CN116522059A - Least square fitting method and motor discrete transmission data processing method - Google Patents
Least square fitting method and motor discrete transmission data processing method Download PDFInfo
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Abstract
The invention discloses a least square fitting method and a processing method of discrete transmission data of a motor, wherein the method adopts a polynomial least square method to fit the encoded discrete data of the input end of the motor and the decoded discrete data of the output end of the motor in the transmission process, and a function model obtained by adopting the first fitting is reduced in bit error rate BER compared with the original transmission process, and the accuracy of data errors is improvedThe reduction, the correlation coefficient of the function model obtained by the second fitting is compared with that obtained by the first fittingImproved data error accuracyReduced bit error rate BER reduction, and correlation coefficientHigher represents better fitting effect and data error accuracyThe lower the transmission accuracy is, the higher the bit error rate BER is, the stronger the transmission anti-interference capability is, the system establishes a memory channel according to the finally obtained fitting function model, different motors have different memory channels, and the discrete data decoded by the motor output end are obtained according to the memory channel without repeated fitting.
Description
Technical Field
The invention belongs to the field of data transmission and data processing, and relates to a least square fitting method and a motor discrete transmission data processing method.
Background
In modern communication technology, discrete data transmission is an important application field, however, in the process of discrete data transmission, the transmission quality is easily degraded due to errors caused by the influence of noise and other interference factors on signals.
Particularly, for the transmission of discrete data, no particularly good mathematical model is used for processing, so that the discrete data after the signal is interfered has larger error precisionThe BER is higher, and the deviation degree of discrete data is more obvious.
The signal interference factor may be the interference of a nearby high-power communication signal, or the signal interference factor may be the interference caused by flaws of hardware of the signal interference factor, such as counting defects caused by the lack of magnetism of a local magnetic signal of an encoder, and the signal interference may be caused by lightning, meteorological anomalies and the like.
The least square method is a classical mathematical optimization method, can solve the optimal solution by minimizing the sum of squares of residual errors, has wide application in the fields of discrete data processing, signal processing and the like, and applies least square fitting to the discrete data transmission process, namely, performs least square fitting on input end coded discrete data and output end decoded discrete data, thereby reducing errors generated when signals are interfered.
However, in the field of fitting processing of discrete data transmission of a motor, few patents or literature reports exist, discrete data are generally disordered, proper mathematical models are not available for optimizing the discrete data of the motor, and the probability of deviation of the discrete data of the motor which is directly transmitted and not subjected to optimization reaches a critical point, so that high-quality control of related hardware is affected.
Disclosure of Invention
The invention aims to provide a least square fitting method and a motor discrete transmission data processing method.
The invention aims to solve the problems that a fitting function model is obtained through a least square fitting algorithm to process discrete data in the transmission process, so that the accuracy of decoding the discrete data at an output end is improved, and the anti-interference capability in the transmission process is improved.
A least square fitting method and a motor discrete transmission data processing method adopt the following technical scheme:
a least square fitting method is provided, which comprises the following steps of:。
least squares description:i.e. functional model->The fitting degree is considered to be best when the sum of the squares of the differences between the ordinate and the ordinate of the scatter value is smallest.
From the least squares and the set function model, it is possible to obtain:wherein->Is the residual error, wherein->Is->、/>Is a number of (3).
Make the following stepsThe result is minimum, then parameter->，/>，…，/>Should satisfy the partial derivatives +.>Thus get +.>The following equations:
。
simplifying and sorting the above equation can be performed by the following matrix equation:
。
a matrix is arrangedIs a vandermonde matrix: />，
If let matrixAnd->Multiplication finds:
，
meanwhile, the method comprises the following steps:from the above, it can be seen that: />Thus push +.>Wherein->For parameter->，/>，…，/>In matrix form,/->Is->In matrix form,/->Is->Is a matrix form of (c).
The matrix equation obtained by simplified arrangement by the least square method is utilizedThenCoefficients can be determined, < >>The matrix is the parameter +.>，/>，…，/>Then a polynomial fitting function can be obtainedIs an expression of (2).
