A data prediction method and device based on kernel partial least squares model

Abstract

The embodiment of the present invention discloses a data prediction method and device based on a kernel partial least squares model. The kernel function in the kernel partial least squares KPLS model is a multidimensional tensor product wavelet kernel function. The sampled data is standardized using the mean and variance of the sampled data obtained online to obtain standardized sampled data; the kernel matrix corresponding to the standardized sampled data is calculated using the multidimensional tensor product wavelet kernel function; the kernel matrix is ​​centralized to obtain the centralized kernel matrix; the centralized kernel matrix is ​​input into the KPLS model; and the KPLS model is used to obtain the quality variable prediction value corresponding to the sampled data. In the embodiment of the present invention, since the kernel function in the KPLS model adopts the multidimensional tensor product wavelet kernel function, the KPLS model has a strong nonlinear mapping ability, so that the quality variable prediction value can be accurately calculated.

Description

Technical Field

[0001] The present invention relates to the field of data processing, and more specifically, to a data prediction method and device based on a kernel partial least squares model. Background Art

[0002] At present, process data needs to be collected in the production process of industrial enterprises. After a lot of data is collected, it is only visualized and its effectiveness is not deeply explored. One of the important reasons is that industrial production is a continuous production process. Each process has a flow that connects the upper and lower processes, and there are process correlations, equipment performance correlations, working condition correlations, etc. There are a large amount of correlation data, which generally contain multivariate coupling, high nonlinearity, time-varying and other characteristics, and do not simply obey the normal distribution. Therefore, the process data collected during the production process cannot effectively predict the quality of the production process. Summary of the invention

[0003] In view of this, an embodiment of the present invention discloses a data prediction method and device based on a kernel partial least squares model to achieve effective prediction of the quality of a production process.

[0004] The technical solution provided by the embodiment of the present invention is as follows:

[0005] A first aspect of an embodiment of the present invention provides a data prediction method based on a kernel partial least squares model, wherein the kernel function in the kernel partial least squares KPLS model is a multidimensional tensor product wavelet kernel function, and the method comprises:

[0006] The sampled data are standardized using the mean and variance of the sampled data obtained online to obtain standardized sampled data;

[0007] Calculating a first kernel matrix corresponding to the standardized sampling data using the multidimensional tensor product wavelet kernel function;

[0008] Centralizing the first kernel matrix to obtain a first kernel matrix after centralization;

[0009] Inputting the first kernel matrix after the centralization process into the KPLS model;

[0010] The KPLS model is used to obtain a predicted value of the first quality variable corresponding to the sampled data.

[0011] In a possible implementation, the method further includes:

[0012] The actual value of the first quality variable corresponding to the sampled data is calculated using the mean and variance of the predicted value of the first quality variable.

[0013] In a possible implementation, the method further includes:

[0014] Calculate the Hotelling T corresponding to the sampled data 2 Statistics and squared prediction error SPE statistics;

[0015] Determine the T corresponding to the sampled data 2 Does the statistic exceed the T of the KPLS model? 2 Statistical control limits;

[0016] Determine whether the SPE statistic corresponding to the sampled data exceeds the SPE statistic control limit of the KPLS model;

[0017] If the T corresponding to the sampling data 2 The statistic exceeds the T 2 If the statistical control limit and / or the SPE statistic corresponding to the sampling data exceeds the SPE statistical control limit, it is determined that a fault exists in the production process corresponding to the sampling data.

[0018] In a possible implementation, the method further includes:

[0019] Establishing the KPLS model;

[0020] The establishing of the KPLS model comprises:

[0021] Standardizing the training data using the mean and variance of the training data to obtain standardized training data;

[0022] Calculating a second kernel matrix corresponding to the standardized training data using the multidimensional tensor product wavelet kernel function;

[0023] Centralizing the second kernel matrix to obtain a centralized second kernel matrix;

[0024] Using the KPLS algorithm and the centralized second kernel matrix, the first score matrix of the input variables and the second score matrix of the output variables are calculated;

[0025] Using the first score matrix and the second score matrix, a regression coefficient matrix is ​​calculated;

[0026] Calculating a second quality variable prediction value corresponding to the training data using the regression coefficient matrix;

[0027] Using the mean and variance of the predicted value of the second quality variable, calculate the actual value of the second quality variable corresponding to the training data;

[0028] Calculate T corresponding to the training data 2 Statistics and SPE statistics;

[0029] According to the T corresponding to the training data 2 The distribution of the statistic determines the T of the KPLS model 2 Statistical control limits;

[0030] The SPE statistic control limit of the KPLS model is determined according to the distribution of the SPE statistic corresponding to the training data.

