CN114383646B - Method and equipment for detecting resolution of continuously-variable measured sensor - Google Patents
Method and equipment for detecting resolution of continuously-variable measured sensor Download PDFInfo
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Abstract
The application discloses a method and equipment for detecting the resolution of a continuously variable type measured sensor, wherein the method comprises the following steps: acquiring monitoring data acquired by the sensor, and acquiring an original data sample based on the monitoring data, wherein the original data sample specifically comprises initial monitoring data and a plurality of data obtained by follow-up continuous monitoring; constructing a step value time array and a measurement model based on the original data sample; determining a classification value based on the step value time sequence, and generating a classification value sequence and a classification value frequency sequence based on the classification value; judging whether monitoring data need to be added or not based on the classification value sequence and the classification value frequency sequence; if not, calculating the resolution of the sensor based on the classification value series. Therefore, the threshold and the cost of the resolution detection operation of various continuous variable type measured sensors are reduced, and the detection efficiency, convenience and universality are improved.
Description
Technical Field
The present application relates to the field of sensors, and more particularly, to a method and apparatus for detecting the resolution of a continuously variable type measured sensor.
Background
Resolution (resolution) was also known earlier, and the definition in ISO GUIDE 99-2007-international metrology vocabulary basic and generic concepts and related terms is "minimal change measured, causing a significant change in the corresponding measured value. The definition in the national measurement technical Specification of the people's republic of China, JF 1001-2011-general measurement term and definition, is: "the smallest change measured that causes the corresponding indication to produce a perceptible change. In the national standard for the people's republic of China, the general term for sensor GB/T7665-2005, the definition of the resolution (rate) of a sensor is expressed as the minimum variation which can be detected by the sensor in a specified measuring range. "
Resolution is the metering performance of the basicity of various sensors, and is a precondition for guaranteeing the sensitivity and accuracy of a measuring system. Many sensors lack a resolution assay; the method has the resolution verification rules, a standard instrument with higher resolution and precision equipment capable of controlling the measured small change are required to be used in a laboratory, and the verification work requires strict working conditions (see JJG 703-2003 electro-optical distance measuring instrument and other rules), so that the detection method has higher economic cost and time cost; there are also sensors that detect nothing. In the detection of the resolution of the sensor, the quantity of measurement samples is generally small, and the uncertainty of detection results is usually rated according to a class B method (see national metrology technical specification of the people's republic, JJF1059.1-2012, which is used for measuring uncertainty rating and representation). The resolution of the measuring tool such as a line ruler and a weighing apparatus is represented by a graduation value (also called a scale interval). The calibration procedure of a part of weighing apparatus measuring instruments gives a corresponding calibration method of the index value, generally, standard weights with 1/10 target resolution specification are gradually increased until the weighing apparatus displays the change of weight quality, and if the index value of the weighing apparatus is increased by 1 metering unit when 10 weights are added, the index value of the weighing apparatus is calibrated to be qualified. This situation is also common in sensor resolution detection works in other countries. The invention direction and scientific research of the patent related to sensor resolution detection are more aimed at inventing a resolution verification instrument with higher measurement accuracy, such as a resolution calibration device 201720576026.X of electro-optical distance meter and a measurement device CN202011544510.7 of EBCMOS resolution parameters, and a new automatic quality comparator of Solecki Michal et al, the resolution of which is 10 nanograms for calibrating quality below 2 milligrams. Liu Junjie et al studied the resolution of liquid particle counters and analyzed 4 domestic and foreign calibration standards, and proposed the idea of improving the resolution of liquid particle counter calibration procedures, but the acquisition of the measured indication still required the careful preparation of 10 μm monodisperse particle size standard substance for the instrument to be calibrated. In summary, most of the sensors are used for detecting the resolution, the measured value is controlled to change according to the designated resolution value under laboratory conditions to cause the change of the measured indication value of the detected instrument, the detection result is mostly the expected value of a small data sample, and the uncertainty of the detection result is mostly assessed according to the class B method.
Therefore, how to improve the detection method of the resolution of the sensor, reduce the threshold and cost of detection operation, and improve the efficiency, convenience and universality of detection is a technical problem to be solved at present.
Disclosure of Invention
The invention provides a method for detecting the resolution of a continuously variable type measured sensor, which is used for solving the problems of high detection operation threshold, high cost, low detection efficiency, low convenience and poor universality of the resolution of the continuously variable type measured sensor in the prior art.
The method comprises the following steps:
acquiring monitoring data acquired by the sensor, and acquiring an original data sample based on the monitoring data, wherein the original data sample specifically comprises initial monitoring data and a plurality of data obtained by follow-up continuous monitoring;
constructing a step value time array and a measurement model based on the original data sample;
determining a classification value based on the step value time sequence, and generating a classification value sequence and a classification value frequency sequence based on the classification value;
judging whether monitoring data need to be added or not based on the classification value sequence and the classification value frequency sequence;
if not, calculating the resolution of the sensor based on the classification value series.
In some embodiments of the present application, the step value time series is specifically:
ΔY＝Δy 1 ，Δy 2 ，...,Δy i ，...,Δy n ；
wherein Δy i Is the i-th step value, and deltay i ＝|y i -y i-1 |，y i Is the i-th measured indication value in the original data Y, Y i-1 Is the measured indication of the i-1 th in the raw data, |y i -y i-1 I is the calculation y i Subtracting y i-1 N is the total number of data of the step value time sequence delta Y, and the total number of data of the step value time sequence delta Y is greater than the total number of data of the original data sequence1 less.
In some embodiments of the present application, the measurement model is specifically:
ΔY＝Re·X+ζ；
wherein Δy is the step value, re is the resolution of the sensor, X is the independent variable and is a natural number, ζ is a random error term.
In some embodiments of the present application, the step value time series is used to determine a classification value, and the classification value time series and the frequency series are generated based on the classification value, specifically:
traversing the time series of step values, taking different step values as classification values, and sequentially arranging the classification values into the classification value series according to the sequence from small to large;
traversing the classification value sequence, counting the occurrence times of each stepping value in the classification value sequence, taking the occurrence times as the frequency of each classification value, and generating the classification value frequency sequence based on the frequency of each classification value.
