RU2117932C1 - Method for calibration of spectral instrument - Google Patents

Abstract

FIELD: methods of initial calibration or recalibration of the second spectrometer in light of the first spectrometer, or, respectively, of itself. SUBSTANCE: during calibration use is made of selection and processing of spectral data obtained both from the first and also from the second instruments. In calibration, use is made of selection and processing of spectral data from the same first instrument which are obtained both, before and after necessity in recalibration arises. Instead of modification of corresponding characteristics of the first and second instruments or the first instrument, before and after arising of necessity in calibration, the present invention modifies the equation of calibration of the second instrument or recalibrated instrument for obtaining results compatible with the results obtained from the first instrument or by the first instrument before it comes out of calibrated state. Equation of calibration is such equation which converts the spectral data of concrete specimen in multitude of wave lengths in compliance with calculated value for some chemical or physical property. Usually the form of such equations of calibration is linear combination of spectral absorbing ability or mathematic conversion of values of absorbing ability measured by the first and second instruments for each specimen. EFFECT: preserved or in some cases even improved accuracy of primary calibration or recalibration of instrument. 10 cl, 8 tbl

Description

 The invention relates to spectrophotometers designed to measure electromagnetic radiation, in particular infrared, near (long wave) infrared, visible radiation, Raman spectra, Rayleigh scattering, etc. More specifically, the invention relates to calibration methods that may be useful in predicting chemical and physical properties based on observed spectral data obtained using a spectrophotometer. Even more specifically, this invention includes near infrared calibration equations suitable for predicting or evaluating physical or chemical properties, for example, octane.

 In a publication in the journal ("J.Sci. Food Agric." 34 (1983) c. 1441-1443) B.G. Osbourne proposes using the equation obtained to calibrate one type of instrument for another instrument.

 In the article "The use of indirect calibration with many variables to control the quality of agricultural products using near infrared spectroscopy", G. Puchwein and A. Eibelguber (Microchim Acta (Vienna), 1986, 11, 43-51) offer a computer program for calibration device. The program selects the appropriate frequency values for the spectral data for a part from a series of samples with which the instrument is calibrated, and then confirms with respect to the remaining samples.

 In the article "Limitations existing in the near infrared region related to the self-calibration of a silicon photodiode" Zh.M. Palmer (SPIE T.499, "Measuring Optical Radiation" (1984), pp. 7-14) describes the self-calibration of silicon photodiode detectors.

 In the article “A Simple Method of Internal Modulation for the Spectral Calibration of Spectrometers with a Circular Variable Filter in the Near IR Spectral Region”, Chandrasekhar, Ashok, Bhatt and Manyan (Physics of infrared radiation, vol. 24, N 6, 1984, pp. 571-572) describe the wavelength calibration of telescopes associated with infrared near-infrared devices for astronomical studies using a frequency-dependent signal from a low-pressure mercury arc lamp.

 Mark and Workman (Spectroscopy: 311, 28) developed a computer algorithm to find isonumerational wavelengths. Isonumerational wavelengths are calibration wavelengths that correspond to the same absorbance readout on the NIR gauge and the NIR slave. Therefore, these wavelengths do not actually vary from one device to another.

 Hackman, Diffie, and Milhouse (Analytica Chemica Acta, 192 (1987), 197) proposed a computer program that transfers calibration equations by calculating the systematic error and slope corrections for each wavelength in the equation. This method of correction for systematic error and slope is actually used in Example 3 of this application. U.S. Patent 4,761,522 to R.D. Rosenthal declared PTFE standard for near infrared radiation and a method of manufacturing this standard. However, this standard is not used in transferring calibration from one instrument to another.

 The article “Standardization of Instruments with Many Variables” by Wang et al. (Anal. Chem., 1991, 63, 2750-2756) describes four standardization methods for either adjusting the primary calibration model for use on a secondary instrument or for correcting spectra obtained with a second instrument to determine the difference in response for both instruments. It was found that a calibration model built on the basis of one group may not be applicable for another group. However, using the mathematical apparatus of the calibration procedure with many variables, four other methods were developed to select the best subset of the available samples for transferring the calibration. Among these methods, there is a known method of correcting spectra by the method of linear transfer of one spectral characteristic by its intensity from one device to the same characteristic of another. This source discloses the use of a calculated dependent variable corresponding to the desired physical property and used to derive coefficients for constant values in the second calibration equation.

 In the article "Calibration of the instrument for near-infrared spectroscopy" (48 Spectroscopy, vol. 4, N 4, p. 48-55) B.G. Osbourne describes in detail the operations for establishing simple patterns using multiple linear regression, as well as the use of derivatives of linear terms. The validation of calibration curves is discussed, in particular, how specific wavelengths are selected to determine the terms in the multiple linear regression equations, as well as the statistical significance of a particular calibration sample. This method can be used in the present invention to determine the calibration equations of an appropriately calibrated instrument for a range of values within which successful prediction can be made, i.e. for the area of interest.

 Other methods for determining calibration equations are described in the Journal of Analytical Chemistry (vol. 60, pp. 1193-1202 (1988)). D.M. Haaland and E.V. Thomas. Methods using inverse least squares, partial least squares, traditional least squares and analysis of the main component of the regression are presented.

 In the article "Liquid Absorption Standards for Ultraviolet, Visible and Near Infrared Spectrophotometry" R.G. Martineka in "J.Am.Med.Technol." (July-August, 1978, pp. 210-216) presents liquid absorption standards having the following desired characteristics: wide absorption peaks, wide wavelength range, high molar absorption capacity, solution stability, easily defined purity characteristics and minimum spectral temperature coefficients . The purpose of using such standards is to calculate the absolute spectral absorbance based on the observed absorbance and to use the correction factor of the instrument.

 The article “Using Statistical Data in the Calibration and Verification of Non-Autonomous Long-Wave Infrared Analyzers” by B. Thompson, (ISA, 1989, document # 88-0116) describes the use of infrared radiation from the long-wave part of the infrared spectrum for process control, including using statistics.

 B. G. Osborne, in his article “Calibration of Instruments for Spectroscopy in the Longwave of the IR Spectrum” (Spectroscopy, 4 (4), pp. 48-50), describes the need for multiplicative scattering correction for solid samples, caused by the difference in particle sizes solids, and computer transfer of complex equations. Osbourne provides methods for deriving calibration equations for specific cases suitable for use in the present invention. The selection of appropriate wavelengths and samples is discussed, and further relevant articles explaining the technology used are provided. The transfer of calibration equations from one instrument to another is described, in which modern instruments require only a change in the capture value, while computerized procedures take into account the difference in spectral data obtained by different instruments. These computerized procedures are not explained in detail, but apparently provide for the conversion of the spectral data of one device so that they are compatible with the spectral data of another device. This should be distinguished from what is provided by the present invention, according to which, instead of converting the spectral data, the corresponding coefficients in the calibration equation for the second device are changed in comparison with the coefficients obtained for the calibration equation of the first device in accordance with the new procedure disclosed in the present description.

 The doctoral dissertation of the author of the present invention, entitled "Chemometric analysis of a magnetic water treatment device" (International University of Microfilms. Thesis Division, N 8919928), discusses linear regression analysis (simple and multiple) to build a linear regression model and transform data that can convert nonlinear data types into data suitable for linear regression modeling. Definitions are presented that establish the degree of reliability according to which the value of one variable (dependent variable) can be found based on the values for other variables (independent variables). In principle, methods for determining the regression constants (or coefficients) for the calibration equations discussed in the above-mentioned doctoral dissertation are used to derive the calibration equations for the first or reference device in the present invention.

 The article "A new approach to identifying portable calibration methods for quantitative near-infrared spectroscopy" (Spectroscopy, vol. 3, No. 11, pp. 28-36, authors H. Mark and D. Workman) showed that the applicability of the characteristics of the device complicates the transfer of calibration data between devices. However, by choosing wavelengths and the corresponding spectral properties for such wavelengths so that they satisfy a certain criterion, it can be achieved that some differences between the devices do not lead to a significant change in the calibration equation obtained for one device when describing the work of another device. However, it does not describe how to make the calibration equation of one device suitable for use in another prior when there are significant changes in the calibration equation suitable for using the second device.

 R.A. Hekman, D.T. Diffie, L.A. Milhouse in the article “Tobacco components associated with deflecting filter devices” (Analytica Chem. Acta, 192 (1987), pp. 197-203) describes the transfer of monochromatic calibration in the near infrared region for tobacco components to a deflecting filter device for use experimental calibration equation for a sensitive but not durable laboratory device to analyze data in a device designed for products that do not require high accuracy in order to predict properties such as humidity, glycerol content, etc. Sawing glycol, nicotine and reducing sugars. A program called MTRAN cannot be used directly until it has been carefully verified that the instrument with the deflection filter is equipped with appropriate filters so that it matches the wavelengths in the primary or reference calibration equation of the laboratory instrument. Therefore, before the primary calibration equation can be converted, the monochromatic data files are compressed to simulate the conditions in the instrument with a deflection filter. The data file is used to restore the calibration equation. With these changes, the CALTRAN program can be used, which previously was used only for transferring calibration between filter devices in order to transfer near-infrared radiation from a monochromatic device to a device with a deflection filter.

 In a typical case, the known methods are aimed at changing the observed spectra (or their mathematical transformation) obtained by one device, in accordance with the changes obtained by a calibrated reference device. Only after the spectra from an uncalibrated instrument coincide with the spectra from a calibrated instrument, can we find ways to transfer the calibration equation from one instrument to another. Experience shows that there is a tendency to errors, uncertainties and numerous computational problems that complicate the use and reduce accuracy, while the invention avoids this.

 US Pat. No. 4,963,745 to Maggard, entitled “Method and Apparatus for Measuring Octane,” discloses how to initially derive a calibration equation for a reference instrument. It is specifically described that spectral features, such as second derivatives, of infrared spectral data at methyl band frequencies in the range of about 1200-1236 nanometers (nm), are significantly correlated with octane values for gasoline-like substances. In the description, numerous patents and articles are mentioned as references, as well as other publications, which, including those specially mentioned, are given in this case specifically by reference.

An example of a linear calibration equation is вид $\genfrac{}{}{0ex}{}{\text{i}}{\text{c}}$ = A ⁱ + Σ _j B $\genfrac{}{}{0ex}{}{\text{i}}{\text{j}}$ X $\genfrac{}{}{0ex}{}{\text{i}}{\text{c}}$ where ϒ $\genfrac{}{}{0ex}{}{\text{i}}{\text{c}}$ - the predicted value of any physical or chemical property, for example, octane values for gasoline, C, from a set called sample-s. As discussed in Example 7, measurements were made on 226 gasoline samples to determine A ⁱ and each B value $\genfrac{}{}{0ex}{}{\text{i}}{\text{jc}}$ for j = 1 - 3 to obtain the multiple regression equation, suitable for predicting the octane values of the excitation of gasoline samples using the first device, device-1, i.e. reference device. The octane excitation value is the average of ASTM D2699 and D2700 methods and commonly known as the (RtM) / 2 value for octane. The predicted reproducibility of this test method is 95% of the confidence limit of ± 0.71 octane numbers per octane range 84 - 94 in the excitation state. From the second device, device-k, in the reflection mode, the spectral absorbance values of gasoline at 1196, 1220 and 1236 nanometers (nm) were used to determine the values for the spectral features in the form of a second derivative of the absorption spectra X $\genfrac{}{}{0ex}{}{\text{k}}{\text{with}}$ in the linear calibration equation to extract the octane value of the excitation. Prediction standard error (PER) is a statistical parameter that is equal to the square root of the average residual variance for unknown samples.

