Nonlinear industrial process quality monitoring method and system

Abstract

The invention discloses a nonlinear industrial process quality monitoring method and system, and the method comprises the steps: collecting an original data set X, and carrying out the mean removal of the original data set X, and obtaining a standard data set Xc; performing nonlinear mapping on the standard data set Xc by using kernel principal component analysis; taking the first k feature variables in the kernel feature space as kernel key component variables, and calculating a nonlinear structure between feature vectors of a kernel matrix K; calculating a projection value Fp of a kernel key component variable in a space where a kernel matrix eigenvector is located, calculating a projection value # imgabs0 # of a kernel matrix K after mean removal by combining the projection value Fp, and constructing a multivariate T2 control chart based on multivariate T2 statistics; and a preset control limit is inserted into the multivariate T2 control chart, and whether the to-be-monitored process is abnormal or not is judged based on the control limit. According to the method, the kernel principal component analysis and the multivariate T2 control chart are combined, complex nonlinear data can be effectively processed and monitored, and the sensitivity and accuracy of anomaly detection are high.

Description

Technical Field

[0001] The present invention relates to a monitoring method, and particularly to a non-linear industrial process quality monitoring method and system. Background Art

[0002] With the rapid development of industrial automation and intelligent manufacturing technologies, modern industrial processes often involve multi-variable and non-linear data characteristics. Traditional monitoring methods, such as Shewhart control charts, CUSUM control charts, and EWMA control charts, are mainly applied to single-variable or linear systems, and have limited monitoring effects on multi-variable and non-linear systems. For example, Shewhart control charts rely on the mean and standard deviation of a single quality characteristic to set control limits, but it is difficult to capture the correlations between variables and potential non-linear structures when dealing with multi-variable or complex non-linear systems, resulting in inaccurate monitoring results. Summary of the Invention

[0003] Object of the Invention: The object of the present invention is to provide a non-linear industrial process quality monitoring method that can efficiently and accurately process multi-variables.

[0004] The second object of the present invention is to provide a non-linear industrial process quality monitoring system.

[0005] Technical Solution: A non-linear industrial process quality monitoring method disclosed by the present invention includes the following steps:

[0006] S1: Collect n sample data of the process to be monitored, and each sample data contains m characteristic variables. The n samples form an original data set X, and the original data set X is de-meaned to obtain a standard data set X c ;

[0007] S2: Use kernel principal component analysis to perform non-linear mapping on the standard data set X c to obtain a kernel matrix K and kernel characteristic variables Φ(t1), Φ(t2), … Φ(t m ) in the kernel feature space, and calculate the covariance matrix W of the kernel matrix K τ ;

[0008] S3: Take the first k characteristic variables in the kernel feature space as kernel key component variables, and combine the kernel key component variables and the covariance matrix W τ to calculate the non-linear structure between the eigenvectors of the kernel matrix K;

[0009] S4: Calculate the projection value F of the kernel key component variables in the space where the eigenvectors of the kernel matrix are located based on the non-linear structure between the eigenvectors of the kernel matrix K p , and combine the projection value F p to calculate the projection value after de-meaning the kernel matrix K

[0010] S5: Based on the projected values after mean removal Calculate the multivariate T 2 statistic, and construct a multivariate T 2 control chart based on the multivariate T 2 statistic;

[0011] S6: Insert the preset control limits into the multivariate T 2 control chart, and based on the distribution of the multivariate T 2 control chart relative to the control limits, determine whether the process to be monitored is abnormal.

[0012] Furthermore, the calculation method of the standard data set X c is as follows:

[0013] The matrix expression of the original data set X is Let x j,i represent the i-th feature variable in the j-th sample data, where 1 ≤ j ≤ n and 1 ≤ i ≤ m;

[0014] Let x i = [x 1,i , …, x n,i T , x i represents the data contained in the i-th column of X, then X = [x 1 , x 2 , …, x m ;

[0015] Perform mean removal on the original data set X to obtain the standard data set after mean removal where represents the mean of all data in the i-th column.

