15/4065—Managing print media, e.g. determining available sheet sizes

 H—ELECTRICITY
 H04—ELECTRIC COMMUNICATION TECHNIQUE
 H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
 H04N1/00—Scanning, transmission or reproduction of documents or the like, e.g. facsimile transmission; Details thereof
 H04N1/00681—Detecting the presence, position or size of a sheet or correcting its position before scanning

 H—ELECTRICITY
 H04—ELECTRIC COMMUNICATION TECHNIQUE
 H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
 H04N1/00—Scanning, transmission or reproduction of documents or the like, e.g. facsimile transmission; Details thereof
 H04N1/00681—Detecting the presence, position or size of a sheet or correcting its position before scanning
 H04N1/00684—Object of the detection
 H04N1/00708—Size or dimensions

 H—ELECTRICITY
 H04—ELECTRIC COMMUNICATION TECHNIQUE
 H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
 H04N1/00—Scanning, transmission or reproduction of documents or the like, e.g. facsimile transmission; Details thereof
 H04N1/00681—Detecting the presence, position or size of a sheet or correcting its position before scanning
 H04N1/00729—Detection means

 H—ELECTRICITY
 H04—ELECTRIC COMMUNICATION TECHNIQUE
 H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
 H04N2201/00—Indexing scheme relating to scanning, transmission or reproduction of documents or the like, and to details thereof
 H04N2201/0077—Types of the still picture apparatus
 H04N2201/0081—Image reader

 H—ELECTRICITY
 H04—ELECTRIC COMMUNICATION TECHNIQUE
 H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
 H04N2201/00—Indexing scheme relating to scanning, transmission or reproduction of documents or the like, and to details thereof
 H04N2201/0077—Types of the still picture apparatus
 H04N2201/0082—Image hardcopy reproducer

 H—ELECTRICITY
 H04—ELECTRIC COMMUNICATION TECHNIQUE
 H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
 H04N2201/00—Indexing scheme relating to scanning, transmission or reproduction of documents or the like, and to details thereof
 H04N2201/0077—Types of the still picture apparatus
 H04N2201/0094—Multifunctional device, i.e. a device capable of all of reading, reproducing, copying, facsimile transception, file transception
Abstract
An operational imaging device and method for sensing a media type in a predetermined media set using a predetermined set of media type determining equations solved using measured values for a set of N variables measured by an operational sensor set in the operational imaging device. The solution of the equation set determines a media type. After a media type is determined, one or more operational parameters of the imaging device is selected for processing of a sheet of the determined media type. The equation set is generated by a training system using a classifier training engine. A plurality of training data sets containing measured variable values for each media type is collected under various conditions by a training sensor set that measures the set of N variables. After generation, the media type determining equation set is stored in memory of the operational imaging device.
Description
 This patent application is related to the U.S. patent application Ser. No. ______, filed June DAY, 2014, entitled “Imaging Device And Method For Determining Operating Parameters” (docket no. P611US2) and assigned to the assignee of the present application.
 None.
 None.
 1. Field of the Disclosure
 The present disclosure relates generally to imaging devices, and, more particularly, to those systems and methods for sensing types or classes of media.
 2. Description of the Related Art
 Incorrectly setting media type is a welldocumented problem for users of imaging devices, such as electrophotographic printers. Setting media properties correctly is difficult for three primary reasons. First, properly identifying media is a subjective decision. Second, paper setting menus are sometimes difficult to locate and navigate. Third, classification of equivalent media is inconsistent. Additionally, media moisture content and environmental factors may invalidate correctly chosen settings. As a consequence of this, it is common for imaging devices to operate suboptimally.
 There are consequences to improperly selected media type settings. The imaging device relies upon media type settings to control media handling, transfer, fusing, and finishing operations. Common failures related to improper media type settings include poor print quality, poor fusing, hot or cold offset, paper jams, media damage, component wear, and wrapping of the fuser by the media. This leads to user dissatisfaction.
 To address this problem, several solutions that incorporate some form of printer control based upon sensed media properties have been developed. Prior art sensor implementations describe devices that measure a single media property, or at most, a few specific properties, such as optical transmission and impedance, to provide limited media identification. Prior art control schemes are limited in scope and are based upon an incomplete characterization of the media. Such prior art systems still rely upon user input and lack a holistic approach. An idealized, fullyfeatured sensing scheme would take a single, direct measurement of all relevant intrinsic media properties and use this information to model and control the imaging device. However, the number of intrinsic property measurements required to adequately control an imaging device, such as an electrophotographic printer, without user input is prohibitive as this approach is neither cost nor space efficient and requires a large number of sensors. Prior art sensing schemes have been incomplete because they have failed to measure some number intrinsic properties of the media needed to more accurately determine the media type.
 It would be advantageous to be able to select a minimum set of sensors for an imaging device based on its intended application, such as retail use, office use, or a general purpose device suitable for a wide range of tasks; measure an extrinsic media property in lieu of several independent intrinsic media properties, and, then determine media type without the need for user intervention.
 Disclosed is a method of media type sensing for use in an operational imaging device such as an electrophotographic printer. The method comprises in one aspect: establishing a media set comprising a plurality of media types M to be used in the operational imaging device; determining a number of variables N needed to determine each media type in the media set; providing a training sensor set for measuring each of the N variables and providing corresponding output signal therefor; using the training sensor set to measure the N variables with a known sample of each media type in the media set and a training imaging device to create a corresponding training data set for each media type in the media set, wherein the measuring includes taking multiple measurements of each of the N variables; inputting each training data set for each media type into a classifier training engine; and generating, using the classifier training engine, a media type determining equation for each media type incorporating corresponding N variable terms to create a set of M media type determining equations for use with an operational set of sensors corresponding to the training set sensors.
 The method in another aspect, in an operational imaging device, comprises: storing in a memory the set of M media type determining equations; providing an operational sensor set for operable communication with the operational imaging device, the operational sensor set measuring a value of each variable in the set of N variables and providing corresponding output signals for the measured N variables for a sheet of media to be processed; converting the received output signals into the N measured normalized variable values; solving the set of M media type determining equations using the N measured normalized variable values to determine a media type from the media set for the media sheet to be processed; and, selecting, based upon the determined media type, from a look up table at least one operational parameter for the operational imaging device.
 The method in another aspect includes the measuring of multiple measurements of each of the N variables by the training sensor set occurs at a plurality of predetermined temperature and relative humidity combinations. The set of N variables comprises at least two variables selected from the group comprising: electrical impedance magnitude, electrical impedance phase, contact resistance, capacitance, optical transmission mean, optical transmission deviation, optical spectral reflectance, optical diffuse reflectance, bending stiffness, acoustic transmission, temperature, media size, relative humidity, media feed motor current, fuser temperature, transfer current, transfer voltage, media holes, preprinted areas, media color, multilayer media, RFID signal, magnetic field, MICR, and further wherein the operational sensor set includes sensors for measuring the at least two selected variables.
 The abovementioned and other features and advantages of the disclosed embodiments, and the manner of attaining them, will become more apparent and will be better understood by reference to the following description of the disclosed embodiments in conjunction with the accompanying drawings.

FIG. 1 is a schematic representation of a training system used with the presently disclosed system and methods. 
FIG. 2 is an illustration of training data sets. 
FIG. 3 is a schematic representation of an operational device employing the presently disclosed system and methods. 
FIGS. 45 illustrate two types of operational parameter ranges schemes. 
FIG. 6 illustrates the use of a matrix of media type determining equation sets to handle faulty sensors. 
FIG. 7 is a simplified block diagram of the present method of using media type determining equation sets in an operational imaging device to determine a media type. 
FIGS. 8A8B are simplified block diagrams of the present method providing for operation in the event of a faulty sensor in an operational imaging device.  It is to be understood that the present disclosure is not limited in its application to the details of construction and the arrangement of components set forth in the following description or illustrated in the drawings. The present disclosure is capable of other embodiments and of being practiced or of being carried out in various ways. Also, it is to be understood that the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of “including,” “comprising,” or “having” and variations thereof herein is meant to encompass the items listed thereafter and equivalents thereof as well as additional items. Unless limited otherwise, the terms “connected,” “coupled,” and “mounted,” and variations thereof herein are used broadly and encompass direct and indirect connections, couplings, and mountings. In addition, the terms “connected” and “coupled” and variations thereof are not restricted to physical or mechanical connections or couplings.
 Spatially relative terms such as “top”, “bottom”, “front”, “back”, “rear”, “side” “under”, “below”, “lower”, “over”, “upper”, and the like, are used for ease of description to explain the positioning of one element relative to a second element. These terms are intended to encompass different orientations of the device in addition to different orientations than those depicted in the figures. Further, terms such as “first”, “second”, and the like, are also used to describe various elements, regions, sections, etc. and are also not intended to be limiting. Like terms refer to like elements throughout the description.
 As used herein, the terms “having”, “containing”, “including”, “comprising”, and the like are open ended terms that indicate the presence of stated elements or features, but do not preclude additional elements or features. The articles “a”, “an” and “the” are intended to include the plural as well as the singular, unless the context clearly indicates otherwise.
 In addition, it should be understood that embodiments of the present disclosure include both hardware and electronic components or modules that, for purposes of discussion, may be illustrated and described as if the majority of the components were implemented solely in hardware. However, one of ordinary skill in the art, and based on a reading of this detailed description, would recognize that, in at least one embodiment, the electronic based aspects of the invention may be implemented in software. As such, it should be noted that a plurality of hardware and softwarebased devices, as well as a plurality of different structural components may be utilized to implement the invention. Furthermore, and as described in subsequent paragraphs, the specific mechanical configurations illustrated in the drawings are intended to exemplify embodiments of the present disclosure and that other alternative mechanical configurations are possible.
 It will be further understood that each block of the diagrams, and combinations of blocks in the diagrams, respectively, may be implemented by computer program instructions. These computer program instructions may be loaded onto a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions which execute on the computer or other programmable data processing apparatus may create means for implementing the functionality of each block or combinations of blocks in the diagrams discussed in detail in the descriptions below.
 These computer program instructions may also be stored in a nontransitory, tangible, computer readable storage medium that may direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable storage medium may produce an article of manufacture including an instruction means that implements the function specified in the block or blocks. Computer readable storage medium includes, for example, disks, CDROMS, Flash ROMS, nonvolatile ROM and RAM. The computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions that execute on the computer or other programmable apparatus implement the functions specified in the block or blocks. Output of the computer program instructions, such as the process models and the combined process models, as will be described in greater detail below, may be displayed in a user interface or computer display of the computer or other programmable apparatus that implements the functions or the computer program instructions.
 The term “image” as used herein encompasses any printed or digital form of text, graphic, or combination thereof. The term “output” as used herein encompasses output from any printing device such as color and blackandwhite copiers, color and blackandwhite printers, and multifunction devices that incorporate multiple functions such as scanning, copying, and printing capabilities in one device. Such printing devices may utilize ink jet, dot matrix, dye sublimation, laser, and any other suitable print formats. The term button as used herein means any component, whether a physical component or graphic user interface icon, that is engaged to initiate an action or event.
 Referring now to
FIG. 1 , a schematic representation of atraining system 10 used with present media type sensing system is illustrated. Included intraining system 10 is atrainer 12 that provides firmware that will be incorporated into one or more operational imaging devices, generally indicated 50, operational imaging devices 501 through 50K as shown. Also included intraining system 10 is a training sensor set 14, a training media set 16 comprised of M different media types, 16116M, arobot 18, atraining imaging device 22, andimaging device subsystems 24. Arobot 18 orrobotic job processor 18 is simply a machine designed to perform a function of anoperational imaging device 50. For example, where theoperational imaging device 50 is an electrophotographic printer,training system 10 may use a fuser robot that performs fusing, a transfer station robot that performs toned image transfer to a media sheet, or a media feed robot that emulates feeding media sheets. Training sensor set 14 is used to measure N different variables related to each media type in the training media set 16 or related to thetraning imaging device 22 or itssubsystems 24 to form training data sets for each media type. Thetraining imaging device 24 would be an imaging device that is substantially the same as anoperational imaging device 50 that would be used by a customer. However, thetraining imaging device 22 would be used in a laboratory or test enclosure so that environmental conditions could be controlled when making measurements as described herein.  A training sensor set 14, consisting of a predetermined collection of sensors, provides data measurement points to
trainer 12. The types and number of sensors used will be described below and will vary dependent upon the media types included in training media set 16, theambient conditions 20 to be measured, the type ofrobots 18 andtraining imaging device 22 used, and functional requirements and customer requirements for theoperational imaging devices 50. The training sensor set 14 is used in conjunction with the training media set 16, comprised of samples of M different media types and provides multiple data points for each variable in a predetermined set of N variables. Possibly included in the set of N variables that training sensor set 14 measures, as illustrated by the reflecting arrows, are those relevant to each media type M in the media set 16; ambient conditions, indicated bycloud 20, such as temperature and relative humidity where the training media set 16 is located, and variables relevant to theoperational imaging device 50 such as electrical, thermal and mechanical properties measured using therobots 18 ortraining imaging device 22. An operational imaging device designer chooses variables that will provide a resolution sufficient to determine each media type M within the training media set 16. The chosen variables N relevant to the distinguishing the media types in the training media set 16 are empirically determined and verified. For a given family ofoperational imaging devices 50, the chosen N variables to be measured using subsystems equivalent to subsystems common to each member of a given family ofoperational imaging devices 50. These subsystems may be provided in atraining imaging device 22 or may be individually provided subsystems, generally indicated 24, such a transfer station 241, fuser 242 or media feed system 243, etc. It will be noted that each media type M is tested with eachrobot 18, thetraining imaging device 22, if present, orsubsystems 24 at several different ambient conditions and measurements are also taken at a plurality of locations within the borders of the media sheet. The use ofrobots 18 and/orsubsystems 24 may obviate the need to use atraining imaging device 22.  Training sensor set 14 comprises direct sensors 141, indirect sensors 142 and subsystem response sensors 143 for one or more subsystems that will be present within the
operational imaging device 50. Such subsystems include a fuser, a toner transfer station, a media feed system, and a finisher, which may also be termed a processing device.  Direct sensor measurements are of a characteristic of the media. These direct measurements include, but are not limited to, optical, electrical impedance, reflectance, thermal capacitance, etc. A more extensive list of direct sensor measurements that may be used with the
present system 10 and operational imaging devices 50150K is provided in Table 3 below.  Indirect measurements include, but are not limited to, temperature, relative humidity, and/or the desired machine state, e.g., process speed. When such indirect measurements are made, each media type in the media set and each imaging device subsystem are measured at the desired indirect measurement points. For example, when temperature and relative humidity are being measured, each media type in the training media set 16 and each
imaging device subsystem 24 are measured at several different temperature and humidity points, such as, for example, 22° C. at 50% relative humidity, 25.6° C. at 80% relative humidity, and 15° C. at 8% relative humidity. These temperature and humidity points are environments in whichoperational imaging devices 50 may be placed. Multiple samples of each media type are measured in these different environments to generate thetraining data set 26. Other temperature and humidity conditions may also be measured.  Subsystem response measurements include change of fuser temperature occurring for each media type in the training media set 16 as they are fed through the fuser, change in transfer nip voltage or current occurring for each media type as they are fed through the transfer nip of the transfer station, media feed motor current for each media type as they are fed through the media path, and/or media location within the media path. Again these measurements may be taken at several different temperatures and relative humidity values and are included in the
training data set 26.  A single sensor in the training sensor set 14 may provide data for two or more variables in the set of N variables. For example, an impedance sensor may provide both magnitude and phase data points. The output of each sensor in the training sensor set 14 may be conditioned and normalized by
trainer 12 so that M data training sets 26 contain normalized data points. This helps to improve performance oftraining system 10.  The data for the N variables for each media type M in the training media set 16 is collected in a data set, generally designated 26, for each media type M, training data sets 261 through 26M as shown. For data in the training data sets 26 the media type or class to which that data belongs is known. For example, should training media set 16 have three media types 161163, three data sets 261263 would be collected. It will be appreciated that the number of data points within each
data set 26 will number in the thousands. In general, as the media types M to be sensed inoperational imaging devices 50 increases in number, the number of variables N measured increases so that each media type M may be determined. The measurements taken for the training data sets 26 may also account for sensor aging, sensor variability, media variability, imaging device subsystem variability to achieve a robust set of media type determining equations flexible enough to handle variability in the operational sensor set 52, in the media types and theoperational imaging devices 50. Further, multiple instances of the same sensor and multiple instances of the same type of media sheet may be used when populating the training data sets 26.  As used herein, the N variables in each
data set 26 for each media type M includes the variables types previously described such as temperature, relative humidity and corresponding imaging device variables, all as selected for inclusion in the predetermined set of N variables.FIG. 2 illustrates a 4×4 matrix of three data sets 261263 for three media types—polyvinyl M1, cardstock M2 and plain paper M3. Note that the data inFIG. 2 has not been normalized. The data points for polyvinyl M1 are indicated by a star, those for cardstock M2 by a triangle, and those for plain media M3 by a cross. For the data sets 261263, the four variables chosen by the imaging device designer to be measured are bending N1 in Watts, impedance magnitude N2 in ohms, impedance phase N3 in degrees and reflectance or gloss N4 in Volts. Clustering of the data points for each of the media types M1M3 can readily be seen. These three data sets 261263 would be processed bytrainer 12 to produce a media type determining equation set 40 having three media type determining equations.  For the purposes of developing a media type determining equation that can successfully classify media type given the different variable input magnitudes, the measured sensor values are normalized prior to training. This is because units of Ohms have no physical comparison to units of optical transmission, degrees of temperature, or percent relative humidity, etc. The goal is to compare how the media is changing with respect to its physical properties and by normalizing the inputs to the same order of magnitude this can be more easily achieved. Before training, these input values are normalized such that the magnitudes of each of the inputs are roughly equivalent over the range expected by the
operational imaging devices 50, the media types expected to be used, expected environments of use, and one or more desired machine states, for example, 40 page per minute (ppm) process speed or 70 ppm process speed. The measured values provided by the operational sensor sets 52 would also be normalized prior tocontrollers 51 solving the media type determining equations sets 40.  The M data sets 26 of N variables each are fed into a
classifier training engine 30. Using the M data sets 26,classifier training engine 30 produces as an output a media type determining equation set 40 containing M media type determining equations, where M is the number of media types and N is the number of variables. It should be understood that the number of variables N does not have to equal the number of media types M. The media type determining equation set 40 will be replicated, 401 through 40K as shown, and installed into each corresponding operational imaging device 50150K. 
Classifier training engine 30 uses a supervised machine learning algorithm used to map inputs (sensed media variables or properties like bending stiffness, electrical impedance, acoustic transmittance, optical reflectance, etc.) to a media type or class. In supervised learning, for a given input data set, the correct output is known. For data in the training data sets 26 the media type or class to which that data belongs is known. With aclassifier training engine 30, results are predicted in a discrete output and input variables are mapped to discrete classes or type—here discrete media types. Once the media type determining equations are formed, these equations, when placed in theoperational imaging devices 50, take measured variable values from the operational sensor set 52 as inputs and use them to determine the best class (i.e. media type). The measured variable values are also termed instances. Classification into one of the several media types may be done by multiclass classification or by combining multiple binary classifiers that deal with only two classes at a time. A classification scheme is advantageous since programs in many existing imaging device controllers are based upon a discrete categorization of media into type, weight, and roughness. 
Classifier training engine 30 may be one of well known classification engines as known in the art that analyze data and recognize patterns for classification. These include a support vector engine 301, a neural network 302, a quadratic classifier 303, a Bayesian network 304, or a learning vector quantizer 305.Classifier training engine 30 operates on the data sets 26126M to produce the multivariable media type determining equation set 40. The media type determining equation set 40 may be constructed many different ways. In one embodiment (created using regression techniques), it resembles a higher order multivariable polynomial. In another embodiment (created using neural networks), it resembles two theta matrices. The form of the media type determining equation will be determined by the type of classifier training engine used intrainer 12. Note that, once determined, the media type determining equation may be manipulated to take any convenient mathematical form.  Two optional elements are shown in
FIG. 1 . These are apolynomial consolidator 32 and expert knowledge cost/value weighter 34. Where the equation set 40 comprises polynomial equations, an optionalpolynomial consolidator 32 may also be provided to operate on each of the M equations in the set ofmedia determining equations 40 to reduce the number of terms in each equation M. Using apolynomial consolidator 32 reduces the number of terms in each polynomial equation in the media type determining media set 40, and, in turn, the memory and processing power needed bycontrollers 53 in operational imaginingdevices 50.  An example implementation of
polynomial consolidator 32 will now be described. The following nomenclature is a representative notation for whenclassifier training engine 30 is a support vector machine, which include examples such as LeastSquares Support Vector Machines (LSSVM) and Fast Support Vector Machines (FSVM) and many others. For the purposes of this illustration of thepolynomial consolidator 32 for use in embedded classification systems to be employed inoperational imaging devices 50, a LSSVM is shown the illustrated implementation where:  p: number of variables;
 x: current set of measurements to be classified, a vector of length p;
 m_{k}: measurement vector from the training data set, with length p, associated with the kth training data point;
 α_{k}: weight associated with the kth training data point;
 y_{k}: true classification (usually coded +1 or −1, but could be another form) associated of the kth training data point;
 b: linear bias offset term; and
 N: number of training data points.
 The method of arriving at these quantities is as follows: generally, the set of N vectors m_{k}, k=1, . . . , N and their corresponding true classifications y_{k }are arrived at through experimentation or other means of creating example data points that characterize the categories, i.e., the media types, that are to be used in the classification. For example, if one were trying to distinguish a class A and a class B, one might measure the characteristics of examples from class A, and also measure the characteristics of examples from class B. For each example, the characteristic features, or measurements, are aggregated in a corresponding vector m_{k}. N would then be the sum of the number of examples from class A and class B. The weights α_{k }are arrived at through a training process, which differs somewhat for different classification algorithms, and, for the purposes of polynomial consolidation, the method by which they are attained is not important.
 The resulting classification function, C(x), may also depend to some degree on the particular classification algorithm. The polynomial consolidation methodology applies to any classification function that one might apply in this manner as long as it is continuous on a bounded interval of interest. By the Weierstrass approximation theorem, it is well known that any function that meets this criteria can be arbitrarily closely approximated by a polynomial function. For example, many implementations of neural network classifiers utilize continuous functions such as the sigmoid function or alternatively the hyperbolic tangent as a key component.
 In the LSSVM with a polynomial kernel implementation the classification function is set for in Eq. 1:

C(x)=sign[Σ _{i=1} ^{N}α_{k} y _{k}(m _{k} ^{T} x+b)^{d}] Eq. 1  In this form, d is an integer that provides the degree of the polynomial, and the other terms are as described previously. This form of classifier can have very high performance depending on the characteristics of the system in which it is operating. However, the level of performance increases as the value of N increases. If the performance desired is obtained only after using N=1000 or more examples, then in order to compute C(x), 1000 sums must be performed. In addition, the values of α_{k}, y_{k}, b and m_{k }must be stored in memory in order to compute the classification function.
 For embedded systems the computational complexity and memory requirement is a significant disadvantage and in many implementations could force the addition of significant cost to a product in order to incorporate the computational power and memory needed to accommodate the classification function. Polynomial consolidation addresses this problem of computational complexity and memory footprint. Instead of evaluating potentially thousands of terms, the function can be represented by a polynomial.
 Certainly, each of the N terms would contribute a different function. In the case of the polynomial form mentioned above, in a LSSVM
classifier training engine 30, each of the N terms would contribute a term as shown in Eq. 2: 
α_{k} y _{k}(m _{k} ^{T} x+b)^{d} Eq. 2  Considering the transposed vector multiplied by another vector is an inner product and assuming the components of m_{k }are [a_{k}, b_{k}, c_{k}, . . . ]^{T }the result is the expression shown in Eq. 3:

α_{k} y _{k}(α_{k} x _{1} +b _{k} x _{2} +c _{k} x _{3} +d _{k} x _{4 } . . . +b)^{d} Eq. 3  This can be expanded via the multinomial theorem's formula, shown in Eq. 4:

$\begin{array}{cc}{\left({s}_{1}+{s}_{2}+\dots +{s}_{q}\right)}^{d}=\sum _{{k}_{1}+{k}_{2}+\dots +{k}_{q}=d}\ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89e\left(\begin{array}{c}d\\ {k}_{1},{k}_{2},\dots \ue89e\phantom{\rule{0.8em}{0.8ex}},{k}_{q}\end{array}\right)\ue89e\prod _{1\le j\le q}\ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89e{x}_{j}^{{k}_{j}}\ue89e\text{}\ue89e\phantom{\rule{1.1em}{1.1ex}}\ue89e\mathrm{where}\ue89e\text{}\ue89e\phantom{\rule{1.1em}{1.1ex}}\left(\begin{array}{c}d\\ {k}_{1},{k}_{2},\dots \ue89e\phantom{\rule{0.8em}{0.8ex}},{k}_{q}\end{array}\right)=\frac{n!}{{k}_{1}!\ue89e{k}_{2}!\ue89e\dots \ue89e\phantom{\rule{0.8em}{0.8ex}}\ue89e{k}_{q}!},& \mathrm{Eq}.\phantom{\rule{0.8em}{0.8ex}}\ue89e4\end{array}$  a binomial coefficient
 Once terms are expanded out for each data point, the result is a list of multivariate polynomials where the coefficients are related to α_{k}, y_{k}, b, d and m_{k}, and the variables are the features or measurements of the data point to be classified, namely x_{1}, x_{2}, . . . , x_{p}, with the number of multivariate polynomials being the number of data points used in the classification (the support vectors).
 As an example, consider a system with a second order polynomial classifier where there is one sensor, whose value to be classified is x, and three data points m_{1}, m_{2}, m_{3 }that were used to train the classifier. Since it has already been trained, we also have the corresponding weights α_{1}, α_{2}, α_{3}, corresponding true values y_{1}, y_{2}, y_{3}, and corresponding offset number T. The classifier would then have the form shown in Eq. 5:

y=sign [α _{1} y _{1}(m _{1} x+τ)^{2}+α_{2} y _{2}(m _{2} x+τ)^{2}+α_{3} y _{3}(m _{3} x+τ)^{2}] Eq. 5  If we consider the portion within the brackets Eq. 6 results:

α_{1} y _{1}(m _{1} x+τ)^{2}+α_{2} y _{2}(m _{2} x+τ)^{2}+α_{3} y _{3}(m _{3} x+τ)^{2}=α_{1} y _{1}(m _{1} ^{2} x ^{2}+2m _{1} τX+τ ^{2})+α_{2} y _{2}(m _{2} ^{2} x ^{2}+2m _{2} τx+τ ^{2})+α_{3} y _{3}(m _{3} ^{2} x ^{2}+2m _{3} τX+τ ^{2}) Eq.6  Due to the multinomial theorem as discussed above, we can then collect like terms in x, resulting in an expression of the form c_{1}x^{2}+c_{2}x+c_{3}. In this case, c_{1}=α_{1}y_{1}m_{1} ^{2}+α_{2}y_{2}m_{2} ^{2}+α_{3}y_{3}m_{3} ^{2}, and similarly the terms can be collected to develop expressions for c_{2 }and c_{3 }and any other constants for the expression.
 In this example, in the final product implementation only c_{1}, c_{2}, and c_{3 }need to be stored in order to classify the new data point, and the savings in both memory footprint and computational complexity are significant, decreasing the potential cost of implementing the classification system in
operational imaging device 50. While this becomes a complicated process for more training data points and more variables, the method illustrated is a framework for solving the problem, which can be automated using computer algebra systems.  The expert knowledge cost/
value weighter 34 may be employed to adjust the weighting of the coefficients in the M media type determining equation set 40. Intrainer 12, generally a cost/value function that is being optimized—that is, starting with some initial “guess” of the best weightings for the function, a cost function is evaluated and properties that are uncovered during this evaluation are used to refine the “guesses” of the weight values until an optimal classifier training engine for that form is found. Generally, the cost/value function lends itself well to optimization, and properties such as convexity of the cost function are very desirable as it leads to a wellstudied set of optimization solution methodologies. In some instances some “allowable” confusion between categories (i.e. media types) may exist, depending on certain conditions. These conditions could be based on areas or ranges of features, or any other sensor or condition for which an expert may have intrinsic knowledge. This may also be referred to as expert knowledge. When an error between two categories is allowable (i.e., a particular type of mistake made may not invalidate the results of the multiclass classification) then the idea is not to penalize that error as harshly. Extending this further, if under different conditions, the importance of correctness differs, then penalties can be adjusted accordingly. This may be implemented using an expert weighting term c_{k} ^{(q) }that comes from an expert weighting matrix, C_{q}, which codifies the expert knowledge and is specific to the ith classifier.  An example of expert knowledge cost/
value weighter 34 for a simplified media set will now be described. The set of q weighting matrices, as an example with media types A, B, and C, might look like the form (the value in the table is what c_{k} ^{(q) }would be):  For q=1