 A calibrated spectrometer can indirectly determine the physical or chemical property of a sample based on spectral responses measured by the spectrometer with respect to a particular sample. The invention relates to a method for calibrating or recalibrating a first spectrometer depending on the second spectrometer or itself, respectively. During calibration, a certain selection and processing of spectral data obtained from both the first and second devices is used. When recalibrating the first device, a certain selection and processing of spectral data from the same first device are used, obtained both before and after the need arises to recalibrate the first choice. Instead of modifying the corresponding characteristics of the first and second devices or the first device before and after it becomes necessary to calibrate the first device, this invention allows you to modify the calibration equation of the second or recalibrated device in order to obtain results that are compatible with the results obtained by the first device for it to exit calibrated state. A calibration equation is an equation that converts the spectral data of a particular sample for a variety of wavelengths to obtain a calculated value for any chemical or chemical property. Typically, such calibration equations are in the form of a linear combination of absorbance values or mathematical transformations of absorbance values measured by the first and second instruments for each sample. An unexpected result, confirmed statistically, was the preservation of the accuracy of a calibrated or re-calibrated instrument, and in some cases even an increase in this accuracy.

 Instruments on the market today use raw spectral data and convert them to digital form or form an analog signal representing them for use in performing calculations. As the main stage in such calculations, the calibration equation together with this signal determines the dependent variable. The dependent variable is either equal to or indicates the value of some physical or chemical property of the material whose raw spectral data are being measured. The calibration equation corresponding to a particular instrument will vary depending on changes in the spectrometer that provides raw spectral data. In order to calibrate the spectrometer, the corresponding calibration equation is determined, which, together with the signal representation of the raw spectrum data measured by the spectrometer for a certain material, must determine the value of its dependent variable to equal or equal to or induce some physical or chemical property of the measured material. In practice, changes in such an equation are directly related to changes in the constants included in such an equation. The present invention is directed in part to how to determine these constants for an uncalibrated instrument using a calibrated instrument and its calibration equation. As soon as such constant values are determined, a calibration equation that is new or transferred to a new instrument is found, which can be used in conjunction with a digitized signal or an analog signal representing raw spectrum data measured with a previously uncalibrated instrument.

For example, if you need to determine the calibration equation for the second device (i.e., equation-2 calibration for device-2) using the calibrated first device and its corresponding calibration equation (i.e., device-1 and equation-1), then carried out to achieve this in accordance with the invention include:
a) determining from calibration equation-1 a value indicative of each dependent variable-1 corresponding to each member of the calibration set, based on spectral data-1 for each member of said calibration set, measured using the device-1, and
b) determination of the constants-2 in the above-mentioned calibration equation-2 so that the sum of the absolute differences between:
(1) the said value, indicative of each dependent variable-2 for each member of said set based on calibration equation-2 and data-2 corresponding to each member, and
(2) the corresponding value of the dependent variable -1 calculated for each term on the basis of calibration equation -1 and the data -1 corresponding to each term was minimal.

 The invention solves the problem of how to use the calibration results of one device to calibrate another device. In addition, the invention can be used to recalibrate the instrument to ensure consistent results after there has been some change in the spectral response of the instrument, which occurs when the light sources change, for example, when replacing burned out incandescent lamps or due to new compounds used to collect data from various sources, such as changes in fiber optics used to transmit light or electromagnetic radiation from one place to another, changes in path length or changed spectroscopic mode, for example, from transparency to reflection.

 The invention in a broad sense relates to the calibration of a new device using a reference device, also provides a method of continuous monitoring of the device, so as to note with confidence that it has not changed so much that it is necessary to derive a new calibration equation in order to obtain reliable prediction for any physical or chemical properties of the investigated material.

 The invention describes methods for indirectly determining a variety of p-properties, such as cetane, octane, aromatic naphthenolifin content, viscosity coefficient, molecular weight and many others using spectroscopic data. It is understood that spectral data broadly includes, but is not limited to, all intensity in comparison with wave spectra that arise when light, widely capturing a wide frequency range, for example, from radio frequencies to ultraviolet, interacts with the material. In principle, any spectral features (as defined in this description) derived from spectral data that can be compared to predict values for any particular chemical or physical property, directly or indirectly, are within the scope of the invention.

Some of the advantages provided by the invention are as follows:
1. Only a small number of samples are required (compared to the number of samples used in the initial calibration of the reference instrument) to determine the calibration equation for an uncalibrated instrument due to the possibility of using the calibration equation of the reference instrument. Example 7 shows that a small calibration sample consisting of only four elements can be used.

 2. The calibration set, sample-s, should not contain any unstable elements that could be included in the initial calibration set of samples, and preferably, in the case of mixtures, such as gasoline or other petroleum fuel, may contain a small amount in the form pure molecules or mixtures thereof easily prepared.

 The restriction on the corresponding elements of sample-s when determining the calibration equation for an ungraded instrument based on its spectral responses depends in part on the statistical processing selected for this data. For multiple linear regressions, the number of elements in sample-s should be at least 1 element larger than the number of wavelengths (independent variables) used in the model, unless correction for systematic error and slope or other error-reducing procedure is applied. For example, at least four samples must be used to transfer the calibration equation with three independent variables.

 It was found that in addition to correcting for systematic error and deviation, other operations can be used to reduce the error, for example, using the least squares, the generalized least sum, and some other methods that can further reduce any remaining error in the resulting equation - 2 calibrations.

 It is preferable that the reference set (sample-s) can be used to transfer the variance, covariance, or function obtained from the variance for a calibrated device, to an uncalibrated device or to the same device at a later point in time, sample-s should reveal the spectral signs that change as the device changes. For the purposes of this invention, sample-s should be defined so that the values of the spectral absorption characteristics show changes at wavelengths of interest when there are changes in the operating characteristics of the device, but the sample must remain constant (within instrumental errors) when the device functions in standard or standard conditions.

 A particular application of one of the solutions arising from the present invention is the calibration of the near infrared IR spectrophotometer using the results obtained from a fully or partially calibrated near infrared reference spectrophotometer. In the present description, references will be made to one or more spectrophotometers. A fully or partially calibrated spectrophotometer or other device, which will be referred to herein as a "reference device" or "reference spectrophotometer", is characterized by a calibration equation that is fully or partially determined. The instrument to be calibrated with respect to the reference instrument will be referred to herein as an “uncalibrated instrument” or “uncalibrated spectrophotometer”. The reference device may become uncalibrated or may leave the calibrated state as a result of various changes in the device itself or the connections between the device and the source from which it receives measured or spectral data.

 The invention provides calibration of an uncalibrated spectrophotometer with respect to a reference spectrophotometer using a much smaller set of calibration samples than was necessary to fully determine the calibration equation for a reference spectrophotometer at the very beginning. The plurality of samples for calibration is here called "plurality-s" or simply "sampling-s". In order to determine the calibration equation for counting octane, aromatic compounds, olefins, polyols, hydroxyl number, etc. for near-infrared radiation, such systems as the NIR Systems 6500 model, the 1200 IT Jndustree model, the 300 Guided Wave model series, the Bran-Luebbe infraredizer or the infrared prover are used, approximately 200 mixtures. Unfortunately, since gasolines are mixtures containing components with different volatilities, it is very difficult, sometimes impossible, to store such samples for processing on an uncalibrated spectrophotometer until a later date. In other words, the samples used to calibrate the reference spectrophotometer should be suitable. The use of materials other than those used to calibrate the reference spectrophotometer increases the difficulty of calibrating an uncalibrated spectrophotometer, since each member of the set of samples from approximately two hundred samples must have an octane number or antiknock characteristic determined in accordance with ASTMD2699 and D2700, etc. P. The procedure for determining octane numbers requires a long time and many operations on the same sample with different engines before reliable results of antiknock characteristics are obtained.

 It is not known from the prior art whether components like pure gasoline, for example, specific hydrocarbon molecules that can be easily reproduced, can be selected for a multitude of samples. The authors of the present invention was found in relation to near infrared radiation with wavelengths in the range of 800 - 2500 nm, which is a lot of sample-s, including as samples: benzene, methyl t-butyl ether, iso-octane, n-decane, I-octene, 2,3,4-trimethylpentane, n-heptane, cyclohexane, n-hexane or toluene, when measured both on a reference instrument and on an uncalibrated instrument in order to obtain spectral data from each instrument, can provide enough data or information to to calibrate uncalibrated when Op. For this description, a calibrated instrument is one that represents stable and reproducible spectral characteristics and has a calibration equation by which the necessary values of the physical or chemical properties of the sample can be obtained with an accuracy equal to or greater than the accuracy of the direct test method (for example, ASTM) , in order to determine such a chemical or physical property.

 In the broadest sense, in order to transfer the calibration equation for octane, any compounds active in the near-infrared region of the spectrum can be used, i.e., they absorb near-infrared radiation in the range 800 - 2500 nm. Examples of such compounds are: n-paraffins, iso-paraffins, aromatic compounds (such as dichlorobenzene or benzene), alcohols (such as methanol or ethanol), olefins (such as I-octene), halogenated alkanes (such as such as trichloroethane), ketones (such as methyl ethyl ketone), ethers (such as methyl t-butyl ether), esters (such as amyl acetate) and naphthenes (such as cyclohexane and methyl cyclohexane). In this description and the claims, the standard error of calculation or prediction is 68% of the confidence limit, unless otherwise indicated. Each error is hereinafter referred to as "SPR" or "SPP".

 The calibration equation for a particular device predicts a physical or chemical property based on spectral responses or spectral data. When measuring octane numbers, specific spectral responses or mathematical transformations corresponding to the values of the spectral features selected to predict the octane numbers for a particular sample are described in detail in US Pat. No. 4,963,745. The equation is preferably linear, but non-linear equations can also be used.

 Spectral features are functionally associated with spectral data, in function, each spectral distinguishing characteristic is determined solely by such spectral data. An example of such functional relationships are mathematical transformations, such as derivatives of the first, second, and higher order; Fourier analysis to determine the frequency components and their contribution; differentiation of spectra; segment integration, etc. The only limitation when choosing such functional relationships or mathematical transformations is that any values obtained by applying them to spectral data must be correlated as independent variables to accurately determine the value for the dependent variable in the calibration equation, which corresponds directly or indirectly to the value of the physical or chemical properties.

 In a detailed discussion of the invention, the following definitions are obtained. For this application, a “function” is a correspondence that associates with each set of values for a set of independent variables, the only value of the dependent variable. In accordance with this definition, the “calibration equation" in this invention is a function that establishes a correspondence between independent variables whose values are determined by spectral characteristics and a dependent variable that corresponds to the value for any chemical and physical property. Any function that determines values for a spectral feature that are uniquely associated with spectral data or that can be used in a calibration equation is within the scope of this invention. The spectral data are uniquely determined by the results of the measured spectral responses of the material with respect to electromagnetic radiation. Examples of electromagnetic radiation are discussed in other parts of this specification. The prior art knows functions that can be used to determine the derived values for spectral features based on spectral data. If a calibration equation exists that contains independent variables equivalent to spectral features defined by a function, then there are no restrictions on specific spectral features or functions for spectral data that define the spectral features that can be used in this invention.