Step value time series in some embodiments of the present application, it is determined whether additional monitoring data is needed based on the classification value series and the classification value frequency series, specifically:
acquiring the frequency of 0 classification value in the classification value frequency sequence, wherein the 0 classification value is a classification value with the value of 0;
when the percentage of the frequency of the 0 classification value to the total number of the step values is smaller than a first preset percentage or the percentage of the frequency of the 0 classification value to the total number of the step values is larger than a second preset percentage or the total number of the classification values is smaller than the first preset value, new data needs to be additionally supplemented or new data samples need to be replaced;
if the percentage of the frequency of the 0 classification value to the total number of the step values is greater than or equal to the first preset percentage, and the percentage of the frequency of the 0 classification value to the total number of the step values is less than or equal to the second preset percentage, and the total number of the classification values is greater than or equal to the first preset value, then the addition of new data or the replacement of new data samples is not needed, and the calculation can be continued.
In some embodiments of the present application, the resolution of the sensor is calculated based on the classification value series, specifically:
calculating a multiple frequency sum of the classification values except the 0 classification value based on the classification value sequence and the classification value frequency sequence;
Based on the multiple frequency sum of the classification values, a class resolution state number sequence and a class resolution state number sequence with polynomial distribution characteristics are constructed;
calculating a class resolution state probability sequence based on the class resolution state sequence and the class resolution state frequency sequence, and estimating the class resolution overall state proportion estimation value sequence;
based on the class resolution state sequence and the class resolution overall state proportion estimation value sequence, a class resolution state with the largest overall state proportion and a class resolution state with the second largest overall state proportion are obtained, and the value of the class resolution state with the largest overall state proportion is primarily judged to be the point estimation value of the sensor resolution Re; carrying out hypothesis test on the difference of the total state proportion maximum class resolution state and the secondary class resolution state in times;
based on the number of times of the maximum class resolution state of the overall state proportion and the number of times of the sub-class resolution state of the overall state proportion, calculating a chi-square value by a chi-square hypothesis test method;
based on the chi-square value, giving a small risk probability standard, inquiring a chi-square critical value table to obtain a critical value, and comparing the chi-square value with the critical value;
If the chi-square value is smaller than or equal to the critical value, judging that the difference is not obvious, adding new data, and then recalculating;
and if the chi-square value is larger than the critical value, judging that the difference is obvious, and finally determining the value of the resolution-like state with the largest overall state proportion, namely the point estimation value of the resolution Re of the sensor.
In some embodiments of the present application, after identifying the resolution of the sensor based on the classification value series, further comprising calculating uncertainty introduced by repeatability, specifically:
calculating integral multiples of each classification value except for a 0 classification value for the resolution based on the classification value and the resolution;
dividing each classification value by a corresponding integer multiple to obtain a quotient serving as a resolution sample measured value corresponding to each classification value, and generating a resolution sample measured value array composed of each resolution sample measured value; based on the resolution sample measurement value sequence, the classification value frequency sequence and the sensor resolution, referring to a Bessel formula, and taking the classification value frequency as the weight of the corresponding resolution sample measurement value, calculating to obtain a sample standard deviation of the sensor resolution;
And calculating uncertainty of the original data sample about the repeatability introduction of the resolution based on the sample standard deviation and taking the difference between the total number of step values and the number of 0 classification values as the degree of freedom.
In some embodiments of the application, the method further comprises:
if yes, continuing to acquire the monitoring data acquired by the sensor, and acquiring a new original data sample based on the monitoring data.
Correspondingly, the application also provides a device for detecting the resolution of the continuously variable type measured sensor, which comprises:
the acquisition module is used for acquiring the monitoring data acquired by the sensor and acquiring an original data sample based on the monitoring data, wherein the original data sample specifically comprises initial monitoring data and a plurality of data obtained by follow-up continuous monitoring;
the construction module is used for constructing a step value time sequence and a measurement model based on the original data sample;
the generation module is used for determining a classification value based on the step value time sequence and generating a classification value sequence and a classification value frequency sequence based on the classification value;
the judging module is used for judging whether the monitoring data need to be added or not based on the classification value sequence and the classification value frequency sequence;
And the determining module is used for calculating the resolution of the sensor based on the classification value series if not.
By applying the technical scheme, the monitoring data acquired by the sensor are acquired, and the original data sample is acquired based on the monitoring data, wherein the original data sample specifically comprises initial monitoring data and a plurality of data obtained by follow-up continuous monitoring; constructing a step value time array and a measurement model based on the original data sample; determining a classification value based on the step value time sequence, and generating a classification value sequence and a classification value frequency sequence based on the classification value; judging whether monitoring data need to be added or not based on the classification value sequence and the classification value frequency sequence; if not, identifying the resolution of the sensor based on the classification value series. Therefore, the threshold and the cost of the resolution detection operation of the continuously-changing type measured sensor are reduced, and the detection efficiency, convenience and universality are improved.
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In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are needed in the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present application, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for detecting the resolution of a continuously variable type measured sensor according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of a step value time sequence and measurement model establishment process according to an embodiment of the present invention;
fig. 3 is a schematic flow chart of a method for generating a classification value sequence and a classification value frequency sequence according to an embodiment of the present invention;
FIG. 4 is a schematic flow chart of determining whether additional monitoring data is needed according to an embodiment of the present invention;
FIG. 5 is a flow chart showing the resolution of an identification sensor according to an embodiment of the invention;
FIG. 6 is a schematic flow chart of a multiple frequency of statistical classification values according to an embodiment of the present invention;
FIG. 7 is a flow chart for verifying that the number of initial sensor resolutions is significantly greater than the number of other resolution states according to an embodiment of the invention;
FIG. 8 is a flow chart of a repeatability introduced uncertainty determination process set forth in an embodiment of the invention;
fig. 9 shows a schematic structural diagram of a device for detecting the resolution of a continuously variable type measured sensor according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present application will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
The embodiment of the application provides a method for detecting the resolution of a continuously variable type measured sensor, which is shown in fig. 1 and comprises the following steps:
step S1, acquiring monitoring data acquired by the sensor, and acquiring an original data sample based on the monitoring data, wherein the original data sample specifically comprises initial monitoring data and a plurality of data obtained by follow-up continuous monitoring.
In this embodiment, when the original data sample for detection is collected from the continuous variable type measured sensor, the operation of the sensor of the measuring system may be under laboratory conditions, or under environmental conditions of the production site, the original data sample may be collected in real time, or may be retained in history;
As for the continuously variable type measured sensor, further illustrated is:
the continuously variable type measured means that the object measured by the sensor is continuously changed with time. For example, the air temperature in a solar greenhouse changes, rises or falls, or is severe or gentle at all times with day-and-night circulation, seasonal changes, production regulation and control. The sensor will show the resolution when measuring and recording the change. Some of the measured goods are not provided with continuous change characteristics, and can be called discrete change type, for example, the loading capacity of a highway truck in and out of the truck, the time of each truck occurrence is discontinuous, the loading capacity of a front truck and a rear truck is irrelevant and discontinuous, and under the use condition, the detection data of a loading capacity weighing system sensor of the truck is not suitable for the method.