TABLE 1 Matrix 1 A B C A 1 0.1 0.5 B 0.1 1 1 C 0.5 1 1  For q=2

TABLE 2 Matrix 2 A B C A 1 1 0.1 B 1 1 1 C 0.1 1 1  There will be a matrix for each q until q=N, with N being the total number of variables. Rows indicate the current classifier, and columns correspond to the true class of a given training data point. In this case, for variable 1 (when q=1,) it is acceptable to confuse A and B, so if we are looking at point k from the perspective of the classifier for media types A or B, the corresponding c_{k} ^{(1)}=c_{k} ^{(2)}=0.1. Similarly, it is less acceptable to confuse media types A and C, so for either of those classifiers, the corresponding classifier will weight that error with c_{k} ^{(1)}=c_{k} ^{(3)}=0.5. For an error that is unacceptable it can be weighted as c_{k} ^{(q)}=1 or even higher. It is only the relative values of these terms that matter, so it is general practice to normalize all of them to 1. Condition 2 (when q=2) has A and C with acceptable confusion, so that is codified c_{k} ^{(1)}=c_{k} ^{(3)}=0.1 but the rest of the cases are deemed unacceptable. The number of different weights is only limited by designer choice, and could also be a continuous or discontinuous function of the variable. The example here is a simple one to make illustration clear.
 Other forms of a
polynomial consolidator 32 may be employed, and the form of polynomial consolidator used should not be considered a limitation of the presently disclosed method. Also other forms of an expert knowledge cost/value weighter 34 may be employed, and the form of the expert knowledge cost/value weighter 34 used should not be considered a limitation of the presently disclosed method.  As part of the training process, a test data set may be used to validate media type determining equation set 40. This is done by separating the entire training data sets 26126M into two subsets. A training data set comprising about ⅔ of the entire data sets 26126M is randomly selected and is used to develop the media type determining equations. A test data set comprising the remaining ⅓ of the entire data sets 26126M is used to empirically evaluate the media type determining equations generated from the ⅔ training data set. This validation technique is well known to one of skill in the art.
 Media type determining equation set 40 is replicated, indicated as 40140K, in firmware, generally indicated 53, to be used in each of the
operational imaging devices 50. As shown, media type determining equation sets 40140K are provided in firmware 53153K of operational devices 501 through 50K, respectively. A single media type determining equation is produced for each type of media M in the training media set 16 so that there are M number of equations in the media type determining equation set 40.  As the number of variables N increases, the complexity and number of terms in each media type determining equation increases. Each media type determining equation is comprised of multiple terms with corresponding constant coefficients for each variable of the N variables. However, where the media type determining equations are polynomial equations, by use of polynomial consolidation techniques such as the one discussed previously, the number of terms and coefficients needed in these equations may be reduced and these consolidated equations form media determining equation sets 40140K used by each controller 51151K to determine media type. Consolidated equations mean a more rapid determination of media type providing real time response in each operational imaging device 50150K to changing media types being processed. As is known in the art, the media type determining equations may be represented in any convenient mathematical manner that closely approximates the solution, for example a Taylor polynomial. In one form
classifier training engine 30 produces a function, comprised of the M media type determining higher order polynomial equations comprising the media type determining equation sets 40140K, that will be used in each operational imaging device 50150K to be used for a given application. Variable measurement values taken by the operational sensor set 52152K in each operational imaging device 50150K are then input to the function (i.e., the M media type determining equations) to determine the type of media sensed.  Using
training system 10 to develop the coefficient matrix for each of the M media type determining equations in the media type determining equation set 40 to control theimaging device 50 easily allows for the inclusion of additional sensors.Training system 10 therefore allows for expansion and/or changes of the selected variables N that may be needed with other imaging products to work optimally.Training system 10 is easily expandable and adaptable to future imaging devices and future media types. 
Operational imaging devices 50 are those that would be provided to users for a specific application, such as a retail application, an office application, or a general purpose application, etc. Operational imaging devices 50150K would be distributed to different locations for use by various end users. Operational imaging devices 50150K would have the same processing devices, e.g., the same fuser types, transfer stations, media feed systems and firmware. Should the processing device hardware or the customer requirements change, then the media type determining equation set 40 would have to be redetermined for the new hardware configuration. Operational devices 50150K include controllers 51151K and an operational sensor set 52152K. Media sheets 60160K are readied to be processed by their corresponding operational imaging devices 50150K. Operational sensor sets 52152K measure the values of the same N variables that were used in the set of N variables that were measured by the training sensor set 14 and provide those measured data values to controllers 51151K. The individual sensors in each of operational sensor sets 52152K may be the same as or similar to those used in training sensor set 14. Controllers 51151K utilize the measured N variable values provided by the operational sensor sets 52152K to solve the media type determining equation sets 40140K stored in firmware 53153K to determine a media type. For example, in operational imaging device 501, operational sensor set 521 provides measured values for the set of N variables as a sheet of media 601 is readied for processing. Controller 511 uses the measured N variable values to solve the media type determining equation set 401, to produce a determined media type 541 which is the highest valued media type determining equation solution found using the variable values measured by operational sensor set 521.  Using the determined media type 541, controller 511 then utilizes lookup table 551 to select a one or more operational parameters 561 to be used by operational imaging device 501 or a subsystem therein to process the readied media sheet 601 to produce a processed media sheet 611. A similar process would be occurring in each of operational imaging devices 50250K to create processed sheets 61261K. However, the operational parameter or parameters selected in those operational imaging devices 50250K will depend on which media type was the determined media type sheets 60260K.
 During training, the extrinsic properties to be measured are selected to closely relate to
operational imaging device 50 functions. This increases success in sensing media types and reduces the number of required sensors. Where theoperational imaging device 50 is an electrophotographic printer, media interacts with three major printer subsystems: media handling, toner transfer, and fusing. It follows that sensed variables or characteristics may be closely related to the fundamental operation of these subsystems. The present media type determining method may also use as a variable one or more of the following variables or characteristics: lumped electrical time response (toner transfer), lumped thermal time response (fusing), mechanical composition (media handling), and other characteristics (e.g., size, temperature, relative humidity).  At a transfer station, an electric field is generated to move charged toner particles from a donor substrate to the media. Electrical characteristics of the media dictate how quickly the electric field will build and what the field strength will be for an applied voltage. Functionally, it is important to know the time response of media to a given voltage input. Appropriate intrinsic measurements for lumped electrical time response may include one or more of a volumetric measure of impedance (magnitude and phase angle), electrical time constant (resistance and capacitance), or some other similar metric.
 In the fuser, temperature and pressure are applied to transfer heat to the media, melt toner, and affix it to the media. The lumped thermal characteristics of the media dictate how quickly heat will transfer into the sheet and how much heat must be transferred to adequately melt toner. Appropriate intrinsic measurements may include a bulk measurement of thermal mass (mass and specific heat), thermal time constant (heat transfer coefficient, specific heat, density, and thickness), thermal diffusivity (density, specific heat, and thermal conductivity), or some other similar metric.
 Within the
operational imaging device 50, media is conveyed through the system via driven rollers. Mechanical characteristics of the media dictate how much drag the media generates in the media path and how much torque the system must provide to transport the media. Appropriate intrinsic measurements might include bending stiffness (elastic modulus and area moment of inertia), coefficient of friction, or some other similar metric.  Media acclimation (temperature and relative humidity) and the desired machine state (process speed) may also affect each of these three media characteristics. For example at high ambient temperature and relative humidity one media type containing more moisture than at standard temperature and relative humidity conditions, may be better processed using settings for another media type.
 An understanding of these three media characteristics (lumped electrical time response, lumped thermal time response, and mechanical composition) is necessary to sufficiently control print processes. If sensors are chosen to closely map to functionallyrelevant extrinsic properties that relate to printer function, adding additional sensors to measure additional characteristics only slightly increases performance of the system. Other measurements that loosely correlate to these intrinsic properties may also be of value. An example would be the imaging device subsystem responses.
 Media properties may be sensed using a wide variety of possible measurement techniques. Using the fundamental media characteristics just discussed as a guidepost helps limit the set of possibilities. Additionally, the measurement technique or sensing methods would be safe, unobtrusive, compact, energy efficient, inexpensive, and sample rapidly. Measurements should avoid containing redundant information. The sensing methods should be sufficiently independent or be decoupled from one another. This general design guideline provides the
classifier training engine 30 with better performance and reduces the number of required sensors and/or measured variables N.  The following describes a variety of sensor types that may be used to make the measurements for the selected variables in the set of N variables. Sensors include those that measure electrical impedance, bending stiffness, optical reflectance, optical transmission, and acoustic transmission. The following extrinsic measurement techniques were selected because they enable the
system 10 andoperational imaging devices 50 to take measurements that closely correlate to the fundamental media properties listed above.  Impedance phase angle and magnitude are derived from media response to an AC voltage applied across the thickness of the sheet while it is staged in a pair of metal rollers. From this, media resistance or capacitance may be calculated. In one embodiment, a 10 KHz wave of 1 volt was sufficient excitation for characterization. This sensor provides an output that closely correlates to lumped electrical time response (electrical impedance or resistance and capacitance).
 Media bending stiffness is measured as a function of a sheet resistance to deformation. The motor current (torque) required to drive a bar that bends a staged sheet is measured. This torque directly correlates to the media modulus of elasticity and area moment of inertia. This sensor provides an output that closely correlates to mechanical composition (bending stiffness). An example of a media stiffness sensor may be found in copending U.S. patent application Ser. No. 14/145,601, entitled “Media Stiffness Sensor Assembly For An Imaging Device,” and Ser. No. 14/145,661, entitled “Method Of Using An Imaging Device Having A Media Stiffness Sensor Assembly” both filed Dec. 31, 2013.
 A pair of photodiodes is used to measure the ratio of specular and diffuse light emitted by an LED and reflected off the surface of a media sheet. The ratio serves as a relative measure of roughness. This sensor provides an output that closely correlates to mechanical composition (coefficient of friction) and loosely correlates to lumped electrical time response and lumped thermal time response (contact resistance).
 An acoustic wave is generated using a piezoelectric transducer or a speaker. The energy content in the wave is dampened as it propagates through the media sheet. The amount of transmitted acoustic energy correlates to the mass of the system. This sensor provides an output that closely correlates to lumped thermal time response (thermal mass).
 An optical transmission sensor measures an amount of light transmitted through a media sheet. The optical transmittance sensor is an infrared LED and a photodetector pair. The infrared LED emits light on one side of the sheet. The photodetector is positioned on the other side of the sheet and measures the quantity of light that is transmitted through the sheet. Several measurements are taken as the sheet is moved by the sensor and an optical average and optical standard deviation are calculated. The transmitted energy is a function of the opacity of the media sheet which correlates to thickness or mass of the media sheet. This sensor provides an output that closely correlates to lumped thermal time response (thermal mass).
 A purpose of the present media sensing system is to use the minimal number of independent extrinsic measurements necessary to develop the media type determining equation set 40 capable of training an
operational imaging device 50 that meets the user application. Applications which use limited sets of known media types or that can accept misclassifications of media types without a significant negative impact can be successfully controlled with fewer sensors. Alternatively, additional measurements and/or sensors may be added to improve accuracy and robustness. Table 3 provides example operational sensor sets that would meet several different levels of performance requirements. 
TABLE 3 Operational Sensor Sets Of Varying Cost And Complexity Sensor Set 1: Sensor Set 2Sensor Set 3Media High Intermediate Low Property Resolution Resolution Resolution Lumped Thermal Diffusivity Acoustic N/A Thermal Acoustic Transmission Transmission Time Microwave Response Transmission Heat Capacity Lumped Impedance Phase Impedance Phase Impedance Electrical Impedance Magnitude Impedance Magnitude Time Resistance Magnitude Response Capacitance Contact resistance Dielectric constant Mechanical Bending Stiffness Optical Optical Composition Thickness Transmission Transmission Acoustic Absorption Mean Mean XRay Optical Optical Optical Transmission Transmission Transmission Mean Deviation Deviation Optical Transmission Optical Deviation Spectral Optical Spectral Reflectance Reflectance Optical Diffuse Reflectance Image Capture/Process Laser Profilometry Other Temperature Temperature N/A Variables Relative Humidity Relative Media Size Humidity Transfer Current Media Feed Motor Transfer Voltage Current Fuser Temperature Media Feed Motor Current RFID Magnetic Field Media Holes MICR Preprinted Areas Media Color Multilayer Media  Table 3 outlines several sensor sets that provide varying degrees of functionality and, in turn, resolution to discern various media types. It should be noted that optical transmission and optical transmision variation may also be listed as being lumped thermal response variables in that media thickness affects both thermal properties and mechanical properties. Optical transmission may also be referred to as optical transmission. For example, sensor set 3 would result in the ability to classify plain paper, cardstock, and polyvinyl labels at ambient environmental conditions. A more fullyfeatured control scheme may incorporate impedance phase, optical spectral reflectance, media feed motor current, and acoustic transmission sensors in addition to a temperature and humidity sensor (sensor set 2). Sensor set 2 would provide the ability to additionally discern light weight, heavy weight, glossy, and bond paper across class B environmental conditions. Sensor set 1 may, for example, be used to distinguish media having holes or perforations, media having preprinted portions, multiweb media, media having magnetic ink or RFID tags, light cardstock, cardstock, heavy cardstock, paper labels, heavy paper labels, vinyl labels, heavy vinyl labels, transparencies, light glossy media, glossy media, heavy glossy media, rough/cotton media, envelopes, heavy envelopes, and polymeric film.
 Use of the image capture, for example, would provide some of the additional capabilities such as recognizing media having holes or preprinted portions. Optical sensors may be used to detect holes. Image capture may be done by use of charge coupled imaging device. Magnetic field may be detected by use of a Hall effect sensor. An RFID reader may be used to sense RFID tags.
 Referring now to
FIG. 3 , there is shown a diagrammatic depiction of an example operational imaging device 50K. Controller 51K is operatively coupled to operational sensor set 52K having a plurality of output signals provided to controller 51K viacommunication link 100. In one form, operational sensor set 52K consists of a base sensor set 52K1 consisting of temperature, relative humidity, impedance and optical transmission sensors S1S4, respectively, and additional sensor set elements consisting of reflectance, media feed motor current, media stiffness sensors S5S7, respectively, through sensor SX where sensor SX is any additional sensor selected by the designer. The composition of the base sensor set 52K1 is a matter of design choice and the intended application of operational imaging device 50K. For example, another base sensor set may be comprised of sensors S3S7. The types of sensors in the base sensor set 52K1 and the additional sensor set elements are meant only to be illustrative, and are not intended to be limited to only those sensors shown. Because one sensor may provide data values for two or more of the variables in the set of N variables, the number of sensors SX may be less than the number of variables N that are measured.  The N signal outputs, designated NSO, from operational sensor set 52K are provided to controller 51K via communications link 100. The NSO are measured values of each variable in the set of N variables. As shown, NSO are provided to signal conditioning circuit 51K1 and signal normalization circuit 51K2 for conditioning and range normalization to produce an input set of N measured variable values 51K3. Note that signal conditioning and normalization steps may also be performed by firmware. At firmware 53K, the set of N measured inputs variables are processed by controller 51K to solve media type determining equation set 40K to produce a determined media type 54K. Using determined media type 54K as a selector for lookup tables 55K, one or more operational parameters 56K are selected by processor 51K. As shown, lookup tables 55K1 through 55KP are provided to select operational parameters 56K156KP. The number and type of operational parameters 56K156KP selected are a matter of design choice and the set of N measured input variable values 51K3. Using
communication link 100, the operational parameters 56K156KP are provided to processing device PDK.  The media sheet 60K which is to be processed is provided to processing device PDK which produces processed media sheet 61K. Media sheet 60K may be media to be printed 60K1 or images to be scanned 60K2. Processing device PDK may, in one form, be a printer or print engine PDK1 or, in another form, a scanner system PDK2. Printer PDK1 may be an electrophotographic printer or an ink jet printer or other printer types as known in the art. Printer PDK1 is illustrated as an electrophotographic printer having a fuser F, a toner transfer station TTS, a finisher unit FU providing hole punching and stapling, and media feed system MFS. Scanner system PDK2 is illustrated as having a media feed system SMFS, an automatic document feeder ADF, a scan bar SB1, and a flatbed scan bar SB2. Where automatic document feeding or duplex scanning are not needed, the ADF and scan bar SB1 are not used. When processing device PDK is printer PDK1, operational parameters 56K may be provided, for example, to fuser F, toner transfer station TTS, finisher unit FU, and media feed system MFS of printer device PDK1. When processing device PDK is scanner PDK2, operational parameters 56K may be provided, for example, to media feed system SMFS, ADF scan bar SB1 and flatbed scan bar SB2.
 As used herein, the term “communications link” is used to generally refer to structure that facilitates electronic communication between multiple components, and may operate using wired or wireless technology. Controller 51K includes a processor unit and associated memory 57K, and may be formed as one or more Application Specific Integrated Circuits (ASIC). Memory 57K may be, for example, random access memory (RAM), read only memory (ROM), and/or nonvolatile RAM (NVRAM). Alternatively, memory 57K may be in the form of a separate electronic memory (e.g., RAM, ROM, and/or NVRAM), a hard drive, a CD or DVD drive, or any memory device convenient for use with controller 51K. Firmware 53K may reside in memory 57K. Controller 51K may be, for example, a combined printer and scanner controller.
 Also illustrated in
FIG. 3 is an alternative approach to determining media type. When the media type determining equation set 40K is being solved by controller 51K, the solution of two or more of the equations in the media type determining equation set 40K may be within a predetermined range of one another. Should this arise, acomparator 58 may be used to determine when two or more of the solutions are within a given range of each other, and, based on the equations involved, a lookup table 59 in memory 53K may be used select one solutionone media type. For example, should media type determining equation set have eight equations andequations equations 
FIGS. 45 illustrate two arrangements for the various operational parameters 56K1 through 56KP that are chosen. In both figures, the abscissa is the range of an operational parameter and the ordinate is a media type. In both figures, three media types M1, M2, M3 are shown in rectangles, the width of which indicates the range of a given operational parameter P. InFIG. 4 , the range of operational parameter P for media type M1 does not overlap range of operational parameter P used for media type M2, and, similarly, between the operational ranges of operational parameter P and media types M2 and M3. InFIG. 5 , the range of operational parameter P for media type M2 overlaps that for media type M1 at one end and that of media type M3 at the other as indicated by RO. While the method shown inFIG. 4 would be more desirable, hardware limitations sometimes preclude setting operational parameters in this manner. When operational parameter range overlap is used, theoperational imaging device 50 should be able to provide acceptable output for either setting for media classified in either type. This may be seen as a simpler form of expert weighting. 
FIG. 6 illustrates a further structure that may be used for the media type determining equation set 40. Occasionally, a sensor within the operational sensor set 52 may fail. The sensor may stop working entirely or the output signal of the sensor may drift outside of an expected range. In either case this may be addressed by providing additional sets of media determining type equation sets. Assuming that all combinations of malfunctioning sensors are detectable, media type determining equation set 40 would be replaced with media type determining equation setmatrix 40′ comprised of a total of S!+1 media type determining equation sets where S is the total number of sensors in operational sensor set 52. The first set operational sensor set SS1 would be one in which all S sensors are functioning. The second operational sensor set SS2 would be one in whichsensor 51 is faulty, the third set SS3 is one where sensor S2 is faulty, and so on where sensor set SSS! is the penultimate faulty sensor set and sensor set SSS!+1 is the final faulty sensor set. In creating the media type determining equation sets for the various combinations of faulty sensors (or conversely for the various combinations of remaining functional sensors),training system 10 would use only that data within each of the training data sets 26126M that corresponds to the remaining functioning sensors within operational sensor set 52. For example, supposesensor 1 andsensor 3 were faulty in operational imaging device 50K, the media type determining equation set withinmatrix 40′ of media type determining equation sets selected for use would be that where the data supplied bysensors matrix 40′ may be reduced to eliminate the reliable sensors when creatingmatrix 40′. Further, if the total number of faulty sensors exceeds a predetermined number, or the expected performance of the system drops below a predetermined acceptable failure threshold,operational imaging device 50 would declare itself to be nonfunctional and issue a service request. 
FIG. 7 provides a simplified flow chart of the present method. For method M100, the actions of blocks B10B50 would occur using thetraining system 10 while those of blocks B60B120 would occur in eachoperational imaging device 50. Method M100 starts at block B10 and proceeds to block B20 where the media set containing M types of media is determined. Next at block B30, a training sensor set for measuring values of a set of N predetermined variables is provided. At block B40, using the training sensor set, normalized training data sets for each media type in the media set is collected. At block B50, a media type determining equation set having M media type determining equations is formed. Thereafter at block B60, the media type determining equation set 40 is stored inmemory 53 of eachoperational imaging device 50. At block B70, an operational sensor set 52 for measuring the values of the set of N variables is provided for eachoperational imaging device 50. At block B80, the values of the set of N variables is measured for a media sheet about to be processed and the values normalized. At block B90, the media type determining equation set is solved using the normalized values of the set of N variables to determine a media type. At block B100, using the determined media type, an operational parameter of the operational imaging device is chosen. At block B110, the media sheet to be processed is processed by the operational imaging device using the selected operational parameter. At block B120, method M100 ends. 
FIGS. 8A8B provide a simplified flow chart of another form of the present method. For method M200, the actions of blocks B220B260 would occur using thetraining system 10 while those of blocks B260B400 would occur in eachoperational imaging device 50. Method M200 starts at block B210 and proceeds to block B220 where the media set containing M types of media is determined. Next at block B230, a training sensor set 14 for measuring values of a set of N predetermined variables is provided. At block B240, using the training sensor set 14, normalized training data sets for each media type in the media set is collected. At block B250, a first media type determining equation set having M media type determining equations is formed where all of the variables in the set of N variables are being measured by the training sensor set 14. The media type determining equation set produced will be selected when all of the sensors in the operational imaging device are functioning properly. At block B260, a number of additional media type determining equation sets are formed from the normalized training data sets 26 that have been modified to remove data values associated with a faulty sensor. The number of modified additional media type determining equation sets will be S! where S is the number of sensors in the training and operational sensor sets 14, 52. For example, if the impedance sensor was determined to be faulty, then the impedance magnitude and phase data values would not be used. If the impedance sensor and bending or stiffness sensor were both faulty, then the impedance magnitude and phase data and the stiffness data would not be used. This process will be repeated for all of the combinations of sensors in the training sensor set 14. As the number of faulty sensors increases, it may still be possible to operate theoperational imaging device 50. However, there will be a point at which theoperational imaging device 50 will no longer be able to determine a media type. This may be taken into account as described with the operations given in blocks B290, and B320B350.  At block B270, the S!+1 media type determining equation sets, where the +1 represents the first media type determining equation set having all sensors functioning, are stored in
memory 53 of eachoperational imaging device 50. At block B280 an operational sensor set 52 for measuring the values of the set of N variables is provided for eachoperational imaging device 50. At block B290 a determination is made to see whether or not any faulty sensor outputs are detected. When it is determined that all of the sensors S in the operational sensor set 52 are functioning, at block B300, method 200 selects the first media type determining equation set where all sensor are functioning. Thereafter, at block B310, method 200 solves the first media type determining equation set using the measured values for the set of N variables. Method M200 then proceeds to block B370.  When it is determined that faulty sensor outputs are presented, the faulty sensors outputs are flagged by
controller 51 which then proceeds to select, based on the combination of the remaining functioning sensors or on the combination of the malfunctioning sensors in the operational sensor set 52, the appropriate additional media type determining equation set from the S! media type determining equations sets that have been stored inmemory 53. At block B330 the confidence level of the selected additional media type determining equation set is checked. The confidence check determines that the appropriate equations are present infirmware 53. When the confidence threshold is not met, i.e., an equation is missing, method M200 declares a fault at block 350 and may issue a service request. When it is determined that the confidence threshold has been met, method M200 proceeds to block B360, the selected additional media type determining equation set is solved using the normalized values of the set of variables that are measured by the remaining functioning sensors in operational sensor set 52 to determine a media type.  At block B370, the solutions provided by the selected additional media type determining equation set or those provided by the first media type determining equation set are checked to determine whether or not two or more of the equation solutions are within a predetermined range of one another. When it is determined that this condition is present, at block B380, a determined media type is selected from lookup table (LUT) 59 stored in
memory 53 based on the combination of which equations in the additional media type determining equation set are within a predetermined range of one another. For example, say the solutions forequations LUT 59.  At block B390, using the determined media type, an operational parameter of the operational imaging device is chosen. At block B400, the media sheet to be processed is processed by the operational imaging device using the selected operational parameter. At block B410, method M200 ends. After completion the process M200 may return to block B290 to recheck for faulty sensors prior to the processing of the next sheet of media. The operations of block B290 may also be performed periodically, such as, prior to beginning a new media processing job.
 Example cases using the
operational imaging devices 50 which are electrophotographic printers will now be described to illustrate the present method and the high degree of flexibility that may be used when developing and implementing the media type determining equations by use of different variables and sensor sets. In each of Tables 48, 1011 and 13, the term “A” is a linear offset term in the media type determining equation. When the media type determining equation set uses polynomial equation form, the number of terms is a function of the polynomial order and the number of variables, or roughly of the number of sensors in each of the sensor sets 52152K assuming each sensor is measuring a single variable. In the simplest case, the polynomial order is one, the decision surface is a constant, and thresholding is used. In the most complex case having a media set having a large number of media types and the form of the equation is a polynomial, a higher order polynomial would be used. However, as the equation order increases, a concern of overfitting of the data may arise if the training data sets do not contain a sufficient number of values. For these reasons, the order of polynomial equations when used will generally have an order between first and fifth. The number of M media type determining equations in the media type determining equation set 40 would be the M number of media types to be classified. Some sensors may be used to make multiple measurements, e.g., impedance magnitude and phase.  The coefficients used for each media type determining equation will be a function of the range normalization as well as the actual design of the hardware in the
operational imaging device 50. Several things about the present system are universal. One of those is that certain sensor term combinations are more important than others in making the media type classification. The number of terms kept in the media type determining equation determines the resolution of the system, but each decreasingly important term makes less of a difference to the media type determination. Another is that while characteristic media properties determine differences between media type, the particular set of sensors chosen will determine which features are used to separate media.  After conditioning and normalization, the measured values of the set of N values are fed into each media type determining equation. The value and sign of the number calculated determines whether the
controller 53 believes the media tested to be of the type measured. Generally, if the sign of the number is positive, then the tested media is classified as “of that type” and if it is negative the media is classified as “not of that type”. If more than one type have a positive sign, the type with the highest positive value is the determined type or as previously discussed the determined type may be found in theLUT 59.  For the following examples the coefficients of each term are given in the coefficient columns, and the sensor input combination in the equation variable column. For example, in Case 1A, for the media type determining equation for polymer, the first term X1 is multiplied by polymer coefficient −0.026359, the second term X2 is multiplied by the coefficient 1.217574 and so on. In each media type determining equation, each term is added to the previous terms. If the coefficients are considered a vector Θ, and the terms a vector of X, then the resultant number is the resultant sum of terms which can be written in vector notation as Θ^{T}X.
 The following nomenclature is used to describe media types that may be sensed using the present methods. The media types include, but are not limited to: plain paper light—6075 g/m^{2}; plain paper standard—>7590 g/m^{2}; plain paper heavy>90120 g/m^{2}; cardstock light 120165 g/m^{2}; cardstock standard—>165220 g/m^{2}; cardstock heavy—220300 g/m^{2}; glossy paper light—105165 g/m^{2}; glossy paper standard—>165220 g/m^{2}; glossy paper heavy>220300 g/m^{2}; paper labels—<=5 mil; paper label heavy >5 mil; plastic label <=5 mil; plastic label heavy >5 mil; polymer (vinyl) labels; envelope standard—<=
sub 24; envelope heavy >sub 24; synthetic polymer—polymer signage 47 mil and transparencies47 mil; and rough/cotton paper—90120 g/m^{2 }(100% cotton or parchment style). Where each of these media types is to be sensed in a single type ofoperational imaging device 50, a corresponding media type determining equation set 40 would be generated and solved as previously described. For the listed examples, media type determining equation set 40 would have 17 media type determining equations. It should also be recognized that variations of a given type may be combined if desired. For example, the three plain paper types can be reduced to a single type covering weights of 60120 g/m^{2 }or two types plain paper light and plain paper heavier covering weights 75120 g/m^{2 }that combines plain paper standard and heavy into one type. Plain paper may also be referred to as office paper or copier paper.  Cases 1A1C provide for media type determination for
operational imaging devices 50 used in a typical retail environment. The media set 16 used in a retail environment generally includes three media types—plain office paper—all weights, a polymeric media, such as, outdoor signage or vinyl labels—all thicknesses, and a thicker media such as cardstock—all weights. The training sensor set 14 and each operational sensor set 52152K used for this three member media set varies in each of the cases 1A1C. Cases 1A1C illustrate various example combinations of measurements and sensors that may be used to determine the media types in this three member media set. Of course, other sets of sensors may also be used to the same effect. Case 1A uses direct and subsystem response sensors to produce three 3^{rd }order polynomial equations which form mediatype determining set 40. In this example the set of N variables comprises two measured variablesmedia feed motor current and optical average. The former being provided by a subsystem response sensor (a motor current sensor) and the latter being provided by a direct sensor (optical sensor). Case 1B uses two direct sensors to produce three 1^{st }order polynomial equations having two measured variables—bending or stiffness and gloss or reflectance. Case 1C uses two direct sensors to produce three fifth order polynomial equations having three variables—impedance magnitude, impedance phase, and acoustic pressure. Based on empirical results, additional sensors may be used but would only increase the cost of theoperational imaging devices 50 used in a retail environment without providing any significant increase in more accurately resolving the three media types.  Tables 46 provide the coefficients for each term in each of the respective media type determining equations sets where one set comprises 3rd order equations, one set comprises first order equations and the last provides fifth order equations. Cases 1A1C help to illustrate the flexibility of the present system where choice of variables measured and selection of corresponding sensors provides a variety of media type determining equation solution sets to determine a media type within a common set of media.