[0031] In a possible implementation, the multidimensional tensor product wavelet kernel function satisfies the Laplace transform Support vector kernel function of

[0032] Wherein, k represents a kernel function, σ represents a scaling factor, K represents a data point in a kernel matrix, K is represented as (x, z), and x and y represent measurement values ​​in K(x, z).

[0033] In a possible implementation, the output expression of any one dimension of the multidimensional tensor product wavelet kernel function is:

[0034]

[0035] Wherein, ω represents the angular velocity of the kernel function, C represents a constant, L represents the Laplace transform, represents the i-th element in the vector of the s-th column in the regression coefficient matrix, where s=1, 2,…, M, k represents a kernel function, and (x, z) represents a data point.

[0036] In a possible implementation, the KPLS model satisfies the following formula:

[0037]

[0038] Among them, the ε i represents the slack variable of the i-th point, represents the estimated value of the slack variable at the i-th point, the μ i represents the Lagrange multiplier of the i-th point, represents the estimated value of the Lagrange multiplier at the i-th point, represents the jth component of the i-th training data, represents the estimated value of the jth component of the i-th training data, represents the estimated value of the i-th element in the vector representing the s-th column in the regression coefficient matrix.

[0039] In a possible implementation, the T 2 The statistics satisfy the following formula:

[0040] T 2 =[t1,t2,…,t A ]Λ -1 [t1,t2,…,t A ] T ;

[0041] Among them, the -1 represents the inverse matrix of the principal component covariance matrix, A represents the number of principal components of the extracted input variable X, T = [t1, t2, ..., t A ] represents the score matrix of input variable X;

[0042] The SPE statistic satisfies the following formula:

[0043]

[0044] The KPLS model maps data from low-dimensional space to high-dimensional space, t i and t j Corresponding to the mapped data coordinates.

[0045] In a possible implementation, the T 2 The statistical control limits satisfy:

[0046]

[0047] Where N is the number of input variables X, F A,N-A,α It is expressed as the value of F distribution with A to NA degrees of freedom and confidence level α;

[0048] The SPE statistic control limits satisfy:

[0049]

[0050] Where g is a constant and h is χ 2 Degrees of freedom of the distribution, g k =v k / 2m k , v k It is expressed as the mean of the SPE statistic at time k, m k Expressed as the variance of the SPE statistic at time k.

[0051] In a second aspect, the present application provides a data prediction device based on a kernel partial least squares model, wherein the kernel function in the kernel partial least squares KPLS model is a multidimensional tensor product wavelet kernel function, and the device comprises:

[0052] A standardization unit, used to standardize the sampled data using the mean and variance of the sampled data obtained online to obtain standardized sampled data;

[0053] A first calculation unit, used for calculating a first kernel matrix corresponding to the standardized sampling data by using the multidimensional tensor product wavelet kernel function;

[0054] A centralization unit, used for performing centralization processing on the first kernel matrix to obtain a first kernel matrix after centralization processing;

[0055] An input unit, used for inputting the first kernel matrix after the centralization process into the KPLS model;

[0056] The prediction unit is used to obtain a predicted value of a first quality variable corresponding to the sampled data by using the KPLS model.

[0057] From the above technical solution, it can be known that the embodiment of the present invention discloses a data prediction method and device based on a kernel partial least squares model. The kernel function in the kernel partial least squares KPLS model is a multidimensional tensor product wavelet kernel function. The sampled data is standardized using the mean and variance of the sampled data obtained online to obtain standardized sampled data; the kernel matrix corresponding to the standardized sampled data is calculated using the multidimensional tensor product wavelet kernel function; the kernel matrix is ​​centralized to obtain the kernel matrix after centralization; the kernel matrix after centralization is input into the KPLS model; and the KPLS model is used to obtain the quality variable prediction value corresponding to the sampled data. In the embodiment of the present invention, since the kernel function in the KPLS model adopts the multidimensional tensor product wavelet kernel function, the KPLS model has a strong nonlinear mapping ability, so that the quality variable prediction value can be accurately calculated. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the disclosed drawings without paying creative work.