Further, the method for processing the discrete transmission data of the motor adopts the least square fitting method, and comprises the following steps of:
step 1: in the process of collecting the discrete data transmission of the motor, the decoded discrete data of the output end and the encoded discrete data of the input end are respectively recorded asAnd->Fitting a function model by using a polynomial least squares method>；
Step 2: encoding discrete data at the input end of a motor in the process of discrete data transmissionRewritten as vandermonde matrix formDecoding discrete data at the output end of a motor in the discrete data transmission process>Rewriting into matrix form->By usingMatrix equation and substitution +.>And->Get parameters->，/>，…，/>；
Step 3: substitution of parameters，/>，…，/>Calculating correlation coefficient of the function model obtained by the first fitting>Error accuracy of data->Bit error rate BER, where->Reflecting the fitting effect of the fitting function model and the original discrete data, and the data error precision>Reflecting the offset degree of the discrete data after fitting and the anti-interference capability of the BER in the transmission process of the fitting model;
step 4: if the correlation coefficient obtained by the first fitting functionError accuracy of data->If BER is not within the allowable error range, performing a second fitting>And->Decoding discrete data and original motor input end coding discrete data for the motor output end obtained after the first fitting, and coding the motor original input end coding discrete data +.>Rewritten as vandermonde matrix form->Decoding discrete data of the motor output end obtained after the first fitting>Rewriting into matrix form->Utilize->Matrix equation and substitution +.>And->Obtaining the parameters after the second fitting +.>，/>，…，/>；
Step 5: the obtained function model after the second least square fittingIn the transmission process, the fitted motor output end decoding discrete data is obtained according to the encoded discrete data of the original input end of the motor and the function model after the secondary fitting;
step 6: substitution of parameters，/>，…，/>Calculating correlation coefficient of function model obtained by the second fitting>Error accuracy of data->Bit error rate BER, where->Reflecting the fitting effect of the fitting function model and the original discrete data, and the data error precision>The deviation degree of the discrete data after fitting and the BER of the error rate reflect the anti-interference capability of the fitting model in the transmission process.
The correlation coefficients calculated in the above steps 3 and 6Error accuracy of data->The BER is calculated as follows:
correlation coefficientThe calculation steps are as follows:
(1) Calculating actual valuesMean value of>；
(2) Calculating fitting valuesAnd (3) the actual value->Residual error between: />；
(3) Calculating a residual square sum:；
(4) Calculating the total sum of squares:；
(5) Calculating a correlation coefficient：/>；
Wherein the actual valueSubstituting the discrete data into the original motor input end to code the discrete data, fitting the value +.>Substituting the output of the motor obtained after the fittingEnd decoding the discrete data;
accuracy of data errorsThe calculation formula is as follows: data error precision->The difference between the decoded discrete data of the motor output end after fitting and the encoded discrete data of the motor original input end/the encoded discrete data of the motor original input end is adopted, wherein the difference takes an absolute value;
the BER calculation formula is as follows: ber=error code number/total code number, where the total code number is substituted into the motor original input end encoded discrete data, and the error code number is substituted into the motor output end decoded discrete data after fitting with the motor original input end encoded discrete data with error accuracy;
wherein the correlation coefficientThe closer to 1, the better the representative fitting effect, the data error accuracy +.>The lower the bit error rate BER, the higher the transmission accuracy, and the stronger the anti-interference capability in the transmission process.
The core idea of the discrete data transmission processing method based on least square fitting is to perform least square fitting on input end coded discrete data and output end decoded discrete data.
Polynomial least squares fitting methods such asIn this form, the best functional match for discrete data can be found by minimizing the sum of squares of the errors.
If the primary fitting result does not reach the error allowable range, the original value and the function model value obtained by the primary fitting can be used for carrying out secondary fitting to obtain a new fitting function model.