TABLE 4 Case 1A Media Type Determining Equation Set  3 Media Types Equations Coefficients for Media Type in Media Set Equation Polymer Cardstock Plain Paper Variables −0.26359 0.674147 −0.41055 X1 1.217574 0.324479 −1.54205 X2 −2.23855 2.852548 −0.614 X1*X2 −0.95171 0.68555 0.266161 X1*X2{circumflex over ( )}2 −0.49302 0.243864 0.24916 X1{circumflex over ( )}2*X2 −0.214 −0.034 0.248008 X1{circumflex over ( )}2 0.435317 −0.48451 0.049195 X1{circumflex over ( )}3 1.972594 −0.64922 −1.32337 X2{circumflex over ( )}2 0.677691 −0.63346 −0.04423 X2{circumflex over ( )}3 1.25E−15 −2.5E−15 2.39E−16 A X1 = media feed motor current X2 = optical average 
TABLE 5 Case 1B Media Type Determining Equation Set  3 Media Types Equations Coefficients for Media Type in Media Set Equation Polymer Cardstock Plain Paper Variables −0.94122 2.550474 −1.60925 X1 2.842086 −1.73038 −1.11171 X2 −2E−15 −6.2E−15 4.07E−15 A X1 = Stiffness X2 = Reflectance 
TABLE 6 Case 1C Media Type Determining Equation Set  3 Media Types Equations Coefficients for Media Type in Media Set Equation Polymer Cardstock Plain Paper Variables 0.521816 0.1541 −0.67592 X1 −0.64239 0.749393 −0.107 X2 −1.1612 0.695437 0.46576 X3 −1.26453 1.679798 −0.41526 X1{circumflex over ( )}2*X2{circumflex over ( )}2 −0.1172 0.143002 −0.0258 X1{circumflex over ( )}2*X2{circumflex over ( )}3 0.090567 0.018989 −0.10956 X1{circumflex over ( )}2*X3{circumflex over ( )}2 −0.29926 0.425474 −0.12621 X1{circumflex over ( )}3*X2{circumflex over ( )}2 1.001712 −1.03542 0.03371 X1{circumflex over ( )}2*X3{circumflex over ( )}3 0.124537 −0.13386 0.009324 X1{circumflex over ( )}3*X3{circumflex over ( )}2 0.259456 0.015051 −0.27451 X2{circumflex over ( )}2*X3{circumflex over ( )}2 0.076292 0.01834 −0.09463 X2{circumflex over ( )}2*X3{circumflex over ( )}3 0.045954 0.00624 −0.05219 X2{circumflex over ( )}3*X3{circumflex over ( )}2 −1.41847 2.231076 −0.8126 X1*X2 −2.1302 2.285888 −0.15569 X1*X3 −0.6697 0.614604 0.055097 X2*X3 −1.31056 1.433568 −0.12301 X1*X2{circumflex over ( )}2 −0.78187 2.459673 −1.6778 X1{circumflex over ( )}2*X2 −0.0319 −0.06375 0.095647 X1*X2{circumflex over ( )}3 −0.65689 −0.01726 0.674151 X1*X3{circumflex over ( )}2 −1.46065 2.601674 −1.14103 X1{circumflex over ( )}2*X3 0.334875 0.562891 −0.89777 X1{circumflex over ( )}3*X2 0.048487 −0.08137 0.032886 X1*X2{circumflex over ( )}4 1.795706 −2.09925 0.303547 X1*X3{circumflex over ( )}3 0.915608 −0.98512 0.069512 X2*X3{circumflex over ( )}2 −0.44722 0.752981 −0.30576 X1{circumflex over ( )}3*X3 −0.11733 0.410803 −0.29347 X2{circumflex over ( )}2*X3 0.231317 −0.08636 −0.14496 X1{circumflex over ( )}4*X2 0.567364 −0.55563 −0.01173 X1*X3{circumflex over ( )}4 0.873347 −0.78357 −0.08977 X2*X3{circumflex over ( )}3 −0.11993 0.021361 0.098573 X1{circumflex over ( )}4*X3 0.183484 −0.10309 −0.08039 X2{circumflex over ( )}3*X3 0.173374 −0.11658 −0.0568 X2*X3{circumflex over ( )}4 0.050166 −0.07365 0.023488 X2{circumflex over ( )}4*X3 1.040249 0.202081 −1.24233 X1{circumflex over ( )}2 0.431391 −0.04736 −0.38403 X1{circumflex over ( )}3 −0.44561 0.599931 −0.15432 X2{circumflex over ( )}2 −0.32854 0.049625 0.278914 X1{circumflex over ( )}4 0.094454 −0.07046 −0.02399 X2{circumflex over ( )}3 −0.97987 0.341256 0.638617 X3{circumflex over ( )}2 −0.20286 0.065434 0.137428 X1{circumflex over ( )}5 0.103064 −0.15184 0.048777 X2{circumflex over ( )}4 0.300238 −0.35632 0.056081 X3{circumflex over ( )}3 0.019829 −0.0389 0.019072 X2{circumflex over ( )}5 0.242616 0.002065 −0.24468 X3{circumflex over ( )}4 0.011345 0.079402 −0.09075 X3{circumflex over ( )}5 1.886901 −2.18008 0.293184 X1*X2*X3{circumflex over ( )}2 −0.30617 0.10599 0.20018 X1*X2{circumflex over ( )}2*X3 −0.53504 1.959913 −1.42487 X1{circumflex over ( )}2*X2*X3 0.878716 −1.0035 0.12478 X1*X2*X3{circumflex over ( )}3 0.135789 −0.23757 0.101777 X1*X2{circumflex over ( )}3*X3 0.1232 0.324937 −0.44814 X1{circumflex over ( )}3*X2*X3 0.30541 −0.45386 0.148451 X1*X2{circumflex over ( )}2*X3{circumflex over ( )}2 0.708467 −0.43527 −0.2732 X1{circumflex over ( )}2*X2*X3{circumflex over ( )}2 −0.36158 0.519538 −0.15796 X1{circumflex over ( )}2*X2{circumflex over ( )}2*X3 −1.03613 1.398758 −0.36263 X1*X2*X3 −4.3E−15 −4.9E−15 1.17E−15 A X1 = Impedance Magnitude X2 = Impedance Phase X3 = Acoustic Energy  As can be seen from Tables 46, the number of terms in the equations forming each of the respective media type determining set of
equations 40 differs but when solved will determine one of the three media types in the three member media set of plain, cardstock, and polyvinyl. For example for Case 1A the form of the equation for polyvinyl would be as set forth in Eq. 7. 
(sign of the number determined by): 1.25E−15−0.26359X1+1.217574X2−2.23855X1*X2−0.95171X1*X2̂2−0.49302X1̂2*X2−0.214X1̂2+0.435317X1̂3+1.972594X2̂2+0.677691X2̂3 Eq. 7  As can be seen, excluding the offset term A, the second, third, fourth, and eighth terms are greater contributors to the solution. A similar trend may also be seen in Tables 5 and 6 (where A is the first term). These larger contributing terms may be empirically determined to be sufficient in determining the three media types and each equation in the media
type determining set 40 may be truncated to use only the larger contributing terms. Here that would be terms whose absolute values are about 1 or greater. Other threshold values may be used. Truncation would reduce the memory and processing requirements needed incontroller 51. 
Case 2 illustrates the use of direct indirect measurement values and subsystem responses values for determining a second media set consisting of polyvinyl labels, cardstock—all weights, plain paper and lightweight media. Light paper is in the range of 6075 g/m^{2 }while plain paper is in the range of 75120 g/m^{2 }(combines standard and heavy plain paper). The measured variables for this case are: Temperature (X1), Relative Humidity (X2), Media Feed Motor Current (X3), Optical Average (X4) and Optical Deviation (X5). 
TABLE 7 Case 2 Media Type Determining Set  4 Media Types Equations Coefficients for Media Type in Media Set Polyvinyl Plain Light Equation Labels Cardstock Paper Paper Variables 0.225062 −1.42402 1.069768 0.129193 X1 −0.15618 0.934353 −0.54642 −0.23175 X2 −0.35749 1.124621 −0.30012 −0.46701 X3 −0.23404 0.142778 2.510928 −2.41967 X4 0.247742 0.121015 −2.16172 1.792964 X5 0.013711 −0.02611 0.213334 −0.20093 X1*X2 −0.03757 −0.1457 0.708307 −0.52503 X1*X3 0.029382 −0.98702 1.502796 −0.54515 X1*X4 −0.22486 1.111549 −1.02779 0.141101 X2*X3 0.376093 −0.55781 −1.23348 1.4152 X1*X5 −0.32806 0.719974 0.003087 −0.395 X2*X4 −0.00795 0.41247 −0.44329 0.038769 X2*X5 −0.18676 0.869611 −0.44871 −0.23414 X3*X4 0.074733 0.602568 −0.44446 −0.23284 X3*X5 −1.15319 0.672746 1.66255 −1.18211 X4*X5 0.057141 −0.30656 0.316332 −0.06691 X1*X2{circumflex over ( )}2 0.022902 −0.1148 0.150146 −0.05825 X1{circumflex over ( )}2*X2 −0.00492 0.006678 −0.06264 0.060885 X1*X3{circumflex over ( )}2 −0.35556 1.318364 −0.66739 −0.29541 X1{circumflex over ( )}2*X3 0.578065 −0.23992 −1.05918 0.721037 X1*X4{circumflex over ( )}2 −0.10378 0.385121 −0.34058 0.059233 X2*X3{circumflex over ( )}2 −0.30339 1.307525 −0.90682 −0.09732 X1{circumflex over ( )}2*X4 0.009997 −0.33628 0.069833 0.256447 X2{circumflex over ( )}2*X3 0.128141 −0.09628 −0.37517 0.343309 X1*X5{circumflex over ( )}2 0.166336 0.214759 −0.86698 0.485889 X2*X4{circumflex over ( )}2 0.041753 0.26703 −0.71493 0.406152 X1{circumflex over ( )}2*X5 0.194437 −0.45359 0.034794 0.224355 X2{circumflex over ( )}2*X4 0.006733 0.163825 −0.12819 −0.04237 X2*X5{circumflex over ( )}2 0.633982 −0.41982 −0.87551 0.661349 X3*X4{circumflex over ( )}2 −0.07855 −0.01776 0.205488 −0.10917 X2{circumflex over ( )}2*X5 −0.18097 0.219188 −0.28608 0.247858 X3{circumflex over ( )}2*X4 0.117892 −0.17781 0.155455 −0.09554 X3*X5{circumflex over ( )}2 −0.00973 0.333001 −0.13092 −0.19235 X3{circumflex over ( )}2*X5 −0.13255 −0.08775 0.249897 −0.0296 X4*X5{circumflex over ( )}2 −0.37573 0.32157 0.598336 −0.54418 X4{circumflex over ( )}2*X5 −0.22778 1.115435 −0.83106 −0.0566 X1{circumflex over ( )}2 −0.11009 0.561379 −0.42405 −0.02724 X1{circumflex over ( )}3 0.047593 −0.24015 0.309609 −0.11705 X2{circumflex over ( )}2 0.035723 −0.19568 0.18612 −0.02616 X2{circumflex over ( )}3 −0.41602 0.962193 −0.5507 0.004526 X3{circumflex over ( )}2 −0.10718 0.167984 −0.12611 0.065301 X3{circumflex over ( )}3 1.632011 −0.36961 −1.49115 0.228747 X4{circumflex over ( )}2 1.026741 −0.38294 −1.39262 0.748819 X4{circumflex over ( )}3 0.273458 −0.34669 −0.78042 0.853651 X5{circumflex over ( )}2 0.023698 −0.15596 0.148829 −0.01657 X5{circumflex over ( )}3 −0.00028 −0.15674 −0.09303 0.250049 X1*X2*X3 0.100456 −0.4077 0.207944 0.099301 X1*X2*X4 −0.04225 0.019812 0.088199 −0.06576 X1*X2*X5 −0.16898 −0.08951 −0.00523 0.263717 X1*X3*X4 0.275793 −0.33318 0.396509 −0.33912 X1*X3*X5 −0.34118 0.70765 −0.70225 0.335783 X2*X3*X4 −0.24481 −0.30138 0.804439 −0.25825 X1*X4*X5 0.092109 −0.0826 0.209463 −0.21897 X2*X3*X5 −0.14553 −0.11924 0.773938 −0.50917 X2*X4*X5 −0.40228 0.740575 0.235175 −0.57347 X3*X4*X5 1.49E−16 7.24E−16 2.06E−16 2.89E−16 A  As can be seen, four third order equations comprise the media type determining equation set for this case. Again truncation may be applied if desired.