The original data sample Y is composed of 1 initial monitoring data and n data obtained by subsequent continuous monitoring, the sampling time interval is not required but is strictly arranged according to the sequence of the generation time, the data with late time is arranged at the back, the total number of the original data samples is n+1, the larger the data quantity of one sample to be detected is, the better, the total number of the data is, the more preferably > =50, and if the influence of random factors on the original data sample is less, the less data can be acquired. It should be noted that the difference of the total data does not affect the protection scope of the present application, and those skilled in the art may determine the total data of the sample to be detected according to the actual situation.
And S2, constructing a step value time sequence and a measurement model based on the original data sample.
To determine the step value time series, in some embodiments of the present application, the step value time series is specifically:
ΔY＝Δy 1 ，Δy 2 ，...,Δy i ，...,Δy n ；
wherein Δy i Is the i-th step value, and deltay i ＝|y i -y i-1 |，i＝1,2，...，n，y i Is the i-th measured indication value in the original data sample Y, Y i-1 Is the measured indication of the i-1 th in the raw data sample, |y i -y i-1 I is the calculation y i Subtracting y i-1 N is the total number of data of the step value time series deltay, and the total number of data of the step value time series deltay is 1 less than the total number of data of the original data sample series.
To determine the measurement model, in some embodiments of the application, the measurement model is specifically:
ΔY＝Re·X+ζ；
wherein Δy is the step value, re is the resolution of the sensor, X is the independent variable and is a natural number, ζ is a random error term.
To illustrate the process of constructing the step value time series and the measurement model based on the raw data sample, the present application is further illustrated by a specific embodiment, as shown in fig. 2, the process of constructing the step value time series and the measurement model based on the raw data sample is specifically:
a sensor of a measuring system, which can measure a measured, a series of measured data Y, which is measured to vary over a period of time, acquired by chronological and designated time intervals, called a time sequence of measured readings of the sensor of the measuring system, Y being a raw data sample that measures the resolution of said sensor:
Y＝y 0 ，y 1 ，y 2 ，...,y i ,...,y n (F01)
In formula (F01): y comprises n+1 ordered indication data Y i ，y i Is the ith data of Y, also Y is at t i Data at time points.
S21: constructing a time series of step values
The time series of step values is denoted as deltay:
ΔY＝Δy 1 ,Δy 2 ，...,Δy i ，...,Δy n (F02)
in the formula (F02), Δy i Is the ith step value of Δy;
Δy i ＝|y i -y i-1 | i＝1,2，...，n (F03)
Δt i ＝t i -t i-1 i＝1,2，...，n (F04)
in formula (F03), Δy i For the i-th step value, y i Is the i-th measured indication value in the original data sample Y, Y i-1 Is the measured indication of the i-1 th in the raw data sample, |y i -y i-1 I is the calculation y i Subtracting y i-1 N is the total number of data of the step value time series deltay, which is 1 less than the total number of data of the original data sample series.
Δy i And Deltat i All positive, Y is usually sampled at equal time intervals deltat, but is influenced by power, communication, human factors and the like of the working site of the measuring system, and the data of Y can be lost, so that any deltat is difficult to ensure i Are all equal, although the intervals of i are all equal; there may also be a small amount of outlier data in Y, but none of these will affect the application of the method.
S22: establishing a measurement model
A measurement model is built for a time series deltay of step values:
ΔY＝Re·X+ζ (F05)
in the expression (F05), Δy is a step value as a dependent variable, re is a resolution of the sensor as a regression coefficient, X is an independent variable and is a natural number, and ζ is a random error term. The model shows that the step value deltay contains an integer number of resolution values Re, and the following calculation steps will be performed on the basis of the variables described by the measurement model and their relationships.
And step S3, determining a classification value based on the step value time sequence, and generating a classification value sequence and a classification value frequency sequence based on the classification value.
In order to accurately obtain the classification value sequence and the frequency sequence, in some embodiments of the present application, the classification value is determined based on the step value time sequence, and the classification value sequence and the frequency sequence are generated based on the classification value, specifically:
traversing the step value time sequence, taking different step values as classification values, and sequentially arranging the classification values into the classification value sequence according to the order from small to large;
traversing the classification value sequence, counting the occurrence times of each stepping value in the classification value sequence, taking the occurrence times as the frequency of each classification value, and generating the classification value frequency sequence based on the frequency of each classification value.
The step value time sequence is shown in fig. 3, and the generated classification value sequence and classification value frequency sequence are divided into 2 substeps:
s31, generating a classification value array: for the step value time data column delta Y, all different step values are extracted, so that no omission and repetition are guaranteed, the extracted step values are called classification values, the classification values are arranged into a sequence in ascending order from small to large, and the sequence is named as a classification value sequence:
dY＝dy 0 ，dy 1 ，...，dy i ，...,dy m (F06)
In the formula (F06), i is the number of the classification value, dy i <dy i+1 M+1 is the number of classification values, the classification value having a value of 0 in the classification value sequence dY is referred to as a 0 classification value, and the other classification values than the 0 classification value are collectively referred to as non-0 classification values.
S32, generating a classification value frequency sequence, and counting each dY corresponding to the classification value sequence dY for the step value time sequence delta Y i The specific method for the classification value frequency sequence consisting of the occurrence frequencies is as follows: for each classification value, traversing the step value time sequence delta Y, counting the number of step values with the same value as the classification value, recording the number as the frequency of the classification value, counting the frequency of all the classification values, and then arranging according to the sequence of the corresponding classification values to generate a classification value frequency sequence:
F＝f 0 ，f 2 ，...,f i ，...,f m (F07)
in formula (F07), F i For the ith classification value dy in the classification value series i The frequency of repeated occurrence in the step value time sequence, i is the sequence number of the classification value frequency, and corresponds to the sequence number of the classification value strictly one by one.
Step S4, judging whether the monitoring data need to be added or not based on the classification value sequence and the classification value frequency sequence.