[0016] Furthermore, the method for obtaining the covariance matrix W τ in step S2 is as follows:

[0017] Use the Gaussian kernel trick feature mapping function of kernel principal component analysis to nonlinearly map the m feature variables of the n samples in the standard data set X c into the kernel feature space to obtain the kernel matrix K, the kernel feature variables Φ(t1), Φ(t2), …, Φ(t m ), and calculate the covariance matrix W τ of the kernel matrix K,

[0018] Furthermore, the method for obtaining the nonlinear structure between the eigenvectors of the kernel matrix K in step S3 is as follows:

[0019] ​S31: Take the first k feature variables in the de-nucleated feature space as the kernel principal feature variables and the kernel key component variables, and then combine the covariance matrix W τ to construct the definition formula of the kernel trick feature mapping function through the characteristic equation of W, where k ∈ [1, m];

[0020] S32: Based on the definition formula of the kernel trick feature mapping function K ki = Φ(t k )·Φ(t i ), calculate all the point values included in the kernel matrix K, and perform de-mean processing on K to obtain

[0021] S33: Assume that the feature coefficients of the corresponding m feature variables in n sample data are α1, α2, …, α m , and then combine the kernel key component variables and the characteristic equation of the covariance matrix W τ to calculate the characteristic equation of the kernel matrix K

[0022] Furthermore, the method for obtaining the definition formula of the kernel trick feature mapping function in step S31 is as follows;

[0023] Assume that the first kernel eigenvalue of W τ is λ and the corresponding first kernel eigenvector is V, then the characteristic equation of W τ is expressed as λV = W τ V, where λ > 0 and V ≠ 0;

[0024] Substitute the formula into the formula λV = W τ V to obtain the following formula:

[0025]

[0026] Take the first k kernel feature variables in the kernel feature space as the kernel key component variables, then the expression of the kernel key component variables is Φ(t k );

[0027] The calculation of the kernel trick feature mapping function is the dot product of two vectors in the feature space. Construct the definition formula of the kernel trick feature mapping function as K ki = Φ(t k )·Φ(t i );

[0028] The method for obtaining in step S32 is as follows:

[0029] First, use K ki = Φ(t k )·Φ(t i ) to calculate all the point values included in the kernel matrix K, K kiThe point value at the $k$-th row and $i$-th column of the kernel matrix $K$;

[0030] Then where

[0031] Furthermore, the method for obtaining the characteristic equation of the kernel matrix $K$ in step S33 is as follows:

[0032] Let the second kernel eigenvalue of $W$ τ be $\lambda'$ and the corresponding second kernel eigenvector be $Z$. Then the characteristic equation of $W$ τ is expressed as $\lambda'Z = W$ τ $Z$, where $\lambda' \gt 0$ and $Z \neq 0$;

[0033] Substitute into $\lambda'Z = W$ τ $Z$ to obtain the following equation:

[0034]

[0035] $\lambda'Z = W$ τ $Z$ can be equivalently expressed as the following equation: $\lambda'(\varPhi(t$ k $)\cdot Z)=\varPhi(t$ k )\cdot(W$ τ $Z)$ (2);

[0036] Let the characteristic coefficients of the $m$ characteristic variables corresponding to $n$ sample data be $\alpha_1,\alpha_2,\cdots,\alpha$ m , then the kernel key component eigenvector $Z$ can be expressed as the following equation:

[0037]

[0038] Combining formulas (2), (3) and obtain the following equation:

[0039]

[0040] Combining the kernel matrix $K$ and equation (4), obtain the following equation:

[0041]

[0042] Let $\alpha$ be the eigenvector of the kernel matrix $K$. Combining equation (5), the characteristic equation of the kernel matrix is $m\lambda'\alpha=\alpha K$.

[0043] Furthermore, the method for obtaining the projection value after removing the mean in step S4 is as follows:

[0044] Normalize the characteristic coefficients $\alpha_1,\alpha_2,\cdots,\alpha$ k corresponding to the kernel key component variables so that $(Z$ P $\cdot Z$ P) = 1, where p ∈ [1, k], and the kernel key component variable Z of the kernel matrix K P is expressed as

[0045] Calculate the projection value F of the kernel key component variable of the kernel matrix K p , and the projection value F p The calculation formula is as follows:

[0046]

[0047] Calculate the projection value after removing the mean

[0048] Based on the definition formula of the kernel trick feature mapping function,[[]] and the projection value F p Calculate the projection value of K after removing the mean

[0049] Furthermore, the way to obtain the multivariate T 2 statistic in step S5 is: based on the projection value after removing the mean of the covariance matrix Calculate the multivariate T 2 statistic

[0050] Furthermore, the control limit in step S5 is set based on the historical data distribution; when the multivariate T 2 in the control chart shows that the upper limit of the multivariate T 2 statistic exceeds the control limit, then the interval exceeding the control limit is determined as an abnormal interval.