 For this description and claims, “calibration equation” means an equation that predicts directly or indirectly, for example, by functional connection, a quantitative assessment of a chemical or physical property (dependent variable) based on one or more spectral features (independent variables) and, possibly, some other parameters, such as temperature.

 A regression model for near-infrared infrared for measuring octane in a gasoline that contains MTBE was published in the book of the American Chemical Society, Department of Fuel Chemistry, vol. 35, No. 1, p. 266-275, written by Stephen M. Maggard and presented at the 199th Conference of the American National Chemical Society in Boston, Massachusetts, April 22-27, 1990. This document specifically describes and presents the use of t-butyl methine combination bands, including color tones, in modules with the aim of predicting octanes of gasoline compounds containing MTBE.

 As used herein, “spectral features” means spectral ability, transparency, reflectivity (diffuse reflection, specular, total, attenuated, etc.), emission, fluorescence, phosphorescence or transflectance, or their mathematical functions, such as derivatives, relationships, Fourier transforms and differences for the ultraviolet part of the spectrum, the visible part, near infrared, medium infrared, far infrared, microwave or electromagnetic radio frequency radiation.

 The text of the description mentions the use of derivatives of spectral absorption data. An example of what is meant by the term “derivative” will be shown. The logic used to take the derivative of the absorbance data is based on the calculation of the finite differences, since the data are determined at regularly spaced intervals, and they are discontinuous between these intervals.

 Absorbance spectral data collected using NIROL-6500 systems can be used. The OL-6500 has a spectral bandwidth of about 9 nm, but the spectral data is digitized so that the recorded data is displayed at intervals of 2 nm. In the general case, two elements can change when the derivative at a point is calculated, the first of them defines the segment, and the second - the gap. A segment determines the number of points that are used to calculate the average number to the right and left of the point at which the derivative is calculated. On the other hand, the gap denotes the number of points near the midpoint (immediately adjacent to the point where the derivative is taken) that are excluded from the calculations of neighboring segments (although the total length of the segment does not change). If we denote the average value of the segment (with higher wavelengths) above the point where the derivative is taken, point A, and the average value of the segment below the point where the derivative is taken, point B, then, in accordance with the calculation of the finite differences, the first derivative at the point is equal to A minus B.

For example, when a segment is 10 in increments of 2 nm per segment, and the span is 0, the first derivative of the absorbance (d ¹ A / dw) at 1170 nm is calculated as follows:
d ¹ A / dw ₁₁₇₀ = {(A ₁₁₇₂ + A ₁₁₇₄ + A ₁₁₇₆ + A ₁₁₇₈ + A ₁₁₈₀ ) / 5} - {(A ₁₁₆₈ + A ₁₁₆₆ + A ₁₁₆₄ + A ₁₁₆₂ + A ₁₁₆₀ ) / 5}
If the segment changes to 6, and the interval to 8, the first derivative has the form:
d ¹ A / dw ₁₁₇₀ = {(A ₁₁₇₆ + A ₁₁₇₈ + A ₁₁₈₀ ) / 3} - {(A ₁₁₆₄ + A ₁₁₆₂ + A ₁₁₆₀ ) / 3}
Typically, for data obtained at intervals of 2 nm, the first derivative of the absorbance at wavelength x is:
d ¹ A / dw _x = Σ _i (A _{(x + (span / 2) + 2i)} / (segment / 2)
- Σ _i (A _{(x + (span / 2) + 2i)} / (segment / 2)
where x is the wavelength in nanometers, for example, 1170 and i = from 1 to segment / 2.

 For the well-known reasons, the above equation is strictly valid only for segments 2, 6, 10, 14, 18, etc., in the NIR, NSAS system software package (near-infrared spectral analysis software package, NIR Systems, Inc.) gaps 0, 4, 8, 12, 16, etc. Segment 0 is treated as segment 2. Similarly, segment 4 is treated as 6, etc. Similarly, span 6 is treated as span 0, and span 6 is treated as span 4, and so on.

Derivatives of a higher order can be simplified to expressions involving only the terms of the first derivative, and solved by the form of the previous equation. In the general case, if the order of the derivative is equal to h, then the desired derivative is equal to:
d ^h A / dw _x = d ^h-1 A / dw _{(x + { (segment + prom a day)} / 2} +1) -d ^h-1 A / dw _{(x- { (segment + prom a day)} / 2} -one)
where the gap is equal to the gap of the derivative of order h, and the segment used to calculate the derivative of order h-1 is the same as the desired value for the derivative of order h.

For example, the fourth derivative of 1170 nm with a segment of 10 and a gap of 4 is equal to:
d ⁴ A / dw ₁₁₇₀ = d ³ A / dw ₁₁₇₈ - d ³ A / dw ₁₁₆₂
= (d ² A / dw ₁₁₈₆ - d ² A / dw ₁₁₇₀ ) - (d ² A / dw ₁₁₇₀ - d ² A / dw ₁₁₅₄ )
= {(d ¹ A / dw ₁₁₉₄ - d ¹ A / dw ₁₁₇₈ ) - (d ¹ A / dw ₁₁₇₈ - d ¹ A / dw ₁₁₆₂ )} - {(d ¹ A / dw ₁₁₇₈ - d ¹ A / dw ₁₁₆₂ ) - (d ¹ A / dw ₁₁₆₂ -d ¹ A / dw ₁₁₄₆ )
= {{[((A ₁₁₉₈ + A ₁₂₀₀ +.. + A ₁₂₀₆ ) / 5) - ((A ₁₁₉₀ + A ₁₁₈₈ + ... + A ₁₁₈₂ ) / 5)] - [((A ₁₁₈₂ + A ₁₁₈₄ + ... + A ₁₁₉₀ ) / 5) - ((A ₁₁₇₄ + A ₁₁₇₂ + ... + A ₁₁₆₆ ) / 5)]} - {[((A ₁₁₈₂ + A ₁₁₈₄ + ... + A ₁₁₉₀ ) / 5) - ((A ₁₁₇₄ + A ₁₁₇₂ + ... + A ₁₁₆₆ ) / 5)] - [((A ₁₁₆₆ + A ₁₁₆₈ +. .. + A ₁₁₇₄ ) / 5) - ((A ₁₁₅₈ + A ₁₁₅₆ + ... + A ₁₁₅₀ ) / 5)]}} - {{[((A ₁₁₈₂ + A ₁₁₈₄ + ... + A ₁₁₉₀ ) / 5) - ((A ₁₁₇₄ + A ₁₁₇₂ +... + A ₁₁₆₆ ) / 5)]} - {[((A ₁₁₆₆ + A ₁₁₆₈ + ... + A ₁₁₇₄ ) / 5) - ((A ₁₁₅₈ + A ₁₁₅₆ + ... + A ₁₁₅₀ ) / 5)] - {[((A ₁₁₆₆ + A ₁₁₆₈ + ... + A ₁₁₇₄ ) / 5) - ((A ₁₁₅₈ + A ₁₁₅₆ +. .. + A ₁₁₅₀ ) / 5)] - [((A ₁₁₅₀ + A ₁₁₅₂ + ... + A ₁₁₅₈ ) / 5) - ((A ₁₁₄₂ + A ₁₁₄₀ + ... + A ₁₁₃₄ ) / 5]}}
where all derivatives of a lower order are also taken using segment 10 and interval 4. It should be noted that it is necessary to adjust the segment and the interval to the actual value before applying one of the generalized formulas (for example, the fourth derivative of segment 8 and interval 6 is adjusted to segment 10 and gap 4 before applying the formula).

 It should be noted that segments of 2 nm were used, but segments with a smaller or larger number of nm or equal to parts of nm can be used. Preferably, the selection depends on the degree of spectral resolution provided by the spectrometer.

 Examples of differentials, finite differentials are presented, but one of many types of finite differentials can be adopted. All methods available for use are in fact based on one theory, however, the specific details of the calculations may vary to some extent. It should also be noted that although finite differentials are discussed, it is possible that differentials with differences approaching zero and not some finite number can also be used. For example, a polynomial power series, such as a Taylor series, based on a series of points of intensity versus wavelength curves or spectral data, may be used.

 This invention describes a means for determining a calibration equation for a primary instrument that uses a significant amount of work previously done to obtain a calibration equation for a reference spectrophotometer. Indeed, the first device can be a reference spectrophotometer that has exited the calibration state for the reasons already mentioned.

 To make the description easier to understand, the following conditions must be accepted. Independent variables corresponding to the calibration equation for the first device will be denoted by -i or -I, for example, independent variable -i or independent variable-I corresponds to one or more members of the set of independent variables in the calibration equation, calibration equation-i or level-I calibration, respectively, for the first device, here called device-i or device-I. In most examples, three wavelengths are used, each of which is named wavelength-i, of which three independent variables-i are obtained using the function based on the spectral features of sample-c. According to a specific set of independent variables-i, there is a dependent variable, referred to here as the dependent variable-i. The value of the dependent variable -i will usually be equal to the predicted value of the -p property of sample-c. Dependent variable-i corresponds to the dependent variable found in calibration equation-i. The constants in the calibration equation-i are named here as constants-i. There are two different kinds of constants-i. One corresponds to slope constant-i, and the other corresponds to bias constant-i. The slope constants-i are the coefficients of the independent variables-i. It is clear that there is a constant-i of steepness for each independent variable-i, which in turn depends on the number of lengths-j of waves included in the grading equation-i. There is only one bias constant-i, which is not a coefficient of any independent variable-i.

 When defining the calibration equation for instrument-k (also called instrument-2) using the calibration equation for instrument-i, a new set of calibration equation constants that correspond to the constants-k is mainly determined. The new values of the constants are determined in at least one or, preferably, in two stages, taking into account the fact that there is already a calibration equation-i, deduced for the device-i.

 To successfully transfer or modify the calibration equation-i in the calibration equation-k, the values of the SPR or SPP for property-p, based on the spectral data of device-k or device-2 by means of calibration equation-k or calibration equation-2, should be practically the same accurate, like the values obtained by instrument-i and calibration equation-i, or alternatively, should be as accurate as the values that could be obtained if instrument-k was calibrated in the same way as instrument-i but in most cases they are up should be at least equal to or better than the DSS for the primary test method for directly measuring values to determine property-p used to calibrate instrument-i. This invention provides the advantage that the number of samples required for processing with either instrument-i, or instrument-k, or both, is significantly less than the number of samples required to obtain a reliable calibration equation for instrument-i or for fully calibrate instrument-k in the same way as instrument-i. In other words, in any case, the value of E (k) in the standard error of predicting the value for determining property-p using the -k device and the calibration equation-k should not significantly exceed the value of the standard forecasting error obtained as a result of determining the values for property-p directly or the primary test method originally used to calibrate instrument-i.

 One, although not the only, way to transfer calibration equation-i to instrument-k is to change the constants of calibration equation-i. These changed constants become k-constants. Preferably, the calibration equation-i is converted into the calibration equation-k in two steps. Step 2 is optimal (given below), but it is preferable depending on whether the correction indicated by step 2 is significant. The symbol “significant” means that the obtained dispersion value in the predicted values does not exceed more than 10% of the value DSS or DSS depending on which one is larger, determined using calibration equation-k without step 2.

Step I: the definition of calibration equation-k (calibration equation-2) using calibration equation-i (calibration equation-1) includes the following sub-steps:
(a) Determine the calibration equation-i by measuring the dependent variables-i directly using the primary test method with a standard error in calculating E and correlating this dependent variable-ic with many independent variables-i. The set of independent variables i may consist of one or more elements.