When we encode the input end in the process of transmitting the discrete data of the motorWhen the scattered data and the output end decoded discrete data are subjected to a least square fitting method, continuous multiple groups of corresponding input end coded discrete data and output end decoded discrete data in the transmission process are collected and used for least square fitting, a function model is obtained after fitting, and the function model is obtained、…、、/>、/>、/>、/>The former coefficients and constant terms.
According to the method for processing the discrete transmission data of the motor, the discrete data are collected aiming at the discrete data of the motor, the discrete data are decoded according to the motor output end after being fitted according to the original input end coding discrete data of the motor obtained through collection and the function model obtained through fitting in the transmission process, a memory channel is built according to the fitted function model, different motors have different memory channels, and the discrete data are decoded according to the memory channel without repeated fitting.
The invention has the beneficial effects that: a fitting function model obtained by twice least square fitting is adopted, fitted output end decoding discrete data is obtained according to the original input end coding discrete data combined with the function model after twice fitting, and compared with the original output end decoding discrete data, the fitted output end decoding discrete data has correlation coefficientsImprovement of data error accuracy->The method has the advantages that the BER is reduced, the fitting degree of the model is high, the transmission precision is improved, the anti-interference capability of transmission is improved, after the model is built, the system builds a memory channel according to the obtained fitting function model, different motors have different memory channels, and the discrete data decoded at the output end of the motor are obtained according to the memory channel without repeated fitting.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 shows a first set of least squares fitting effects;
FIG. 3 illustrates the effect of a first set of conventional fit functions;
FIG. 4 shows a portion of raw discrete data for a first set of least squares fits and a conventional function fit;
FIG. 5 shows a second set of least squares fitting effects;
FIG. 6 illustrates the effect of a second set of conventional fit functions;
FIG. 7 shows a portion of raw discrete data for a second set of least squares fits and conventional function fits;
FIG. 8 shows a third set of least squares fitting effects;
FIG. 9 illustrates the effect of a third set of conventional fit functions;
fig. 10 shows a third set of partially original discrete data for least squares fitting and conventional function fitting.
Detailed Description
The present invention will be further described more fully hereinafter, but the scope of the invention is not limited thereto.
A least square fitting method and a motor discrete transmission data processing method adopt the following technical scheme:
the least square fitting method is characterized in that a polynomial model obtained by fitting is set as follows:。
according to least squaresThe equation and the set function model can be obtained:。
make the following stepsThe result is minimum, then parameter->，/>，…，/>Should satisfy the partial derivatives +.>Thus, 6 equations are obtained:
。
simplifying and sorting the above equation can be performed by the following matrix equation:
。
reuse ofMatrix equation solution parameter +.>，/>，…，/>，/>Is->In matrix form,/->Is->Is a matrix form of (c).
Further, the discrete data processing method of the motor discrete transmission data adopts the discrete data processing method of least square fitting, and comprises the following steps:
step 1: in the process of collecting the discrete data transmission of the motor, the decoded discrete data of the output end and the encoded discrete data of the input end are respectively recorded asAnd->Fitting a function model by using a polynomial least squares method>；
Step 2: encoding discrete data at the input end of a motor in the transmission processRewritten as vandermonde matrix form->Decoding discrete data +.>Rewriting into matrix form->Utilize->Matrix equation and substitution;
step 3: substitution of parameters，/>，…，/>Calculating correlation coefficient of the function model obtained by the first fitting>Error accuracy of data->Bit error rate BER, where->Reflecting the fitting effect of the fitting function model and the original discrete data, and the data error precision>Reflecting the offset degree of the discrete data after fitting and the anti-interference capability of the BER in the transmission process of the fitting model;
step 4: performing a second fitting usingAnd->Decoding discrete data and original motor input end coding discrete data for the motor output end obtained after the first fitting, and coding the motor original input end coding discrete data +.>Rewritten as vandermonde matrix form->Decoding discrete data of the motor output end obtained after the first fitting>Rewriting into matrix form->Utilize->Matrix equation and substitution +.>And->Obtaining the parameters after the second fitting +.>，/>，…，/>；
Step 5: the obtained function model after the second least square fittingIn the transmission process, the fitted motor output end decoding discrete data is obtained according to the encoded discrete data of the original input end of the motor and the function model after the secondary fitting;
step 6: substitution of parameters，/>，…，/>Calculating correlation coefficient of function model obtained by the second fitting>Error accuracy of data->Error codeRate BER, wherein>Reflecting the fitting effect of the fitting function model and the original discrete data, and the data error precision>The deviation degree of the discrete data after fitting and the BER of the error rate reflect the anti-interference capability of the fitting model in the transmission process.