[0051] Based on the same inventive concept, the present invention also provides a non - linear industrial process quality monitoring system, which is characterized in that it includes,

[0052] A sample acquisition module, which is used to collect m sample data of the process to be monitored, and each sample data contains n feature variables. The m samples form the original data set X, and calculate the covariance matrix W of the original data set X;

[0053] A non - linear mapping module, which uses kernel key component analysis to perform non - linear mapping on the standard data set X c to obtain the kernel matrix K, the kernel feature variables Φ(t1), Φ(t2), … Φ(t m ) in the kernel feature space, and calculate the covariance matrix W τ ;

[0054] Nonlinear structure construction module, taking the first k feature variables in the kernel feature space as kernel key component variables, and combining the kernel key component variables and the covariance matrix W τ Calculate the nonlinear structure between the eigenvectors of the kernel matrix K;

[0055] Projection value calculation module, calculating the projection value F of the kernel key component variables in the space where the eigenvectors of the kernel matrix are located p , combining the projection value F p , calculating the projection value after de - meaning the kernel matrix K

[0056] Multivariate T 2 Control chart construction module, capable of calculating the multivariate T statistic based on the de - meaned projection value 2 , and constructing a multivariate T 2 control chart based on the multivariate T 2 statistic;

[0057] Judgment module, capable of inserting a preset control limit into the multivariate T 2 control chart, and judging whether the process to be monitored is abnormal based on the distribution of the multivariate T 2 control chart relative to the control limit.

[0058] Beneficial effects: Compared with the prior art, the present invention has the following remarkable advantages: The present invention combines kernel principal component analysis and multivariate T 2 control chart, and can effectively process and monitor complex nonlinear data. Compared with traditional methods, the present invention can capture the nonlinear features in the data, significantly improving the sensitivity and accuracy of anomaly detection; and the present invention can achieve efficient and accurate anomaly detection by calculating the projection value of the key components after the kernel principal component analysis transformation in real - time and combining the T 2 statistic, and enhancing the overall real - time monitoring ability and robustness. The present invention extracts the kernel key component variables, which can not only timely identify the minor anomalies in the nonlinear process, but also effectively adapt to high - dimensional data, having strong industrial adaptability and broad application prospects. Brief description of the drawings

[0059] Figure 1 is the flow chart of the method of the present invention;

[0060] Figure 2 is the 3D scatter plot of the original data X of the embodiment of the present invention;

[0061] Figure 3 is the multivariate T 2 control chart of the embodiment of the present invention;

[0062] Figure 4 is the structural schematic diagram of the system of the present invention. Detailed implementation manners

[0063] The technical solutions of the present invention will be further described below with reference to the accompanying drawings.

[0064] Embodiment 1

[0065] A non - linear industrial process quality monitoring method disclosed by the present invention, as Figure 1 shown, includes the following steps:

[0066] S1: Collect m sample data of the process to be monitored, and each sample data contains n characteristic variables. The m samples constitute the original data set X, and the original data set X is processed by removing the mean value to obtain the standard data set X c ; where m>n>0. A non - linear industrial process refers to a process in a complex industrial environment where, due to the interaction of various factors such as process parameters, material diversity, and changes in operating conditions, the system exhibits non - linear behavior. These processes are usually difficult to effectively model and predict through traditional linear models, so more complex algorithms and methods need to be adopted for analysis and control. In such systems, common applications include welding processes, chemical reaction processes, machining processes, etc. In these processes, the changes in key parameters such as temperature, pressure, and flow rate may have highly non - linear characteristics and complex correlations with each other.

[0067] The sample data is obtained by real - time monitoring and data collection in the industrial process, and usually includes a large amount of multi - dimensional and time - series data. These data may contain variables such as temperature, pressure, flow rate, speed, etc., and there are complex interdependent relationships among these variables. Due to the non - linear characteristics of the data, traditional methods based on linear assumptions are difficult to process such data. Therefore, how to effectively extract valuable information from these high - dimensional and non - linear data has become the key to realizing efficient process quality monitoring and fault diagnosis.