In order to accurately determine whether additional monitoring data is needed, in some embodiments of the present application, whether additional monitoring data is needed is determined based on the classification value sequence and the classification value frequency sequence, specifically:
Acquiring the frequency of the 0 classification value in the classification value frequency sequence, wherein the 0 classification value is a classification value with the value of 0;
when the percentage of the frequency of the 0 classification value to the total number of the step values is smaller than a first preset percentage or the percentage of the frequency of the 0 classification value to the total number of the step values is larger than a second preset percentage or the total number m of the classification values is smaller than the first preset value, new data needs to be added or new data samples need to be replaced;
if the percentage of the frequency of the 0 classification value to the total number of the step values is greater than or equal to the first preset percentage, and the percentage of the frequency of the 0 classification value to the total number of the step values is less than or equal to the second preset percentage, and the total number of the classification values is greater than or equal to the first preset value, then no new data need to be added or new data samples need to be replaced.
As shown in fig. 4, the raw data sample is obtained from the sensor operation of the measurement system, and the measured change is not carefully designed but is a natural change in a period of time, so that the measured change may not be enough to fully exhibit the real resolution when the data volume of the raw data sample is small, and the step makes a judgment by using the information such as the classification value frequency and the like so as to supplement the data in time, increase the volume of the raw data sample and increase the opportunity of the resolution of the sensor to be exposed in the sample.
In the classified value sequence, the 0 classified value is obtained, the serial number is extracted to be z, and in the classified value frequency sequence, the classified value frequency f with the serial number z is obtained z Calculating f z Percentage of total number n of step values: p is p z ＝f z /n﹒100；
For example, the first preset percentage is set to be 5%, the second preset percentage is set to be 95%, the first preset value is set to be 3, and p is checked z If p z <5% or p z >95, determining that new data should be added or a new data sample should be replaced, and proceeding to step S1;
if the total number m of the classification values is less than 3, judging that new data should be added or new data samples should be replaced, and turning to the step S1;
if p is z More than or equal to 5 percent and p z And if the m is not less than 95 percent and the m is not less than 3, judging that the data is available.
As shown in fig. 4, in order to present the user with the reason that additional data is needed, it may be performed in sub-steps:
s41, checking whether the proportion of the 0 classification value is too large.
Analyzing the classification value sequence and the classification value frequency sequence to obtain the frequency f of the 0 classification value z Calculating p z ＝f z N is 100, judge:
if p is z >95%, go to S42, if p z And (3) not more than 95%, turning to S43.
S42, warning is provided: "data does not reflect the significant changes measured, and additional data is needed. "to return to step S1, additional data continues to be acquired.
S43, checking whether the proportion of the 0 classification value is too small.
If p is z <5, go to S44, if p z And (5) or more, turning to S45.
S44, warning is provided: "lack of measured 0 change, need supplemental data. "
Turning back to step S1, additional data continues to be acquired.
S45, checking the number of the classified values.
Extracting the total number of the classification values, if the total number of the classification values is less than 3, the measured change amplitude of the time period is too small, the resolution Re of the sensor may not be exposed, and an alarm needs to be provided: the measured change amplitude is smaller, and the data is needed to be supplemented. And returning to the step S1, and continuously collecting additional data.
And if the total number of the classification values is more than or equal to 3, continuing the step S5.
And S5, if not, calculating the resolution of the sensor based on the classification value series.
It is necessary to explain that: p is p z Data samples of =100% or the total number of classification values =1 are certainly not available, and the set values of 95%, 5%, 3 are adjustable.
In order to accurately calculate the resolution of the sensor, in some embodiments of the application, the resolution of the sensor is calculated based on the classification value series, in particular:
calculating a multiple frequency sum of the classification values except the 0 classification value based on the classification value sequence and the classification value frequency sequence;
Based on the multiple frequency sum of the classification values, a class resolution state number sequence and a class resolution state number sequence with polynomial distribution characteristics are constructed;
calculating a class resolution state probability sequence based on the class resolution state sequence and the class resolution state frequency sequence, and estimating the class resolution overall state proportion estimation value sequence;
based on the class resolution state sequence and the class resolution overall state proportion estimation value sequence, a class resolution state with the largest overall state proportion and a class resolution state with the second largest overall state proportion are obtained, and the value of the class resolution state with the largest overall state proportion is primarily judged to be the point estimation value of the sensor resolution Re;
carrying out hypothesis test on the difference of the total state proportion maximum class resolution state and the secondary class resolution state in times;
based on the number of times of the maximum class resolution state of the overall state proportion and the number of times of the sub-class resolution state of the overall state proportion, calculating a chi-square value by a chi-square hypothesis test method;
based on the chi-square value, giving a small risk probability standard, inquiring a chi-square critical value table to obtain a critical value, and comparing the chi-square value with the critical value;
If the chi-square value is smaller than or equal to the critical value, judging that the difference is not obvious, adding new data, and then recalculating;
and if the chi-square value is larger than the critical value, judging that the difference is obvious, and finally determining the value of the resolution-like state with the largest overall state proportion, namely the point estimation value of the resolution Re of the sensor.
The raw data sample Y is only one sample of the sensor output over a period of monitoring run time, and is not the population of the sensor data, and the invention uses the data of one sample to estimate the true value of the resolution of the population of the sensor. The original data sample output by the sensor under the influence of the random factor has random errors, and the errors are transmitted to the step value time sequence and the classification value sequence, so that a part of resolution Re becomes a plurality of pseudo resolution Re after being influenced by the random factor. These pseudo-resolutions Re, which are more or less than resolution Re, are more formally characterized by the smallest step value of resolution, which are frequently distributed in dY which is a multiple of resolution Re, and we put together the unidentified resolution Re and these pseudo-resolutions as a class of resolution. Table 1 below shows various cases where the resolution Re and the pseudo resolution Re based on the (F05) measurement model coexist:
TABLE 1
From table 1, it can be seen that the remainder of different values of re, N, ζ affect Δy/class resolution, 5 types can be seen: (1) When the independent variable N is 0, the values of the stepping values delta Y, re and zeta are all 0; independent variable N>At 0: (2) when ζ is 0, Δy can be divisible by Re; (3) When zeta is a value of zeta 1 In the class, the condition that delta Y cannot be divided by Re; (4) When zeta is a value of zeta 2 In class, it may happen that ΔY is resolved by some class resolution re j The situation of integer division; (5) When zeta is a value of zeta 3 In the class, then, it appears that ΔY cannot be resolved by any class resolution re j And (3) the whole division. Since the true value of the resolution of the sensor is an intrinsic property of the sensor, the probability of occurrence of the (2) th condition is high; while the resolution re of each category in the (4) th case occurring under the influence of the random factor j The probability of occurrence is small, which is in accordance with the central limit theorem and periodThe mode characteristic of the expected value is an important basis for identifying the resolution Re according to the scheme, and is proved in the detection of data samples of a plurality of sensors. As shown in fig. 5, the specific method for calculating the resolution of the sensor includes the following sub-steps:
and S51, calculating the multiple frequency sum of the classification values.