[0059] Figure 1 A flow chart of a data prediction method based on a kernel partial least squares model disclosed in an embodiment of the present invention;

[0060] Figure 2 A flow chart of a data prediction method based on a kernel partial least squares model disclosed in an embodiment of the present invention;

[0061] Figure 3 The present invention is a schematic diagram of the structure of a data prediction device based on a kernel partial least squares model disclosed in an embodiment of the present invention. DETAILED DESCRIPTION

[0062] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0063] The embodiment of the present invention discloses a data prediction method and device based on a kernel partial least squares model. The kernel function in the kernel partial least squares KPLS model is a multidimensional tensor product wavelet kernel function. The sampled data is standardized using the mean and variance of the sampled data obtained online to obtain standardized sampled data; the kernel matrix corresponding to the standardized sampled data is calculated using the multidimensional tensor product wavelet kernel function; the kernel matrix is ​​centralized to obtain the centralized kernel matrix; the centralized kernel matrix is ​​input into the KPLS model; and the KPLS model is used to obtain the quality variable prediction value corresponding to the sampled data. In the embodiment of the present invention, since the kernel function in the KPLS model adopts the multidimensional tensor product wavelet kernel function, the KPLS model has a strong nonlinear mapping ability, so that the quality variable prediction value can be accurately calculated.

[0064] See also Figure 1 , a flow chart of a process monitoring method based on a kernel partial least squares KPLS model disclosed in an embodiment of the present invention, wherein the kernel function in the KPLS model is a multidimensional tensor product wavelet kernel function, and the method comprises:

[0065] Step S101, standardizing the sampled data using the mean and variance of the sampled data obtained online to obtain standardized sampled data;

[0066] It should be noted that the standardization process performed in the embodiment of the present invention can eliminate the influence of the sample amplitude on the modeling.

[0067] Step S102, using the multidimensional tensor product wavelet kernel function to calculate a first kernel matrix corresponding to the standardized sampling data;

[0068] It can be understood that the multidimensional tensor product wavelet kernel function is used to calculate the standardized sampling data x _new ,t∈R m ,t=1,2,…,N t The corresponding first kernel matrix K t ∈R 1×N , that is, mapping the standardized sampling data to the high-dimensional feature space, introducing the multi-dimensional tensor product wavelet kernel function to obtain the first kernel matrix.

[0069] It should be noted that the basic idea of ​​kernel partial least squares (KPLS) is to map the linearly inseparable data in the original input space to the high-dimensional feature space through the kernel function to make it linearly separable, and then perform partial least squares (PLS) operation to achieve the linear transformation of the nonlinear correlation between variables. Most of the existing KPLS methods use the Gaussian radial basis kernel function, that is, σ is a scaling factor used to control the radial direction of the function. However, experiments have shown that it is not applicable in most cases and the fitting accuracy is relatively low.

[0070] In the embodiment of the present application, a multidimensional tensor product wavelet kernel function is designed based on the Gaussian radial basis kernel function, and the multidimensional tensor product wavelet kernel function is constructed by the following three theorems:

[0071] Theorem 1: A kernel function that is translation invariant is a kernel function that allows support vectors. In the process of constructing the function, considering the possible suddenness of the production process and the complexity of the data transformation process, the model is designed as a complex frequency domain transformation, which can not only obtain the frequency spectrum but also increase the complex dimension based on the transformation of the original function.

[0072] The multidimensional tensor product wavelet kernel function satisfies the Laplace transform The support vector kernel function.

[0073] Wherein, k represents a kernel function, σ represents a scaling factor, K represents a data point in a kernel matrix, K is represented as (x, z), and x and y represent measurement values ​​in K(x, z).

[0074] It can be seen that the Laplace transform is used in Theorem 1 in the embodiment of the present application, and a complex frequency function is obtained. Compared with the Fourier transform, better analysis can be performed when processing data of sudden events.

[0075] Theorem 2: The tensor product wavelet kernel that satisfies the translation invariance theorem is the support vector kernel function of the admissible multidimensional tensor product.

[0076]

[0077] Where σ,x,z∈R N , h(.) represents the mother wavelet function, and ω represents the scaling factor.

[0078] Theorem 3: The kernel function is a support vector kernel function that allows multi-dimensional tensor products. When there are multi-dimensional inputs and multi-dimensional outputs, it enters the KPLS model after the integral transformation of the data.

[0079] The output expression of any one dimension of the multidimensional tensor product wavelet kernel function is:

[0080]

[0081] Among them, ω represents the angular velocity of the kernel function, C represents a constant, and L represents the Laplace transform. represents the i-th element in the vector of the s-th column in the regression coefficient matrix, s=1, 2, ..., M, k represents the kernel function, and (x, z) represents the data point.

[0082] The characterization conditions of the slack variables in the sample are added to the KPLS model, and the function f constructed by the data s (x) are all positive functions.