[0068] During actual operation, install n sampling sensors on the process to be monitored. The detection signals of the n sensors at the same moment constitute a sample data, and the samples obtained at m moments constitute the original data set X. When actually collecting sample data, the sampling time interval or sampling step size can be set according to needs.

[0069] Preferably, filter and denoise the detection signals in the original data set X.

[0070] The matrix expression of the original data set X is Use x j,i to represent the i - th characteristic variable in the j - th sample data, 1≤j≤n, 1≤i≤m;

[0071] Let x i =[x 1,i,…,x n,i T , x i denotes the data contained in the i-th column of X, then X = [x 1 , x 2 ,…, x m ;

[0072] Perform mean removal on the original data set X to obtain the standardized data set after mean removal where denotes the mean of all data in the i-th column.

[0073] S2: Use kernel principal component analysis to perform non-linear mapping on the standardized data set X c to obtain the kernel matrix K and the kernel feature variables Φ(t1), Φ(t2), … Φ(t m ) in the kernel feature space, and calculate the covariance matrix W of the kernel matrix K τ .

[0074] Gaussian kernel trick feature mapping function (RBF): K(x, x') = exp(-σ * ||x - x'|| 2 ), where σ * refers to the bandwidth parameter. In this embodiment, σ * takes 1, and ||x - x'|| represents the Euclidean distance between different rows of the matrix.

[0075] The expression for non-linear mapping is x ∈ R m → Φ(x) ∈ R h , where Φ(·) is the non-linear mapping function, m represents the dimension of the original data space, that is, the number of feature variables contained in the sample data, h represents the dimension of the kernel feature space, and h ≥ m; the non-linear mapping maps the m feature variables in the sample data to h feature variables in the kernel feature space.

[0076] Adopt the Gaussian kernel trick feature mapping function of kernel key component analysis to non-linearly map the m feature variables of n samples in the standardized data set X c into the kernel feature space to obtain the kernel matrix K, the kernel feature variables Φ(t1), Φ(t2), … Φ(t m ), and calculate the covariance matrix W of the kernel matrix K τ ,

[0077] S3: Take the first k feature variables in the kernel feature space as the kernel key component variables, and combine the kernel key component variables and the covariance matrix W τ to calculate the non-linear structure between the eigenvectors of the kernel matrix K. ​

[0078] S31: Take the first k eigenvariables in the kernel feature space as the kernel key component variables, and then combine with the covariance matrix W τ to construct the definition formula of the kernel trick feature mapping function through the characteristic equation of W, where k ∈ [1, m];

[0079] Let the first kernel eigenvalue of W τ be λ (λ > 0), and the corresponding first kernel eigenvector be V (V ≠ 0), then the characteristic equation of W τ is expressed as:

[0080] λV = W τ V

[0081] Substitute the formula into the formula λV = W τ V to get

[0082]

[0083] Take the first k kernel eigenvariables in the kernel feature space as the kernel key component variables, k = 1, 2, …, n, the maximum value of k can be n, and the minimum value is 1, then the kernel main feature data corresponding to the kernel key component is expressed as Φ(t k ); Take the first k eigenvectors of the kernel matrix K, that is, perform dimensionality reduction processing, reducing from n dimensions to k dimensions.

[0084] The kernel trick feature mapping function needs to calculate the dot product of two vectors in the feature space. The matrix of size m×m can be defined as K ki = Φ(t k )·Φ(t i ).

[0085] S32: Based on the definition formula of the kernel trick feature mapping function K ki = Φ(t k )·Φ(t i ), calculate all the point values included in the kernel matrix K, and perform mean removal processing on K to obtain

[0086] First, use K ki = Φ(t k ·)Φ(t i ) to calculate all the point values included in the kernel matrix K. K ki refers to the point value of the k-th row and the i-th column of the kernel matrix K;

[0087] Then where

[0088] S33: Let the characteristic coefficients of the m eigenvariables corresponding to n sample data be α1, α2, …, α m, and then combine the nuclear key component variables and the covariance matrix W τ Calculate the characteristic equation of the kernel matrix K based on the characteristic equation of τ .