 (b) Obtain, respectively, instrument-i and instrument-k spectral data-i and spectral data-k, respectively, for each sample element-c that should be used in step (c) (including at least one element c), determine using the function value-k and value-i, respectively (equal respectively to each spectral attribute-k and -i) for each element of the sample-c, corresponding to each independent variable-k and -i, respectively.

 (c) Determine (in accordance with calibration equation-i) the value for this dependent variable-i for each sample element-c. The value defined for the dependent variable -i, or the value determined using some function -f using this value defined for the dependent variable -i, is entered into the calibration equation-k for the value of the dependent variable -k in the calibration equation-k . The values of spectral features-k found for each sample element-c are also entered into the calibration equation-k. (Recall that the spectral features -k are determined functionally using the spectral data -k determined by measurements made by the -k instrument for each sample element -c. Therefore, the only unknowns in the calibration equation -k will be the constants -k). The values for the constants-k, which should be substituted into the calibration equation-k, form the calibration equation-k, the sum of all the absolute differences between each defined value of the property-p for sample c, corresponding to the dependent variable-k for sample c, and the specific value of property-p for sample-c, corresponding to the dependent variable -i for sample-c, is minimized so that the values for property-p for sample-U, the values of which for property-p do not go beyond the required limits, are obtained based deduced a calibration equation-k, wherein NGN actually exceeds the SEE or SEP of E for determining dependent variable at-i directly by some primary test method. As soon as the constants-k are determined, which allows us to obtain the value of the dependent variables-k for the elements of the sample-c, having the values for the property-p within the required limits, within the DSS or DSS for E with the direct or primary test method, the equation is obtained - k calibration in light of the preceding calibration equation-i. The absolute difference is the difference between the two numbers obtained as a result of the first squaring and taking the positive square root. (Recall that instrument-k, the first instrument, may in fact be a reference instrument that has exited the calibration state, or it may actually be a completely different instrument).

The value for the dependent variable-i, which should be substituted in the calibration equation-k for the dependent variable-k, can be functionally related to the dependent variable-i using the function-f such as, for example, the logarithm (log) for any reason ( e.g. natural or decimal), such as ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$ = n • log ϒ $\genfrac{}{}{0ex}{}{\text{i}}{\text{c}}$ + m or linear function ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$ = n • ϒ $\genfrac{}{}{0ex}{}{\text{i}}{\text{c}}$ + m, where n and m are constants, or their linear combination, or generally any function, such as a polynomial or geometric series, provided that within the required range of values ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{s}}$ the function is essentially linear.

Range of Required Values ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{s}}$ represents a range of values that determine a chemical or physical property that have been calibrated using calibration equation-k together with device-k to predict when values of SPR or SPP are lower than SPR or SPP of the primary test method.

For clarity, if ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$ = n • ϒ $\genfrac{}{}{0ex}{}{\text{i}}{\text{c}}$ + m and n = 1 and m = 0, then ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$ = ϒ $\genfrac{}{}{0ex}{}{\text{i}}{\text{c}}$ . However, for any other values of n and m, the corresponding constants will be related to the constants defined in a different way for n = 1 and m = 0 as follows:
A ^k = nA $\genfrac{}{}{0ex}{}{\text{k}}{\text{o}}$ B $\genfrac{}{}{0ex}{}{\text{k}}{\text{j}}$ = nB $\genfrac{}{}{0ex}{}{\text{k ′}}{\text{jo}}$ ,
Where
A $\genfrac{}{}{0ex}{}{\text{k}}{\text{o}}$ is the constant value for n = 1 and m = 0 and
B $\genfrac{}{}{0ex}{}{\text{k ′}}{\text{jo}}$ is the constant value for n = 1 and m = 0.

In other words, whatever the values for n and m are, the dependent variable -k will be functionally related to the dependent variable -i. To determine the value for the corresponding physical or chemical property, measured directly, you just need to perform an inverse transformation from ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$ to ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{∞}}$ when for any value of m and n except n = 0. ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{∞}}$ = (ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{cm}}$ ) / n.

 Instrument-k and its spectral data are used in this invention if instrument-k can be calibrated in an identical way to such an instrument that can be used to successfully calibrate instrument-i.

 Preferably, equation −i and calibration equation −k are linear. In the generalized method discussed above for the present invention, it is not necessary that both equations-i and -k be of the same kind or both are linear. By the same form is meant the same functional dependence on the same number of independent variables with the corresponding constants defining the dependent variable.

где
ϒ $\genfrac{}{}{0ex}{}{\text{i}}{\text{s}}$ - зависимая переменная-i в уравнении-i калибровки, которая предпочтительно приобретает значение, фактически равное свойству-p любого элемента, S, образца-S, а ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{s}}$ - зависимая переменная-k в уравнении-k калибровки, которая функционально связана с ϒ $\genfrac{}{}{0ex}{}{\text{i}}{\text{s}}$ посредством функции-f;
A^k и Aⁱ - каждое является соответственно константами-i и -k пересечения или смещения в уравнениях-i и -k калибровки;
X $\genfrac{}{}{0ex}{}{\text{i}}{\text{js}}$ и X^k является каждое одним значением по меньшей мере одной независимой переменной-i и -k в уравнениях калибровки, соответственно i- и -k, величина которого равна по меньшей мере одному спектральному признаку-i и -k, соответственно элемента, S, при длине волны-j, и
B $\genfrac{}{}{0ex}{}{\text{i}}{\text{j/}}$ и B $\genfrac{}{}{0ex}{}{\text{k}}{\text{j}}$ - соответственно константы-i и -k крутизны, соответствующие коэффициентам для каждой по меньшей мере одной независимой переменной-i и -k, соответствующей спектральным признакам-i и -k, соответственно при длине волны-j.Preferably, the grading equations for instrument-i and instrument-k have the following linear form:

Where
ϒ $\genfrac{}{}{0ex}{}{\text{i}}{\text{s}}$ - the dependent variable-i in the calibration equation-i, which preferably acquires a value that is actually equal to the property-p of any element, S, sample-S, and ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{s}}$ - dependent variable -k in the calibration equation -k, which is functionally related to ϒ $\genfrac{}{}{0ex}{}{\text{i}}{\text{s}}$ through the function f;
A ^k and A ⁱ - each is respectively the constants-i and -k of the intersection or bias in the calibration equations-i and -k;
X $\genfrac{}{}{0ex}{}{\text{i}}{\text{js}}$ and X ^k is each one value of at least one independent variable-i and -k in the calibration equations, respectively, i- and -k, the value of which is equal to at least one spectral characteristic-i and -k, respectively, of the element, S, for wavelength j, and
B $\genfrac{}{}{0ex}{}{\text{i}}{\text{j /}}$ and B $\genfrac{}{}{0ex}{}{\text{k}}{\text{j}}$ - respectively, the steepness constants-i and -k, corresponding to the coefficients for each at least one independent variable-i and -k, corresponding to the spectral features-i and -k, respectively, at wavelength-j.

 There can be an infinite number of ways of substituting values for the constants-k, which lead to a calibration equation-k with an SPR value that actually does not exceed the SPR or SPP value, which is necessarily present in the direct method used at some point to obtain the calibration equation-i directly or indirectly . By “practically not exceeding” is meant 30% more, preferably 20% more, and most preferably 10% more. The directly defined values of property-p must be obtained at least once using any primary or direct test method for calibrating the device by determining its calibration equation to predict the values of the physical or chemical property, property-p, for a number of materials based on spectral data for such materials. However, once the first instrument has been calibrated, it can be used to calibrate other instruments without the need to re-measure property-p using the primary test method. Instrument-i has a directly defined calibration equation-i if some or all of the constants-i in it are determined using values directly found as a result of the primary test method. However, if only the values used to determine the constants-k are obtained based on the prediction of values previously calibrated by the device without taking into account the values from the primary test method for property-p, then device-k is calibrated indirectly. In all cases, there will be at least one device, the calibration equation of which is determined primarily on the basis of the values for its dependent variable, determined by the primary test method. Mentioned above of the SPR or SPP of this primary test method.

However, it has been found that the following criteria are particularly suitable for determining the k constants, given that the calibration equations k and -i are linear in shape, as noted above. According to one criterion, the corresponding B $\genfrac{}{}{0ex}{}{\text{k}}{\text{j}}$ and A ^{k, the} constants-k, respectively, actually extremely reduced to the maximum possible extent the following expression: Σ _c (ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$ -A ^k -Σ _j B $\genfrac{}{}{0ex}{}{\text{k}}{\text{j}}$ X $\genfrac{}{}{0ex}{}{\text{k}}{\text{jc}}$ ) ² .

Alternatively, B values may be used. $\genfrac{}{}{0ex}{}{\text{k}}{\text{j}}$ and A ^k , which essentially satisfy simultaneously the following two equations:
B $\genfrac{}{}{0ex}{}{\text{k}}{\text{j}}$ = B $\genfrac{}{}{0ex}{}{\text{i}}{\text{j}}$ Σ _c X $\genfrac{}{}{0ex}{}{\text{i}}{\text{jc}}$ X $\genfrac{}{}{0ex}{}{\text{k}}{\text{jc}}$ / Σ _c (X $\genfrac{}{}{0ex}{}{\text{k}}{\text{jc}}$ ) ²
and
A ^k = Σ _c (ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$ -Σ _j B $\genfrac{}{}{0ex}{}{\text{k}}{\text{j}}$ / X $\genfrac{}{}{0ex}{}{\text{k}}{\text{jc}}$ ) / n ;,
Where
n = number of sample items-c.

In the end, a particularly acceptable criterion was also found for determining the k constants corresponding to B $\genfrac{}{}{0ex}{}{\text{k}}{\text{j}}$ and A ^k , which essentially satisfies the two following equations simultaneously:
B $\genfrac{}{}{0ex}{}{\text{k}}{\text{j}}$ = B $\genfrac{}{}{0ex}{}{\text{i}}{\text{j}}$ Σ _c X $\genfrac{}{}{0ex}{}{\text{i}}{\text{jc}}$ / Σ _c (X $\genfrac{}{}{0ex}{}{\text{k}}{\text{jc}}$ )
and
A ^k = Σ _c (ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$ -Σ _j B $\genfrac{}{}{0ex}{}{\text{k}}{\text{j}}$ X $\genfrac{}{}{0ex}{}{\text{k}}{\text{jc}}$ ) / n ;,
Where
n = number of sample items-c.

где
ϒ $\genfrac{}{}{0ex}{}{\text{a}}{\text{c}}$ - прямо или косвенно определенное значение для свойства-p конкретного элемента, c, выборки-p, которое определено с принятой стандартной погрешностью расчета, не превышающей E первичного способа испытания, причем указанное значение для свойства-p не выходит за требуемую область значений;
n - число элементов выборки-p;
v - стандартная погрешность расчета от использования значений уравнения-k калибровки с целью определения зависимой переменной-k для элемента выборки, c, причем v незначительно превышает E.Stage 2 entails an adjustment for slope and offset. The requirements for samples regarding the correction for slope and offset are discussed in the examples. Mainly, the correction for slope and offset is obtained from the definition of values for "m" and "b", which satisfy the following expression:

Where
ϒ $\genfrac{}{}{0ex}{}{\text{a}}{\text{c}}$ - directly or indirectly a certain value for the property-p of a particular element, c, of the sample-p, which is determined with the accepted standard calculation error not exceeding E of the primary test method, and the specified value for property-p does not go beyond the required range of values;
n is the number of sample elements-p;
v is the standard error of the calculation from the use of the values of the calibration equation-k in order to determine the dependent variable-k for the sample element, c, and v is slightly greater than E.