Calculating a multiple frequency sum of the classification values except the 0 classification value based on the classification value sequence and the classification value frequency sequence;
As shown in fig. 5, the specific steps of calculating the multiple frequency sum of the classification values are as follows:
s511, starting from the 1 st non-0 classification value to the maximum classification value, the classification values are used as divisors dy one by one based on the classification value series i ；
S512, starting from the 1 st non-0 classification value to the maximum classification value based on the classification value array, and taking each classification value as a divisor dy one by one j ；
S513 based on the dividend dy i Sum divisor dy j Dy is calculated i /dy j Rem remainder of i,j If dy i Not marked "used" and remainder rem i,j =0, give dy j Frequency of multiples of ft j Adding dy to i Frequency f of (f) i And dy is combined with i Marked as "used" for the divisor dy j Traversing the full dividend dy i The dy can be obtained j Frequency of multiples of ft j If the divisor is marked "used" as a dividend, the divisor does not participate in the calculation;
s514, traversing all divisors dy based on the classification value series j Completing the calculation of the sum of the multiple frequencies if the divisor has been regarded as the dividend dy i Divided by integer, i.e. marked as "used", the divisor dy j Not taking part in calculation, and finally obtaining all divisors dy j Is a multiple of the sum of the frequencies;
s52, constructing a class resolution state sequence and a sub-sequence thereof.
Based on the above calculation, the multiple frequency is added to a value greater than 1The divisor dy j Named class resolution state re k The corresponding multiple frequency sum is named as the resolution state re of the class k Times of times(s) k Namely, the number of times of occurrence in the step value time sequence, namely, naming the counted class resolution state number as q, and obtaining 1-q states possibly including the sensor resolution state; to meet the need for maximum likelihood estimation, the 0-class value is then named class resolution state re 0 And the times are counted 0 Equal to its frequency f 0 The method comprises the steps of carrying out a first treatment on the surface of the Finally, the frequency and the divisors equal to 1 are combined into 1 nominal class resolution state-the state which can not be divided is recorded as re q+1 ，re q+1 The corresponding number of times is re q+1 The number of (1) is recorded as time q+1 Thus, the frequency of all classification values becomes the frequency of a certain state, and the state sequence of the complete polynomial distribution, namely the class resolution state sequence, is formed without omission and repetition:
RE＝re 0 ，re 1 ，re 2 ，...，re k ，...，re q ，re q+1 (F08)
a corresponding sequence of class resolution status times:
TIMES＝times 0 ，times 1 ，...，times k ，...，times q ，times q+1 (F09)
in the formula (F09), the amino acids are represented by,
times of each k The sum is equal to the total number n of the stepping values and the total frequency of the classification values.
S53, calculating a class resolution state probability sequence.
Based on the class resolution state time sequence, each time is calculated k Dividing the total number n of the step values to obtain a corresponding class resolution state probability sequence:
P＝p 0 ，p 1 ，...，p k ，...，p q ，p q+1 (F10)
it should be noted that, the scheme does not strictly divide the states which cannot be divided, which may cause that a part of classification values which cannot be divided by any other classification values are divided into the range of class resolution states, so that the advantage is that the number of class resolution states is very small, the resolution states of the sensor cannot be omitted, the difficulty of dividing the class resolution states is reduced, and the recognition range of the resolution of the sensor is enlarged.
S54, calculating an estimated value of the resolution of the sensor.
Based on the class resolution state sequence and the class resolution state probability sequence, in the formula (F10), the probability p of each state k Sum=1, satisfies key features of polynomial distribution, according to principle of maximum likelihood estimation, each state re in the original data sample k Probability p of (2) k Is a maximum likelihood estimate of the proportion of each state in the population; thus, p can be derived from the sample k The class resolution state with the maximum probability value, namely the maximum overall proportion, is obtained and is recorded as re p-max The invention re according to the mode characteristic of the resolution of the sensor p-max As the only candidate for the resolution Re of the sensor, a quasi-resolution state Re is noted quasi ：
Re quasi ＝re p-max (F11)
Incidentally, the overall proportional state can also be acquired next to re p-max The next highest class resolution state, denoted re p-second 。
S55 test Re quasi And re p-second Is a difference in (a) between the two.
The quasi-resolution state Re quasi Is estimated by the sample probability, whether it can be significantly larger than the other class resolution state re j Is also required to make a difference significance check, taking into account re 0 、 re q+1 Are not true class resolution states, do not need to participate in the verification, and are considered in re 1 ～re q Class resolution re with the next highest medium probability p-second Can represent other types of resolution states, thus detecting Re quasi And re p-second The difference significance of (3);
for utensilFor the original data sample of the volume, the sample probability and the value of the overall proportion are the same, and the proportion difference and the frequency difference of each state are equivalent, so the scheme extracts Re from the resolution-like frequency sequence respectively quasi And re p-second Is used to replace the overall ratio and sample probability for the difference test, in particular using the chi-square hypothesis test method, if q=1, the next highest resolution re is desirable p-second Is 0. As shown in fig. 7, the present invention uses a data sample of an air carbon dioxide concentration sensor as an example to illustrate the specific steps:
S551 proposes the assumption
H 0 : zero assumption: quasi-resolution state Re quasi The number of times and re of (2) p-second No significant difference between the times of (1) i.e. according to a theoretical ratio of 1:1;
H A : alternative assumptions: quasi-resolution state Re quasi Is significantly greater than re p-second I.e. not in accordance with a theoretical ratio of 1:1.
