CN108549732B - Roller kiln temperature modeling method based on local quadratic weighting kernel principal component regression - Google Patents

Roller kiln temperature modeling method based on local quadratic weighting kernel principal component regression Download PDF

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CN108549732B
CN108549732B CN201711370985.7A CN201711370985A CN108549732B CN 108549732 B CN108549732 B CN 108549732B CN 201711370985 A CN201711370985 A CN 201711370985A CN 108549732 B CN108549732 B CN 108549732B
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CN108549732A (en
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陈宁
田爽
桂卫华
李旭
吴昌宝
戴佳阳
袁小峰
谢滨
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Hunan Shanshan New Energy Co ltd
Central South University
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Central South University
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Abstract

The invention discloses a roller kiln temperature soft measurement modeling method based on local quadratic weighting kernel principal component regression. Respectively introducing the techniques of nuclear skill, instant learning and the like by using local sample data with higher similarity and combining the characteristics of high dimension, nonlinearity, process time variation and the like of the roller kiln, and establishing a roller kiln temperature soft measurement model based on local weighted nuclear principal component regression; and finally, considering different degrees of influence of input variables of local modeling sample data on output variables, secondarily weighting the local modeling variables, establishing a roller kiln temperature soft measurement model based on local secondary weighted kernel principal component regression, and realizing accurate prediction of the roller kiln temperature. The model obtained by the invention can better track the state change of the process and provide a good guiding function for the temperature control of the roller kiln, thereby improving the production quality and the qualification rate of products.

Description

Roller kiln temperature modeling method based on local quadratic weighting kernel principal component regression
Field of the invention
The invention belongs to the field of roller kiln smelting, and particularly relates to a roller kiln temperature soft measurement modeling method.
Background
The lithium battery has the characteristics of high working voltage, large specific energy, long cycle life, light weight, less environmental pollution and the like, and has wide application in various fields around the world, such as mobile phones, electric automobile technologies, medical instrument power supplies and the like. The representative battery is a lithium battery which takes a roller kiln as a production platform and lithium cobaltate as a positive electrode material. The roller kiln for producing the sintering device of the lithium battery anode material is a light continuous industrial kiln, has the characteristics of low energy consumption, short sintering period, good furnace temperature uniformity and the like, is a distributed system of a thermal flow field, and is divided into three large areas, namely a heating section, a constant temperature section and a cooling section, wherein each large area is divided into a plurality of small areas. The temperature of the roller kiln is a most critical parameter in system operation, the adverse effect on the product quality can be brought when the temperature is too high or too low, and the necessary condition for ensuring the product quality is to maintain the temperature stability.
At present, due to the limitation of working conditions and environments, running information and process parameters such as oxygen flow distribution and furnace burden distribution in a roller kiln are difficult to obtain. Considering that the actual process often has a complex physical structure and an internal reaction mechanism, it is difficult to accurately obtain a mechanism model thereof. In order to predict the temperature variation trend of the roller kiln, researchers establish partial differential equations from the perspective of a temperature field and a flow field in recent years. However, the partial differential equation established from the field angle brings difficulty to the solution, and the model can only analyze the partial differential equation off-line, so that the on-line prediction of the temperature is difficult to realize. Therefore, establishing a data-driven model which is convenient to solve and can better estimate the temperature of the roller kiln is a problem to be solved currently.
Disclosure of Invention
The invention aims to provide a roller kiln temperature soft measurement modeling method based on local quadratic weighting kernel principal component regression, which is characterized in that the local sample data with higher similarity is utilized, and the characteristics of high dimension, nonlinearity, process time variation and the like of the roller kiln are combined, so that the techniques of kernel skill, instant learning and the like are respectively introduced; and finally, secondarily weighting the local modeling variable according to different influence degrees of the input variable of the local modeling sample data on the output variable, establishing a roller kiln temperature soft measurement model based on local secondary weighted kernel principal component regression, and realizing the prediction of the roller kiln temperature. Therefore, the problems in the prior art are solved.