Case 3 represents a media set that would be important to corporate “office” usage: plain paper—all weights, bond paper, cardstock—all weights, polyvinyl labels—all thicknesses, paper labels—all thicknesses, envelopes—all types and transparencies. In this case an extra sensor type, a reflectance sensor has been added such that more information is available to the classifier algorithm to separate the greater number of media types in this case. In Table 8 below, an example of coefficients for each media type and the corresponding sensor term are given. As in the previous case, there is a separate equation for each media type. The number of terms is a function of the number of sensors whereas the number of equations is the number of media types to be classified. The variables (normalized) represent Temperature (X1), Relative Humidity (X2), Impedance Magnitude (X3), Impedance Phase (X4), Reflectance (X5), Optical transmission Average (X6), and Optical transmission variation (X7). Reflectance sensing was added to increase the resolution of the system. 
TABLE 8 Case 3 Media Type Determining Equation Set  7 Media Types Equation Coefficients Polyvinyl Paper Bond Equation Envelopes Labels Transparencies Plain Paper Cardstock Labels Paper Terms 0.242808151 −0.3022667 −0.0491579 0.654057468 −0.97351965 0.168457672 0.259620957 X1 −0.01330176 0.84585723 −0.120025 −1.22077225 −0.33500161 −0.553407974 1.396651357 X2 −1.37489733 −0.1298633 0.15315162 −4.07078138 1.47210184 0.150420275 3.799868243 X3 0.159805392 −0.4530109 −0.0328607 0.007380524 −0.37329899 0.337221897 0.354762809 X4 −0.03137718 −0.7627554 0.48495245 0.68890323 0.456535275 0.50658056 −1.34283896 X5 −0.23703325 1.25760707 −0.1833756 −0.00038332 0.292820153 −1.699788598 0.570153552 X6 −0.08842941 −0.0659294 −0.1038132 0.691897028 0.756912349 0.386522154 −1.57715955 X7 −0.03774966 0.2083204 −0.0408547 −0.38572795 −0.32021909 −0.085178173 0.661409181 X1 * X2 −0.46825036 −0.0416872 −0.0059438 −1.17095757 −0.4726776 0.205245122 1.954271358 X1 * X3 0.090469474 −0.3713271 0.04878452 0.657499323 0.367081558 −0.00901844 −0.78348931 X1 * X4 0.6267451 0.55035809 0.02516059 −0.45452791 −1.08095652 −0.610545198 0.943765848 X2 * X3 −0.10970869 −0.584089 −0.0792134 0.76115018 0.116950171 0.555621583 −0.6607109 X1 * X5 0.036304219 0.166694 0.00240912 −0.58742405 0.204803565 −0.013396524 0.190609669 X2 * X4 −0.19386352 0.20576049 0.18077901 0.35145225 −0.36387624 −0.535897777 0.355645785 X1 * X6 −0.16572491 −0.1069755 −0.0516899 0.015388638 0.532614986 0.210944798 −0.43455809 X2 * X5 −0.3828572 0.006038 −0.018257 −0.50987861 0.619603254 0.197328854 0.088022667 X3 * X4 −0.01038755 −0.3310865 0.02464473 0.170773931 0.121501059 0.54130573 −0.51675144 X1 * X7 0.087358187 2.13665827 0.06906835 −1.42352942 −0.18670512 −1.746199137 1.06334887 X2 * X6 −1.13859457 −0.5354781 0.41314087 −1.3457852 3.642512513 0.37668805 −1.41248355 X3 * X5 0.214018404 −0.0602839 −0.0463747 −0.33748569 −0.2677048 −0.080954315 0.578784994 X2 * X7 0.008227289 −0.6078817 −0.1542212 −1.93635588 1.261053994 0.022504261 1.4066732 X3 * X6 −0.10772428 0.33797076 −0.1912707 0.506630077 0.499212018 −0.186427521 −0.85839036 X4 * X5 −1.11533626 0.72260049 −0.1025189 −0.9098379 2.238050338 0.059829784 −0.89278759 X3 * X7 0.623613057 −1.2446447 0.08504447 0.27708983 −1.02386944 0.752172688 0.530594112 X4 * X6 −0.33746245 −0.1676835 0.05569619 −0.6716702 −0.0349193 0.462651255 0.693387976 X4 * X7 0.198677045 −1.7136494 −1.1122608 2.707697972 −0.49570898 0.530774916 −0.11553077 X5 * X6 −0.44830534 0.37979146 −0.477535 0.169566611 1.754798417 −0.216351379 −1.16196479 X5 * X7 0.060861078 −0.9303548 0.26464063 −0.42059107 0.59975339 0.159996521 0.265694281 X6 * X7 −0.06642697 −0.400875 0.07595577 0.427777369 0.216408286 0.316872893 −0.5697124 X1 * X2{circumflex over ( )}2 −0.03033115 −0.1089005 0.02039878 0.0884261 0.023469737 0.099593952 −0.0926569 X1{circumflex over ( )}2 * X2 1.104164442 −0.1375385 0.01430879 0.910564031 −0.36090926 0.065321852 −1.59591135 X1 * X3{circumflex over ( )}2 −0.28610152 0.32555398 −0.0215696 −0.40451992 0.722334335 −0.28029139 −0.05540585 X1{circumflex over ( )}2 * X3 −0.05679468 0.29508389 0.01500337 0.065384349 0.306876345 −0.380851788 −0.24470148 X1 * X4{circumflex over ( )}2 0.968134856 −0.0875256 0.00368472 1.047335379 −0.68055834 −0.417423169 −0.83364785 X2 * X3{circumflex over ( )}2 0.106984082 −0.0273801 −0.0038711 0.536250953 −0.02571888 −0.092027394 −0.49423754 X1{circumflex over ( )}2 * X4 −0.46911341 −0.6210633 −0.0262951 −0.02215315 0.742307301 0.551758423 −0.15544073 X2{circumflex over ( )}2 * X3 0.029959315 0.30676346 −0.0018093 0.004508407 0.062845066 −0.221896672 −0.18037031 X1 * X5{circumflex over ( )}2 −0.02495464 0.53998496 −0.0539299 0.091485987 0.130652518 −0.524101755 −0.15913714 X2 * X4{circumflex over ( )}2 −0.03221472 −0.0367792 −0.0204677 −0.13394671 −0.08007686 −0.011930464 0.315415614 X1{circumflex over ( )}2 * X5 0.218460659 0.19533822 −0.0288234 0.484929557 −0.37665004 −0.104732257 −0.38852272 X2{circumflex over ( )}2 * X4 −0.31298873 −0.0796939 −0.0110477 0.05870185 0.093799545 0.759061335 −0.50783245 X1 * X6{circumflex over ( )}2 0.023256249 −0.1369177 0.13074052 0.444100204 0.036162466 0.017104908 −0.51444669 X2 * X5{circumflex over ( )}2 −0.13532985 0.17431111 0.01702134 0.168393669 0.287371468 −0.128914797 −0.38285294 X3 * X4{circumflex over ( )}2 −0.05764968 0.25950249 −0.1055292 −0.02277384 0.64040572 −0.2961302 −0.41782531 X1{circumflex over ( )}2 * X6 0.144736128 0.20520264 0.01876379 0.075086074 −0.26439205 −0.277476654 0.098080074 X2{circumflex over ( )}2 * X5 −0.01295648 0.21266324 −0.0062756 0.291283396 0.358857085 −0.177690646 −0.66588097 X3{circumflex over ( )}2 * X4 0.315586948 0.18030758 0.00016429 0.19996937 −0.79907586 −0.293808336 0.396856013 X1 * X7{circumflex over ( )}2 0.218973731 0.22531613 0.08264195 0.316699388 −0.31314516 −0.050307601 −0.48017844 X2 * X6{circumflex over ( )}2 −0.00244836 0.48193641 0.24934533 −0.37691143 0.338010386 −0.388013626 −0.30191871 X3 * X5{circumflex over ( )}2 −0.35227415 0.05331815 0.03809078 −0.13670761 0.802073614 0.109739074 −0.51423985 X1{circumflex over ( )}2 * X7 −0.52443353 −1.3907833 −0.1651325 0.744962068 0.961085722 1.17244877 −0.79814722 X2{circumflex over ( )}2 * X6 −0.2566956 −0.0365632 0.07185654 −0.32597867 1.622202025 −0.041289211 −1.03353191 X3{circumflex over ( )}2 * X5 0.150880012 0.02016158 0.01913804 0.0932972 −0.29390751 −0.276697418 0.287128093 X2 * X7{circumflex over ( )}2 0.715717405 −0.6505444 0.04942693 0.460706029 −1.05818782 1.312283869 −0.82940203 X3 * X6{circumflex over ( )}2 −0.06172227 0.24009602 −0.0287398 −0.18907301 0.009040378 −0.162248061 0.192646726 X4 * X5{circumflex over ( )}2 −0.25833591 0.02168096 0.04734084 0.193850486 0.858138335 −0.100312335 −0.76236239 X2{circumflex over ( )}2 * X7 2.048616532 −0.4801869 −0.0381019 2.19872312 −1.81707289 −0.468959887 −1.44301803 X3{circumflex over ( )}2 * X6 −0.06147092 0.22879508 0.02734446 0.026662595 0.237054069 −0.211083078 −0.2473022 X4{circumflex over ( )}2 * X5 0.019018286 0.35534086 −0.0293189 0.327874074 −0.47389923 0.011003144 −0.21001828 X3 * X7{circumflex over ( )}2 0.263794229 −1.2885052 0.11419223 −0.03300695 −0.80374925 1.333696103 0.413578835 X4 * X6{circumflex over ( )}2 0.27963138 0.24083357 −0.0534372 −0.12149756 −0.13741223 −0.023846008 −0.18427194 X3{circumflex over ( )}2 * X7 0.044749075 0.02489239 0.0432358 0.447757539 0.164636166 −0.297332654 −0.42793831 X4{circumflex over ( )}2 * X6 −0.02399799 −0.0855735 0.0283726 −0.02278462 −0.20840843 −0.020831413 0.33322337 X4 * X7{circumflex over ( )}2 0.05329374 −1.6061004 −0.0509634 0.193624208 −0.85812634 1.534707715 0.733564474 X5 * X6{circumflex over ( )}2 −0.20329684 −0.1136408 0.00892198 −0.8077009 0.085471081 0.238507852 0.791737606 X4{circumflex over ( )}2 * X7 0.249965119 0.99639693 −0.6997549 0.938787384 −0.58629349 −1.088674948 0.189573854 X5{circumflex over ( )}2 * X6 −0.05624124 0.05621629 −0.0382949 −0.11591467 0.041698835 −0.032089637 0.144625319 X5 * X7{circumflex over ( )}2 −0.00839996 0.26646453 −0.1639763 0.026170868 0.084923933 −0.2049962 −0.00018684 X5{circumflex over ( )}2 * X7 0.28163397 −0.087712 0.06309944 0.402808555 −0.90243212 0.065790681 0.176811511 X6 * X7{circumflex over ( )}2 0.386273884 −0.519215 0.08960004 −0.20972974 −0.40100835 −0.131217004 0.785296176 X6{circumflex over ( )}2 * X7 0.142529438 0.33749117 −0.0080187 −0.44783953 0.126016081 −0.28859151 0.138413088 X1{circumflex over ( )}2 0.036334313 0.12216315 0.00910985 −0.18454767 0.169883929 −0.104638169 −0.04830541 X1{circumflex over ( )}3 −0.07066936 −0.284715 0.05589571 0.252305977 0.117436606 0.247913939 −0.31816788 X2{circumflex over ( )}2 −0.0398291 −0.2773847 0.05271931 0.309902861 0.167959018 0.212456695 −0.42582404 X2{circumflex over ( )}3 0.909644173 0.08440005 0.03466067 −0.0260951 0.240063123 −0.535929951 −0.70674296 X3{circumflex over ( )}2 1.068296553 0.13004595 −0.0123454 1.347391959 −1.03492607 −0.458305795 −1.04015724 X3{circumflex over ( )}3 −0.17521611 0.17517023 0.06231885 −0.21474491 0.373652076 −0.251374791 0.030194659 X4{circumflex over ( )}2 −0.06605909 0.0723524 0.00328255 −0.13066688 0.106342931 −0.083581399 0.098329478 X4{circumflex over ( )}3 0.312102004 0.80158207 0.96882362 −0.91623853 −1.02160195 −0.562009997 0.417342786 X5{circumflex over ( )}2 0.123171561 0.15007733 0.48102528 −0.5519628 −0.50960591 −0.050435888 0.357730429 X5{circumflex over ( )}3 −0.53887541 1.61379721 0.10504467 −0.31556109 0.488544753 0.266720262 −1.61967039 X6{circumflex over ( )}2 −0.25639983 0.35075975 0.07883228 −0.32546733 −0.28205864 1.239843522 −0.80550975 X6{circumflex over ( )}3 0.367050626 0.16798992 0.05675556 0.69868854 −1.06549399 −0.18297778 −0.04201288 X7{circumflex over ( )}2 0.162316766 −0.0089132 0.02342981 −0.00583392 −0.53889923 −0.103534971 0.471434709 X7{circumflex over ( )}3 −0.10779052 −0.3436667 −0.0149956 −0.05648475 0.016226244 0.280247575 0.226463781 X1 * X2 * X3 0.162739258 0.18592952 −0.0146728 0.163175444 −0.16835845 −0.082884162 −0.24592884 X1 * X2 * X4 0.053107567 0.1009162 −0.0243086 0.126345382 −0.027035 −0.108823967 −0.12020157 X1 * X2 * X5 −0.54721799 −0.1107567 −0.0090108 −0.28058423 0.920530688 0.238391661 −0.21135254 X1 * X3 * X4 −0.3689005 −0.4467775 −0.0637423 0.152615471 0.526974547 0.395448384 −0.19561819 X1 * X2 * X6 −0.38771626 −0.0542216 0.07289316 −0.34806928 0.78396724 0.082003032 −0.14885628 X1 * X3 * X5 −0.45089733 0.01311599 0.01066731 −0.67449927 0.957117362 0.343771508 −0.19927557 X2 * X3 * X4 −0.07334702 −0.0386646 0.0216881 0.05110817 0.427787692 −0.081419426 −0.30715292 X1 * X2 * X7 0.693727149 −0.8897513 −0.0614786 0.261172037 −0.42403462 0.798914114 −0.37854884 X1 * X3 * X6 −0.12759699 0.21168643 −0.0413005 0.330100921 0.775088044 −0.144140058 −1.00383785 X1 * X4 * X5 0.134162986 0.17267197 0.05671629 −0.24113209 0.289122875 −0.117606636 −0.29393541 X2 * X3 * X5 −0.60536881 0.67849644 −0.0388384 0.623385535 0.880769098 −0.502027315 −1.03641659 X1 * X3 * X7 0.128413047 −0.9850029 0.13365049 0.490639439 0.019561605 0.343550075 −0.13081176 X1 * X4 * X6 1.185281201 −0.0519245 −0.0176642 1.049481512 −0.68351136 −0.653399454 −0.82826321 X2 * X3 * X6 −0.1563354 0.47360594 −0.0499928 0.219737277 0.878147712 −0.330207418 −1.03495531 X2 * X4 * X5 −0.18197796 0.03153822 −0.0091941 −0.46035895 0.110668281 0.209663912 0.299660627 X1 * X4 * X7 −0.25557672 −1.2530535 0.2945048 −0.54476269 0.194645313 1.224383089 0.339859741 X1 * X5 * X6 0.32911471 0.58463128 0.01280195 0.911020371 −0.22261648 −0.533906046 −1.08104578 X2 * X3 * X7 0.243204546 −1.036637 0.08133881 −0.24571052 −0.41147512 0.595739638 0.77353967 X2 * X4 * X6 −0.13276077 0.19299011 −0.0956321 0.180770017 0.696891148 −0.038718484 −0.80353996 X3 * X4 * X5 −0.19839175 0.11970146 −0.1294672 −0.46678533 0.561396374 0.002562748 0.110983683 X1 * X5 * X7 −0.42659867 0.1628119 −0.0940231 −0.5472644 0.595759866 0.277665679 0.031648729 X2 * X4 * X7 −0.06960141 0.60321056 0.01119979 −1.86649281 0.481986914 −0.15435873 0.994055683 X2 * X5 * X6 0.083469304 −0.8463705 0.03634371 −0.00261979 −0.1789313 0.866965472 0.041143097 X3 * X4 * X6 0.000404245 −0.4776174 0.072095 0.194514726 −0.24542735 0.218205362 0.237825398 X1 * X6 * X7 −0.01372983 −0.0524225 −0.1602315 −0.35306244 0.123927487 0.17980322 0.275715526 X2 * X5 * X7 −0.46966518 0.58347487 0.01063821 0.067900488 1.130370871 −0.188545099 −1.13417416 X3 * X4 * X7 −0.47015211 −1.3645586 −0.2574877 −0.31219992 1.906092833 0.918031528 −0.41972609 X3 * X5 * X6 0.282659953 0.16435012 0.03221158 0.031144009 −0.44180809 −0.025267221 −0.04329036 X2 * X6 * X7 −0.60137204 0.49042391 −0.1294754 −0.13264599 2.083689039 −0.296493343 −1.41412616 X3 * X5 * X7 0.25694826 0.10016521 −0.2401126 0.81570113 −0.22345036 −0.133936214 −0.57531541 X4 * X5 * X6 0.561703289 −0.3617383 0.00757938 −0.46358326 −0.33602152 −0.367632643 0.959693056 X3 * X6 * X7 −0.06207154 0.10055074 −0.0140666 −0.28123819 0.027665815 0.045761125 0.183398653 X4 * X5 * X7 −0.28564421 0.10939144 0.05276535 −0.64976654 0.562086993 0.234468818 −0.02330185 X4 * X6 * X7 −0.19245128 0.01241731 −0.125598 0.027315036 1.196398231 −0.214711911 −0.70336938 X5 * X6 * X7 4.57465E−14 −6.748E−14 −2.509E−15 −7.0855E−15 −1.1269E−13 −4.98299E−14 1.02708E−13 A  This set of terms is handled exactly like the terms in the
Case 2. There are more terms in this model (120) because a sensing method (reflectance) has been added.  As with the equations in the prior cases, certain terms are more significant than others, and it is possible to either expand or contract the number of terms depending on the resolution desired. In this case the empirically determined higher contributing terms are set out in Table 9.

TABLE 9 Higher Contributing Terms For Case 3X2 X3 X6 X1*X3 X2*X3 X2*X6 X3*X5 X3*X6 X3*X7 X4*X6 X5*X6 X1*X3{circumflex over ( )}2 X2*X3{circumflex over ( )}2 X2{circumflex over ( )}2*X6 X3{circumflex over ( )}2*X5 X3*X6{circumflex over ( )}2 X4*X6{circumflex over ( )}2 X5*X6{circumflex over ( )}2 X5{circumflex over ( )}2*X6 X5{circumflex over ( )}2 X3{circumflex over ( )}2 X6{circumflex over ( )}2 X7{circumflex over ( )}2 X1*X4*X5 X1*X3*X7 X2*X3*X6 X2*X4*X5 X1*X5*X6 X2*X3*X7 X2*X4*X6 X3*X4*X7 X3*X5*X6 X3*X5*X7 X5*X6*X7  While information about the temperature and relative humidity did not factor in significantly to a limited set of media types, as the media types that need to be separated becomes larger in number, the environmental measurements linked with electrical properties (example: X1*X3 and X2*X3) become more important in helping make the media type determination.
 Case 4 illustrates an imaging device which is designed to be useful for a wide variety of tasks. This system will classify the following paper types: plain paper light; plain paper standard; plain paper heavy; cardstock light; cardstock heavier weight—165300 g/m^{2 }(combined standard and heavy weight cardstock); glossy paper—all weights; paper labels—all thicknesses; polymer (vinyl) labels—all thicknesses; envelopes—all types; polymer signage; transparencies; and bond paper.
 For Case 4 the training sensor set includes: Temperature (X1), Relative Humidity (X2), Impedance Magnitude (X3), Impedance Phase (X4), Reflectance (X5), Media Feed Motor Current (X6), Optical transmission Average (X7), and Optical transmission Variation (X8). As in earlier cases each media type to be classified has an equation. Here there are 165 terms in each equation and eleven equations in the media type determining equation set 40. These equations are broken into Table 10 and Table 11 due to the large number of terms.