S552 calculating theoretical times
Detection value: state Re quasi (＝1.831cm 3 ﹒m -3 ) Number A of times (A) 1 16504 times, state re p-second (＝20.142cm 3 ﹒m -3 ) Number A of times (A) 2 =520 times, sum of times of two states=16504 times;
theoretical value: theoretical times are calculated according to theoretical ratio 1:1: re (Re) quasi Theoretical number of times = T 1 =16504. 1/2=8372 times; re is re p-second Theoretical number of times = T 2 =16504. 1/2=8372 times;
list the list of associations, see table 2:
| i | detection value A i | Theoretical value T i | A i -T i |
| 1 | 16224 | 8372 | 7852 |
| 2 | 520 | 8372 | -7852 |
| Totalizing | 16744 | 16744 | 0 |
TABLE 2
S553, calculating a chi-square value X C 2
X C 2 ＝(|A 1 -T 1 |-0.5) 2 /T 1 +(|A 2 -T 2 |-0.5) 2 /T 2 ＝(|16504-8372|-0.5) 2 /8372+(|520 -8372|-0.5) 2 /8372＝7363.36028+7363.36028＝14726.7。
S554 Chart X C 2 Threshold table, making inferences:
since the number of states involved in the test is known to be k=2, the degree of freedom df=k-1=1 of the lookup table is shown as a small risk probability criterion, which is exemplified by α=0.005, and the chi-square X C 2 The critical value table can know the critical value X 0.005 2 ＝7.88；
Making an inference: because of the calculated X c 2 ＝14726.7>>7.88＝X 0.005 2 So can override H 0 Alternative hypothesis H is approved for hypothesis of (1) A I.e. in the population state Re quasi (1.831) is much larger than the sub-resolution state re p-second Is a ratio of (3);
if can turn over H 0 Assuming that the difference is not significant, it can be considered that the quasi-resolution Re quasi The resolution Re. If not turn over H 0 The assumption that the difference is not significant also requires recalculation of the added monitoring data for the sample;
three further points are described: firstly, the number of times of the class resolution state is equal to the product of the class resolution state probability and the total number n of sample data, and when the data number is more than 5, the comparison probability is equivalent to the comparison number of times, so that the number of times is used for replacing the probability to carry out difference significance hypothesis test is equivalent and feasible; secondly, in the technical scheme, the states of any original data sample participating in chi-square test are only 2, so the degree of freedom df of the table lookup is always=1; thirdly, the small risk probability standard can generally take different values of 0.01, 0.05, 0.1 and the like, and the smaller the value, the higher the test standard and the higher the reliability are, and the small risk probability standard can be determined according to actual needs.
Based on the test Re quasi If significant, the point estimate of the sensor resolution Re can be finally identified:
Re＝Re quasi (F12)
the above method is also fully effective for use in raw data samples that are not affected by random factors.
In order to ensure the accuracy of the resolution, in some embodiments of the present application, after recognizing the resolution of the sensor based on the classification value series, further includes calculating uncertainty of repeatability introduction, specifically:
Based on the classification value sequence and the resolution of the sensor, calculating and determining integral multiples of the non-0 classification value for the resolution of the sensor, and generating an integral multiple sequence according to the integral multiples corresponding to the non-0 classification value and the order of the classification values in the classification value sequence;
generating a resolution sample measurement value array based on each non-0 classification value and integer multiple array;
calculating a sample standard deviation based on the array of resolved sample measurements and the resolution of the sensor;
and evaluating the uncertainty introduced by the repeatability of the resolution measurement according to the standard deviation of the sample.
According to the requirements of general verification standards of sensor resolution, the uncertainty of the resolution Re needs to be assessed on the basis of identifying the resolution point to estimate Re.
As shown in fig. 8, the present invention provides a class a assessment method for resolution measurement repeatability introducing uncertainty:
and S61, determining an integer multiple sequence of the classification value.
From non-0 classification value dy in the classification value series 1 Initially, the classification value dy is used i Dividing by resolution Re, taking the integer part of the quotient as integral multiple, and naming the integral multiple as integral multiple x i I.e. the independent variables in the measurement model, are calculated to the maximum classification value dy n The whole-multiple sequence of classification values was obtained:
X＝x 1 ，x 2 ，...,x i ，...,x n (F13)
and S62, generating a resolution sample measured value array.
Dividing each classification value by a corresponding integer multiple to obtain a quotient serving as a resolution sample measured value corresponding to each classification value:
rE i ＝dy i /x i i＝1,2,…,n (F14)
generating a resolution sample measurement value array consisting of individual resolution sample measurement values:
rE＝rE 1 ,rE 2 ,…,rE i ,…,rE m F(15)
s63, calculating a sample standard deviation.
Based on the resolution sample measurement value sequence and the classification value frequency sequence, the sensor resolution Re, a sample standard deviation s is calculated according to the following formula (F16) by following the bessel formula:
in the formula (F16), s is the standard deviation of the sample, sigma is the sum sign, F i For the frequency of classification values corresponding to rEi, f 0 For the frequency of the 0 classification value, n is the total number of data of the step value, n-f 0 -1 is the degree of freedom of the sample standard deviation.
And S65, calculating uncertainty introduced by the repeatability of the measurement of the resolution sample.
Calculating a resolution sample measurement repeatability-induced uncertainty based on the sample standard deviation s:
in the formula (F17), U (Re) is uncertainty of repetitive introduction of the sensor resolution Re, and s is sample standard deviation.
In the verification of the resolution of the sensor, it may be necessary to determine other assessments than repeatability based on the specific characteristics of the sensor of the measurement system being verified, factors affecting the resolution verification, and the uncertainty may be assessed by a class B standard, which need not be described in detail herein.
By applying the technical scheme, compared with the prior art, the invention has the advantages that:
1. detection equipment such as a higher-resolution etalon and the like and a laboratory-level strictly controllable measured change condition are not needed, the threshold and the cost of detection operation are reduced, and the detection of an online sensor is realized at any time and any place.
2. The monitoring data of the sensor to be detected in daily operation is used, the data with N times of resolution is used, the quality of an original data sample is not strictly required, the data can be accumulated at any moment, the time intervals between successive data can be the same or different, the data can be online real-time data or offline historical data, new data can be sequentially added, and a data source with a large sample size is easy to obtain.
3. The probability of the resolution state is calculated based on the basic principle of maximum likelihood estimation, so that the resolution estimation value with the maximum probability is obtained, the error caused by taking the average value of the samples as the resolution point estimation is reduced, and the resolution obtained by the scheme is closer to the overall true value.
4. The method is strong in universality, is not only applied to a certain sensor, but also applied to various measured sensors with continuous change characteristics such as air temperature, air relative humidity, air carbon dioxide concentration, soil temperature, soil moisture, sunlight illuminance, total sunlight radiation, rainfall, water temperature, hearth temperature and the like, and has accurate detection results, so that the method can be widely applied to the fields of design, production, verification, calibration, maintenance and the like of sensor resolution, and has wide application prospects at home and abroad.
In order to further explain the technical idea of the application, the technical scheme of the application is described with specific application scenarios.