A roller kiln temperature soft measurement modeling method based on local quadratic weighting kernel principal component regression is characterized by comprising the following steps:
1) model input/output selection: according to mechanistic analysis, the model input variables are: the temperature x of the upper and lower temperature zones of each temperature zonei1、xi2The temperature of each temperature zone at the moment before the upper and lower temperature zones
Figure BDA0001513737750000011
Voltage and current u of upper and lower temperature zones of each temperature zonei1,ui2,ii1,ii2The flow of the atmosphere v into each temperature zoneiWherein i is 1,2, …, and M represents the number of temperature zones; and (3) arranging the input/output data by using the model output variable as the current temperature of the temperature zone, storing the input/output data in a database, and using the obtained data as sample data for identifying the model parameters, establishing a roller kiln temperature soft measurement model and carrying out simulation verification.
2) Modeling roller kiln temperature soft measurement based on local weighted kernel principal component regression:
firstly, sample data in a database is classified and standardized: training samples, validating samples, testing samples, and normalizing according to formula (1):
Figure BDA0001513737750000021
wherein μ is the mean and σ is the standard deviation;
secondly, obtaining a weight coefficient according to the distance between each sample and the test sample, namely the similarity, wherein the distance between the history sample and the test sample and the designated weight value adopt the formula (2)
Figure BDA0001513737750000022
Wherein x isi∈RmFor history samples, xq∈RmTo test the specimen, diRepresenting the distance between the history sample and the test sample, mu representing the parameter of the adjusting weight changing with the distance, wiRepresents a specified weight value; the larger the weight value is, the more similar the sample is to the test sample, and the sample closest to the test sample is used for establishing a local data model, so that the higher-precision predicted temperature can be obtained.
Let the historical sample used for modeling be xiWhere i is 1,2, …, N indicates the number of samples, and y is the corresponding output sampleiI is 1,2, …, N, and if the mapping function of the input variable to the high-dimensional space is phi, the corresponding high-dimensional sample space is phi (x)i) I is 1,2, …, N, and the input matrix is X ═ X1,x2,…,xN]TThe output matrix is Y ═ Y1,y2,…,yN]TObtaining a weighted training sample phi of the nonlinear high-dimensional space through projectionw(xi)＝wiφ(xi) 1, 2.., N, resulting in a weighted covariance matrix as follows:
Figure BDA0001513737750000023
for covariance matrix CW,KPerforming characteristic decomposition to obtain principal component vector of high-dimensional space,
Λw,KVw,K＝CW,KVw,K (4)
wherein, Λw,KAs a matrix of eigenvalues, Vw,KIs CW,KThe feature vector matrix of (2).
Because the specific form of the mapping function phi is difficult to obtain, C cannot be directly calculatedW,KLet V bew,KAnd Λw,KCannot be directly acquired, and for this reason, nuclear skills are introduced for non-threadsAnd (3) extracting the sexual characteristics:
is provided with CW,KHas a maximum eigenvalue of λw,KThe corresponding feature vector is vw,KThen there is λw,Kvw,K＝CW,Kvw,KTrue, vw,KMapping phi from each sample non-linearly in a high-dimensional spacew(xi) N linear combinations are represented as follows:
Figure BDA0001513737750000024
order to
Figure BDA0001513737750000025
At λw,Kvw,K＝CW,Kvw,KBoth sides simultaneously multiplying by phiw(xi)TTo obtain
λw,K(φw(xk)Tvw,K)＝φw(xk)T(CW,Kvw,K),k＝1,2,…,N (6)
Simplifying two sides of the variable to obtain:
Figure BDA0001513737750000026
the elements defining the kernel matrix K are as follows:
K(i,j)＝φ(xi)Tφ(xj) (8)
likewise, define KW(i,j)＝φw(xi)Tφw(xj) Represents a weighted kernel matrix having
KW(i,j)＝wiK(i,j)wj (9)
In combination of formulae (7), (8) and (9) have
Nλw,Kαw,K＝KWαw,K (10)
From the above formula, αw,KIs namely KWCorresponding feature vector to fill the projection vectorFoot | | | vw,K1 for aw,KIs standardized to
Figure BDA0001513737750000031
From this, the projection vector of each high-dimensional sample Φ (xk), k ═ 1, 2.