The correlation coefficients calculated in the above steps 3 and 6Error accuracy of data->The BER is calculated as follows:
correlation coefficientThe calculation steps are as follows:
(1) Calculating actual valuesMean value of>；
(2) Calculating fitting valuesAnd (3) the actual value->Residual error between: />；
(3) Calculating a residual square sum:；
(4) Calculating the total sum of squares:；
(5) Calculating a correlation coefficient：/>；
Wherein the actual valueSubstituting the discrete data into the original motor input end to code the discrete data, fitting the value +.>Substituting the discrete data into the motor output end obtained after the fitting;
accuracy of data errorsThe calculation formula is as follows: data error precision->The difference between the decoded discrete data of the motor output end after fitting and the encoded discrete data of the motor original input end/the encoded discrete data of the motor original input end is adopted, wherein the difference takes an absolute value;
the BER calculation formula is as follows: ber=error code number/total code number, where the total code number is substituted into the motor original input end encoded discrete data, and the error code number is substituted into the motor output end decoded discrete data after fitting with the motor original input end encoded discrete data with error accuracy.
Embodiment one:
the fitting function model obtained by the traditional method of the decoded discrete data of the output end of the first group of motors and the encoded discrete data of the input end of the original motors is that，，Three function models obtained by adopting a traditional method and correlation coefficient +.>0.904337311, 0.964391561 and 0.93947625, respectively, calculate the data error accuracy one by one>Error accuracyMaximum of 5.23%, 2.35%, 3.57%, respectively, according to the error accuracy +.>To calculate bit error rates BER, respectively、/>、/>。
Error precision in original motor discrete data transmission processMaximum 6.54%, BER of error rate +.>。
The first group of motor output end decoding discrete data and the original motor input end encoding discrete data adopt least square fitting:
first fitting utilizationMatrix equation and substitution +.>And->Get parameters->，/>，…，/>Solving to obtain，/>，/>，，/>，The obtained first fitting function model isCorrelation coefficient->For 0.975389243, calculate data error precision one by one +.>Error accuracy->Max 1.23%, according to the error accuracy +.>To calculate the bit error rate BER, which is +.>Compared with a function model obtained by fitting by a traditional method, the correlation coefficientHigh, the fitting effect is good, compared with the function model obtained by the fitting of the traditional method and the original transmission process, the error precision is +.>Low, high transmission accuracy, low BER, and high anti-interference capability.
Second fitting utilizationMatrix equation and substitution +.>And->Get parameters->，/>，…，/>Solving to obtain，/>，/>，，/>，The obtained first fitting function model isCorrelation coefficient->For 0.985989243, calculate data error precision one by one +.>Error accuracy->0.65%, according to the error accuracy +.>To calculate the bit error rate BER, which is +.>Correlation coefficient +.>The fitting effect is better, and the error precision is improved>The reduction of the BER, the transmission accuracy and the BER are higher, and the improvement of the anti-interference capability is indicated.