TABLE 10 Case 4 Media Type Determining Equation Set  11 Media Types (Part 1) Equation Coefficients Lighter Heavier Weight Weight Paper Bond Equation Cardstock Cardstock Labels Paper Envelopes Terms −0.10215 −0.96693 0.359736 0.363189 0.1646867 X1 −0.00735 0.726339 −0.46402 0.293542 −0.173118 X2 −0.50142 0.257461 0.156373 4.016341 −0.6041163 X3 −0.39654 0.397066 0.115222 −0.24473 0.0732896 X4 0.204041 −0.2667 0.235262 −1.19166 0.2337414 X5 −0.38159 0.435812 −0.08037 −0.964 0.2995665 X6 0.260921 −0.053 −1.37083 1.283396 −0.4634386 X7 −0.32533 0.500724 0.39651 −1.26373 0.225797 X8 −0.06565 0.033339 −0.08807 0.24662 −0.0307321 X1*X2 −0.13495 −0.76728 0.087931 2.654338 −0.3326146 X1*X3 −0.36356 −0.05836 −0.13407 −0.24047 0.3409796 X1*X4 −0.05893 0.52864 −0.43036 0.634368 0.1450806 X2*X3 0.070669 −0.45792 0.44908 0.187372 0.1620274 X1*X5 −0.12211 0.123223 −0.06857 −0.1776 −0.0373728 X2*X4 −0.02833 −0.25859 −0.35674 −0.8934 −0.0380259 X1*X6 0.062907 0.265196 0.271402 −0.39663 −0.0026142 X2*X5 0.909783 −0.43324 0.372216 1.2813 −0.0811195 X3*X4 0.272906 −0.73372 −0.68953 0.642533 −0.181046 X1*X7 −0.30487 0.84623 −0.50478 −0.20065 −0.0324242 X2*X6 −0.28482 −0.08269 0.035914 −1.76024 −0.6419247 X3*X5 −0.50572 −0.03866 0.565644 −0.02227 0.2127391 X1*X8 −0.0795 0.695273 −0.74671 0.890684 −0.2712677 X2*X7 1.762335 0.14588 −0.28552 0.825141 −1.3209074 X3*X6 −0.28597 0.443505 −0.11064 −0.53588 0.0163182 X4*X5 0.33312 −0.00724 −0.12219 0.233576 −0.0586616 X2*X8 −0.94669 1.302532 −0.44448 0.924754 0.4573673 X3*X7 1.015426 0.082229 0.151306 −1.45905 −0.0372243 X4*X6 0.930716 −0.39203 0.458681 0.431552 −0.1594392 X3*X8 −0.45028 −0.03084 1.133179 0.750633 0.3492999 X4*X7 −0.31051 0.295385 0.116376 −0.1335 0.1778553 X5*X6 0.547048 −0.54746 0.014396 0.32587 −0.2449667 X4*X8 0.226614 −0.61915 0.372392 0.05312 0.0077516 X5*X7 0.108459 0.355198 −0.1466 −0.29784 0.1623835 X5*X8 −0.39451 0.247612 0.150887 −0.06514 −0.1133357 X6*X7 0.457813 −0.14817 −0.03302 −0.95241 −0.0531792 X6*X8 −0.55816 1.133495 0.277864 0.782589 0.2767174 X7*X8 −0.00515 −0.22679 0.175352 −0.26889 0.0622672 X1*X2{circumflex over ( )}2 −0.01301 −0.07598 0.048155 −0.05488 0.0171917 X1{circumflex over ( )}2*X2 0.079203 −0.36796 −0.18077 −1.21195 1.0751652 X1*X3{circumflex over ( )}2 0.238941 0.491853 −0.18625 0.065917 −0.4338321 X1{circumflex over ( )}2*X3 0.045677 −0.00292 −0.34546 −0.21611 −0.0315138 X1*X4{circumflex over ( )}2 0.283617 0.055458 −0.27218 −1.18334 0.4441188 X2*X3{circumflex over ( )}2 −0.15339 0.131654 0.028356 −0.03497 0.2354653 X1{circumflex over ( )}2*X4 −0.02984 −0.35992 0.27291 −0.07621 −0.3547497 X2{circumflex over ( )}2*X3 0.050466 0.094552 0.06311 0.251497 −0.037331 X1*X5{circumflex over ( )}2 0.160558 −0.00512 −0.36186 0.010888 −0.0582474 X2*X4{circumflex over ( )}2 −0.35751 0.638837 −0.4005 −0.1836 0.1813197 X1{circumflex over ( )}2*X5 −0.00668 0.072938 0.161304 0.011111 0.1833463 X2{circumflex over ( )}2*X4 −0.24437 0.76841 −0.44347 −0.00191 0.0889477 X1*X6{circumflex over ( )}2 −0.06228 0.260589 −0.00207 0.089108 −0.0937767 X2*X5{circumflex over ( )}2 0.343692 −0.48027 −0.20402 −0.21273 −0.0598696 X3*X4{circumflex over ( )}2 −0.28517 1.887516 −0.07392 −0.7279 −0.2333632 X1{circumflex over ( )}2*X6 0.084384 −0.15658 −0.22951 0.10896 0.0828668 X2{circumflex over ( )}2*X5 0.675777 −0.33885 0.172613 0.160238 0.0892832 X3{circumflex over ( )}2*X4 0.027775 −0.39694 0.862114 −0.39186 −0.0011708 X1*X7{circumflex over ( )}2 −0.45755 1.329883 −0.32686 −0.22937 0.2083025 X2*X6{circumflex over ( )}2 −0.02147 −0.00847 −0.24347 −0.79733 −0.1234555 X3*X5{circumflex over ( )}2 −0.17592 0.72296 0.809169 −0.16073 −0.2975119 X1{circumflex over ( )}2*X7 −0.32326 −0.11596 0.107446 −0.03323 0.0322397 X2{circumflex over ( )}2*X6 0.083391 −0.20866 −0.05538 −1.05817 −0.2742538 X3{circumflex over ( )}2*X5 −0.20365 −0.04443 0.051339 0.167066 −0.1248242 X1*X8{circumflex over ( )}2 0.181533 −0.09063 0.167089 −0.53324 0.1843593 X2*X7{circumflex over ( )}2 0.337674 0.389601 −0.11578 0.117904 −0.2955719 X3*X6{circumflex over ( )}2 −0.12465 0.021421 0.120407 0.451322 −0.2821513 X4*X5{circumflex over ( )}2 0.710402 −0.08486 −0.56394 −0.41194 −0.1154069 X1{circumflex over ( )}2*X8 0.069376 −0.37973 0.661899 −0.21212 −0.2148755 X2{circumflex over ( )}2*X7 1.477739 −0.69285 −0.18726 −0.19059 −0.5402833 X3{circumflex over ( )}2*X6 0.078293 −0.16992 0.045211 −0.00863 −0.2433564 X4{circumflex over ( )}2*X5 −0.02801 −0.03375 −0.27549 0.482277 0.0558407 X2*X8{circumflex over ( )}2 −0.51609 0.330651 0.554524 −1.79683 0.6795722 X3*X7{circumflex over ( )}2 0.374891 0.277379 0.127821 −0.41041 0.0139804 X4*X6{circumflex over ( )}2 0.028317 0.135954 0.077471 −0.11418 −0.0061094 X2{circumflex over ( )}2*X8 −0.45718 0.443713 −0.20604 −2.26695 1.4871733 X3{circumflex over ( )}2*X7 0.382353 −0.43679 −0.29453 −0.59778 −0.0753872 X4{circumflex over ( )}2*X6 0.547306 −0.85813 0.159545 −0.59204 −0.2305444 X3*X8{circumflex over ( )}2 −0.40737 −0.20638 1.286032 0.502435 0.2459154 X4*X7{circumflex over ( )}2 −0.49848 0.966306 −0.20128 0.087834 0.147961 X5*X6{circumflex over ( )}2 0.803535 −0.55223 0.21879 −0.22361 0.158234 X3{circumflex over ( )}2*X8 0.082115 −0.13336 −0.59163 −0.65502 −0.0609128 X4{circumflex over ( )}2*X7 0.315409 −0.51715 0.056125 0.538094 −0.0209327 X5{circumflex over ( )}2*X6 −0.05057 0.056377 −0.20692 0.431149 0.0259592 X4*X8{circumflex over ( )}2 −0.13122 −0.34741 0.668695 0.737777 0.1328341 X5*X7{circumflex over ( )}2 −0.12 0.190068 0.361689 0.793499 −0.003278 X4{circumflex over ( )}2*X8 0.47021 −0.01416 −0.59154 −0.18966 −0.1802951 X5{circumflex over ( )}2*X7 0.110789 −0.15229 −0.12374 0.003351 −0.0324989 X5*X8{circumflex over ( )}2 −0.02503 −1.46202 2.115192 0.842059 −0.1288026 X6*X7{circumflex over ( )}2 −0.0313 0.045946 −0.03697 0.193474 −0.0168117 X5{circumflex over ( )}2*X8 −0.53931 0.053701 0.66336 0.519137 0.2487398 X6{circumflex over ( )}2*X7 0.345938 −0.96856 0.231235 −0.36603 −0.0527204 X6*X8{circumflex over ( )}2 0.265951 −0.11526 −0.48219 −0.3034 −0.0189186 X6{circumflex over ( )}2*X8 0.206863 −0.52847 0.182014 −0.4704 −0.1333772 X7*X8{circumflex over ( )}2 −0.67686 0.9898 −0.22295 0.563122 0.2116338 X7{circumflex over ( )}2*X8 0.188171 0.791867 −0.30372 −0.90642 −0.1022968 X1{circumflex over ( )}2 0.090529 0.390991 −0.13762 −0.44375 −0.0496673 X1{circumflex over ( )}3 −0.01882 −0.16481 0.11995 −0.18406 0.0422425 X2{circumflex over ( )}2 0.002369 −0.14932 0.120972 −0.19565 0.0429012 X2{circumflex over ( )}3 0.355354 −0.49245 −0.06932 −0.27671 0.9429658 X3{circumflex over ( )}2 0.155078 −0.32116 −0.13668 −1.26564 0.7533977 X3{circumflex over ( )}3 −0.10408 0.057916 −0.22639 −0.21782 −0.1307067 X4{circumflex over ( )}2 −0.04858 0.141545 −0.02966 0.121084 −0.0309203 X4{circumflex over ( )}3 0.080835 0.085359 −0.27947 0.351041 0.070428 X5{circumflex over ( )}2 −0.00531 0.096888 0.062116 0.532437 0.0385223 X5{circumflex over ( )}3 −0.54744 0.966933 −0.3685 −0.83533 0.5047912 X6{circumflex over ( )}2 −0.30219 0.105289 0.024698 −0.11067 0.1926124 X6{circumflex over ( )}3 0.33342 −0.22375 −0.65974 −1.44193 −0.2861917 X7{circumflex over ( )}2 0.280755 −0.59172 0.588902 −1.07438 −0.1014826 X7{circumflex over ( )}3 −0.32083 −0.13641 −0.22931 −0.78865 −0.0244664 X8{circumflex over ( )}2 −0.28887 0.161116 −0.13442 0.178944 −0.0048997 X8{circumflex over ( )}3 −0.07031 −0.25978 0.101222 0.228322 −0.166292 X1*X2*X3 −0.03949 0.0539 0.079318 −0.05521 0.1205788 X1*X2*X4 0.135352 −0.16249 0.0041 0.046921 0.0411474 X1*X2*X5 0.578589 −0.49445 0.156758 0.835545 −0.1344985 X1*X3*X4 −0.28539 −0.1429 −0.09598 −0.02693 0.0341592 X1*X2*X6 −0.00595 −0.3858 0.044057 −0.21352 −0.4854171 X1*X3*X5 0.512641 −0.56394 0.117315 0.334152 −0.0941368 X2*X3*X4 0.069186 −0.24225 0.132578 0.154435 −0.20241 X1*X2*X7 1.127602 −0.12103 −0.27445 −0.28795 −0.5877396 X1*X3*X6 0.046281 0.081032 −0.16733 −0.00978 0.0411183 X1*X4*X5 −0.01015 −0.25057 0.243957 −0.55575 0.2706885 X2*X3*X5 −0.01464 0.090724 0.141612 0.092853 0.0055111 X1*X2*X8 −0.53849 0.208679 0.519656 −0.67111 0.9142973 X1*X3*X7 0.815422 −0.84809 −0.45894 −0.88413 0.0181859 X1*X4*X6 0.493878 0.203547 −0.2528 −0.43569 −0.1958555 X2*X3*X6 0.256557 −0.06237 −0.25877 −0.0125 −0.2319322 X2*X4*X5 0.220871 −0.61282 −0.2669 −0.02175 0.0929956 X1*X3*X8 0.064053 −0.1714 −0.30714 −0.05011 0.3667094 X1*X4*X7 −0.29289 0.039687 −0.23128 0.180217 −0.0177572 X1*X5*X6 0.078293 0.408937 −0.12917 −1.16226 0.6496404 X2*X3*X7 0.898708 −1.03228 −0.48039 −0.78522 −0.0401139 X2*X4*X6 0.0915 0.310086 −0.27633 −0.62971 0.3183238 X3*X4*X5 −0.04935 −0.21242 0.415688 0.466658 −0.1247571 X1*X4*X8 0.0159 −0.00464 −0.14939 0.896552 0.0378157 X1*X5*X7 0.30737 −0.07851 −0.4287 −0.73647 0.1885984 X2*X3*X8 0.0024 0.024689 −0.34584 0.093854 0.2585262 X2*X4*X7 −0.31307 0.301737 −0.04528 −0.18058 0.0528011 X2*X5*X6 1.402584 −0.09761 0.49176 −0.40266 −0.2453313 X3*X4*X6 −0.18872 0.235094 0.048899 0.625176 0.0348824 X1*X5*X8 −0.32083 −0.07229 0.938313 0.455732 −0.0572186 X1*X6*X7 0.080238 −0.22238 0.599487 0.489494 −0.178889 X2*X4*X8 0.072749 −0.59915 0.596198 1.112758 −0.3587823 X2*X5*X7 0.252546 −0.38424 1.430512 1.112136 0.3324322 X3*X4*X7 −0.25503 0.888144 −0.19559 −0.54327 −0.4024524 X3*X5*X6 0.724351 −0.69733 −0.21961 0.047505 −0.4312239 X1*X6*X8 0.036301 0.042267 0.155748 0.27004 −0.0609612 X2*X5*X8 −0.58043 0.010051 0.814339 1.055985 0.0129246 X2*X6*X7 1.348292 −1.13073 −0.30939 −0.40764 −0.2969597 X3*X4*X8 −0.35205 −0.1986 0.428399 −0.84829 −0.3945412 X3*X5*X7 0.131113 0.220836 −0.21382 −0.34778 0.0344171 X4*X5*X6 −0.27941 0.033886 −0.11227 −0.08138 0.4043953 X1*X7*X8 0.780671 −0.27468 −0.30045 −0.12618 −0.310726 X2*X6*X8 0.154203 0.367461 −0.34601 −0.32021 0.0957328 X3*X5*X8 0.400996 0.238667 0.874774 0.761336 −0.7695738 X3*X6*X7 −0.12892 0.050188 0.010194 0.006645 0.2199706 X4*X5*X7 −0.09432 0.302933 0.062928 −0.52523 0.218943 X2*X7*X8 2.373327 −1.48476 −0.53495 −0.11611 −0.6172811 X3*X6*X8 0.086311 −0.11863 0.131575 0.058383 −0.0353397 X4*X5*X8 0.277093 −0.26721 1.421102 0.10983 0.0088814 X4*X6*X7 −0.18165 0.969705 −0.03391 0.753953 0.3524887 X3*X7*X8 1.218325 −0.77491 −0.13311 −0.51012 −0.297565 X4*X6*X8 −0.71351 1.069155 −0.20616 0.182572 0.0452514 X5*X6*X7 0.807241 −0.7179 0.15679 −0.14507 −0.2137711 X4*X7*X8 −0.10985 0.735279 −0.40728 −0.19674 0.0527789 X5*X6*X8 −0.33354 0.669541 −0.18949 0.303635 0.3290144 X5*X7*X8 0.362289 0.386427 −0.96376 0.404961 −0.2324204 X6*X7*X8 4.27E−15 4.12E−13 −1.4E−13 1.36E−13 −3.866E−14 A 