Figure BDA0001513737750000032
Wherein, define Kw(i,j)＝wjK (i, j) is Kw＝K·diag(w1,w2,...wN)；
To KWPerforming characteristic decomposition:
KWαW,K＝ΛW,KαW,K (12)
wherein ΛW,KIs a diagonal matrix whose diagonal elements are represented by KWThe characteristic values of (A) are arranged from big to small, aW,KFor corresponding feature vectors, in order to realize data dimension reduction, the first l-dimension data is selected according to the variance contribution rate to be projected to a high-dimension feature space, namely a is selectedW,KThe first column of (1), is noted
Figure BDA0001513737750000033
The projections of the training sample and the test sample in the high-dimensional feature space are as follows:
Figure BDA0001513737750000034
after the kernel principal component is extracted, establishing an output variable y and a nonlinear feature t in a feature spaceT∈RlLeast squares regression model between:
y＝tθ (14)
the regression coefficient θ can be calculated from the training samples:
θ＝[(TW,K)TTW,K]-1(TW,K)TY (15)
the predicted output of the query sample is obtained as:
Figure BDA0001513737750000035
3) roller kiln temperature soft measurement modeling based on local quadratic weighting kernel principal component regression
When the sintering temperature of the lithium ion battery anode material is predicted, the greater the correlation with a prediction variable, the more representative the extracted main component and the higher the prediction precision, the secondary weighting processing is performed on sample data for establishing a local model, a correlation coefficient is obtained by means of common Pearson correlation analysis, and then new weight distribution is performed according to the correlation degree, and the specific process is as follows:
first, a correlation coefficient r between each input variable and a predicted variable is calculated:
Figure BDA0001513737750000041
where E represents the mathematical expectation, X represents the model input variables, and Y represents the output variables.
The larger the value of r, the greater the correlation between coefficients, so that the quadratic weight p can be calculated from the formula (18)
Figure BDA0001513737750000042
The weighted input variables are: xP＝[z1,z2,…,zi]T·diag(p1,p2,…pi). Wherein z is1,z2,…ziRepresenting the input variables of the model after one weighting, i being the dimension of the input, piRepresenting the weight value;
then, after the second weighting process, the kernel is functionalized as:
Figure BDA0001513737750000043
likewise, define KPW(i,j)＝φw(xi w)Tφw(xj w) Then there is
KPW(i,j)＝wiKP(i,j)wj (20)
To KPWPerforming feature decomposition
KPWαPW,K＝ΛPW,KαPW,K (21)
Definition Kpw(i,j)＝wjKP(i, j) to extract features to reduce the dimension of the data, the first l columns of the feature vectors are selected and recorded as
Figure BDA0001513737750000044
Then the projection of the training sample in the high-dimensional feature space is:
Figure BDA0001513737750000045
for query sample xqProjected into a high-dimensional space by a kernel transform, the elements of the kernel matrix of the projected space being represented as
Figure BDA0001513737750000046
Query sample xqThe projection in the feature space is:
Figure BDA0001513737750000047
after the kernel principal component is extracted, the output variable y and the nonlinear feature t can be established in the feature spaceT∈RlLeast squares regression model between:
y＝tθ (24)
the regression coefficient θ can be calculated from the training samples:
θ＝[(TPW,K)TTPW,K]-1(TPW,K)TY (25)
thus, the predicted output of the available query samples is:
Figure BDA0001513737750000048
finally, the model parameters are optimized and identified by using the sample data in the database, the simulation verification is carried out, the root mean square error RMSE and the average absolute value error MAE are used as performance indexes to evaluate the prediction performance of the model,
Figure BDA0001513737750000049
Figure BDA00015137377500000410
wherein, yiRepresenting the actual data sample values and,
Figure BDA00015137377500000411
and expressing the predicted value established according to the established prediction model. The invention has the following beneficial effects:
1) the method is based on deep analysis of the roller kiln, covers main influencing factors/variables in the sintering process, and finally obtains a result closer to reality.