We substitute the indicated values for m and b into the following expression, as a result of which we obtain a simplified calibration equation for the dependent variable -k for the device -k, which has the form:
ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$ = [mA ^k + b] + Σ _j [mB $\genfrac{}{}{0ex}{}{\text{k}}{\text{j}}$ X $\genfrac{}{}{0ex}{}{\text{k}}{\text{jc}}$ ]
In some cases, step 2 may be omitted because the correction assumed or required when using the slope or bias correction does not cause a significant change in the constant-k for the calibration equation-k. But it is preferable to carry out the steps in accordance with the slope and bias correction in order to determine whether or not a significant correction exists. In most cases, it has been found that steepness and offset correction is necessary.

 Regarding stage 2, it should be noted that when the correction for steepness or bias is used, even a significant change in the values of the constant k required by the correction or due to the correction does not mean that an error was made during the implementation of stage 1, It was found that an error it takes place, at stage 1 they are actually corrected by adjusting for the steepness or displacement and vice versa (see example 1). Moreover, it was found that the number of samples required to implement the correction for steepness and bias, even if they are added to the samples necessary for stage 1, is much less than they are necessary to determine the calibration equation-i for the device-i. This seems completely unexpected and cannot be foreseen in advance. Indeed, when a slope correction indicates a significant correction in constants, prior art methods (see near-infrared spectral analysis, publ. NIR Systems, Inc., Silver Spring, Maryland, 1989) require that the instrument must be re-calibrated -k in the same way that was used for initial calibration of instrument-i.

 Of interest is a more detailed analysis of what happens to the k-constants in the calibration equation-k in step 1 or 2. In step 1, each constant changes essentially independently to satisfy the set of numerical criteria mentioned above. In step 2, the bias constants change together by an amount defined as "m". The intersection constant k is affected by both m and increment b. When applied together, the calibration equation-k for the device-k preferably makes it possible to determine the value of the SPP for the dependent variable -k, which is more accurate and often much better than the value obtained from the calibration equation-i using the data measured by the device- i or at least an SPP that is equal to an E value or more precisely than this value, taking the SPP value for the direct test method to determine the values used to calibrate instrument-i. Shown in the examples, this result is completely unexpected.

 This invention also describes an indirect method for determining property-p for sample-u using spectral data-k measured with instrument-k, making it possible to determine such spectral data-k for sample-u. Although many methods are known for identifying the instrument’s calibration equation, so far they have not provided the ability to easily convert the calibration equation-i corresponding to the device-i to the calibration equation-k corresponding to the device-k.

Здесь Y $\genfrac{}{}{0ex}{}{\text{i}}{\text{c}}$ и Y $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$ - расчетные или предсказанные значения для зависимых переменных на основе уравнений калибровки для приборов-i и -k, соответственно оба для каждого элемента, c, выборки-c.The new form for the calibration equation -k or -i entails the use of next-order differentials as spectral features. For example, each of the calibration equations for instrument-k and instrument-i has the form:

Here y $\genfrac{}{}{0ex}{}{\text{i}}{\text{c}}$ and Y $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$ - calculated or predicted values for dependent variables based on calibration equations for instruments-i and -k, respectively, for each element, c, sample-c.

X $\genfrac{}{}{0ex}{}{\text{i}}{\text{jc}}$ and X $\genfrac{}{}{0ex}{}{\text{k}}{\text{jc}}$ are the second derivatives of the found values of the spectral absorbance for devices-i and -k, respectively, both for each element, c, of sample-c at a wavelength of-j.

X $\genfrac{}{}{0ex}{}{\text{/ i}}{\text{jc}}$ and X $\genfrac{}{}{0ex}{}{\text{/ k}}{\text{jc}}$ are the third derivative of the observed values of spectral absorbance for instruments-i and -k, respectively, both for sample-c at wavelength-j.

 Using calibration equations in the form of derivatives of neighboring orders of spectral data, it was found that unexpectedly a correction for the slope and offset causes a change in the constant-k of the calibration equation, which leads to obtaining values for the property-p of the sample, c, based on the spectral data measured for the sample -c with instrument-k, which show excellent agreement with the results obtained from instrument-i and calibration equation-i.

Example 1. The calibration equation for an uncalibrated instrument is derived based on the calibration equation established for the reference instrument. The solutions for the following equations determine: B $\genfrac{}{}{0ex}{}{\text{k}}{\text{js}}$ and A ^k in the linear calibration equation for instrument-k, an uncalibrated instrument of the form ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$ = A ^k + Σ _j B $\genfrac{}{}{0ex}{}{\text{k}}{\text{j}}$ X $\genfrac{}{}{0ex}{}{\text{k}}{\text{jc}}$ which takes the calibration equation ϒ $\genfrac{}{}{0ex}{}{\text{i}}{\text{c}}$ = A ⁱ + Σ _j B $\genfrac{}{}{0ex}{}{\text{i}}{\text{j}}$ X $\genfrac{}{}{0ex}{}{\text{i}}{\text{jc}}$ for a calibrated or reference instrument, instrument-i.

Three different mathematical criteria are used independently. Since only three wavelengths are used, then J = 1 - 3, and since 25 is the total number of sample elements-c, then c = 1 - 25. Independent variables, X $\genfrac{}{}{0ex}{}{\text{k}}{\text{jc}}$ (where k identifies device-k) have values for spectral features obtained from the spectral response of device-k at wavelength-j. Each wavelength is in the wavelength range 800 - 2500 nm. Here, the spectral features are the second derivative of the absorbance at three wavelengths-j: 1196, 1220 and 1286 nm.

Прибор-i калибруется с использованием множественной линейной регрессии второй производной спектральной поглощательной способности при длине волны 1196, 1220 и 1236 нм путем модулирования зависимой переменной октан (R+M)/2 на 72 газолиновых образцах, заключающих октановый диапазон 86-93 с примерно равномерным распределением. Прибор представляет собой NIR Systems 6500, функционирующий в режиме отражения с использованием волоконной оптики с длиной пробега 18 мм.Mathematical Criterion 1
Σ _c (ϒ $\genfrac{}{}{0ex}{}{\text{i}}{\text{c}}$ -A ^k -Σ _j B $\genfrac{}{}{0ex}{}{\text{k}}{\text{j}}$ X $\genfrac{}{}{0ex}{}{\text{k}}{\text{jc}}$ ) = 0;
provided ϒ $\genfrac{}{}{0ex}{}{\text{i}}{\text{c}}$ = ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{c /}}$

Instrument-i is calibrated using multiple linear regression of the second derivative of the absorbance at a wavelength of 1196, 1220 and 1236 nm by modulating the dependent variable octane (R + M) / 2 on 72 gasoline samples containing an octane range of 86-93 with an approximately uniform distribution . The device is a NIR Systems 6500 operating in reflection mode using fiber optics with a path length of 18 mm.

 From the regression equation for the device, the values of 25 calibration transfer standards are obtained and then these values are taken as the octane (R + M) / 2 dependent variable for 25 standard calibration transfer values. The same standards are presented in example 2.

 25 standard calibration transfer values and 10 samples with a known octane rating are processed by the -k instrument. The results are presented in table. one.

 Alternatively, it is also determined that it is possible to indirectly derive the calibration equation-k from the transferred calibration equation-k when the step of reducing the least square error is used instead of adjusting for the slope and offset. When the errors were modeled as a dependent variable -k using spectral data -k, again, as an independent variable, it became possible to add the obtained contacts with constants from the transferred calibration equation -k and indirectly derive the least squares determination (mathematical criterion I).

Mathematical Criterion II
B $\genfrac{}{}{0ex}{}{\text{k}}{\text{r}}$ = [B $\genfrac{}{}{0ex}{}{\text{i}}{\text{r}}$ Σ _c X $\genfrac{}{}{0ex}{}{\text{i}}{\text{rc}}$ X $\genfrac{}{}{0ex}{}{\text{k}}{\text{rc}}$ ] / [Σ _c (X $\genfrac{}{}{0ex}{}{\text{k}}{\text{rc}}$ ) ² ]
A ^k = Σ _c (ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$ -Σ _r B $\genfrac{}{}{0ex}{}{\text{k}}{\text{r}}$ X $\genfrac{}{}{0ex}{}{\text{k}}{\text{rc}}$ ) / n
Provided ϒ $\genfrac{}{}{0ex}{}{\text{i}}{\text{c}}$ = ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$
It should be noted that c = 1 - 25, only three wavelengths of 1196, 1220 and 1236 are used, and n = 25, since the number of elements in sample-c is 25.

 Instrument-i is calibrated using multiple linear regression of the second derivative of spectral absorbance at 1196, 1220 and 1236 nm by modeling the octane (R + M) / 2 dependent variable on 72 gasoline samples containing the octane range 86-93 with an approximately uniform distribution . Instrument-i is a type of NIR Systems 6500 operating in reflection mode using fiber optics with a path length of 18 mm.

 The values of the 25 standard calibration transfer values are derived from the regression equation for instrument-i, after which these values are taken as the octane (R + M) / 2 values of the dependent variable for the 25 standard calibration transfer values. The same standards are presented in example 2.

Вышеупомянутые константы в уравнении калибровки предсказывают значение 10-и образцов с известным октановым числом. Отмечается жесткое смещение октановых чисел (R+M)/2. Компьютерная программа устанавливает необходимость поправки на крутизну, равную 0,56741, и необходимость поправки на пересечение, равную 36,646. Эти поправки дают значение конечной крутизны и уравнение калибровки с поправкой на смещение для прибора-k и демонстрируют стандартную погрешность расчета, равную 0,184, и смещение 0,0265 октановых чисел (R+M)/2 для остальных 62-х образцов.Instrument-k processes 25 standard calibration transfer values. Regression constants are calculated as follows:

The above constants in the calibration equation predict the value of 10 samples with a known octane number. A marked shift in octane numbers (R + M) / 2 is noted. The computer program establishes the need for a slope correction of 0.56741, and the need for an intersection correction of 36.646. These corrections give the value of the final slope and the calibration equation with an offset correction for the instrument-k and demonstrate a standard calculation error of 0.184 and an offset of 0.0265 octane numbers (R + M) / 2 for the remaining 62 samples.

 Mathematical Criterion III.

B $\genfrac{}{}{0ex}{}{\text{k}}{\text{r}}$ = B $\genfrac{}{}{0ex}{}{\text{i}}{\text{r}}$ Σ _c X $\genfrac{}{}{0ex}{}{\text{i}}{\text{jc}}$ / Σ _c X $\genfrac{}{}{0ex}{}{\text{k}}{\text{jc}}$
A ^k = Σ _c (ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$ -Σ _r B $\genfrac{}{}{0ex}{}{\text{k}}{\text{r}}$ X $\genfrac{}{}{0ex}{}{\text{k}}{\text{rc}}$ ) / n
Provided ϒ $\genfrac{}{}{0ex}{}{\text{i}}{\text{c}}$ = ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$
It should be noted that r = 1 - 3, since only three wavelengths are used, n = 25, since the number of elements in the sample is 25. The above criterion III is used in the same way as criterion II. The results of all methods are presented in table. 1.

 To demonstrate the expected accuracy from the octane calibration equation transferred from one instrument, instrument-i to another instrument-k, the following is true.