[0089] Let W τ The second nuclear eigenvalue be λ' (λ' > 0), and the corresponding second nuclear eigenvector be Z (Z ≠ 0), then the characteristic equation of W τ is expressed as:

[0090] λ'Z = W τ Z;

[0091] Substitute into λ'Z = W τ Z to get:

[0092]

[0093] λ'Z = W τ Z can be equivalently expressed as:

[0094] λ'(Φ(t k ·)Z) = Φ(t k )·(W τ Z) (2)

[0095] Let the characteristic coefficients of the m characteristic variables corresponding to n sample data be α1, α2, … α m , then the nuclear key component eigenvector Z,

[0096]

[0097] Combined with formulas (2), (3) and to get:

[0098]

[0099] Substitute the kernel matrix K into the left side of equation (4) to get:

[0100]

[0101] Substitute the kernel matrix K into the right side of equation (4) to get:

[0102]

[0103] Combined with the above two left and right equations, the following expression is obtained:

[0104]

[0105] Let α be the eigenvector of the kernel matrix K, and α is used to construct the projection direction. By simplifying equation (5) into the following matrix form, we get:

[0106] mλ'α = αK。

[0107] S4: Calculate the projection value F of the nuclear key component variable in the space where the eigenvector of the nuclear matrix lies p , combined with the projection value F p , calculate the projection value after de - meaning the nuclear matrix K

[0108] Select the second nuclear eigenvector corresponding to the largest second nuclear eigenvalue in the second nuclear eigenvalues λ'. Usually, the first few second nuclear eigenvectors can also be selected to retain most of the information of the data while reducing redundancy. For non - zero first nuclear eigenvalues, performing nuclear key component analysis in the feature space is equivalent to solving the second nuclear eigenvalue problem in mλ'α = αK.

[0109] After solving the eigenvalue problem, the eigen - coefficients α1, α2, … α k and eigenvalues λ1'≥λ2'≥…λ k ' can be determined. By selecting the first k second nuclear eigenvectors for dimensionality reduction, the coefficients α1, α2, … α k can be further normalized to satisfy (Z P ·Z P ) = 1, where p ∈ [1, k], and the nuclear key component variable Z P of the nuclear matrix K has the expression

[0110] The nuclear key component variables correspond one - to - one with the solved second nuclear eigenvectors. According to the selected nuclear key component variables, project the original data onto these key component variables, and calculate the projection value of each sample data on each nuclear key component variable. The projection value represents the projection value of the sample data in the direction of the nuclear key component variable. For each sample data, its projection value on the nuclear key component variable can be calculated through the inner product (defined by the kernel - trick feature mapping function). The projection value F P of the nuclear key component variable is calculated by projecting Φ(t i ) onto the eigenvector Z P (where P = 1, 2, …, l), and the calculation expression is as follows:

[0111]

[0112] The nuclear matrix after de - meaning through the defined formula of the constructed kernel - trick feature mapping function and the projection value F P , calculate the projection value after de - meaning

[0113]

[0114] S5: Based on the projection value after de - meaning Calculate the multivariate T 2 statistic, and construct a multivariate T 2 control chart based on the multivariate T 2 statistic.

[0115] Based on the covariance matrix of the projection values after mean removal calculate the multivariate T statistic for each sample data 2 statistic

[0116] S6: Insert the preset control limits into the multivariate T 2 control chart, and based on the distribution of the multivariate T 2 control chart relative to the control limits, determine whether the process to be monitored is abnormal.

[0117] The control limits are set based on the historical data distribution. Preferably, the critical values of the Fisher distribution are used to set the control limits.

[0118] When a multivariate T 2 statistic in the control chart exceeds the control limit, then the interval exceeding the control limit is determined as an abnormal interval. In practical applications, when an abnormality is detected, an external alarm device can be connected to conveniently feedback the monitoring result to the administrator and prompt the administrator to conduct further analysis or take corresponding corrective measures. 2 statistic in the control chart exceeds the control limit, then the interval exceeding the control limit is determined as an abnormal interval. In practical applications, when an abnormality is detected, an external alarm device can be connected to conveniently feedback the monitoring result to the administrator and prompt the administrator to conduct further analysis or take corresponding corrective measures.