[0083] The KPLS model satisfies the following formula:

[0084]

[0085] Among them, the ε i represents the slack variable of the i-th point, represents the estimated value of the slack variable at the i-th point, the μ i represents the Lagrange multiplier of the i-th point, represents the estimated value of the Lagrange multiplier at the i-th point, represents the jth component of the i-th training data, represents the estimated value of the jth component of the i-th training data, represents the estimated value of the i-th element in the vector representing the s-th column in the regression coefficient matrix.

[0086] It can be seen that Theorem 3 in the embodiment of the present application uses support vector regression to process data, and introduces slack variables and Laplace multipliers, which can greatly improve the inclusiveness and accuracy of the model. This solves the problem that the kernel function is obtained by multiplying Gaussian functions, which causes the inability to include all functions that may be constructed in the actual data processing process, especially in the process of processing mutation events, and it is often impossible to construct a specific function.

[0087] The multidimensional tensor product wavelet kernel function constructed based on the above three definitions can greatly improve the fitting accuracy. At the same time, the covariance information between input and output is combined with latent variables to further improve the fitting accuracy and kernel model characteristics.

[0088] Step S103, performing centralization processing on the first kernel matrix to obtain a first kernel matrix after centralization processing;

[0089] It is understandable that by centralizing the data in the first kernel matrix, predictions can be made based on a small number of samples, thereby solving the problem of being unable to model and analyze due to time and cost constraints and the number of samples available being often less than the number of variables, thereby improving the availability of the model.

[0090] Step S104: input the first kernel matrix after the centralization process into the KPLS model.

[0091] Step S105: using the KPLS model to obtain a predicted value of a first quality variable corresponding to the sampled data.

[0092] It should be noted that in, represents the predicted value of the first quality variable, Φ represents the first kernel matrix, B represents the regression coefficient matrix, K t represents the first kernel matrix after centralization, T represents the score matrix of the input variable, U represents the score matrix of the output variable, K represents the data points in the first kernel matrix, T T Represents the transposed matrix of the score matrix.

[0093] The embodiment of the present invention discloses a data prediction method based on a kernel partial least squares model, wherein the kernel function in the kernel partial least squares KPLS model is a multidimensional tensor product wavelet kernel function, wherein the sampled data is standardized by using the mean and variance of the sampled data obtained online to obtain standardized sampled data; the kernel matrix corresponding to the standardized sampled data is calculated by using the multidimensional tensor product wavelet kernel function; the kernel matrix is ​​centralized to obtain the centralized kernel matrix; the centralized kernel matrix is ​​input into the KPLS model; and the KPLS model is used to obtain the quality variable prediction value corresponding to the sampled data. In the embodiment of the present invention, since the kernel function in the KPLS model adopts the multidimensional tensor product wavelet kernel function, the KPLS model has a strong nonlinear mapping capability, thereby being able to accurately calculate the quality variable prediction value.

[0094] To further optimize the above embodiment, the data prediction method based on the kernel partial least squares model in the embodiment of the present invention further includes:

[0095] Step S106: Calculate the actual value of the first quality variable corresponding to the sampled data using the mean and variance of the predicted value of the first quality variable.

[0096] It should be noted that in, represents the actual value of the first quality variable, S t represents the variance of the predicted value of the first quality variable, Y mean Represents the mean of the predicted values ​​of the first quality variable.

[0097] In the embodiment of the present invention, the mean and variance of the quality variable prediction value are used to calculate the actual value of the quality variable corresponding to the sampled data, so that the quality variable corresponding to the sampled data finally predicted is more accurate, further improving the accuracy of quality prediction in the production process.

[0098] To further optimize the above embodiment, the data prediction method based on the kernel partial least squares model in the embodiment of the present invention further includes:

[0099] Step S201: Calculate the Hotelling T corresponding to the sampled data. 2 Statistics and squared prediction error SPE statistics;

[0100] It should be noted that T 2 The statistics satisfy the following formula:

[0101] T 2 =[t1, t2, …, t A ]Λ -1 [t1, t2, …, t A ] T ;

[0102] Among them, Λ -1 represents the inverse matrix of the principal component covariance matrix, A represents the number of principal components of the input variable X extracted, T = [t1, t2, ..., t A ] represents the score matrix of input variable X.

[0103] The SPE statistic satisfies the following formula:

[0104]

[0105] Among them, the KPLS model maps data from low-dimensional space to high-dimensional space, t i and t j Corresponding to the mapped data coordinates.