Embodiment two:
the fitting function model obtained by the traditional method of the decoding discrete data of the output end of the second group of motors and the encoding discrete data of the input end of the original motors is that，，Three obtained by the traditional methodA function model, correlation coefficient->0.913410953, 0.851919698 and 0.798589401, respectively, calculate the data error accuracy one by one>Error accuracy->Maximum of 5.89%, 6.19%, 7.23%, respectively, according to the error accuracy +.>To calculate bit error rates BER of +.>、/>、/>。
Error rate error precision in original motor discrete data transmission processMaximum 8.23%, BER is +.>。
The second group of motor output end decoding discrete data and the original motor input end encoding discrete data adopt least square fitting:
first fitting utilizationMatrix equation and substitution +.>And->Get parameters->，/>，…，/>Solving to obtain，/>，/>，，/>，The obtained first fitting function model isCorrelation coefficient->For 0.961059252, calculate data error precision one by one +.>Error accuracy->Maximum 1.78%, according to the error accuracy +.>To calculate the bit error rate BER, which is +.>Fitting with the traditional methodThe correlation coefficient is compared with the obtained function model>High, the fitting effect is good, compared with the function model obtained by the fitting of the traditional method and the original transmission process, the error precision is +.>The method has the advantages of low transmission precision, low bit error rate BER, and high anti-interference capability.
Second fitting utilizationMatrix equation and substitution +.>And->Get parameters->，/>，…，/>Solving to obtain，/>，/>，，/>，Obtaining the productThe first-order fitting function model of (2) isCorrelation coefficient->For 0.973307938, calculate data error precision one by one +.>Error accuracy->Max 0.64%, according to the error accuracy +.>To calculate the bit error rate BER, which is +.>Correlation coefficients compared to the functional model obtained by the first fittingThe fitting effect is better, and the error precision is improved>The reduction indicates high transmission precision, reduced BER, and improved anti-interference capability.
Embodiment III:
the fitting function model obtained by the traditional method of the decoded discrete data of the output end of the third group of motors and the encoded discrete data of the input end of the original motors is that，，Three function models obtained by adopting a traditional method and correlation coefficient +.>0.911866042, 0.954286974 and 0.937683535, respectively, calculate the data error accuracy one by one>Error accuracy->Maximum 5.32%, 2.15%, 3.56% respectively, according to the error accuracy +.>To calculate bit error rates BER, respectively、/>、1.56/>。
Error precision in original motor discrete data transmission processMaximum 6.21%, BER of error rate +.>。
The third group of motor output end decoding discrete data and the original motor input end encoding discrete data adopt least square fitting:
first fitting utilizationMatrix equation and substitution +.>And->Get parameters->，/>，…，/>Solving to obtain，/>，/>，，/>，The obtained first fitting function model isCorrelation coefficient->For 0.971234563, calculate data error precision one by one +.>Error accuracy->Maximum 1.13% according to the error accuracy +.>To calculate the bit error rate BER, which is +.>Compared with a function model obtained by fitting by a traditional method, the correlation coefficient +.>High, the fitting effect is good, compared with the function model obtained by the fitting of the traditional method and the original transmission process, the error precision is +.>Low, high transmission accuracy, low BER, and high anti-interference capability.
Second fitting utilizationMatrix equation and substitution +.>And->Get parameters->，/>，…，/>Solving to obtain，/>，/>，，/>，The obtained first fitting function model isCorrelation coefficient->For 0.973307938, calculate data error precision one by one +.>Error accuracy->Max 0.46%, according to the error accuracy +.>To calculate the bit error rate BER, which is +.>Correlation coefficient +.>The fitting effect is better, and the error precision is improved>The reduction indicates that the transmission precision is improved, the BER is reduced, and the anti-interference capability is improved.
According to the method for processing the discrete transmission data of the motor, the discrete data are collected aiming at the discrete data of the motor, the discrete data are decoded according to the motor output end after being fitted according to the original input end coding discrete data of the motor obtained through collection and the function model obtained through fitting in the transmission process, a memory channel is built according to the fitted function model, different motors have different memory channels, and the discrete data are decoded according to the memory channel without repeated fitting.