2) Considering that the actual process often has a complex physical structure and an internal reaction mechanism, it is difficult to accurately obtain a mechanism model thereof. Therefore, by utilizing local sample data with high similarity and combining the characteristics of high dimension, nonlinearity, process time variation and the like of the roller kiln, the techniques of nuclear skill, instant learning and the like are respectively introduced, and a roller kiln temperature soft measurement model based on local weighted nuclear principal component regression is established; and finally, secondarily weighting the local modeling variable according to different degrees of influence of the input variable of the local modeling sample data on the output variable, and establishing a roller kiln temperature soft measurement model based on local secondary weighted kernel principal component regression, wherein the model uses local secondary weighting, so that the projection of the sample in a characteristic space is changed, and the final output result is more accurate.
3) The model can better track the state change of the process and provide a good guiding function for controlling the temperature of the roller kiln, thereby improving the production quality and the qualification rate of products.
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FIG. 1 is a schematic diagram of a roller kiln temperature soft measurement model based on local quadratic weighting kernel principal component regression according to the present invention; FIG. 2 is a schematic diagram of the effect of the roller kiln temperature soft measurement model output by the local weighted kernel principal component regression in the lower temperature region of the 3 rd temperature region according to the present invention;
FIG. 3 is a schematic diagram of the effect of the roller kiln temperature soft measurement model output by the local secondary weighted kernel principal component regression in the lower temperature region of the 3 rd temperature region according to the present invention;
FIG. 4 is a schematic diagram of the effect of the roller kiln temperature soft measurement model output by the local weighted kernel principal component regression in the lower temperature region of the 12 th temperature region;
FIG. 5 is a schematic diagram of the effect of the roller kiln temperature soft measurement model output by the local secondary weighted kernel principal component regression in the lower temperature region of the 12 th temperature region.
Detailed Description
To better illustrate the present invention, a preferred embodiment is described in detail with reference to the accompanying drawings, in which:
example 1
Step 1: data preprocessing: and performing early-stage arrangement on the process operation data of the roller kiln, including displaying wrong data, missing data and the like, and storing the sorted data in the created database. The obtained data is used as training sample data for identifying model parameters, establishing a temperature soft measurement model and carrying out simulation verification;
step 2: training sample selection: first, considering a lower temperature zone of the i-th to 3-12 temperature zones as a research object, it is known through mechanism analysis that the temperature change of the temperature zone is mainly affected by several factors including: upper temperature zone x of ith temperature zonei1The temperature of the ith temperature zone at the moment before the temperature zone
Figure BDA0001513737750000051
Temperature x of the i-1 th temperature zone(i-1)2Temperature x of the (i + 1) th lower temperature zone(i+1)2Voltage u of upper and lower temperature zones of ith temperature zonei1,ui2Current ii1,ii2And the flow volume v of the atmosphere introduced into each temperature zonei. Taking 2000 data containing the above variables as sample data: four fifths of the samples were used as training samples and one fifth of the samples were used as verification samples and test samples.
And step 3: modeling roller kiln temperature soft measurement based on local quadratic weighting kernel principal component regression:
first, a weight coefficient is obtained according to the distance between each sample and the test sample, i.e., the similarity, wherein the distance between the history sample and the test sample and the designated weight value are expressed by the following formula (1)
Figure BDA0001513737750000061
Wherein x isi∈Rm(m-1, …,6) is a history sample, xq∈Rm(m-1, …,6) is a test specimen, diRepresenting the distance between the historical sample and the test sample, sigma representing the parameter of the adjusting weight changing with the distance, wiDenotes a specified weight value, i ═ 1, 2.
Next, considering that the degree of influence of the input variable selected at the time of prediction on the output variable differs, the greater the correlation with the output variable, the more representative the extracted principal component, and the higher the prediction accuracy when the sintering temperature of the lithium ion battery positive electrode material is predicted. For this reason, the sample data for building the local model needs to be subjected to the second weighting process. At present, a relatively common method for establishing a relation between an input variable and an output variable is a method based on partial least squares feature extraction. Here, the correlation coefficient will be obtained by correlation analysis by means of Pearson in common use, and then new weight assignment is made according to the degree of correlation.