[0106] Step S202: Determine the T corresponding to the sampled data. 2 Does the statistic exceed the T of the KPLS model? 2 Statistical control limits;

[0107] It should be noted that T is approximately normally distributed, T2 statistic follows F distribution, and T 2 The statistical control limits satisfy:

[0108]

[0109] Where N is the number of input variables X, F A，N-A，α Expressed as the value of the F distribution with A to NA degrees of freedom and a confidence level of α.

[0110] It should be noted that the T of the KPLS model 2 Statistical control limits can be calculated from training data.

[0111] Step S203, determining whether the SPE statistic corresponding to the sampled data exceeds the SPE control limit of the KPLS model;

[0112] It should be noted that the SPE control limits meet the following requirements:

[0113]

[0114] Where g is a constant and h is χ 2 Degrees of freedom of the distribution, g k =v k / 2m k , v k It is expressed as the mean of the SPE statistic at time k, m k Expressed as the variance of the SPE statistic at time k.

[0115] It should be noted that the SPE statistic control limit of the KPLS model can be calculated using training data.

[0116] Step S204: If the T corresponding to the sampled data 2 The statistic exceeds the T 2 If the statistical control limit and / or the SPE statistic corresponding to the sampling data exceeds the SPE control limit, it is determined that a fault exists in the production process corresponding to the sampling data.

[0117] In the embodiments of the present application, by calculating and monitoring statistical quantities, the capability of "static statistics" can be added during online data processing. If there is no relevant function, the constructed model is likely to diverge during operation. Another point is that by adding this part of the content to pre-process the data, less computing power is invested, and hardware costs are reduced. At the same time, a modular assembly model is adopted, and a certain function can be "suspended" during actual debugging, avoiding the need to adjust the overall structure of the system to deal with a bug in a function, thereby improving debugging efficiency.

[0118] To further optimize the above embodiment, the data prediction method based on the kernel partial least squares model in the embodiment of the present invention further includes:

[0119] Step S301, establishing the KPLS model;

[0120] The establishing of the KPLS model comprises:

[0121] Step S3001, standardizing the training data using the mean and variance of the training data to obtain standardized training data;

[0122] Step S3002, using the multidimensional tensor product wavelet kernel function to calculate a second kernel matrix corresponding to the standardized training data;

[0123] It can be understood that the second kernel matrix [K] ij =Φ(x i ),in:

[0124] K(x i ,x j )=<Φ(x i ),Φ(x j )> represents the parameters of the vertical and horizontal axes in the kernel matrix.

[0125] Step S3003, performing centralization processing on the second kernel matrix to obtain a centralized second kernel matrix;

[0126] It should be noted that the formula used in the embodiment of the present invention is Centralize the data in the second kernel matrix to satisfy in, represents the second kernel matrix after centralization, E represents the residual matrix, and E N represents the N-point residual matrix value, Represents the transposed matrix of the N-point residual matrix value, where N represents a value of the residual matrix and T represents the transposed matrix of the matrix.

[0127] Step S3004: Use the KPLS algorithm and the centralized second kernel matrix to calculate a first score matrix of input variables and a second score matrix of output variables;

[0128] Step S3005: Calculate a regression coefficient matrix using the first score matrix and the second score matrix;

[0129] It should be noted that the regression coefficient matrix B = Φ T U(T T KU) -1 T T Y. Among them, Φ T represents the transposed matrix of the kernel matrix, the first score matrix T represents the score matrix of the input variable X, the second score matrix U represents the score matrix of the output variable Y, K represents the data points in the second kernel matrix, and Y represents the input variable.

[0130] Step S3006, using the regression coefficient matrix to calculate the predicted value of the second quality variable corresponding to the training data;

[0131] It should be noted that in, Represents the predicted value of the second quality variable.

[0132] Step S3007: using the mean and variance of the predicted value of the second quality variable, calculate and obtain the actual value of the second quality variable corresponding to the training data;

[0133] It should be noted that in, Represents the actual value of the second quality variable, S r represents the variance of the predicted value of the second quality variable, Y _mean Represents the mean of the predicted values ​​of the second quality variable.

[0134] Step S3008: Calculate T corresponding to the training data 2 Statistics and SPE statistics;

[0135] It should be noted that T 2 The statistics satisfy the following formula:

[0136] T 2 =[t1, t2, …, t A ]Λ -1 [t1, t2, …, t A ] T ;

[0137] Among them, Λ -1 represents the inverse matrix of the principal component covariance matrix, A represents the number of principal components of the input variable X extracted, T = [t1, t2, ..., t A ] represents the score matrix of input variable X.

[0138] The SPE statistic satisfies the following formula:

[0139]

[0140] Among them, the data is mapped from low-dimensional space to high-dimensional space, t i and t j Corresponding to the mapped data coordinates.