Claims (4)
1. A least squares fitting method, comprising the steps of:
s1: output end decoding discrete number in discrete data acquisition transmission processThe data and the input end code discrete data are recorded asAnd->Let a function model->The least square fitting method is adopted for the function model, which isWherein->Representing that the sum of the squares of the differences between the ordinate of the fitted function model and the ordinate of the scatter is minimal,/->，/>，…，/>Is a parameter;
s2: combining least squaresModelObtain->，/>Is the residual error, wherein->Is->、/>Number, parameters->，/>，…，/>Satisfy partial derivatives->；
S3: obtaining a matrix equation，
Has the following componentsAt the same time there is->Obtain->Then->WhereinFor parameter->，/>，…，/>In matrix form,/->Is->Is in the form of a vandermonde matrix,/>Is->Is a matrix form of (a);
s4: by means ofMatrix equation and substitution +.>And->Get parameters->，/>，…，/>。
2. A method for processing discrete transmission data of a motor, which is characterized in that a least squares fitting method as set forth in claim 1 is adopted, and the method comprises the following steps:
step 1: output end decoding discrete number in process of collecting discrete data transmission of motorThe data and the input end coded discrete data are respectively recorded asAnd->Fitting a function model by using a polynomial least squares method>；
Step 2: encoding discrete data at input end in discrete data transmission process of motorRewritten as vandermonde matrix form->Decoding discrete data of output end in discrete data transmission process of motor>Rewriting into matrix form->Utilize->Matrix equation and substitution +.>And->Get parameters->，/>，…，/>；
Step 3: substitution of parameters，/>，…，/>Calculating correlation coefficient of the function model obtained by the first fitting>Error accuracy of data->Bit error rate BER, where->Reflecting the fitting effect of the fitting function model and the original discrete data, and the data error precision>Reflecting the offset degree of the discrete data after fitting and the anti-interference capability of the BER in the transmission process of the fitting model;
step 4: performing a second fitting usingAnd->Decoding discrete data of the motor output end and encoding discrete data of the original motor input end, which are obtained after the first fitting, respectively, and encoding the discrete data of the original motor input end +.>Rewritten as vandermonde matrix form->Decoding discrete data of the motor output end obtained after the first fitting>Rewriting into matrix form->By usingMatrix equation and substitution +.>And->Obtaining the parameters after the second fitting +.>，/>，…，/>；
Step 5: the obtained function model after the second least square fittingIn the transmission process, the fitted motor output end decoding discrete data is obtained according to the encoded discrete data of the original input end of the motor and the function model after the secondary fitting;
step 6: substitution of parameters，/>，…，/>Calculating correlation coefficient of function model obtained by the second fitting>Error accuracy of data->Bit error rate BER, where->Reflecting the fitting effect of the fitting function model and the original discrete data, and the data error precision>The deviation degree of the discrete data after fitting and the BER of the error rate reflect the anti-interference capability of the fitting model in the transmission process.
3. The method of claim 2, wherein the correlation coefficients calculated in step 3 and step 6Error accuracy of data->The BER is calculated as follows:
correlation coefficientThe calculation steps are as follows:
(1) Calculating actual valuesMean value of>；
(2) Calculating fitting valuesAnd (3) the actual value->Residual error between: />；
(3) Calculating a residual square sum:；
(4) Calculating the total sum of squares:；
(5) Calculating a correlation coefficient：/>；
Wherein the actual valueSubstituting the discrete data into the original motor input end to code the discrete data, fitting the value +.>Substituting the discrete data into the motor output end obtained after the fitting;
accuracy of data errorsThe calculation formula is as follows: data error precision->The difference between the decoded discrete data of the motor output end after fitting and the encoded discrete data of the motor original input end/the encoded discrete data of the motor original input end is adopted, wherein the difference takes an absolute value;
the BER calculation formula is as follows: ber=error code number/total code number, where the total code number is substituted into the motor original input end encoded discrete data, and the error code number is substituted into the fitted motor output end decoded discrete data which has an excessive difference from the motor original input end encoded discrete data error accuracy.
4. The method for processing discrete transmission data of a motor according to claim 2, wherein the discrete data acquisition is performed on discrete data of the motor, the discrete data are decoded according to the motor output end after being acquired by combining the acquired coded discrete data of the original input end of the motor with a fitted function model in the transmission process, the system establishes memory channels according to the fitted function model, different motors have different memory channels, and the discrete data are decoded according to the memory channels without repeated fitting.
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