Firstly, calculating a correlation coefficient r between each input variable and each output variable as shown in formula (2):
Figure BDA0001513737750000062
where E represents the mathematical expectation.
Considering that the larger the value of r, the larger the correlation between coefficients, the quadratic weight p can be calculated from the definitional equation (3)
Figure BDA0001513737750000063
Weighted input variables: xP＝[z1,z2,…,zi]T·diag(p1,p2,…pi). Wherein z is1,z2,…ziRepresenting the input variables of the model before weighting. p is a radical ofiRepresenting the magnitude of the weight.
Then, constructing a secondary weighted training sample after nonlinear high-dimensional space projection, and calculating a weighted covariance matrix
Figure BDA0001513737750000064
Wherein the content of the first and second substances,
Figure BDA0001513737750000065
expressed as a weighted input variable, and,
Figure BDA0001513737750000066
the method is a secondary weighted training sample after nonlinear high-dimensional space projection.
Thirdly, a Gaussian kernel function is introduced to extract the nonlinear characteristic (5)
Figure BDA0001513737750000067
Where δ is the nuclear parameter, φ (x)i) Is a high-dimensional space sample, and K is a kernel matrix.
Let KPW(i,j)＝φw(xi p)Tφw(xj p) Then there is
Figure BDA0001513737750000071
To KPWPerforming characteristic decomposition: kPWαPW,K＝ΛPW,KαPW,K。
Wherein, ΛPW,KAnd alphaPW,KAre respectively a quadratic weighting kernel matrix KPWAn eigenvalue matrix and an eigenvector matrix.
Reducing dimension of data for extracting feature, selecting the first d columns of feature vectors, and recording as
Figure BDA0001513737750000072
The projection of the training/test sample in the feature space is (7)
Figure BDA0001513737750000073
Then, a least squares regression model between the output variables of the test samples and the nonlinear characteristics is established, and the calculation formula (8)
Figure BDA0001513737750000074
And finally, performing optimized identification on the parameters of the data driving model by using sample data in the database by adopting a cross validation method, and performing simulation validation.
According to the test, the number of samples required by local modeling is as follows: n is 20, principal component parameters: d is 3, nuclear parameters: delta optimization range: [ 0.060.10.150.20.250.30.350.40.511.52510 ], distance variation parameter: sigma optimizing range: [0.050.10.511.522.533.544.55810]. The predicted performance of the model is evaluated using the root mean square error RMSE and the mean absolute error MAE as performance indicators.
Figure BDA0001513737750000075
Figure BDA0001513737750000076
Wherein, yiRepresenting the actual data sample values and,
Figure BDA0001513737750000077
and expressing the predicted value established according to the established prediction model.
The simulation results are shown in fig. 2 and 3, which are a roller kiln temperature prediction and actual temperature effect graph of the 3 rd temperature zone low-temperature zone local weighted nuclear principal component regression, and a roller kiln temperature prediction and actual temperature effect graph of the 3 rd temperature zone low-temperature zone local secondary weighted nuclear principal component regression. Fig. 4 and 5 are a graph of the roller kiln temperature prediction and actual temperature effect of the local weighted nuclear principal component regression of the lower temperature zone of the 12 th temperature zone, and a graph of the roller kiln temperature prediction and actual temperature effect of the local secondary weighted nuclear principal component regression of the lower temperature zone of the 12 th temperature zone, respectively. Graph 1 shows the root mean square error RMSE and mean absolute error MAE simulation statistics.
TABLE 1 root mean square error RMSE and mean absolute error MAE simulation statistics
Figure BDA0001513737750000078
Figure BDA0001513737750000081
From the simulation results, the obtained local quadratic weighting can realize more accurate temperature prediction by obtaining a correlation coefficient through common Pearson correlation analysis and then performing new weight distribution according to the degree of correlation.