The embodiment of the application also provides a device for detecting the resolution of the continuously variable type measured sensor, as shown in fig. 9, the device comprises:
the acquiring module 701 is configured to acquire monitoring data acquired by the sensor, and acquire an original data sample based on the monitoring data, where the original data sample specifically includes an initial monitoring data and a plurality of data obtained by subsequent continuous monitoring;
a construction module 702, configured to construct a step value time series and a measurement model based on the raw data samples;
a generating module 703, configured to determine a classification value based on the step value time sequence, and generate a classification value sequence and a classification value frequency sequence based on the classification value;
a judging module 704, configured to judge whether additional monitoring data is needed based on the classification value sequence and the classification value frequency sequence;
a determining module 705, configured to calculate the resolution of the sensor based on the classification value sequence if not.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present application, and are not limiting; although the application has been described in detail with reference to the foregoing embodiments, it will be appreciated by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not drive the essence of the corresponding technical solutions to depart from the spirit and scope of the technical solutions of the embodiments of the present application.
Claims (6)
1. A method for detecting the resolution of a continuously variable measured sensor, the method comprising:
acquiring monitoring data acquired by the sensor, and acquiring an original data sample based on the monitoring data, wherein the original data sample specifically comprises initial monitoring data and a plurality of data obtained by follow-up continuous monitoring;
constructing a step value time array and a measurement model based on the original data sample;
determining a classification value based on the step value time sequence, and generating a classification value sequence and a classification value frequency sequence based on the classification value;
judging whether monitoring data need to be added or not based on the classification value sequence and the classification value frequency sequence;
if not, calculating the resolution of the sensor based on the classification value series;
the step value time sequence specifically comprises the following steps:
ΔY＝Δy 1 ，Δy 2 ，...,Δy i ，...,Δy n ；
wherein Δy i Is the i-th step value, and deltay i ＝|y i -y i-1 |，y i Is the i-th indication value measured in the original data Y, Y i-1 Is an indication of the i-1 st measured value in the raw data, |y i -y i-1 I is the calculation y i Subtracting y i-1 N is the step value timeThe total number of data of the number sequence delta Y, and the total number of data of the step value time number sequence delta Y is 1 less than the total number of data of the original data number sequence;
The measurement model specifically comprises the following steps:
ΔY＝Re·X+ζ；
wherein Δy is the step value, re is the resolution of the sensor, X is the independent variable and is a natural number, ζ is a random error term;
determining a classification value based on the step value time sequence, and generating a classification value sequence and a classification value frequency sequence based on the classification value, wherein the classification value sequence comprises the following specific steps:
traversing the step value time sequence, taking different step values as classification values, and sequentially arranging the classification values into the classification value sequence according to the order from small to large;
traversing the classification value sequence, counting the occurrence times of the classification value in the step value time sequence, taking the occurrence times as the frequency of the classification value, and generating the classification value frequency sequence based on the frequency of each classification value;
the 0 classification value is a classification value with the value of 0;
calculating the resolution of the sensor based on the classification value array, specifically:
calculating the multiple frequency sum of all classification values except for 0 classification value based on the classification value sequence and the classification value frequency sequence;
based on the multiple frequency sum of the classification values, a class resolution state sequence and a class resolution state frequency sequence with polynomial distribution characteristics are constructed;
Calculating a class resolution state probability sequence based on the class resolution state sequence and the class resolution state frequency sequence, and estimating a class resolution overall state proportion estimation value sequence;
based on the class resolution state sequence and the class resolution overall state proportion estimation value sequence, a class resolution state with the largest overall state proportion and a class resolution state with the second largest overall state proportion are obtained, and the value of the class resolution state with the largest overall state proportion is primarily judged to be the point estimation value of the sensor resolution Re;
calculating the multiple frequency sum of all the classification values except the 0 classification value based on the classification value sequence and the classification value frequency sequence, wherein the specific steps of calculating the multiple frequency sum of the classification values are as follows:
starting from the 1 st non-0 classification value to the maximum classification value, each classification value is used as the dividend dy based on the classification value series one by one i ；
Based on the classification value sequence, starting from the 1 st non-0 classification value to the maximum classification value, each classification value is used as a divisor dy one by one j ；
Based on the dividend dy i Sum divisor dy j Dy is calculated i /dy j Rem remainder of i,j If dy i Not marked "used" and remainder rem i,j =0, give dy j Frequency of multiples of ft j Adding dy to i Frequency f of (f) i And dy is combined with i Marked as "used" for the divisor dy j Traversing the full dividend dy i The dy can be obtained j Frequency of multiples of ft j If the divisor is marked "used" as a dividend, the divisor does not participate in the calculation;
traversing all divisors dy based on the classification value series j Completing the calculation of the sum of the multiple frequencies if the divisor has been regarded as the dividend dy i Divided by integer, i.e. marked as "used", the divisor dy j Not taking part in calculation, and finally obtaining all divisors dy j Is a multiple of the sum of the frequencies;
adding the multiple frequency to the divisor dy greater than 1 j Named class resolution state re k The corresponding multiple frequency sum is named as the resolution state re of the class k Times of times(s) k ；
Based on the class resolution state time sequence, each time is calculated k Dividing the total number n of the step values to obtain a corresponding class resolution state probability sequence:
P＝p 0 ，p 1 ，...，p k ，...，p q ，p q+1 ；
based on the class resolution state sequence and the class resolution state probability sequence, p of the slave sample k The class resolution state with the maximum probability value, namely the maximum overall proportion, is obtained and is recorded as re p-max Re is based on the mode characteristic of the resolution of the sensor p-max As the only candidate for the resolution Re of the sensor, a quasi-resolution state Re is noted quasi 。
2. The method of claim 1, wherein determining whether additional monitoring data is needed based on the classification value sequence and the classification value frequency sequence is specifically:
acquiring the frequency of the 0 classification value from the classification value frequency sequence;
when the percentage of the frequency of the 0 classification value to the total number of the step values is smaller than a first preset percentage or the percentage of the frequency of the 0 classification value to the total number of the step values is larger than a second preset percentage or the total number of the classification values is smaller than the first preset value, new data needs to be added or new original data samples need to be replaced;
if the percentage of the frequency of the 0 classification value to the total number of the step values is greater than or equal to the first preset percentage, and the percentage of the frequency of the 0 classification value to the total number of the step values is less than or equal to the second preset percentage, and the total number of the classification values is greater than or equal to the first preset value, then no new data need to be added or new data samples need to be replaced.