[0119] The present invention is applicable to the quality monitoring of non - linear industrial processes in fields such as chemical industry, digital production lines, pharmaceutical products, semiconductors, etc. When applied to different technical fields or different non - linear industrial process quality monitoring, the characteristic coefficients α1, α2, … α m and the bandwidth parameter σ of the Gaussian kernel - based feature mapping function (RBF) * can be set according to the actual situation, which is beneficial to improving the accuracy and response speed of monitoring.

[0120] Example 2

[0121] A non - linear industrial process quality monitoring method disclosed by the present invention is used for the quality inspection of a welding process.

[0122] By collecting the welding feed speed, welding current, and welding temperature data during the welding process through real - time monitoring sensors, the welding feed speed, welding current, and welding temperature data are the characteristic variables, the number of characteristic variables is 3, sampling is performed once per second, and a total of 150 sample data are collected. Preferably, the collected sample data are removed of outliers and noise to ensure the data quality. The 3D scatter plot of the original data X collected is as Figure 2 shown.

[0123] The original data X collected is subjected to mean removal processing to obtain the standard data set X c The mean removal processing is to eliminate the influence of different variable dimensions, and the standardized data has a zero mean.

[0124] The Gaussian kernel trick feature mapping function (RBF) is used to map the standard data set X c to the kernel feature space. Perform the steps corresponding to obtaining the covariance matrix W in Embodiment 1 τ That is, by calculating the three dimensions of the welding feed speed, welding current, and welding temperature during the welding process, the covariance matrix of the data in the kernel feature space is obtained as follows:

[0125]

[0126] Take the first 3 feature variables in the kernel feature space as the kernel key component variables, and combine the kernel key component variables and the covariance matrix W τ Calculate the non-linear structure between the eigenvectors of the kernel matrix K.

[0127] Successively perform steps S3 and S4 in Embodiment 1 to obtain the projected values after mean removal

[0128]

[0129] And the projected values after mean removal are shown in Table 1 below:

[0130] Table 1

[0131]

[0132] Based on the projected values after mean removal shown in Table 1 Based on the projected values after mean removal Covariance matrix Calculate the multivariate T 2 statistic

[0133] According to the multivariate T 2 statistic value, draw the multivariate T Figure 3 as shown 2 control chart. By calculating the historical data distribution of the statistic, determine the control limit, and in this embodiment, the critical value of the Fisher distribution is adopted.

[0134] Calculate and determine the confidence interval of the multivariate T 2 control chart as UCL, that is, calculate the control limit, and the calculation formula of UCL is:

[0135]

[0136] Among them, the significance level α of the embodiment of the present invention is 0.05.

[0137] Based on the distribution of the multivariate T 2 control chart relative to the control limit, it is judged whether the process to be monitored is abnormal, and whether the following statistical situations occur in sequence as shown in Table 2 below:

[0138] Table 2

[0139] Sample number <![CDATA[Multivariate T 2 statistic]]> Control limit Is it abnormal? 1 324.31 527.2852 No 2 444.53 527.2852 No … … … … 150 637 527.2852 Yes

[0140] From Figure 3 analysis, the method of combining KPCA and T 2 statistic has a detection rate of up to 96.04% for the abnormal detection of the welding process, indicating that the method of nonlinear system process quality monitoring based on kernel principal component analysis (KPCA) and multivariate T 2 control chart is feasible.

[0141] Embodiment 3

[0142] A nonlinear industrial process quality monitoring system disclosed by the present invention, as Figure 4 shown, includes a sample acquisition module, a nonlinear mapping module, a nonlinear structure construction module, a projection value calculation module, a multivariate T 2 control chart construction module and a judgment module.

[0143] The sample acquisition module is used to collect m sample data of the process to be monitored, and each sample data contains n characteristic variables. The m samples constitute the original data set X, and the covariance matrix W of the original data set X is calculated. The sample acquisition module executes step S1 in Embodiment 1.

[0144] The nonlinear mapping module uses kernel principal component analysis to perform nonlinear mapping on the standard data set X c to obtain the kernel matrix K, the kernel characteristic variables Φ(t1), Φ(t2), … Φ(t m ) in the kernel feature space, and calculates the covariance matrix W τ of the kernel matrix K. The nonlinear mapping module executes step S2 in Embodiment 1.

[0145] The nonlinear structure construction module takes the first k characteristic variables in the kernel feature space as the kernel principal component variables, combines the kernel key component variables and the covariance matrix W τ to calculate the nonlinear structure between the eigenvectors of the kernel matrix K. The nonlinear structure construction module executes step S3 in Embodiment 1.