 Both devices-i and -k are independently calibrated using the same 72 samples. As a result of calibration, a linear calibration equation is derived, which can be used to predict octane values. The standard prediction error for each of these equations is derived for 10 known samples.

 The calibration transfer equation for instrument-k is derived from calibration equation-i and one of the following criteria: I, II, or III.

 Each transferable equation is adjusted for slope and offset with 10 patterns representing the equation adjusted for slope and offset.

 The results of the above steps are shown in table. 1. It is especially important that the SPP changes dramatically as a result of adjustments for slope and bias. However, the final SPP after adjusting for the slope and offset in case of criterion 1 gives the SPP identical to the value of the SPP of the initial calibration equation-i.

 In this case, the exact calculation of the best value of the SPP, which we can hope for, will be the value of the SPP equal to 0.146, which is the value of the SPP for the device-k in full calibration using 72 samples.

 Example 2. In this example, the mathematical criterion I of example 1 (multiple linear regression) is used, the calibration equation has a linear form, but for independent variables, the spectral features defined by the second and third derivatives of the spectral data, respectively, for each selected frequency are used.

Здесь ϒ $\genfrac{}{}{0ex}{}{\text{i}}{\text{c}}$ и ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$ - расчетные или прогнозируемые значения для зависимых переменных на основе уравнений калибровки для приборов-i и -k, соответственно оба для каждого элемента, с, из выборки-с с 8-ю элементами.

Here ϒ $\genfrac{}{}{0ex}{}{\text{i}}{\text{c}}$ and ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$ - calculated or predicted values for dependent variables based on calibration equations for instruments-i and -k, respectively, for each element, s, from a sample-s with 8 elements.

X $\genfrac{}{}{0ex}{}{\text{i}}{\text{jc}}$ and X $\genfrac{}{}{0ex}{}{\text{k}}{\text{jc}}$ - the second derivatives of the observed values of the spectral absorption capacity for devices-i and -k, respectively, both for each element, s, sample-s at a wavelength-j, where j = 1 - 3.

X $\genfrac{}{}{0ex}{}{\text{/ i}}{\text{jc}}$ and X $\genfrac{}{}{0ex}{}{\text{/ k}}{\text{jc}}$ - the third derivative for the observed values of the spectral absorption capacity for the devices-i and -k, respectively, both for the sample-s at the wavelength-j, where j = 1 - 3.

 The wavelengths are the same as in example 1.

 Device-i analyzed 72 gasoline samples to obtain their spectral absorbing characteristics. In addition, 25 samples of standard calibration transfer values were also processed. Then the second and third derivatives of the spectra are derived using segment lengths of 10 and gaps of 0 by NSAS (NIR Sysfems, Juc. Software package for spectral analysis of near infrared radiation). Compositions of 25 standard calibration transfer values are presented in table. 7, they are specially selected, since they include most of the variability of 72 gasoline samples at the wavelength used for calibration. The octane number of 72 gasoline samples is in the range of 86.3 - 93.2 octane numbers (R + M) / 2, the samples are distributed in this range in an approximately uniform distribution. Each sample is analyzed 4 times by four different laboratory detonation engines (APAL, Control Lab., District Control Lab. And St. Paul Control Lab) using ASTM methods 2699 and 2700 to obtain accurate octane (R + I) / 2 calculations.

Значения членов B_i представлены в табл. 2. В табл. 2 приведены также множественный коэффициент определения (R²), множественный коэффициент корреляции (R) и стандартная погрешность расчета. Из табл. 2 может быть сделано заключение о том, что уравнение калибровки является очень точным.Files of the second and third derivatives of 72 gasoline samples are sent to a universal computer and multiple linear regression in accordance with mathematical criterion 1 is performed using conventional computer programs using SAS statistics (SAS Institute, Inc. Carey, North Carolina) for the second derivative absorbance at 1196, 1220 and 1236 nm by modeling the dependent variable of octane (R + M) / 2. Data analysis by this method gives a model of multiple linear regression of the form:

The values of the members B _{i are} presented in table. 2. In the table. 2 also shows the multiple determination coefficient (R ² ), the multiple correlation coefficient (R) and the standard error of calculation. From the table. 2, it can be concluded that the calibration equation is very accurate.

 The calibration transfer standards from the calibration equation of instrument-i are then predicted and the predicted values are used as the dependent octane variable (R + M) / 2, and the absorbance data for calibration transfer standards on the -k instrument are converted into a second derivative and a third derivative and used for values of independent variables -k to determine the corresponding constants -k according to the classical least-squares method or mathematical criterion 1. The results are shown in table. 3.

в сравнении с октановым числом приближается к прямой линии. Обычно это связано с тем, что первоначальное уравнение калибровки, линейное или нелинейное, преобразовано таким образом, чтобы получить линейную зависимость. При анализе данных ясно, что поправка на крутизну оправдана, так как зависимость стремится к прямой линии. При использовании программы ПК Бейсик показано, что необходимы поправка на крутизну для m, равная 0,86406, и поправка на смещение для b, равная 12,5590.Then 72 gasoline samples were processed by instrument-k and the files of the second and third derivatives were obtained, as indicated above. The new calibration equation from table. 3 is used to predict the octane (R + M) / 2 of 72 samples (it should be noted that these samples are identical to the original calibration set processed on instrument-i) using the same octane number that was used in the initial calibration of instrument-i. These calculations are performed on a PC using the Basic program. The calculated octane values show an offset of -0.431 and have a standard prediction error of 0.586. These errors are quite high, considering that the initial standard error of calculation on the device-i is only 0.145. It can also be seen from the predicted octane values that the error for predicting low octane numbers ((R + M) / 2 is approximately equal to 86) is quite high, i.e. about -0.8 when compared to predicting a higher octane number ((R + M) / 2 approximately 93), for example, much closer to zero, approximately 0.1. This type of behavior is similar to the variance depending on another random variable, when the calculated forecast values tend to have errors by a value that represents the function of the calculated octane number. For example, lower octane numbers gave higher error values, and higher octane numbers gave lower error values. When the behavior described above is observed, the slope and bias correction is justified because the graph

in comparison with the octane number is approaching a straight line. This is usually due to the fact that the original calibration equation, linear or non-linear, is transformed in such a way as to obtain a linear relationship. When analyzing the data, it is clear that the slope correction is justified, since the dependence tends to a straight line. When using the BASIC software, it is shown that a slope correction for m of 0.86406 and an offset correction for b of 12.5590 are needed.

В табл. 5 приведены конечные константы регрессии для прибора-k с использованием переноса калибровки, затем следует поправка на крутизну и смещение.

In the table. Figure 5 shows the final regression constants for instrument-k using calibration transfer, followed by a correction for slope and bias.

 It was found that this equation has a standard error of calculation of 0.190 on instrument-k compared with the standard error of 0.145 instrument-i for 72 gasoline samples.

 Example 3. This example defines the slope and bias correction mentioned above in this description (Anal.Chem.Acta, 192 (1987) 197).

 The different members are defined earlier in the description, ϒ is a calculated or predicted dependent variable taking into account independent variables equivalent to one or more spectral features defined as members of X.

- значение с поправкой на крутизну и смещение, прогнозируемое для физического свойства, как показано далее.Depending on the magnitude of the slope and offset corrections corresponding to m and b, where m is the slope correction and b is the bias correction, you can decide not to change the calibration equation for the uncalibrated instrument.

- the value adjusted for the slope and offset predicted for the physical property, as shown below.

In a special example, ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$ is the predicted octane number from calibration equation-k before adjusting for slope and bias and ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$ - The measured octane number of the sample (or the octane predicted by the calibrated NIR instrument) is used to determine the slope and offset corrections. In the calibration set, which is used to make corrections for slope and bias, it is necessary that the set:
1. Represented the required range for a particular property, for example, octane. Then the sample should have current octane values (measured in accordance with TSTM D 2699 and D 2700) in approximately the range of octane values of interest.

 2. There was an octane number measured for each sample, and so that this current octane value was then correlated (using a plot) in comparison with the calculated octane value for each sample, determined using the calibration equation, in which the slope should be adjusted and bias.

3. The number n of samples for adjusting the slope and offset should be 2 in order to determine both m and b, but the examples usually use the number 10. The calibration equation for the device-k has the form: ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$ = A ^k + Σ _c B $\genfrac{}{}{0ex}{}{\text{k}}{\text{j}}$ X $\genfrac{}{}{0ex}{}{\text{k}}{\text{jc}}$ , ϒ $\genfrac{}{}{0ex}{}{\text{a}}{\text{c}}$ is a directly defined or current property, here is the ASTM measured octane number.

Результаты являются следующими:

• b = 1/n{Σ_cϒ $\genfrac{}{}{0ex}{}{\text{a}}{\text{c}}$ -mΣ_cϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$ }

Пример 4. Математическая обработка переходит от множественной линейной регрессии к частичным наименьшим квадратам для переноса калибровки от прибора-i к прибору-k.4. Find m and b, solve the equation for m and b that satisfy the following mathematical criteria:

The results are as follows:

• b = 1 / n {Σ _c ϒ $\genfrac{}{}{0ex}{}{\text{a}}{\text{c}}$ -mΣ _c ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$ }

Example 4. Mathematical processing goes from multiple linear regression to partial least squares to transfer the calibration from device-i to device-k.

 In this example, instrument-i is a bench measuring device of the NIR Systems 6500 type, operating in reflection mode using fiber optics. The device is calibrated, as shown in example 1, using 72-x samples. Calibration is carried out as before modeling the octane (R + M) / 2 using the second derivative of the absorbance at 1220, 1196 and 1236 nm as independent variables of the multiple regression calibration equation. The standard calibration transfer values are the same 25 values shown in Example 5.

 Instrument-k is an uncalibrated instrument of the NIR Systems OL-6500 type, operating in reflection mode using fiber optics. On this instrument, 25 standard calibration transfer values are processed using calculated octane values from instrument-i as a dependent variable. Thanks to the invention, it is possible to calibrate the device-k, resorting to a different mathematical approach, different from the approach that was used on the device-i (multiple linear regression). Partial Least Squares (ChNKs) are selected as an alternative calibration method for instrument-k. ChNK principles are well known (Harold Martens and Tormod Nes, Multidimensional Calibration, John Wiley & Sons, New York, 1989, ISBN 471-90979-3).

 The CNS method is performed by modeling the dependent variable of the calculated octane value for 25 standard calibration values at the level of the second derivatives of the spectral absorbance in the wavelength range of 1190 - 1240 nm (with intervals of 2 nm, i.e. 1190, 1192, 1194. .. 1240). Cross validation of the results is carried out using 4 groups of the subset. Models are built using one, two, three, four, five and six hidden variables. The model of the four hidden variables obviously gives the best calculation of the octane excitation number for instrument-k and a correlation of 0.9994 octane values calculated by instrument-i. The fourth latent variable CLC model is used to predict the values of the first 10 samples from the calibration set for the initial 72 samples. The predicted values show a significant bias of 0.433 of octane numbers (R + M) / 2 and a standard error of 0.468. A correction is made for the slope of 0.940 and a correction for the intersection of 5.77 octane numbers (R + M) / 2. The remaining 62 samples are predicted to be unknown. The 62 samples show a shift of 0.0156 octane numbers and a standard prediction error of 0.153 for octane numbers for unknowns.