[0141] Step S3009: According to the T corresponding to the training data 2 The distribution of the statistic determines the T of the KPLS model 2 Statistical control limits;

[0142] It should be noted that T is approximately normally distributed, T2 statistic follows F distribution, and T 2 The statistical control limits satisfy:

[0143]

[0144] Where N is the number of input variables X, F A，N-A，α Expressed as the value of the F distribution with A to NA degrees of freedom and a confidence level of α.

[0145] Step S3010: Determine the SPE control limit of the KPLS model according to the distribution of the SPE statistic corresponding to the training data.

[0146] It should be noted that the SPE statistic follows the weighted distribution χ 2 , the SPE statistic control limits satisfy:

[0147]

[0148] Where g is a constant and h is χ 2 Degrees of freedom of the distribution, g k =v k / 2m k , v k It is expressed as the mean of the SPE statistic at time k, m k Expressed as the variance of the SPE statistic at time k.

[0149] In an embodiment of the present invention, a KPLS model is constructed by training data. The KPLS model can decompose and screen the data information in the system, extract the comprehensive variables with the strongest explanatory power for quality variables, identify information and noise in the system, and better overcome the adverse effects of multiple correlations of variables in system modeling, so that the subsequent use of the model can perform accurate quality prediction and process monitoring.

[0150] See also Figure 2 , a flow chart of a data prediction method based on a kernel partial least squares model disclosed in an embodiment of the present invention, the kernel function in the kernel partial least squares KPLS model is a multidimensional tensor product wavelet kernel function, and the method includes two parts: offline modeling and online monitoring and quality prediction.

[0151] In offline modeling, normal historical data is first obtained; then the historical data is mapped into a high-dimensional space based on the multidimensional tensor product wavelet kernel function; a PLS statistical model is established; monitoring statistics are designed and a quality monitoring model is established; and control limits are determined.

[0152] In online monitoring and quality prediction, data is first sampled in real time; then mapped to the KPLS model space; the monitoring statistics are calculated, and the control limits determined in the offline modeling are used to determine whether a failure occurs in the production process. If a failure occurs, the failure point is determined to be the control limit, and the data above the control limit is normal historical data; the predicted quality variables are calculated, and the predicted quality variables are used to determine whether a failure occurs in the production process. If a failure occurs, the failure point is determined to be the control limit, and the data above the control limit is normal historical data. It should be noted that the inventor has demonstrated through experiments that if all data are mapped to the model, the hardware load is extremely large. In order to reduce investment, the control limit can be dynamically adjusted with the failure point as the boundary.

[0153] See also Figure 3 , a schematic diagram of the structure of a data prediction device based on a kernel partial least squares model disclosed in an embodiment of the present invention, wherein the kernel function in the kernel partial least squares KPLS model is a multidimensional tensor product wavelet kernel function, and the device comprises:

[0154] A first standardization unit 301 is used to standardize the sampled data using the mean and variance of the sampled data obtained online to obtain standardized sampled data;

[0155] A first calculation unit 302, used for calculating a first kernel matrix corresponding to the standardized sampling data by using the multidimensional tensor product wavelet kernel function;

[0156] A first centralization unit 303 is used to perform centralization processing on the first kernel matrix to obtain a first kernel matrix after centralization processing;

[0157] An input unit 304, used to input the first kernel matrix after the centralization process into the KPLS model;

[0158] The first prediction unit 305 is used to obtain a first quality variable prediction value corresponding to the sampled data by using the KPLS model.

[0159] The embodiment of the present invention discloses a data prediction device based on a kernel partial least squares model, wherein the kernel function in the kernel partial least squares KPLS model is a multidimensional tensor product wavelet kernel function, wherein the sampled data is standardized by using the mean and variance of the sampled data obtained online to obtain standardized sampled data; the kernel matrix corresponding to the standardized sampled data is calculated by using the multidimensional tensor product wavelet kernel function; the kernel matrix is ​​centralized to obtain the centralized kernel matrix; the centralized kernel matrix is ​​input into the KPLS model; and the KPLS model is used to obtain the quality variable prediction value corresponding to the sampled data. In the embodiment of the present invention, since the kernel function in the KPLS model adopts the multidimensional tensor product wavelet kernel function, the KPLS model has a strong nonlinear mapping capability, thereby being able to accurately calculate the quality variable prediction value.

[0160] To further optimize the above embodiment, the data prediction device based on the kernel partial least squares model in the embodiment of the present invention further includes:

[0161] The second calculation unit is used to calculate the actual value of the first quality variable corresponding to the sampled data by using the mean and variance of the predicted value of the first quality variable.