3. The method according to claim 1, further comprising performing a hypothesis test for the difference in number of times between the overall state-ratio maximum class resolution state and the overall state-ratio sub-maximum class resolution state, in particular:
Based on the number of times of the maximum class resolution state of the overall state proportion and the number of times of the sub-class resolution state of the overall state proportion, calculating a chi-square value by a chi-square hypothesis test method;
based on the chi-square value, giving a small risk probability standard, inquiring a chi-square critical value table to obtain a critical value, and comparing the chi-square value with the critical value;
if the chi-square value is smaller than or equal to the critical value, judging that the difference is not obvious, adding new data, and then recalculating;
and if the chi-square value is larger than the critical value, judging that the difference is obvious, and finally determining the value of the resolution-like state with the largest overall state proportion, namely the point estimation value of the resolution Re of the sensor.
4. The method according to claim 1, further comprising calculating uncertainty of the repeatability introduction after calculating the resolution of the sensor based on the classification value series, in particular:
calculating integer multiples of each classification value other than the 0 classification value for the resolution based on the classification value and the resolution;
using a quotient obtained by dividing each classification value except the 0 classification value by a corresponding integer multiple as a resolution sample measurement value corresponding to each classification value, and generating a resolution sample measurement value sequence composed of each resolution sample measurement value;
Based on the resolution sample measured value sequence, the classification value frequency sequence and the sensor resolution, taking the classification value frequency as the weight of the corresponding resolution sample measured value, and calculating to obtain the sample standard deviation of the sensor resolution;
and calculating uncertainty of the original data sample about the repeatability introduction of the resolution based on the sample standard deviation and taking the difference between the total number of step values and the number of 0 classification values as the degree of freedom.
5. The method of claim 1, wherein the method further comprises:
if yes, continuing to acquire the monitoring data acquired by the sensor, and acquiring a new original data sample based on the monitoring data.
6. A device for detecting the resolution of a continuously variable measured sensor, the device comprising:
the acquisition module is used for acquiring the monitoring data acquired by the sensor and acquiring an original data sample based on the monitoring data, wherein the original data sample specifically comprises initial monitoring data and a plurality of data obtained by follow-up continuous monitoring;
the construction module is used for constructing a step value time sequence and a measurement model based on the original data sample;
The generation module is used for determining a classification value based on the step value time sequence and generating a classification value sequence and a classification value frequency sequence based on the classification value;
the judging module is used for judging whether the monitoring data need to be added or not based on the classification value sequence and the classification value frequency sequence;
a determining module, configured to calculate a resolution of the sensor based on the classification value sequence if not;
the step value time sequence specifically comprises the following steps:
ΔY＝Δy 1 ，Δy 2 ，...,Δy i ，...,Δy n ；
wherein Δy i Is the i-th step value, and deltay i ＝|y i -y i-1 |，y i Is the i-th indication value measured in the original data Y, Y i-1 Is an indication of the i-1 st measured value in the raw data, |y i -y i-1 I is the calculation y i Subtracting y i-1 N is the total number of data of the step value time sequence delta Y, and the total number of data of the step value time sequence delta Y is 1 less than the total number of data of the original data sequence;
the measurement model specifically comprises the following steps:
ΔY＝Re·X+ζ；
wherein Δy is the step value, re is the resolution of the sensor, X is the independent variable and is a natural number, ζ is a random error term;
determining a classification value based on the step value time sequence, and generating a classification value sequence and a classification value frequency sequence based on the classification value, wherein the classification value sequence comprises the following specific steps:
traversing the step value time sequence, taking different step values as classification values, and sequentially arranging the classification values into the classification value sequence according to the order from small to large;
Traversing the classification value sequence, counting the occurrence times of the classification value in the step value time sequence, taking the occurrence times as the frequency of the classification value, and generating the classification value frequency sequence based on the frequency of each classification value;
the 0 classification value is a classification value with the value of 0;
calculating the resolution of the sensor based on the classification value array, specifically:
calculating the multiple frequency sum of all classification values except for 0 classification value based on the classification value sequence and the classification value frequency sequence;
based on the multiple frequency sum of the classification values, a class resolution state sequence and a class resolution state frequency sequence with polynomial distribution characteristics are constructed;
calculating a class resolution state probability sequence based on the class resolution state sequence and the class resolution state frequency sequence, and estimating a class resolution overall state proportion estimation value sequence;
based on the class resolution state sequence and the class resolution overall state proportion estimation value sequence, a class resolution state with the largest overall state proportion and a class resolution state with the second largest overall state proportion are obtained, and the value of the class resolution state with the largest overall state proportion is primarily judged to be the point estimation value of the sensor resolution Re;
Calculating the multiple frequency sum of all the classification values except the 0 classification value based on the classification value sequence and the classification value frequency sequence, wherein the specific steps of calculating the multiple frequency sum of the classification values are as follows:
starting from the 1 st non-0 classification value to the maximum classification value, each classification value is used as the dividend dy based on the classification value series one by one i ；
Based on the classification value sequence, starting from the 1 st non-0 classification value to the maximum classification value, dividing each part one by oneClass value as divisor dy j ；
Based on the dividend dy i Sum divisor dy j Dy is calculated i /dy j Rem remainder of i,j If dy i Not marked "used" and remainder rem i,j =0, give dy j Frequency of multiples of ft j Adding dy to i Frequency f of (f) i And dy is combined with i Marked as "used" for the divisor dy j Traversing the full dividend dy i The dy can be obtained j Frequency of multiples of ft j If the divisor is marked "used" as a dividend, the divisor does not participate in the calculation;
traversing all divisors dy based on the classification value series j Completing the calculation of the sum of the multiple frequencies if the divisor has been regarded as the dividend dy i Divided by integer, i.e. marked as "used", the divisor dy j Not taking part in calculation, and finally obtaining all divisors dy j Is a multiple of the sum of the frequencies;
adding the multiple frequency to the divisor dy greater than 1 j Named class resolution state re k The corresponding multiple frequency sum is named as the resolution state re of the class k Times of times(s) k ；
Based on the class resolution state time sequence, each time is calculated k Dividing the total number n of the step values to obtain a corresponding class resolution state probability sequence:
P＝p 0 ，p 1 ，...，p k ，...，p q ，p q+1 ；
based on the class resolution state sequence and the class resolution state probability sequence, p of the slave sample k The class resolution state with the maximum probability value, namely the maximum overall proportion, is obtained and is recorded as re p-max Re is based on the mode characteristic of the resolution of the sensor p-max As the only candidate for the resolution Re of the sensor, a quasi-resolution state Re is noted quasi 。
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