[0146] The projection value calculation module calculates the projection value F of the core key component variables in the space where the eigenvectors of the kernel matrix are located. p , combines the projection value F p , and calculates the projection value after the kernel matrix K is de-meaned The projection value calculation module executes step S4 in Embodiment 1.

[0147] Multivariate T 2 The control chart construction module can, based on the de-meaned projection value calculate the multivariate T 2 statistic, and construct a multivariate T 2 control chart based on the multivariate T 2 statistic. The multivariate T 2 control chart construction module executes step S5 in Embodiment 1.

[0148] The judgment module can insert a preset control limit into the multivariate T 2 control chart, and judge whether the process to be monitored is abnormal based on the distribution of the multivariate T 2 control chart relative to the control limit. The judgment module executes step S6 in Embodiment 1.

Claims

1. A non - linear industrial process quality monitoring method, characterized in that: Including the following steps: S1: Collect n sample data of the process to be monitored, and each sample data contains m feature variables. The n samples constitute the original data set X, and the original data set X is de-meaned to obtain the standard data set X c ; S2: Use kernel principal component analysis for the standard data set X c to perform non-linear mapping to obtain the kernel matrix K and the kernel feature variables Φ(t1), Φ(t2), … Φ(t m ), and calculate the covariance matrix W of the kernel matrix K τ ; S3: Take the first k eigenvariables in the kernel feature space as kernel key component variables, and combine the kernel key component variables and the covariance matrix W τ Calculate the nonlinear structure among the eigenvectors of the kernel matrix K; S4: Calculate the projection value F of the kernel key component variable in the space where the eigenvectors of the kernel matrix K are located based on the non-linear structure between the eigenvectors of the kernel matrix K p , combined with the projection value F p , calculate the projection value after the kernel matrix K is de-meaned S5: Based on the projected values after mean removal Calculate the multivariate T 2 statistic, and based on the multivariate T 2 statistic, construct a multivariate T 2 control chart; S6: Insert the preset control limits into the multivariate T 2 control chart, and based on the distribution of the multivariate T 2 control chart relative to the control limits, determine whether the process to be monitored is abnormal.

2. The non-linear industrial process quality monitoring method according to claim 1, characterized in that: The standard data set X c is calculated as follows: The matrix expression of the original dataset X is Let x j,i represent the i-th feature variable in the j-th sample data, where 1 ≤ j ≤ n and 1 ≤ i ≤ m; Let x i = [x 1,i , …, x n,i T , where x i represents the data contained in the i-th column of X, then X = [x 1 , x 2 , …, x m ;​ The original dataset X is de-meaned to obtain the standardized dataset after de-meaning. where represents the mean of all data in the i-th column.