[0162] To further optimize the above embodiment, the data prediction device based on the kernel partial least squares model in the embodiment of the present invention further includes:

[0163] The third calculation unit is used to calculate the Hotelling T corresponding to the sampled data. 2 Statistics and squared prediction error SPE statistics;

[0164] The first judgment unit is used to judge the T corresponding to the sampled data. 2 Does the statistic exceed the T of the KPLS model? 2 Statistical control limits;

[0165] A second judgment unit is used to judge whether the SPE statistic corresponding to the sampled data exceeds the SPE statistic control limit of the KPLS model;

[0166] A determination unit is used to determine the T corresponding to the sampling data. 2 The statistic exceeds the T 2 If the statistical control limit and / or the SPE statistic corresponding to the sampling data exceeds the SPE statistical control limit, it is determined that a fault exists in the production process corresponding to the sampling data.

[0167] To further optimize the above embodiment, the data prediction device based on the kernel partial least squares model in the embodiment of the present invention further includes:

[0168] An establishing unit, used for establishing the KPLS model;

[0169] The establishing unit specifically includes:

[0170] A second standardization unit is used to standardize the training data using the mean and variance of the training data to obtain standardized training data;

[0171] A fourth calculation unit, used for calculating a second kernel matrix corresponding to the standardized training data by using the multidimensional tensor product wavelet kernel function;

[0172] A second centralization unit, used for performing centralization processing on the second kernel matrix to obtain a centralized second kernel matrix;

[0173] a fifth calculation unit, configured to calculate a first score matrix of input variables and a second score matrix of output variables by using a KPLS algorithm and the centralized second kernel matrix;

[0174] a sixth calculation unit, configured to calculate a regression coefficient matrix using the first score matrix and the second score matrix;

[0175] A second prediction unit, used to calculate a second quality variable prediction value corresponding to the training data using the regression coefficient matrix;

[0176] a seventh calculation unit, configured to calculate an actual value of the second quality variable corresponding to the training data by using the mean and variance of the predicted value of the second quality variable;

[0177] An eighth calculation unit is used to calculate T corresponding to the training data 2 Statistics and SPE statistics;

[0178] The first control limit determination unit is used to determine the control limit according to the T corresponding to the training data. 2 The distribution of the statistic determines the T of the KPLS model 2 Statistical control limits;

[0179] The second control limit determination unit is used to determine the SPE statistic control limit of the KPLS model according to the distribution of the SPE statistic corresponding to the training data.

[0180] It should be noted that the specific working principles of each component in the device embodiment can be found in the corresponding part of the method embodiment, which will not be repeated here.

[0181] Finally, it should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.

[0182] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0183] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A data prediction method based on kernel partial least squares model, characterized in that: The kernel function in the kernel partial least squares KPLS model is a multidimensional tensor product wavelet kernel function, and the method comprises: The sampled data are standardized using the mean and variance of the sampled data obtained online to obtain standardized sampled data, wherein the sampled data is process data collected during the industrial production process; Calculating a first kernel matrix corresponding to the standardized sampling data using the multidimensional tensor product wavelet kernel function; Centralizing the first kernel matrix to obtain a first kernel matrix after centralization; Inputting the first kernel matrix after the centralization process into the KPLS model; Using the KPLS model, obtaining a predicted value of a first quality variable corresponding to the sampled data; The output expression of any one dimension of the multidimensional tensor product wavelet kernel function is: Wherein, ω represents the angular velocity of the kernel function, C represents a constant, L represents the Laplace transform, represents the i-th element in the vector of the s-th column in the regression coefficient matrix, where s=1, 2, ..., M, k represents a kernel function, and (x, z) represents a data point; The KPLS model satisfies the following formula: Among them, the ε i represents the slack variable at the i-th point, represents the estimated value of the slack variable at the i-th point, the μ i represents the Lagrange multiplier of the i-th point, represents the estimated value of the Lagrange multiplier at the i-th point, represents the jth component of the i-th training data, represents the estimated value of the jth component of the i-th training data, Represents the estimated value of the i-th element in the vector in the s-th column of the regression coefficient matrix.

2. The method according to claim 1, characterized in that The method further comprises: The actual value of the first quality variable corresponding to the sampled data is calculated using the mean and variance of the predicted value of the first quality variable.