TABLE 11 Case 4 Media Type Determining Equation Set (Part 2) Equation Coefficients Plain Paper Plain Paper Plain Paper Vinyl Light Standard Heavy Equation Glossy Labels Transparency weight Weight Weight Variables 0.008334 −0.26056 −0.07356 0.483513 0.099907 −0.16058 X1 −0.15216 0.381826 −0.05868 0.328938 −0.87234 −0.15998 X2 −0.21507 −0.33809 0.324886 −1.78166 −1.38446 −0.01608 X3 0.065257 −0.31483 −0.1304 −1.27301 1.951628 0.003238 X4 0.143846 −0.42946 0.626293 −0.80779 0.226054 0.831227 X5 −0.01532 −0.2415 −0.02236 −0.47534 0.460518 1.080084 X6 0.22925 1.26534 −0.27918 −2.3858 1.271585 0.526066 X7 0.032057 −0.3214 −0.13438 2.017673 −0.89928 −0.45866 X8 −0.05885 0.10932 −0.01756 0.13558 −0.27366 −0.09209 X1 * X2 0.249592 −0.27014 −0.014 −1.00513 −0.42268 −0.01302 X1 * X3 −0.32841 −0.32345 0.060776 −1.16952 1.647236 0.590506 X1 * X4 0.31468 −0.14485 0.05872 −0.41512 −0.61973 −0.22517 X2 * X3 0.101336 −0.5882 −0.03299 −0.24967 0.737523 −0.2588 X1 * X5 −0.12249 0.845214 0.017806 1.967854 −1.30142 −1.10405 X2 * X4 0.037748 0.219486 −0.0124 0.150201 −0.13297 1.073289 X1 * X6 −0.25424 −0.46771 −0.0121 −0.17734 0.584121 0.197559 X2 * X5 0.163602 −1.49172 −0.01524 −0.78121 −0.18121 0.36917 X3 * X4 0.05025 0.428918 0.147655 −0.66706 0.529668 0.154754 X1 * X7 −3.8E−05 0.592474 0.008519 0.143424 −0.42899 −0.09884 X2 * X6 −2.16129 2.095748 0.802578 −0.22818 0.513063 1.602894 X3 * X5 −0.03415 −0.11482 0.014012 0.748159 −0.07097 −0.71833 X1 * X8 −0.20669 0.448149 0.10001 −0.28985 −0.19341 −0.42956 X2 * X7 0.00677 1.538433 −0.01333 −0.4441 −0.75426 −1.3176 X3 * X6 0.056374 0.379234 −0.19786 0.109105 −0.13145 0.199614 X4 * X5 −0.19214 0.037302 −0.01236 0.710697 −1.09759 0.187459 X2 * X8 −0.05303 0.128428 −0.33012 −0.19522 −1.06511 0.237839 X3 * X7 −0.0511 −0.18173 −0.08708 0.29394 −0.9022 0.949176 X4 * X6 0.211277 −0.80354 −0.14112 −0.8314 −0.13327 0.261181 X3 * X8 −0.05405 −1.96166 0.15335 −0.43197 0.451299 0.446387 X4 * X7 0.223471 −0.40578 0.011947 −0.05765 0.009363 0.018909 X5 * X6 0.194725 0.22561 0.022762 −1.5557 1.672419 −0.62536 X4 * X8 1.266961 −0.45986 −1.37587 0.03446 −0.03855 0.437501 X5 * X7 0.205098 −0.34798 −0.50868 1.285024 −1.46681 0.475909 X5 * X8 0.05542 −0.30394 −0.04178 −0.21152 −0.38779 1.038434 X6 * X7 0.039114 0.273978 −0.01833 0.137346 1.018175 −0.97071 X6 * X8 −0.24973 −1.66504 0.355351 0.324745 0.580843 −0.70371 X7 * X8 0.063588 −0.12122 0.054512 −0.27418 0.414275 0.149677 X1 * X2{circumflex over ( )}2 0.012887 −0.02506 0.016639 −0.07566 0.102618 0.038228 X1{circumflex over ( )}2 * X2 −0.02061 −0.20967 0.014708 0.049554 0.641834 0.143778 X1 * X3{circumflex over ( )}2 −0.18344 0.464822 0.001586 0.235528 −0.41629 −0.22781 X1{circumflex over ( )}2 * X3 −0.14428 0.410198 0.051384 −0.45615 0.200308 0.320078 X1 * X4{circumflex over ( )}2 0.15409 0.047776 0.016326 0.069817 0.454578 −0.12246 X2 * X3{circumflex over ( )}2 0.031268 −0.73471 −0.00025 −1.26533 1.15006 0.663161 X1{circumflex over ( )}2 * X4 −0.31814 0.563877 −0.00529 0.242756 −0.06576 0.170893 X2{circumflex over ( )}2 * X3 0.035858 0.066749 −0.09848 0.503014 −0.29418 −0.50306 X1 * X5{circumflex over ( )}2 0.057447 0.294363 −0.01279 −0.65789 0.099669 0.269076 X2 * X4{circumflex over ( )}2 0.05231 0.11786 0.068118 −0.17303 −0.38447 0.417128 X1{circumflex over ( )}2 * X5 0.31291 −0.565 −0.04447 −0.21447 0.162069 −0.02296 X2{circumflex over ( )}2 * X4 −0.06061 −0.32829 0.043306 −0.12123 0.216557 −0.04844 X1 * X6{circumflex over ( )}2 −0.12999 −0.17929 0.009317 −0.06933 0.151816 0.175465 X2 * X5{circumflex over ( )}2 0.084364 0.431634 −0.01714 0.220313 −0.4163 0.344879 X3 * X4{circumflex over ( )}2 −0.02618 −0.25743 −0.01656 0.386359 −0.50979 −0.17594 X1{circumflex over ( )}2 * X6 0.459398 0.190069 0.065599 −0.00811 −0.42418 −0.20331 X2{circumflex over ( )}2 * X5 0.111737 −0.73338 0.009857 −0.0407 0.133934 −0.26779 X3{circumflex over ( )}2 * X4 −0.02604 −0.15869 0.055637 0.135586 −0.05356 0.072599 X1 * X7{circumflex over ( )}2 −0.08806 −0.22499 0.081568 −0.25256 0.561151 −0.58836 X2 * X6{circumflex over ( )}2 −1.00914 0.606562 0.284071 0.046102 0.41409 0.873323 X3 * X5{circumflex over ( )}2 −0.01178 −0.44601 −0.05595 0.391251 −0.32461 −0.41315 X1{circumflex over ( )}2 * X7 0.106834 −0.12442 −0.05607 0.028828 0.004795 0.457357 X2{circumflex over ( )}2 * X6 −0.52803 1.651051 0.058907 0.309708 0.281509 −0.24423 X3{circumflex over ( )}2 * X5 −0.00389 0.201007 −0.00094 −0.20202 −0.13431 0.354544 X1 * X8{circumflex over ( )}2 0.015187 −0.34769 0.08246 0.06451 0.168016 0.228432 X2 * X7{circumflex over ( )}2 0.025258 0.087945 −0.0199 0.185455 −0.1782 −0.50353 X3 * X6{circumflex over ( )}2 0.134832 0.483539 −0.09509 0.093434 −0.54972 −0.26446 X4 * X5{circumflex over ( )}2 0.099871 0.45514 0.006394 −0.49104 0.28598 0.126216 X1{circumflex over ( )}2 * X8 0.149625 −0.24469 −0.21991 0.101241 0.099611 0.223656 X2{circumflex over ( )}2 * X7 0.19227 1.058495 −0.06144 0.363287 −0.27438 −1.13555 X3{circumflex over ( )}2 * X6 −0.27758 0.548618 0.051733 0.143376 0.006174 −0.17219 X4{circumflex over ( )}2 * X5 0.007275 −0.0924 −0.00598 0.239579 −0.63768 0.493799 X2 * X8{circumflex over ( )}2 −0.05416 −0.13084 0.005373 1.114014 0.091439 −0.41398 X3 * X7{circumflex over ( )}2 −0.00549 −0.21343 0.018918 0.140419 −0.13873 −0.22254 X4 * X6{circumflex over ( )}2 0.057689 −0.27348 −0.00569 −0.31628 0.310727 0.195745 X2{circumflex over ( )}2 * X8 0.145137 −0.77182 −0.07505 1.084537 0.625498 −0.01611 X3{circumflex over ( )}2 * X7 −0.05073 0.581663 −0.00916 0.428506 −0.77022 0.678208 X4{circumflex over ( )}2 * X6 0.024305 0.626202 −0.04456 −0.48323 0.609525 0.162889 X3 * X8{circumflex over ( )}2 −0.0503 −1.54554 0.162741 0.647692 −0.76602 0.1703 X4 * X7{circumflex over ( )}2 0.112733 −0.36342 0.050533 0.004786 −0.00474 −0.30701 X5 * X6{circumflex over ( )}2 0.095975 −0.28424 −0.08675 −0.36332 −0.22922 0.374847 X3{circumflex over ( )}2 * X8 −0.13475 0.882325 0.052756 0.383859 −0.42301 0.595427 X4{circumflex over ( )}2 * X7 0.332893 0.017863 −0.13432 0.125973 −0.16843 −0.63801 X5{circumflex over ( )}2 * X6 0.069911 −0.18661 0.016286 −0.83682 0.260991 0.414219 X4 * X8{circumflex over ( )}2 −0.05127 −1.19265 0.225417 0.090162 0.143798 −0.21253 X5 * X7{circumflex over ( )}2 0.090659 −0.66751 0.022032 −0.47209 −0.12008 −0.1908 X4{circumflex over ( )}2 * X8 0.998142 1.054438 −1.18461 1.04276 −1.06041 −0.48463 X5{circumflex over ( )}2 * X7 −0.05968 0.151483 −0.03563 0.339599 −0.51738 0.269677 X5 * X8{circumflex over ( )}2 −0.15425 −0.91742 0.153801 0.440071 0.040726 −1.02964 X6 * X7{circumflex over ( )}2 0.3314 0.063172 −0.25876 0.163682 −0.52787 0.026504 X5{circumflex over ( )}2 * X8 −0.02894 −1.41937 0.070566 0.020657 0.199328 0.154472 X6{circumflex over ( )}2 * X7 0.005695 0.376493 0.021879 −0.35252 0.694648 −0.14486 X6 * X8{circumflex over ( )}2 0.004863 0.480603 −0.00331 −0.13929 0.073886 0.152801 X6{circumflex over ( )}2 * X8 −0.10047 0.386874 0.067126 0.661709 −0.22279 0.017461 X7 * X8{circumflex over ( )}2 −0.06321 −0.54661 0.144013 −0.60518 0.102708 0.35643 X7{circumflex over ( )}2 * X8 −0.03717 0.194313 0.003083 0.009743 −0.27426 0.314884 X1{circumflex over ( )}2 −0.00768 0.086649 0.012692 −0.06566 −0.07393 0.161754 X1{circumflex over ( )}3 0.038819 −0.0695 0.044076 −0.21003 0.282245 0.112001 X2{circumflex over ( )}2 0.046229 −0.08778 0.03684 −0.18937 0.291741 0.104975 X2{circumflex over ( )}3 0.213497 −0.34489 0.080422 −0.25713 0.058924 −0.37002 X3{circumflex over ( )}2 0.095259 −0.28107 −0.00637 0.364989 0.377389 0.201308 X3{circumflex over ( )}3 −0.09989 0.53888 0.043301 −0.46934 0.395873 0.081419 X4{circumflex over ( )}2 −0.04436 −0.08594 0.018229 −0.34727 0.073934 0.093728 X4{circumflex over ( )}3 0.787932 −0.06127 0.749871 −0.69131 −0.57711 −0.61321 X5{circumflex over ( )}2 0.316445 −0.43198 0.332211 −0.26148 −0.07632 −0.54564 X5{circumflex over ( )}3 −0.02888 −0.8167 0.031787 −0.24029 0.200737 1.087402 X6{circumflex over ( )}2 −0.01576 −0.35017 0.003052 −0.03722 −0.01958 0.473513 X6{circumflex over ( )}3 −0.04754 2.19229 0.189532 −0.38815 −0.3681 0.408095 X7{circumflex over ( )}2 −0.03171 0.751564 0.067412 0.58956 −0.28391 −0.45187 X7{circumflex over ( )}3 −0.04099 0.712215 0.069639 −0.54337 0.556039 0.481705 X8{circumflex over ( )}2 −0.00864 0.059843 0.032812 −0.86241 0.715074 0.112728 X8{circumflex over ( )}3 −0.08322 0.298577 0.000794 −0.0088 −0.16956 0.091655 X1 * X2 * X3 0.160214 −0.07112 −0.01747 0.580289 −0.37512 −0.40644 X1 * X2 * X4 0.263306 −0.05903 0.009309 −0.02912 −0.02022 −0.20826 X1 * X2 * X5 0.193875 −0.60161 −0.05888 −0.5636 −0.33581 0.459821 X1 * X3 * X4 0.088528 0.158979 −0.0375 0.040853 −0.08436 0.399633 X1 * X2 * X6 −0.26512 0.763972 −0.03223 −0.34436 1.088783 −0.06016 X1 * X3 * X5 −0.00742 0.349736 −0.0529 0.615873 −0.86956 −0.26218 X2 * X3 * X4 0.046114 0.014618 −0.10225 −0.04571 0.064741 0.090462 X1 * X2 * X7 0.063517 0.517846 −0.03157 0.006537 0.322928 −0.66546 X1 * X3 * X6 −0.23607 0.172301 0.035039 0.290442 −0.19931 −0.06287 X1 * X4 * X5 −0.20104 −0.47338 −0.11842 0.4372 0.414599 0.322441 X2 * X3 * X5 −0.03576 −0.26087 −0.00283 0.051125 −0.12461 0.137984 X1 * X2 * X8 −0.03923 −0.71525 −0.10156 0.439384 0.182428 −0.01363 X1 * X3 * X7 −0.114 0.465199 −0.01425 0.32004 −0.99512 1.390954 X1 * X4 * X6 0.230703 0.667971 −0.01642 −0.37826 0.837159 −0.97283 X2 * X3 * X6 0.129692 0.727401 0.038007 0.263506 −0.55616 −0.33523 X2 * X4 * X5 0.140268 0.230195 −0.04605 −0.27446 0.173738 0.398033 X1 * X3 * X8 −0.16733 −0.62232 0.177315 −0.47542 −0.24262 1.317815 X1 * X4 * X7 0.156772 0.64452 0.031884 −0.01695 0.242023 −0.76439 X1 * X5 * X6 0.033416 −0.56853 −0.05077 0.271349 0.473032 0.12496 X2 * X3 * X7 −0.12838 0.87972 −0.04811 0.654619 −1.1611 1.006712 X2 * X4 * X6 −0.20147 −0.39774 0.010047 0.08196 −0.21442 0.744706 X3 * X4 * X5 0.003435 −0.01086 0.012796 −0.4701 0.58065 −0.5819 X1 * X4 * X8 0.576581 −0.00706 0.016747 0.154406 −0.61813 −0.81063 X1 * X5 * X7 0.180499 0.34086 0.009898 −0.24055 0.529418 −0.1564 X2 * X3 * X8 −0.03514 0.293551 0.081938 0.171135 −0.51066 −0.1078 X2 * X4 * X7 −0.30396 0.203527 0.031144 −0.00716 0.311411 0.022828 X2 * X5 * X6 0.05101 −0.39829 −0.02456 0.135604 −0.20543 −0.69227 X3 * X4 * X6 −0.04741 −0.09161 −0.09508 0.132019 −0.19861 −0.41266 X1 * X5 * X8 −0.0819 −1.07915 0.048662 0.164458 −0.29504 0.191655 X1 * X6 * X7 0.046107 −0.22552 −0.06191 1.723596 −1.88341 −0.34188 X2 * X4 * X8 −0.43232 −0.1591 −0.10727 0.162957 −0.00579 −0.18417 X2 * X5 * X7 0.135992 −2.58045 0.034051 0.342312 −0.51695 −0.06008 X3 * X4 * X7 −0.59868 1.111615 0.08758 0.287463 0.003834 −0.18646 X3 * X5 * X6 −0.07846 0.681727 −0.01024 0.069342 0.382232 −0.45796 X1 * X6 * X8 −0.26168 −0.12156 −0.06269 0.001624 0.125841 −0.10503 X2 * X5 * X8 −0.16413 −0.37255 0.073576 −0.28546 0.443843 −0.88881 X2 * X6 * X7 0.154197 0.810208 −0.01472 −0.75301 0.900955 −0.23687 X3 * X4 * X8 −0.77757 1.312509 −0.55074 0.704606 0.268034 0.41796 X3 * X5 * X7 −0.18703 0.138185 −0.05783 0.209536 −0.41074 0.32196 X4 * X5 * X6 −0.14313 −0.33643 0.140057 0.004691 1.02762 −0.64629 X1 * X7 * X8 −0.05905 0.660023 −0.02037 0.040803 0.281258 −0.62077 X2 * X6 * X8 −0.10889 −0.15184 −0.09955 0.164032 −0.34715 0.4481 X3 * X5 * X8 0.069664 0.261902 −0.1005 0.613685 −0.20535 −1.95732 X3 * X6 * X7 −0.12915 −0.23787 0.046583 0.207981 −0.38276 0.401301 X4 * X5 * X7 0.028585 0.128449 0.096828 0.36848 0.297074 −0.98261 X2 * X7 * X8 0.089988 0.792047 −0.07317 −0.22195 −0.25763 −0.134 X3 * X6 * X8 0.012718 0.0203 −0.01428 0.257937 −0.07241 −0.34114 X4 * X5 * X8 −0.12118 −1.20935 0.095071 0.900399 −1.15467 −0.03173 X4 * X6 * X7 −0.01389 −1.23558 0.039361 −0.55595 −0.60764 0.760828 X3 * X7 * X8 0.036954 0.675967 −0.00634 −0.44508 0.52597 −0.38792 X4 * X6 * X8 0.284669 −0.53585 −0.11066 0.244735 0.190827 −0.59387 X5 * X6 * X7 0.038589 0.559155 0.0745 −0.3852 1.094862 −1.06848 X4 * X7 * X8 0.095748 0.038007 −0.11768 0.04489 −0.05278 −0.17255 X5 * X6 * X8 0.179035 −0.85389 −0.01738 −0.10464 0.084094 −0.01803 X5 * X7 * X8 −0.10711 0.275223 0.112764 −0.14654 −0.40869 0.532016 X6 * X7 * X8 3.22E−14 −5.1E−13 −1.7E−14 −5.6E−14 −1.4E−13 2.28E−13 A  Because there are so many crossidentifications that need to be made, the number of significant terms increases substantially with the number of media types which need to be differentiated. It is not necessary, however, to have the same terms in each equation. The following table shows the most significant terms for each media type. These are organized into terms for which increased sensor output is a positive indicator, and those for which increased sensor signal is a negative indicator.