The above disclosure is only one specific embodiment of the present application, but the present application is not limited to any variations that can be made by those skilled in the art, and the present application is intended to fall within the scope of the present application.

Claims (1)

1. A roller kiln temperature soft measurement modeling method based on local quadratic weighting kernel principal component regression is characterized by comprising the following steps:
1) model input/output selection: according to mechanistic analysis, the model input variables are: the temperature x of the upper and lower temperature zones of each temperature zonei1、xi2The temperature of each temperature zone at the moment before the upper and lower temperature zones
Figure FDA0001513737740000011
Voltage and current u of upper and lower temperature zones of each temperature zonei1,ui2,ii1,ii2The flow of the atmosphere v into each temperature zoneiWherein i is 1,2, …, and M represents the number of temperature zones; the model output variable is the current temperature zone temperature, the input/output data are sorted and stored in a database, and the obtained data are used as sample data for identifying model parameters, establishing a roller kiln temperature soft measurement model and performing simulation verification;
2) modeling roller kiln temperature soft measurement based on local weighted kernel principal component regression:
firstly, sample data in a database is classified and standardized: training samples, validating samples, testing samples, and normalizing according to formula (1):
Figure FDA0001513737740000012
wherein μ is the mean and σ is the standard deviation;
secondly, obtaining a weight coefficient according to the distance between each sample and the test sample, namely the similarity, wherein the distance between the history sample and the test sample and the designated weight value adopt the formula (2)
Figure FDA0001513737740000013
Wherein x isi∈RmFor history samples, xq∈RmTo test the specimen, diRepresenting the distance between the history sample and the test sample, mu representing the parameter of the adjusting weight changing with the distance, wiRepresents a specified weight value; the greater the weight value is, the more similar the sample is to the test sample, and the sample closest to the test sample is used for establishing a local data model, so that the higher-precision predicted temperature can be obtained;
let the historical sample used for modeling be xiWhere i is 1,2, …, N indicates the number of samples, and y is the corresponding output sampleiI is 1,2, …, N, and if the mapping function of the input variable to the high-dimensional space is phi, the corresponding high-dimensional sample space is phi (x)i) I is 1,2, …, N, and the input matrix is X ═ X1,x2,…,xN]TThe output matrix is Y ═ Y1,y2,…,yN]TObtaining a weighted training sample phi of the nonlinear high-dimensional space through projectionw(xi)＝wiφ(xi) 1, 2.., N, resulting in a weighted covariance matrix as follows:
Figure FDA0001513737740000014
for covariance matrix CW,KPerforming characteristic decomposition to obtain principal component vector of high-dimensional space,
Λw,KVw,K＝CW,KVw,K (4)
wherein, Λw,KAs a matrix of eigenvalues, Vw,KIs CW,KA feature vector matrix of (a);
because the specific form of the mapping function phi is difficult to obtain, C cannot be directly calculatedW,KLet V bew,KAnd Λw,KIt cannot be directly obtained, and for this reason, a kernel technique is introduced to extract nonlinear features:
is provided with CW,KHas a maximum eigenvalue of λw,KCorresponding feature vectorV isw,KThen there is λw,Kvw,K＝CW,Kvw,KTrue, vw,KMapping phi from each sample non-linearly in a high-dimensional spacew(xi) N linear combinations are represented as follows:
Figure FDA0001513737740000021
order to
Figure FDA0001513737740000022
At λw,Kvw,K＝CW,Kvw,KBoth sides simultaneously multiplying by phiw(xi)TTo obtain
λw,K(φw(xk)Tvw,K)＝φw(xk)T(CW,Kvw,K),k＝1,2,...,N (6)
Simplifying two sides of the variable to obtain:
Figure FDA0001513737740000023
the elements defining the kernel matrix K are as follows:
K(i,j)＝φ(xi)Tφ(xj) (8)
likewise, define KW(i,j)＝φw(xi)Tφw(xj) Represents a weighted kernel matrix having
KW(i,j)＝wiK(i,j)wj (9)
In combination of formulae (7), (8) and (9) have
Nλw,Kαw,K＝KWαw,K (10)
From the above formula, αw,KIs namely KWCorresponding feature vector so that the projection vector satisfies | | vw,K1 for aw,KIs standardized to