3. The method according to claim 1, characterized in that The method further comprises: Calculate the Hotelling T corresponding to the sampled data 2 Statistics and squared prediction error SPE statistics; Determine the T corresponding to the sampled data 2 Does the statistic exceed the T of the KPLS model? 2 Statistical control limits; Determine whether the SPE statistic corresponding to the sampled data exceeds the SPE statistic control limit of the KPLS model; If the T corresponding to the sampling data 2 The statistic exceeds the T 2 If the statistical control limit and / or the SPE statistic corresponding to the sampling data exceeds the SPE statistical control limit, it is determined that a fault exists in the production process corresponding to the sampling data.

4. The method according to claim 1, characterized in that The method further comprises: Establishing the KPLS model; The establishing of the KPLS model comprises: Standardizing the training data using the mean and variance of the training data to obtain standardized training data; Calculating a second kernel matrix corresponding to the standardized training data using the multidimensional tensor product wavelet kernel function; Centralizing the second kernel matrix to obtain a centralized second kernel matrix; Using the KPLS algorithm and the centralized second kernel matrix, the first score matrix of the input variables and the second score matrix of the output variables are calculated; Using the first score matrix and the second score matrix, a regression coefficient matrix is ​​calculated; Calculating a second quality variable prediction value corresponding to the training data using the regression coefficient matrix; Using the mean and variance of the predicted value of the second quality variable, calculate the actual value of the second quality variable corresponding to the training data; Calculate T corresponding to the training data 2 Statistics and SPE statistics; According to the T corresponding to the training data 2 The distribution of the statistic determines the T of the KPLS model 2 Statistical control limits; The SPE statistic control limit of the KPLS model is determined according to the distribution of the SPE statistic corresponding to the training data.

5. The method according to claim 1, characterized in that The multidimensional tensor product wavelet kernel function satisfies the Laplace transform Support vector kernel function of Wherein, k represents a kernel function, σ represents a scaling factor, K represents a data point in a kernel matrix, K is represented as (x, z), and x and y represent measurement values ​​in K(x, z).

6. The method according to claim 3 or 4, characterized in that: The T 2 The statistics satisfy the following formula: T 2 =[t1,t2,…,t A ]Λ -1 [t1,t2,…,t A ] T ; Among them, the -1 represents the inverse matrix of the principal component covariance matrix, the t1, the t2, the t A represents the principal element of the extracted input variable X, A represents the number of principal elements of the extracted input variable X, T=[t1, t2, …, t A ] represents the score matrix of input variable X; The SPE statistic satisfies the following formula: The KPLS model maps data from low-dimensional space to high-dimensional space, t i and t j Corresponding to the mapped data coordinates, M is a positive integer, and N is a positive integer.

7. The method according to claim 3 or 4, characterized in that: The T 2 The statistical control limits satisfy: Where N is the number of input variables X, F A,N-A,α It is expressed as the value of F distribution with A to NA degrees of freedom and confidence level α; The SPE statistic control limits satisfy: Among them, g represents a constant and h represents X 2 Degrees of freedom of the distribution, g k =v k / 2m k , ν k It is expressed as the mean of the SPE statistic at time k, m k Expressed as the variance of the SPE statistic at time k.

8. A data prediction device based on a kernel partial least squares model, characterized in that: The kernel function in the kernel partial least squares KPLS model is a multidimensional tensor product wavelet kernel function, and the device comprises: A standardization unit, used to standardize the sampled data using the mean and variance of the sampled data obtained online to obtain standardized sampled data, wherein the sampled data is process data collected during the industrial production process; A first calculation unit, used for calculating a first kernel matrix corresponding to the standardized sampling data by using the multidimensional tensor product wavelet kernel function; A centralization unit, used for performing centralization processing on the first kernel matrix to obtain a first kernel matrix after centralization processing; An input unit, used for inputting the first kernel matrix after the centralization process into the KPLS model; A prediction unit, configured to obtain a predicted value of a first quality variable corresponding to the sampled data by using the KPLS model; The output expression of any one dimension of the multidimensional tensor product wavelet kernel function is: Wherein, ω represents the angular velocity of the kernel function, C represents a constant, L represents the Laplace transform, represents the i-th element in the vector of the s-th column in the regression coefficient matrix, where s=1, 2, ..., M, k represents a kernel function, and (x, z) represents a data point; The KPLS model satisfies the following formula: Among them, the ε i represents the slack variable at the i-th point, represents the estimated value of the slack variable at the i-th point, the μ i represents the Lagrange multiplier of the i-th point, represents the estimated value of the Lagrange multiplier at the i-th point, represents the jth component of the i-th training data, represents the estimated value of the jth component of the i-th training data, Represents the estimated value of the i-th element in the vector in the s-th column of the regression coefficient matrix.

Images