 It should be noted that a different spectral region can be selected, rather than 1190 - 1240, provided that it is functionally related to the octane number with at least the same reliability as when measured directly. This also clearly shows that the wavelengths used in equation-1 need not be the same as the values in equation-2, which indicates additional advantages of the invention.

 Example 5. This example describes the transfer of the calibration equation, which can be used when transferring from one refinery to another, from one detonation engine to another, from one device after changing the configuration and changing the lamp to another device with a significantly reduced prediction error by double transfer calibration.

 This example clearly demonstrates the advantages of the present invention, for example, instrument-k is fully calibrated using only gasolines that did not contain MTBE (methyl t-butyl ether). Congress recently passed an act on a new fuel composition, and since device-k operates in a refinery that is located on a site that does not have CO (carbon monoxide), the act on a new fuel composition requires MTBE (or whatever) to be added to the refinery or other raw materials saturated with oxygen) to gasoline mixtures of such a number. Since instrument-k is calibrated without MTBE, this should be expected to lead to significant errors if the current instrument-k calibration is used on unknown samples that contain MTBE. In order not to re-calibrate the k-instrument completely, it would be advisable to transfer the calibration equation, which can take into account the MTBE intake as it is added to the gasoline feed of the refinery at some future date. In this example, instrument-k is a type of NIR Systems OL-6500 operating in reflective mode using fiber optics.

 The type NIR Systems OL 6500 was chosen for instrument-i, since it was once calibrated on the basis of 226 samples, some of which contained MTBE, and with it you can select samples containing P-15% by volume of MTBE.

 The problem is somewhat complicated by the fact that only standard calibration values are processed by instrument-i when calibrating it with MTBE, these values are 8 pure mixtures (and calculated octane numbers) shown in Table. 6. These 8 mixtures are not processed by the -k instrument, so direct calibration transfer is not possible.

 To carry out the transfer, 8 standard calibration values are processed again by the -i instrument. Since the calibration of instrument-i is carried out taking into account MTBE, instrument-i is tuned from transmittance measurements at a path length of 20 mm to a reflection measurement at a path length of 18 mm using fiber optics. The gain of the lamp and detector also changes.

 Given the new set of conditions, using 8 standard calibration values, the calibration for MTBE is transferred from instrument-i in transmit mode to instrument-i in reflective mode. Then its equation without correction for slope and offset or other methods of error (for example, the least squares method) is used to calculate the predicted octane values for 25 standard calibration values, which are also processed by device-i in reflective mode and device-k also in reflective mode.

 Multiple linear regression according to 25 standard values of the table. 7 on instrument-k, using calculated octane values as dependent variables and the second derivative of absorbance at 1220, 1196, and 1236 nm, produces a new calibration equation for instrument-k, which can be used to predict the octane numbers of gasoline mixtures containing MTBE.

 The new equation is corrected for steepness and displacement for 10 gasoline samples. Four of these samples are higher unleaded gasoline mixtures ((R + M) / 2 octane = 92), the remaining 6 are normal unleaded gasoline mixtures ((R + M) / 2 = 87). These samples show an offset of 0.919 and a standard error of 0.946 (R + M) / 2 octane numbers.

 Based on these data, a slope correction of 0.950 and an offset correction of 5.30 are performed. The resulting equation demonstrates an offset of 0.0401 and a standard prediction error of 0.122 for 30 unknown gasoline samples. Some relevant data is provided below.

 The summary table shows a very interesting phenomenon, which consists in the fact that the transferred calibration equation is approximately 2 times more accurate than the original equation. This is most likely due to the fact that the octane values used in the correction for slope and offset for instrument-k are known with greater accuracy than the calibration samples used on instrument-i.

 This example is contrary to the conventional wisdom of some NIR systems experts. These scientists believe that the equation derived for one refinery cannot be used for forecasting at another plant. In this example, calibration for MTBE instrument-i was performed at the Ashland Refinery in Catletsburg. It is a very sophisticated refinery operating in accordance with industry standards, it has 12 gasoline miscible components. On the other hand, instrument-k processes data from a refinery in Ashland's St. Paul's Park in Minnesota, which has only 6 gasoline-miscible components and is therefore considered less complex. Moreover, the refineries in Catletsburg and St. Paul's Park have almost no overlap in terms of crude oil compositions.

Example 6. This example shows that if ϒ _{k, s} is a linear function of ϒ _{i, s} , then the transferred calibration equation turns out to be as efficient or almost as effective as the equation obtained from the direct calibration transfer of the previous examples (i.e. e. where ϒ _{i, s (forecast)} = ϒ _{k, s (current)} Here we will consider the linear function ϒ _{i, s} , where ϒ _{k, s} = 3 (ϒ _{i, s} ) _forecast. +25.
The previous example shows the calibration for octane (R + M) / 2 on 226 samples, which predicts the octane values (R + M) / 2 of 8 calibration standards (isooctane, n-decane, 1-octene 2,4,3- trimethylpentane, n-heptane, cyclohexane, n-hexane and toluene). This calibration was developed on the NIR Systems Model 6500, which operates in transmission mode with a range of 20 mm.

Subsequently, this device was adapted for fiber optics using reflectivity at a path length of 18 mm after the amplification factors of the lamp and detector were changed. The 8 calibration standards are processed on the instrument using three times the octane value determined from the transmission measurements plus 25 as the value of the dependent variable. Multiple linear regression results are as follows:
A _k - = 286.951
B _{k, 1220} - = 283,252
B _{k, 1196} - = 70,020
B _{k, 1236} - = 84.185
Then the values are predicted for 10 gasoline samples.

The predicted values for 10 gasoline samples are adjusted using three equivalent methods. Method 1 entails subtracting 25 from the value predicted for gasoline samples (R + M) / 2, dividing the result by 3 and adjusting for slope and offset. Method 2 requires an adjustment for the slope and bias using the currently measured octane value of the sample. Method 3 requires the use of three times the octane value of gasoline samples plus 25 for the samples used in the slope and bias correction, and the correction of the values predicted for subsequent unknowns, subtracting 25 and dividing by 3. In each of these three methods, a bias of 0.0281 is noted and the standard prediction error of 0.240 octane numbers (R + M) / 2 using an unknown set consisting of 62 unknowns
It should be noted that the final equation for direct calibration transfer (ϒ _{i, s forecast} = ϒ _{k, s current} ) shows a slightly lower error and bias than any of the previous methods (bias = 0.0237, SPP = 0.223 octane (R + M) / 2). ϒ _{k, s} multiplied by a constant and with the addition of some other constants, gave a value for the dependent variable for the transfer, which affected the error term (ϒ _{k, s prediction.} -ϒ _{i, s tech.} ), which cannot be deleted using the inverse mathematical function or by adjusting for slope and offset.

However, if we formulate the calibration transfer equation (without correction for slope and bias) and multiply the regression constants (A _k , B _{k, 1220} , B _{k, 1196} and B _{k, 1236} ) by 3 and add 25 to A _k , with the exact the answer we can come to the conclusion that the direct method (ϒ _{k, s forecast.} = ϒ _{i, s tech.} ) after using the correction for the slope and offset with the current octane values (R + M) / 2 of 10 samples or using adjustments for slope and offset, produces an equation using three times the octane value plus 25 and subtracting 25 from each predicted octane value and dividing it by 3.

Example 7. The calibration equation for an uncalibrated instrument is obtained based on the calibration equation derived for the reference instrument. The solutions for the following equations determine: B $\genfrac{}{}{0ex}{}{\text{k}}{\text{j}}$ and A ^k in the linear calibration equation for the uncalibrated instrument-k, having the form: ϒ $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$ = A ^k + Σ _j B $\genfrac{}{}{0ex}{}{\text{k}}{\text{j}}$ X $\genfrac{}{}{0ex}{}{\text{k}}{\text{jc}}$ that uses the calibration equation: ϒ $\genfrac{}{}{0ex}{}{\text{i}}{\text{c}}$ = A ⁱ + Σ _j B $\genfrac{}{}{0ex}{}{\text{i}}{\text{j}}$ X $\genfrac{}{}{0ex}{}{\text{i}}{\text{jc}}$ for calibrated or reference instrument, instrument-i.

The mathematical criterion I is used - the classical least squares method. But since only three wavelengths are used, then J = 1 - 3, since 4 is the total number of elements in the sample-c, then c = 1 - 4. Independent variables X $\genfrac{}{}{0ex}{}{\text{k}}{\text{jc}}$ (where k stands for device-k), the spectral characteristics obtained from the spectral data of device-k at a wavelength-j have values. Each wavelength j is within the wavelength range of 800 - 2500. Here, the spectral features represent the second derivative of the spectral absorbance determined at three wavelengths: 1196, 1220 and 1286 nm.

Следует отметить, что в математическом критерии I форма уравнения калибровки для эталонного прибора-i может отличаться от формы уравнения для неоткалиброванного прибора-k.Mathematical Criterion I

It should be noted that in mathematical criterion I, the form of the calibration equation for the reference device-i may differ from the form of the equation for the uncalibrated device-k.

 Even after changing the lamp, which usually changes the spectral characteristics of the device, and adapting the device to fiber optics, operating in reflective mode at different path lengths, it was possible to recalibrate such a device using the steps of this invention.

Calibration is performed on instrument-i for the octane excitation value. The calibration set includes 226 samples. These samples are analyzed on instrument-i and multiple linear regression is performed by modeling the octane (R + M) / 2 at the level of the second derivative of absorbance at 1220, 1196 and 1236 nm. Device-i operates in transmission mode using a total path length of 20 mm. The resulting regression constants are as follows:
A ⁱ - = 87.925
B $\genfrac{}{}{0ex}{}{\text{i}}{\text{1}}$ - = 69.864
B $\genfrac{}{}{0ex}{}{\text{i}}{\text{2}}$ - = 18.581
B $\genfrac{}{}{0ex}{}{\text{i}}{\text{3}}$ - = 27.664
The standard calculation error for the equation is 0.330. It should be noted that these results were obtained from different detonation engine operators testing samples on the same detonation engines. These results are believed to be good, since the permissible ASTM limit values for (R + M) / 2 are a standard calculation error of approximately 0.35. These samples are characterized by an approximately uniform distribution of 84-94 octane (R + M) / 2.

 The values of the calibration equation derived from multiple regression are predicted for 4 calibration transfer standards. These standards and their calculated values of octane (R + M) / 2 are given in table. nine.

 It should also be noted that the device-i was calibrated over a four-month period (i.e., the samples were processed as they entered the laboratory), and this is not an optimal calibration option. The fact that these calibration standards were not processed on the device immediately or simultaneously with the initial calibration, but not later than 1 month after the calibration was not optimal, was also not optimal.

 After that, the lamp on the device-i burns out and a new lamp is inserted. The device also adapts to fiber optics, operating in reflective mode with different total path lengths (≈ 18 mm). After changes in the nature of the configuration and the path length, the detector gain must also change to accommodate the new lamp and lower the bandwidth of the fiber optics configuration (as opposed to the transmission).

 Standard samples for calibration transfer are again processed on instrument-i and the calibration transfer equation is derived by modeling the calculated octane as a function of the second derivative of spectral absorbance at 1220, 1196 and 1236 nm.