Figure FDA0001513737740000024
From this, each high-dimensional sample phi (x) can be obtainedk) 1,2, the projection vector of N is:
Figure FDA0001513737740000025
wherein, define Kw(i,j)＝wjK (i, j) is Kw＝K·diag(w1,w2,...wN)；
To KWPerforming characteristic decomposition:
KWαW,K＝ΛW,KαW,K (12)
wherein ΛW,KIs a diagonal matrix whose diagonal elements are represented by KWThe characteristic values of (A) are arranged from big to small, aW,KFor corresponding feature vectors, in order to realize data dimension reduction, the first l-dimension data is selected according to the variance contribution rate to be projected to a high-dimension feature space, namely a is selectedW,KThe first column of (1), is noted
Figure FDA0001513737740000027
The projections of the training sample and the test sample in the high-dimensional feature space are as follows:
Figure FDA0001513737740000026
after the kernel principal component is extracted, establishing an output variable y and a nonlinear feature t in a feature spaceT∈RlLeast squares regression model between:
y＝tθ (14)
the regression coefficient θ can be calculated from the training samples:
θ＝[(TW,K)TTW,K]-1(TW,K)TY (15)
the predicted output of the query sample is obtained as:
Figure FDA0001513737740000031
3) modeling roller kiln temperature soft measurement based on local quadratic weighting kernel principal component regression:
when the sintering temperature of the lithium ion battery anode material is predicted, the greater the correlation with a prediction variable, the more representative the extracted main component and the higher the prediction precision, the secondary weighting processing is performed on sample data for establishing a local model, a correlation coefficient is obtained by means of common Pearson correlation analysis, and then new weight distribution is performed according to the correlation degree, and the specific process is as follows:
first, a correlation coefficient r between each input variable and a predicted variable is calculated:
Figure FDA0001513737740000032
wherein E represents a mathematical expectation, X represents a model input variable, and Y represents an output variable;
the larger the value of r, the greater the correlation between coefficients, so that the quadratic weight p can be calculated from the formula (18)
Figure FDA0001513737740000033
The weighted input variables are: xP＝[z1,z2,…,zi]T·diag(p1,p2,...pi) Wherein z is1,z2,…ziRepresenting the input variables of the model after one weighting, i being the dimension of the input, piRepresenting the weight value;
then, after the second weighting process, the kernel is functionalized as:
Figure FDA0001513737740000034
likewise, define KPW(i,j)＝φw(xi w)Tφw(xj w) Then there is
KPW(i,j)＝wiKP(i,j)wj (20)
To KPWPerforming feature decomposition
KPWαPW,K＝ΛPW,KαPW,K (21)
Definition Kpw(i,j)＝wjKP(i, j) to extract features to reduce the dimension of the data, the first l columns of the feature vectors are selected and recorded as
Figure FDA0001513737740000035
Then the projection of the training sample in the high-dimensional feature space is:
Figure FDA0001513737740000036
for query sample xqProjected into a high-dimensional space by a kernel transform, the elements of the kernel matrix of the projected space being represented as
Figure FDA0001513737740000037
Query sample xqThe projection in the feature space is:
Figure FDA0001513737740000038
after the kernel principal component is extracted, the output variable y and the nonlinear feature t can be established in the feature spaceT∈RlLeast squares regression model between:
y＝tθ (24)
the regression coefficient θ can be calculated from the training samples:
θ＝[(TPW,K)TTPW,K]-1(TPW,K)TY (25)
thus, the predicted output of the available query samples is:
Figure FDA0001513737740000041
finally, the model parameters are optimized and identified by using the sample data in the database, the simulation verification is carried out, the root mean square error RMSE and the average absolute value error MAE are used as performance indexes to evaluate the prediction performance of the model,
Figure FDA0001513737740000042
Figure FDA0001513737740000043
wherein, yiRepresenting the actual data sample values and,
Figure FDA0001513737740000044
and expressing the predicted value established according to the established prediction model.
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