3. The non-linear industrial process quality monitoring method according to claim 1, characterized in that: Obtain the covariance matrix W in step S2 τ The method is as follows: The Gaussian kernel trick feature mapping function using kernel principal component analysis nonlinearly maps the m feature variables of n samples in the standard dataset X c into the kernel feature space to obtain the kernel matrix K and the kernel feature variables Φ(t1), Φ(t2), …, Φ(t m ), and calculates the covariance matrix W of the kernel matrix K τ , 4. The non-linear industrial process quality monitoring method according to claim 3, characterized in that: The method for obtaining the non-linear structure between the eigenvectors of the kernel matrix K in step S3 is as follows: S31: Take the first k eigenvariables in the kernel feature space as kernel key component variables, and then construct the definition formula of the kernel technique feature mapping function in combination with the characteristic equation of the covariance matrix W τ where k ∈ [1, m]; S32: Based on the definition formula K of the kernel trick feature mapping function ki = Φ(t k ) · Φ(t i ), calculate all the point values included in the kernel matrix K, and perform mean removal processing on K to obtain S33: Let the feature coefficients of the corresponding m feature variables in n sample data be α1, α2, …, α m , and then combine the kernel key component variables and the covariance matrix W τ to calculate the characteristic equation of the kernel matrix K according to the characteristic equation of 5. The non-linear industrial process quality monitoring method according to claim 4, characterized in that: The method for obtaining the defining formula of the kernel trick feature mapping function in step S31 is; Let W τ have a first core eigenvalue of λ and a corresponding first core eigenvector of V, then the characteristic equation of W τ is expressed as λV = W τ V, where λ > 0 and V ≠ 0; Substitute the formula into the formula λV = W τ to obtain the following equation for V: Take the first k kernel feature variables in the kernel feature space as the kernel key component variables, and the expression of the kernel key component variables is Φ(t k ); The calculation of the kernel trick feature mapping function is the dot product of two vectors in the feature space. The definition formula of the kernel trick feature mapping function is constructed as K ki = Φ(t k ) · Φ(t i ); Obtained in step S32 The method is as follows: First, use K ki = Φ(t k )·Φ(t i ) to calculate all the point values contained in the kernel matrix K. K ki refers to the point value at the k-th row and the i-th column of the kernel matrix K; Then wherein 6. The non-linear industrial process quality monitoring method according to claim 5, characterized in that: The method for obtaining the characteristic equation of the kernel matrix K in step S33 is: Let W τ have a second core eigenvalue λ' and a corresponding second core eigenvector Z, then for W τ the characteristic equation is expressed as λ'Z = W τ Z, where λ' > 0 and Z ≠ 0; Substitute into λ'Z = W τ for Z to obtain the following equation: λ'Z = W τ Z can be equivalently expressed as the following formula: λ'(Φ(t k )·Z) = Φ(t k )·(W τ Z) (2); Let the feature coefficients of the m feature variables corresponding to n sample data be α1, α2, …, α m , then the kernel key component feature vector Z can be expressed as the following formula: Combined with formulas (2), (3) and the following formula is obtained: Combining the kernel matrix K and equation (4), the following equation is obtained: Let α be the eigenvector of the kernel matrix K. Combining equation (5), the characteristic equation of the kernel matrix is mλ'α = αK.

7. The non-linear industrial process quality monitoring method according to claim 6, characterized in that: Step S4 obtains the projection value after mean removal The method is as follows: Normalize the characteristic coefficients α1, α2, …, α corresponding to the nuclear key component variables k so that (Z P ·Z P ) = 1, where p ∈ [1, k], and the expression of the nuclear key component variable Z P of the nuclear matrix K is Calculate the projection value F of the key component variables of the kernel matrix K p , the projection value F p is calculated as follows: Calculate the projected value after mean removal Based on the definition formula of the kernel trick feature mapping function, and the projection value F p Calculate the projection value of K after mean removal 8. The quality monitoring method for nonlinear industrial processes according to claim 7, characterized in that: Obtain the multivariate T in step S5 2 The method for obtaining the statistic is: based on the projection values after mean removal of the covariance matrix Calculate the multivariate T 2 statistic 9. The non-linear industrial process quality monitoring method according to claim 1, characterized in that: The control limits in step S5 are set based on the historical data distribution; when the upper limit of the multivariate T 2 in the control chart exceeds the control limit, the interval where the upper limit of the multivariate T 2 statistic exceeds the control limit is determined as an abnormal interval.

10. A non-linear industrial process quality monitoring system, characterized in that: Including A sample acquisition module, configured to collect m sample data of the process to be monitored, and each sample data includes n characteristic variables. The m samples constitute the original data set X, and the covariance matrix W of the original data set X is calculated; Nonlinear mapping module, which uses kernel principal component analysis for the standard data set X c to perform nonlinear mapping to obtain the kernel matrix K, kernel feature variables Φ(t1), Φ(t2), … Φ(t m ), and calculate the covariance matrix W of the kernel matrix K τ ; Nonlinear structure construction module, taking the first k eigenvariables in the kernel feature space as kernel key component variables, and combining the kernel key component variables and the covariance matrix W τ Calculating the nonlinear structure among the eigenvectors of the kernel matrix K; The projection value calculation module calculates the projection value F of the kernel key component variables in the space where the eigenvectors of the kernel matrix are located p , combines the projection value F p , and calculates the projection value after de - meaning the kernel matrix K Multivariate T 2 A control chart construction module that can calculate the multivariate T statistic based on the projected values after mean removal 2 and construct a multivariate T 2 control chart based on the multivariate T 2 statistic; A judgment module capable of inserting a preset control limit into a multivariate T 2 control chart and, based on the distribution of the multivariate T 2 control chart relative to the control limit, judge whether an abnormality occurs in the process to be monitored.

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