The resulting regression constants were as follows:
A ^k - = 87,717
B $\genfrac{}{}{0ex}{}{\text{k}}{\text{1}}$ - = 92,471
B $\genfrac{}{}{0ex}{}{\text{k}}{\text{2}}$ - = 24,079
B $\genfrac{}{}{0ex}{}{\text{k}}{\text{3}}$ - = 32,054
B $\genfrac{}{}{0ex}{}{\text{k}}{}$$\genfrac{}{}{0ex}{}{}{\text{1}}$ very different from B ₁ whereas A ^k , B $\genfrac{}{}{0ex}{}{\text{k}}{}$$\genfrac{}{}{0ex}{}{}{\text{2}}$ and B $\genfrac{}{}{0ex}{}{\text{k}}{}$$\genfrac{}{}{0ex}{}{}{\text{3}}$ are within the octane values of 6 (R + M) / 2 from respectively A ⁱ , B $\genfrac{}{}{0ex}{}{\text{i}}{}$$\genfrac{}{}{0ex}{}{}{\text{2}}$ and B $\genfrac{}{}{0ex}{}{\text{i}}{}$$\genfrac{}{}{0ex}{}{}{\text{3}}$ .

Then, an analysis of 97 samples for octane (R + M) / 2 was performed. All samples were different from the previous ones. Moreover, they were analyzed by many operators on different detonation engines other than previously used engines. The calibration transfer equation shows a slight mix of 0.0392 octane (R + M) / 2 values (note that the offset between two different detonation engines is usually much higher than this value) and a standard calculation error of 0.371 octane (R + M) / 2. The offset and slope correction was performed using two samples: one with an octane number of 87.4 and the other with an octane number of 92.5, the slope correction was 0.9402 and the intersection correction or offset correction was 5.297, and the final equation was obtained :
A ^k - = 87,774
B $\genfrac{}{}{0ex}{}{\text{k}}{\text{1}}$ - = 86.945
B $\genfrac{}{}{0ex}{}{\text{k}}{\text{2}}$ - = 22,640
B $\genfrac{}{}{0ex}{}{\text{k}}{\text{3}}$ - = 30,139
The equation adjusted for slope and bias has a bias of 0.0 and a standard prediction error of 0.343.

 In order to show that this cannot be done directly from the initial calibration equation, taking into account the transmission data, the initial calibration equation is used to predict the octane (R + M) / 2 for each sample of 97 gasoline samples. The result shows an offset of 0.482 octane. Setting the bias and slope using only 97 samples, respectively, according to the initial calibration equation, shows bias 0 and the standard error of calculation is 1.96 (R + M) / 2 octane.

 It should also be noted that the steepness of the two points and the offset adjustment can also be considered as a step that reduces the error of the generalized smallest sum, in the sense that it can be performed equivalently using the geometric approach.

 For example, using a line through measured current values, you can determine constants to get a line between predicted values before you make adjustments to ensure that both lines are equivalent. Therefore, this is the generalized smallest sum since squares are not used in this approach.

 The specific compositions, discussed methods or embodiments are provided in the description for illustration only. Changes to these compositions, methods or embodiments are apparent to those skilled in the art and therefore should be included within the scope of the invention described.

For example, a method equivalent to the methods described in the examples, not going beyond the scope of the claimed invention, determines the offset value, for example, for A ^k in the calibration equation-k for the device-k based on the calibration equation-i for the device-i, into account that A ⁱ is equal to some arbitrary value, for example, zero, or a value determined depending on A ⁱ and the function A ⁱ , i.e. partially calibrated instrument. The correct value for A ^k is a value that, when used in equation-k, determines the value for the dependent variable -k, which is essentially equal to the current value of the desired physical or chemical property. The correct value for A ^k can be obtained by applying the slope and bias corrections to the equation obtained by using an arbitrary value for A or a value determined by any function A. Another method equivalent to the above occurs when the final equation , which will be derived from the equation of slope and bias, functions of m or b (terms described in Example 6) can be used. This will clearly change the calculated or predicted value of the dependent variable. However, just as it was shown in the description for using the calibration function YΨ of the calibration equation-i, the function m or b can be used, and then the resulting dependent variable can be converted back to a value that will be essentially equal to the current value for the chemical or physical property of the desired range.

 Another change within the scope of this invention is how the values are assigned to the -k dependent variable. These values for the dependent variable -k, which can be used to determine the constants -k in the calibration equation -k or to perform the correction for the slope and offset, can be found without using the primary test method, but can be determined using the- i calibration and spectral data-i received from device-i or possibly any other calibrated device, together with its corresponding calibration equation, which covers virtually the same required range and corresponding with ektralnye data.

 Another variant of this invention is the use of different spectral features in the calibration equation-i, different from the characteristics in the calibration equation-k, for example, different wavelengths or different mathematical transformations, or both of these approaches, provided that each difference is correlated with the necessary physical or chemical property.

 In most examples, only three wavelengths are used. However, this number may vary depending on the desired or desired statistical reliability. If for any property the indirect method has an SPP with respect to V, the value of which is less than the reliability interval for the direct method when determining such a property, then there is a practical limit to how little this value of V can be and how many wavelengths may be needed.

 Another modification relates to spectral features that can be derived from absorption spectra. In the examples, both the second derivative and the derivative of higher orders of intensity depending on wavelengths or absorption capacity were used. Specifically, derivatives of higher orders, such as first, second, third, fourth, fifth, etc., are also contemplated as contemplated by this invention. The values of the spectral characteristics can simply be equal to the value determined for a particular wavelength or range of wavelengths, relative to the reference wavelength, for example, absorbance values. Spectral features do not imply mandatory differences from spectral data in their values. Obviously, they can be more complex and that using a linear combination of spectral features or their mathematical transformations is also within the scope of the invention.

 It is also obvious, as a variant of this invention, a linear combination of derivatives of higher orders, for example derivatives of the third and fourth or higher order spectral data (see example 5).

 Moreover, the set of elements or a range of numbers described herein may include any element or number within such a set or range, respectively, including any subset or subrange within any of the named sets or ranges.

Claims (10)

 1. A method of calibrating a spectral device to determine the property value of an unknown sample, comprising using constants in calibration equation-2 for said device using a spectral device that corresponds to calibration equation-1, characterized in that it includes, in any order, the determination from calibration equation-1 values of the dependent variable-1, respectively, to each element of the set of standards for transferring calibration based on spectral data-1 for each element of the said set of standards for transferring calibration and determining constants-2 in said calibration equation-2 from the condition of minimizing the sum of the absolute differences between each value of dependent variable-2 for each element of the set of standards for transferring calibration using spectral data-2 measured by the said instrument and the corresponding value dependent variable-1, defined for each element of the set of standards for transferring calibration according to calibration equation-1, determination of the values of the mentioned property is unknown single sample using said instrument.  2. A method for calibrating a spectral device to determine the property value of an unknown sample, comprising using constants in calibration equation-2 for a second device using a first spectral device having calibration equation-1, characterized in that the method includes in any order the determination from equation-1 calibration of the value of the dependent variable-1, respectively, to each element of the set of standards for transferring calibration based on spectral data-1 for each element of the set of standards for transferring calibration, measured using the first device, and the definition of constants-2 in equation-2 calibration from the condition of minimizing the sum of the absolute differences between each value of the dependent variable-2 for each element of the set of standards for transferring calibration using spectral data-2, measured by the said second device , and the corresponding value of the dependent variable-1, defined for each element of the set of standards for calibration transfer, measured by the first device, determining the values of the above properties in an unknown sample using a second instrument.  3. A method for calibrating a spectral device to determine the property value of an unknown sample, including calibrating the first device with a second device in the range of required values for the corresponding property, characterized in that the method includes, in any order, obtaining spectral data corresponding to the first device and the second device data-1 and data-2, respectively, for each element of the set of standards for transferring the calibration, the determination using the calibration equation-1 of the first device is for dependent variable-1, respectively, for each element of the set of standards for transferring calibration, determining the value for dependent variable-2, functionally related to the defined property, for each element of the set of standards for transferring calibration, choosing values for constants-1 in calibration equation-1 such so that the sum of the absolute differences between each dependent variable-1 defined by calibration equation-1 with selected constants-1 and data-1 for each element of the set of standards for transfer calibration, and the corresponding dependent variable-2 for identical elements of many standards for transferring calibration is essentially minimized, the determination of the values of the mentioned properties in an unknown sample.  4. The method according to claims 1, 2 or 3, characterized in that many standards for calibration transfer have values of the dependent variable that differ from the values of the dependent variable that could be obtained using the initial benchmark test, and many standards for calibration transfer have compositions that differ from the composition of the sample, and the determination of constants-2 is carried out using partial least squares, multiple linear regression and / or regression of the main component.  5. The method according to claims 1, 2 or 3, characterized in that the spectral data-1 and spectral data-2 include infrared spectral data, the sample includes liquid, many standards for calibration transfer include at least one composition other than the compositions, used to calibrate the first instrument.  6. The method according to claim 1, characterized in that the set of standards for transferring calibration includes at least one standard, which is a pure compound or a mixture of pure compounds.  7. The method according to claim 1, characterized in that many standards for transferring calibration have at least one element that provides spectral data-2 when measured by a second device, which together with calibration equation-2 determines the value for dependent variable-2 from for at least one element having a characteristic value that differs significantly from the value determined by direct testing, for which calibration equation-1 and calibration equation-2 were derived for the purpose of modeling. 8. The method according to p. 1, characterized in that the calibration equation-2 has the following form:

where y $\genfrac{}{}{0ex}{}{\text{1}}{\text{s}}$ - dependent variable-1 for the sample element s based on calibration equation-1 for the first device;
Y $\genfrac{}{}{0ex}{}{\text{2}}{\text{s}}$ - dependent variable-2 for the sample element s;
A ² - transfer constant-2;
B $\genfrac{}{}{0ex}{}{\text{2}}{\text{j}}$ - constant-2 slope for each sample element at a wavelength j;
I $\genfrac{}{}{0ex}{}{\text{2}}{\text{js}}$ - an independent variable, determined on the basis of spectral data-2, corresponding to the sample element s at a wavelength j,
and said minimization of absolute differences is provided by minimizing the following expression:
Σ _s {Y $\genfrac{}{}{0ex}{}{\text{1}}{\text{s}}$ -A ² -Σ _j (B $\genfrac{}{}{0ex}{}{\text{2}}{\text{j}}$ • I $\genfrac{}{}{0ex}{}{\text{2}}{\text{js}}$ )} ² ,
the independent variable is determined based on spectral data-2 by converting the absorption capacity, which includes determining the differential of the absorption spectra. 9. The method according to any one of claims 1 to 8, characterized in that corrections for slope and offset are introduced to increase the accuracy of the dependent variable Y $\genfrac{}{}{0ex}{}{\text{1}}{\text{s}}$ before

in this case, the values for m and b are substituted into the following expression:

where m and b are determined from the following expressions:

b = 1 / n {Σ _c Y $\genfrac{}{}{0ex}{}{\text{a}}{\text{c}}$ -mΣ _c Y $\genfrac{}{}{0ex}{}{\text{k}}{\text{c}}$ },
where the dependent variable (ac) Y $\genfrac{}{}{0ex}{}{\text{a}}{\text{c}}$ selected from the group of values consisting of directly determined values for property-p of element c, the predicted value for property-p of element c using the calibration equation for property-p within the range for which the calibration equation is obtained by modeling, each value for property-p does not go beyond the limits for which calibration equation-1 was obtained by modeling, and their combinations, and n is the number of elements in the set of samples adjusted for the slope and offset, to which the calculated values Achen representing values within which the modeling obtained calibration equation-1.  10. The method according to any one of claims 1 to 8, characterized in that it includes the step of reducing the error.

Images