TABLE 12 Case 4 Highest Contributing Terms For Each Media Type Media Type Positive Equation Terms Negative Equation Terms Glossy X5*X7 X3*X5, X3*X5{circumflex over ( )}2 Vinyl Labels X7, X3*X5, X3*X6, X7*X8, X3*X4*X7, X3*X7*X8, X3{circumflex over ( )}2*X6, X5{circumflex over ( )}2*X7, X7{circumflex over ( )}2, X4*X6*X7 X3*X5*X6, X3*X5*X7 Transparency X3*X5 X5*X7, X5{circumflex over ( )}2*X7 Plain Paper, Light X8, X2*X4, X2*X4*X8, X7, X4*X8, X1{circumflex over ( )}2*X4, X1*X4, X3*X7{circumflex over ( )}2, X3{circumflex over ( )}2*X7, X1*X3, X3, X4 X5{circumflex over ( )}2*X7, X5*X8 Plain Paper, Medium X4, X7, X1*X4, X4*X8, X3, X2*X4, X2*X8, X3*X7, X6*X8, X1{circumflex over ( )}2*X4, X5*X8, X5{circumflex over ( )}2*X7, X2*X4*X6, X1*X7*X8, X4*X7*X8 X2*X4*X8, X4*X6*X7 Plain Paper, Heavy X6, X1*X6, X3*X5, X6*X7, X2*X4, X3*X6, X3{circumflex over ( )}2*X6, X1*X4*X6, X2*X4*X6 X6*X7{circumflex over ( )}2, X4*X7*X8 Cardstock, lighter X3*X6, X4*X6, X3{circumflex over ( )}2*X6, X3*X7, X5*X6*X7 X1*X3*X6, X3*X4*X6, X3*X4*X8, X3*X6*X8, X4*X6*X8 Cardstock, heavier X3*X7, X7*X8, X1{circumflex over ( )}2*X6, X6*X7{circumflex over ( )}2, X2*X4*X6, X3*X4*X8, X2*X6{circumflex over ( )}2, X5*X6*X7 X3*X6*X8 Paper Labels X4*X7{circumflex over ( )}2, X6*X7{circumflex over ( )}2, X7 X3*X4*X7, X4*X6*X7 Bond X3, X7, X1*X3, X2*X5*X7, X5, X8, X3*X5, X4*X6, X3*X4*X7, X2*X6*X7 X1*X3{circumflex over ( )}2, X2*X3{circumflex over ( )}2, X3{circumflex over ( )}2*X5, X3*X7{circumflex over ( )}2, X3{circumflex over ( )}2*X7, X3{circumflex over ( )}2,, X7{circumflex over ( )}2 Envelopes X1*X3{circumflex over ( )}2, X3{circumflex over ( )}2*X7 X3*X6 
Case 5 illustrates a further facet of the present system in its ability to empirically provide for unique but measureable characteristics. Here the media type is one of Current Tray Setting or Not Current Tray Setting. The sensors are: temperature (X1), relative humidity (X2), bending stiffness (X3), impedance magnitude (X4), impedance phase (X5), piezoelectric (X6), gloss (X7), media feed motor current (X8), optical average (X9), and optical deviation (X10). The use of this media type determining equation set is to confirm that the media type present in the tray is actually the media type that the imagining device has been set to expect via a default setting or by user input. 
TABLE 13 Case 5 Media Type Determining Equation Terms and Coefficients Equation Coefficients Not Media Media Tray Tray Equation Setting Setting Terms 0.392198 −0.3922 X1 −0.21532 0.215322 X2 −0.34959 0.349589 X3 −1.61869 1.618695 X4 0.649465 −0.64947 X5 −0.20153 0.201533 X6 0.095659 −0.09566 X7 0.41543 −0.41543 X8 0.74879 −0.74879 X9 −0.66235 0.662346 X10 −0.09979 0.099786 X1*X2 −0.32922 0.329224 X1*X3 −0.11913 0.119131 X1*X4 0.037662 −0.03766 X2*X3 0.593923 −0.59392 X1*X5 −0.39819 0.398186 X2*X4 −0.03036 0.030365 X1*X6 0.227733 −0.22773 X2*X5 0.714031 −0.71403 X3*X4 0.351761 −0.35176 X1*X7 −0.52856 0.528565 X2*X6 −0.45134 0.451339 X3*X5 0.152689 −0.15269 X1*X8 0.471173 −0.47117 X2*X7 −0.38101 0.381006 X3*X6 −0.5 0.499997 X4*X5 0.166312 −0.16631 X1*X9 −0.28433 0.284328 X2*X8 −0.40146 0.401462 X3*X7 −0.82183 0.821829 X4*X6 −0.11683 0.116833 X1*X10 0.029629 −0.02963 X2*X9 −0.4343 0.434298 X3*X8 0.823381 −0.82338 X4*X7 0.404232 −0.40423 X5*X6 0.034223 −0.03422 X2*X10 −0.03628 0.036278 X3*X9 −0.08499 0.084995 X4*X8 0.10603 −0.10603 X5*X7 0.387408 −0.38741 X3*X10 −1.57542 1.575417 X4*X9 0.174785 −0.17478 X5*X8 −0.17738 0.177377 X6*X7 −0.12492 0.124916 X4*X10 0.422478 −0.42248 X5*X9 0.955331 −0.95533 X6*X8 −0.67126 0.671263 X5*X10 1.642136 −1.64214 X6*X9 −0.19022 0.190223 X7*X8 −1.07103 1.071031 X6*X10 −0.09467 0.094671 X7*X9 0.585393 −0.58539 X7*X10 0.350863 −0.35086 X8*X9 −0.20693 0.206927 X8*X10 −0.24222 0.24222 X9*X10 −0.00424 0.004238 X1*X2{circumflex over ( )}2 −0.01849 0.018489 X1{circumflex over ( )}2*X2 −0.07571 0.075706 X1*X3{circumflex over ( )}2 −0.16202 0.162018 X1{circumflex over ( )}2*X3 0.023809 −0.02381 X1*X4{circumflex over ( )}2 −0.06483 0.064831 X2*X3{circumflex over ( )}2 0.143068 −0.14307 X1{circumflex over ( )}2*X4 0.017994 −0.01799 X2{circumflex over ( )}2*X3 −0.14988 0.149876 X1*X5{circumflex over ( )}2 −0.07459 0.074586 X2*X4{circumflex over ( )}2 0.248391 −0.24839 X1{circumflex over ( )}2*X5 0.559786 −0.55979 X2{circumflex over ( )}2*X4 −0.43422 0.434218 X1*X6{circumflex over ( )}2 −0.23801 0.238015 X2*X5{circumflex over ( )}2 0.765897 −0.7659 X3*X4{circumflex over ( )}2 −0.04636 0.046359 X1{circumflex over ( )}2*X6 0.16869 −0.16869 X2{circumflex over ( )}2*X5 0.206799 −0.2068 X3{circumflex over ( )}2*X4 −0.39389 0.393892 X1*X7{circumflex over ( )}2 −0.12102 0.121018 X2*X6{circumflex over ( )}2 −0.12624 0.126241 X3*X5{circumflex over ( )}2 −0.33551 0.335508 X1{circumflex over ( )}2*X7 0.034876 −0.03488 X2{circumflex over ( )}2*X6 −0.1061 0.106103 X3{circumflex over ( )}2*X5 −0.07525 0.075246 X1*X8{circumflex over ( )}2 0.299633 −0.29963 X2*X7{circumflex over ( )}2 0.050744 −0.05074 X3*X6{circumflex over ( )}2 0.043682 −0.04368 X4*X5{circumflex over ( )}2 0.005082 −0.00508 X1{circumflex over ( )}2*X8 −0.65839 0.658391 X2{circumflex over ( )}2*X7 −0.15007 0.15007 X3{circumflex over ( )}2*X6 −0.44138 0.441375 X4{circumflex over ( )}2*X5 −0.2356 0.235603 X1*X9{circumflex over ( )}2 −0.09121 0.091206 X2*X8{circumflex over ( )}2 0.014659 −0.01466 X3*X7{circumflex over ( )}2 0.144011 −0.14401 X4*X6{circumflex over ( )}2 −0.2481 0.248105 X1{circumflex over ( )}2*X9 −0.03678 0.036785 X2{circumflex over ( )}2*X8 −0.18586 0.185861 X3{circumflex over ( )}2*X7 −0.29367 0.293665 X4{circumflex over ( )}2*X6 0.26522 −0.26522 X1*X10{circumflex over ( )}2 −0.11792 0.117918 X2*X9{circumflex over ( )}2 −0.28022 0.280216 X3*X8{circumflex over ( )}2 0.569179 −0.56918 X4*X7{circumflex over ( )}2 −0.12589 0.125893 X5*X6{circumflex over ( )}2 0.049607 −0.04961 X1{circumflex over ( )}2*X10 0.139017 −0.13902 X2{circumflex over ( )}2*X9 −0.27999 0.279991 X3{circumflex over ( )}2*X8 0.400057 −0.40006 X4{circumflex over ( )}2*X7 −0.40352 0.403516 X5{circumflex over ( )}2*X6 0.272747 −0.27275 X2*X10{circumflex over ( )}2 0.125748 −0.12575 X3*X9{circumflex over ( )}2 −0.04443 0.044431 X4*X8{circumflex over ( )}2 −0.38804 0.388044 X5*X7{circumflex over ( )}2 0.010946 −0.01095 X2{circumflex over ( )}2*X10 0.026099 −0.0261 X3{circumflex over ( )}2*X9 0.128374 −0.12837 X4{circumflex over ( )}2*X8 −0.0977 0.097698 X5{circumflex over ( )}2*X7 0.112268 −0.11227 X3*X10{circumflex over ( )}2 −0.57072 0.570721 X4*X9{circumflex over ( )}2 −0.02157 0.021574 X5*X8{circumflex over ( )}2 −1.17249 1.172486 X6*X7{circumflex over ( )}2 0.177258 −0.17726 X3{circumflex over ( )}2*X10 −0.48689 0.48689 X4{circumflex over ( )}2*X9 −0.02917 0.02917 X5{circumflex over ( )}2*X8 0.351264 −0.35126 X6{circumflex over ( )}2*X7 0.172658 −0.17266 X4*X10{circumflex over ( )}2 −0.21287 0.212866 X5*X9{circumflex over ( )}2 −0.02781 0.027815 X6*X8{circumflex over ( )}2 0.191457 −0.19146 X4{circumflex over ( )}2*X10 0.053537 −0.05354 X5{circumflex over ( )}2*X9 0.394465 −0.39447 X6{circumflex over ( )}2*X8 −0.01713 0.017129 X5*X10{circumflex over ( )}2 0.504408 −0.50441 X6*X9{circumflex over ( )}2 −0.16856 0.168563 X7*X8{circumflex over ( )}2 −0.54755 0.547553 X5{circumflex over ( )}2*X10 0.589201 −0.5892 X6{circumflex over ( )}2*X9 −0.3931 0.393102 X7{circumflex over ( )}2*X8 0.325506 −0.32551 X6*X10{circumflex over ( )}2 0.027363 −0.02736 X7*X9{circumflex over ( )}2 −0.45764 0.45764 X6{circumflex over ( )}2*X10 −0.66756 0.667563 X7{circumflex over ( )}2*X9 0.232242 −0.23224 X7*X10{circumflex over ( )}2 −0.12155 0.121549 X8*X9{circumflex over ( )}2 −0.03118 0.031175 X7{circumflex over ( )}2*X10 0.087035 −0.08704 X8{circumflex over ( )}2*X9 −0.05629 0.056286 X8*X10{circumflex over ( )}2 −0.17974 0.179739 X8{circumflex over ( )}2*X10 −0.26172 0.261719 X9*X10{circumflex over ( )}2 0.237149 −0.23715 X9{circumflex over ( )}2*X10 0.068742 −0.06874 X1{circumflex over ( )}2 0.001726 −0.00173 X1{circumflex over ( )}3 −0.03659 0.036588 X2{circumflex over ( )}2 0.005717 −0.00572 X2{circumflex over ( )}3 −0.22425 0.224245 X3{circumflex over ( )}2 −0.11607 0.116067 X3{circumflex over ( )}3 −1.08999 1.089989 X4{circumflex over ( )}2 0.004207 −0.00421 X4{circumflex over ( )}3 −0.15123 0.151232 X5{circumflex over ( )}2 −0.26763 0.267628 X5{circumflex over ( )}3 −0.72407 0.724066 X6{circumflex over ( )}2 −0.45835 0.458355 X6{circumflex over ( )}3 −1.1929 1.192896 X7{circumflex over ( )}2 −0.42005 0.420047 X7{circumflex over ( )}3 −0.04523 0.045227 X8{circumflex over ( )}2 −0.06928 0.069284 X8{circumflex over ( )}3 0.033054 −0.03305 X9{circumflex over ( )}2 −0.26327 0.263266 X9{circumflex over ( )}3 0.073182 −0.07318 X10{circumflex over ( )}2 0.264724 −0.26472 X10{circumflex over ( )}3 0.031831 −0.03183 X1*X2*X3 0.325466 −0.32547 X1*X2*X4 0.19262 −0.19262 X1*X2*X5 0.360998 −0.361 X1*X3*X4 −0.1275 0.127503 X1*X2*X6 −0.22275 0.222751 X1*X3*X5 0.356181 −0.35618 X2*X3*X4 −0.27042 0.270415 X1*X2*X7 0.146347 −0.14635 X1*X3*X6 0.054064 −0.05406 X1*X4*X5 −0.23348 0.233479 X2*X3*X5 −0.1187 0.118696 X1*X2*X8 −0.11296 0.112962 X1*X3*X7 0.30988 −0.30988 X1*X4*X6 0.109666 −0.10967 X2*X3*X6 0.180193 −0.18019 X2*X4*X5 0.138588 −0.13859 X1*X2*X9 −0.16146 0.161457 X1*X3*X8 0.618789 −0.61879 X1*X4*X7 0.041566 −0.04157 X1*X5*X6 0.335233 −0.33523 X2*X3*X7 −0.40252 0.40252 X2*X4*X6 −0.09183 0.09183 X3*X4*X5 0.025335 −0.02533 X1*X2*X10 −0.18679 0.186789 X1*X3*X9 0.077534 −0.07753 X1*X4*X8 −0.06461 0.064615 X1*X5*X7 −0.08829 0.088292 X2*X3*X8 0.864694 −0.86469 X2*X4*X7 −0.02159 0.021592 X2*X5*X6 0.182978 −0.18298 X3*X4*X6 0.218334 −0.21833 X1*X3*X10 −0.34019 0.340194 X1*X4*X9 −0.00043 0.000427 X1*X5*X8 0.10574 −0.10574 X1*X6*X7 0.004416 −0.00442 X2*X3*X9 0.00611 −0.00611 X2*X4*X8 −0.58429 0.584295 X2*X5*X7 0.371243 −0.37124 X3*X4*X7 −0.04809 0.048086 X3*X5*X6 0.428082 −0.42808 X1*X4*X10 0.115725 −0.11573 X1*X5*X9 0.303479 −0.30348 X1*X6*X8 −0.02667 0.026671 X2*X3*X10 0.054578 −0.05458 X2*X4*X9 −0.12133 0.121326 X2*X5*X8 0.074864 −0.07486 X2*X6*X7 0.256921 −0.25692 X3*X4*X8 −0.30341 0.303408 X3*X5*X7 0.007407 −0.00741 X4*X5*X6 −0.44697 0.446969 X1*X5*X10 0.122725 −0.12272 X1*X6*X9 −0.01008 0.010077 X1*X7*X8 0.318501 −0.3185 X2*X4*X10 −0.19568 0.195683 X2*X5*X9 0.022128 −0.02213 X2*X6*X8 0.859187 −0.85919 X3*X4*X9 −0.21601 0.216007 X3*X5*X8 −0.55128 0.551277 X3*X6*X7 0.078494 −0.07849 X4*X5*X7 −0.17216 0.172155 X1*X6*X10 −0.25009 0.250095 X1*X7*X9 −0.36721 0.367207 X2*X5*X10 −0.23975 0.239747 X2*X6*X9 0.094702 −0.0947 X2*X7*X8 0.662477 −0.66248 X3*X4*X10 −0.36267 0.362669 X3*X5*X9 −0.44733 0.447328 X3*X6*X8 −0.14987 0.149866 X4*X5*X8 −0.19691 0.196906 X4*X6*X7 0.497398 −0.4974 X1*X7*X10 −0.14898 0.148985 X1*X8*X9 0.342745 −0.34274 X2*X6*X10 −0.16357 0.163575 X2*X7*X9 −0.04455 0.044553 X3*X5*X10 −0.33785 0.337846 X3*X6*X9 −0.32596 0.325962 X3*X7*X8 −0.64484 0.644836 X4*X5*X9 0.174275 −0.17428 X4*X6*X8 0.029496 −0.0295 X5*X6*X7 0.070413 −0.07041 X1*X8*X10 0.415767 −0.41577 X2*X7*X10 −0.54171 0.541714 X2*X8*X9 0.263033 −0.26303 X3*X6*X10 0.079443 −0.07944 X3*X7*X9 0.021509 −0.02151 X4*X5*X10 −0.45956 0.459559 X4*X6*X9 0.227948 −0.22795 X4*X7*X8 0.264222 −0.26422 X5*X6*X8 −0.08646 0.086464 X1*X9*X10 0.173404 −0.1734 X2*X8*X10 −0.11982 0.119819 X3*X7*X10 0.099572 −0.09957 X3*X8*X9 0.079014 −0.07901 X4*X6*X10 0.854689 −0.85469 X4*X7*X9 0.371977 −0.37198 X5*X6*X9 −0.03903 0.039028 X5*X7*X8 0.087049 −0.08705 X2*X9*X10 0.066701 −0.0667 X3*X8*X10 0.169131 −0.16913 X4*X7*X10 0.011573 −0.01157 X4*X8*X9 −0.37003 0.370029 X5*X6*X10 −0.26829 0.268288 X5*X7*X9 −0.27338 0.273379 X6*X7*X8 0.289892 −0.28989 X3*X9*X10 0.137863 −0.13786 X4*X8*X10 −0.00124 0.001243 X5*X7*X10 −0.26242 0.262417 X5*X8*X9 −0.70348 0.70348 X6*X7*X9 −0.0233 0.023298 X4*X9*X10 −0.03544 0.035437 X5*X8*X10 0.749406 −0.74941 X6*X7*X10 0.569549 −0.56955 X6*X8*X9 −0.16385 0.163854 X5*X9*X10 −0.2438 0.243799 X6*X8*X10 −0.03367 0.033668 X7*X8*X9 −0.4882 0.488196 X6*X9*X10 −0.06464 0.064645 X7*X8*X10 0.029627 −0.02963 X7*X9*X10 0.063429 −0.06343 X8*X9*X10 −2.1E−14 −7.8E−14 A  It is possible to either expand or contract the number of terms used in each equation depending on the resolution desired in discerning different media types by adjusting the selection criteria used for the coefficients. The media type determining equations may be condensed when certain terms are found to be insignificant contributors to the solution. This would be empirically determined. This is a matter of design choice and the number of terms chosen is influenced by processing power of the controller, memory available, sensor cost, space within the operational device to accommodate the sensor set.
 Types are not limited to different types of media. A type may be media color, the presence of perforations in the media, the presence of an RFID strip on the media, the presence of a magnetic strip on the media, the presence of holes, preprinted media such as a form, media size. A type can be any distinguishing feature or characteristic provided that there is a corresponding sensor within the sensor sets 14 and 52 to detect these features or characteristics.
 The foregoing description of several methods and an embodiment of the invention has been presented for purposes of illustration. It is not intended to be exhaustive or to limit the invention to the precise steps and/or forms disclosed, and obviously many modifications and variations are possible in light of the above teaching. It is intended that the scope of the invention be defined by the claims appended hereto.
Claims (33)
1. In an operational imaging device having a media set consisting of M types of media and an operational sensor set for measuring values of a predetermined set of N variables related to a media sheet and the processing thereof by a processing device of the operational imaging device, a method of determining a media type from the M types of media for a media sheet to be processed by the processing device in the imaging device, the method comprising:
storing in memory of the imaging device a predetermined media type determining equation set incorporating the predetermined set of N variables wherein each equation corresponds to one media type of the M types of media in the media set;
measuring, using the operational sensor set, a value of each variable in the set of N variables, the operational sensor set providing corresponding output signals representative of the measured values for the set of N variables, the operational sensor set being in operative communication with a controller; and
at the controller:
converting the output signals received from the operational sensor set into measured normalized variable values for the set of N variables;
solving the media type determining equation set using the measured normalized variable values to determine a media type for the media sheet to be processed; and,
selecting, based upon the determined media type, at least one operational parameter for the processing device for processing the media sheet.
2. The method of claim 1 , wherein solving further comprises determining whether or not the solutions of at least two of the media types determining equations are within a predetermined range of one another, and, when it is determined that the at least two solutions are within the predetermined range, using a lookup table to select the determined media type based on the combinations of the at least two media type determining equations.
3. The method of claim 1 , wherein the selecting the at least one operational parameter is performed using a look up table.
4. The method of claim 1 , wherein each equation in the media type determining equation set is a polynomial equation.
5. The method of claim 4 , wherein an order of each polynomial equation is selected to be in the range of a first order through a fifth order.
6. The method of claim 1 , wherein each equation in the media type determining equation set is a Taylor polynomial.
7. The method of claim 1 , wherein the operational sensor set includes one or more direct sensors.
8. The method of claim 1 , wherein the operational sensor set includes one or more indirect sensors.
9. The method of claim 1 , wherein the operational sensor set includes one or more imaging subsystem response sensors.
10. The method of claim 1 , wherein the processing device is an electrophotographic printer and the set of N variables comprises at least two variables selected from the group comprising: electrical impedance magnitude, electrical impedance phase, contact resistance, capacitance, optical transmission mean, optical transmission deviation, optical spectral reflectance, optical diffuse reflectance, bending stiffness, acoustic transmission, temperature, media size, relative humidity, media feed motor current, fuser temperature, transfer current, transfer voltage, media holes, preprinted areas, media color, multilayer media, RFID signal, magnetic field, MICR, and, further wherein, the operational sensor set includes sensors for measuring the at least two selected variables.
11. The method of claim 1 , wherein the processing device is an electrophotographic printer and the set of N variables comprises at least two variables selected from the group comprising: impedance phase, impedance magnitude, optical spectral reflection mean, optical spectral reflection deviation, optical transmission mean, optical transmission deviation, temperature, relative humidity, media feed motor current, and, further wherein, the operational sensor sets includes sensors for measuring the at least two selected variables.
12. The method of claim 11 , wherein the M media types comprise a plain paper light type, a plain paper standard type, a plain paper heavy type, a cardstock light type, a cardstock standard type, a cardstock heavy type, a glossy paper light type, a glossy paper standard type, a glossy paper heavy type, a paper label type, a paper label heavy type, a plastic label type, a plastic label heavy type, a polymer label type, an envelope standard type, an envelope heavy type, a synthetic polymer type, and a rough/cotton paper type, and, further wherein, the at least two variables comprise at least four variables.
13. The method of claim 12 , wherein for each of the M media types, the media type determining equation set contains a media type determining equation corresponding to each of the M media types.
14. The method of claim 11 , wherein the M media types comprise a polymeric media type, a cardstock media type and a plain paper media type.
15. The method of claim 14 , wherein the set of M media determining equations comprises a polymeric media type determining equation, a cardstock media type determining equation and a plain paper media type determining equation.
16. The method of claim 1 , wherein the processing device is an electrophotographic printer and the set of N variables comprises at least two variables selected from the group comprising: optical transmission mean, optical transmission deviation, temperature, relative humidity, media feed motor current, and, further wherein, the operational sensor sets includes sensors for measuring the at least two selected variables.
17. The method of claim 16 , wherein the M media types comprise a polymeric media type, a cardstock media type, a plain paper media type, and a light plain paper media type.
18. The method of claim 17 , wherein the set of M media determining equations comprises a polymeric media type determining equation, a cardstock media type determining equation, a plain paper media type determining equation and a light plain paper media type determining equation.
19. The method of claim 1 , wherein each equation in the set of M media type determining equations comprises a plurality of terms with each term having a coefficient wherein the coefficients of a larger absolute value in comparison to the other coefficients in each equation have a greater weight in determining the media type.
20. The method of claim 19 , wherein each equation of the media type determining equation set is truncated so that the remaining terms in each equation of the media type detrmining equation set have coefficients of a larger absolute value when compared to the coefficients of the truncated terms from that equation.
21. The method of claim 1 , wherein the media type determining equation set stored in memory is generated by:
determining the M media types forming the media set to be used in the operational imaging device;
determining the number of variables in the set of N variables needed to determine each media type in the media set;
providing a training sensor set for measuring the set of the N variables and providing corresponding output signals therefor;
using the training set of sensors to measure the set of N variables with a known sample of each media type in the media set and a training imaging device to create a corresponding training data set for each media type in the media set;
inputting each training data set for each media type into a classifier training engine; and
generating, using the classifier training engine, the media type determining equation for each media type in the media set forming the media type determining equation set.
22. The method of claim 21 , wherein the classifier training engine is one of a support vector engine, a neural network, a quadratic classifier, a Bayesian network, and a learning vector quantizer.
23. The method of claim 22 , wherein when the media type determining equation set consists of polynomial equations.
24. The method of claim 23 , wherein the number of terms in each equation in the set of M media type determining equations is reduced using a polynomial consolidator.
25. The method of claim 23 , further comprising weighting the terms of each equation in the media type determining equation set using an expert knowledge cost/value weighter.
26. A method of media type sensing for use in an operational imaging device, the method comprising:
establishing a media set comprising a plurality of media types M to be used in the operational imaging device;
determining a number of variables N needed to determine each media type in the media set;
providing a training sensor set for measuring each of the N variables and providing corresponding output signal therefor;
using the training sensor set to measure the N variables with a known sample of each media type in the media set and a training imaging device to create a corresponding training data set for each media type in the media set, wherein the measuring includes taking multiple measurements of each of the N variables;
inputting each training data set for each media type into a classifier training engine;
generating, using the classifier training engine and each training data set for each media type, a media type determining equation for each media type incorporating corresponding N variable terms to create a set of M media type determining equations for use with an operational set of sensors corresponding to the training set sensors; and
in an operational imaging device:
storing in a memory the set of M media type determining equations;
providing the operational sensor set in operable communication with the operational imaging device, the operational sensor set measuring a value of each variable in the set of N variables and providing corresponding output signals for the measured N variables for a sheet of media to be processed;
converting the received output signals into the N measured normalized variable values;
solving the set of M media type determining equations using the N measured normalized variable values to determine a media type from the media set for the media sheet to be processed; and,
selecting, based upon the determined media type, from a look up table at least one operational parameter for the operational imaging device.
27. The method of claim 26 , wherein the measuring of multiple measurements of each of the N variables by the training sensor set occurs at a plurality of predetermined temperature and relative humidity combinations.
28. The method of claim 26 , wherein the operational imaging device is an electrophotographic printer and the set of N variables comprises at least two variables selected from the group comprising: electrical impedance magnitude, electrical impedance phase, contact resistance, capacitance, optical transmission mean; optical transmission deviation, optical spectral reflectance, optical diffuse reflectance, bending stiffness, acoustic transmission, temperature, media size, relative humidity, media feed motor current, fuser temperature, transfer current, transfer voltage, media holes, preprinted areas, media color, multilayer media, RFID signal, magnetic field, MICR, and, further wherein, the operational sensor set includes sensors for measuring the at least two selected variables.
29. In an operational imaging device having a media set consisting of M types of media and an operational sensor set having S number of sensors for measuring a value for each variable in a set of N variables related to a media sheet and the processing thereof by a processing device of the operational imaging device, a controller in operative communication with the operational sensor set and receiving the corresponding output signals representative of the measured values for the set of N variables, a method of determining a media type from the media set for the media sheet to be processed by the processing device in the operational imaging device, the method comprising:
storing in memory of the imaging device a predetermined matrix consisting of a first media type determining equation set and S! additional sets of media type determining equation sets, wherein the first media type determining equation set in the matrix comprises M media type determining equations using measured variable values from the S number of sensors and the remaining S! additional media type determining equation sets each comprise a plurality of media type determining equations where one or more variables in the set of N variables is missing; and,
determining whether or not all S number of sensors in the operational sensor set are functioning and, when it is determined that all S number of sensors are functioning:
converting the received output signals into the N measured normalized variable values;
solving the first media type determining equation set using the received N measured normalized variable values to determine a media type from the media set for the media sheet to be processed; and
selecting, based upon the determined media type, at least one operational parameter for the processing device for processing the media sheet.
30. The method of claim 29 , wherein, when it is determined that one or more of the S number of sensors are nonfunctioning:
selecting from the S! additional media type determining equation sets a corresponding media type determining equation set having media type determining equations that use measured variable values from the remaining functioning sensors in the operational sensor set;
converting the received output signals from the remaining functioning sensors into measured normalized variable values;
solving the selected additional media type determining equation set using the measured normalized variable values to determine a media type from the media set for the media sheet to be processed; and,
selecting, based upon the determined media type, at least one operational parameter for the processing device for processing the media sheet.
31. An imaging device comprising:
a controller;
a fuser;
an image transfer station
an input area having a media set consisting of M types of media;
an output area for receiving processed a media sheet;
a media feed system for conveying a media sheet to be processed from the input area past the image transfer station and the fuser to the output area;
an operational sensor set for measuring values of a predetermined set of N variables related to the media sheet to be processed and the processing thereof and providing corresponding output signals representative of the measured set of N variables;
a memory containing a predetermined media set of M media type determining equations incorporating the predetermined set of N variables wherein each media type determining equation corresponds to one media type in the media set; and
the fuser, the image transfer station, the media feed system, the operational sensor set and the memory in operative communication with the controller with the controller being configured to:
receive the output signals of the operational sensor set and convert the received output signals into corresponding normalized values for each variable in the set of N variables;
solve the M media equations using the received values for the set of N variables to determine a type of media for the media sheet to be processed;
select, based upon the determined media type, at least one operational parameter for the processing device; and
process the media sheet to be processed using the at least one operational parameter.
32. The imaging device of claim 31 , wherein the set of N variables comprises at least two variables selected from the group comprising: electrical impedance magnitude, electrical impedance phase, contact resistance, capacitance, optical transmission mean; optical transmission deviation, optical spectral reflectance, optical diffuse reflectance, bending stiffness, acoustic transmission, temperature, media size, relative humidity, media feed motor current, fuser temperature, transfer current, transfer voltage, media holes, preprinted areas, media color, multilayer media, RFID signal, magnetic field, MICR, and, further wherein, the operational sensor set includes sensors for measuring the at least two selected variables.
33. The imaging device of claim 31 wherein the at least one operational parameter is one of a transfer voltage, a fuser temperature, a media process speed, and a combination of two or more of foregoing operational parameters.
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JP2021062565A (en) *  20191016  20210422  セイコーエプソン株式会社  Information processor, leaning device, control method of information processor, and program 
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