Chemical data missing process fault detection method and system

Abstract

The invention discloses a chemical data missing process fault detection method and system, and the method comprises the steps: converting two-dimensional data into a three-dimensional tensor through employing MDT, and carrying out the linear prediction and nonlinear prediction of an incomplete value through employing linear smooth CP and CP-SAE, and carrying out the reconstruction of normal data. And extracting a residual error and a feature space of the data in the data missing process through CP-SAE. And combining features extracted by smooth CP-decomposition and CP-SAE, and establishing three statistical magnitudes to realize fault detection. According to the method, the MDT and smooth CP decomposition method is used for solving the problems of data missing and time delay of data sample sampling, and the timeliness is high. The CP-SAE feature extraction robustness is high, and compared with a conventional linear method, the precision is high, and the response speed is high. The method is simple to operate, does not need repeated operation, and can extract the key features of the data while reconstructing the complete data set only by operating on the incomplete data set. The missing data can be effectively supplemented, the process monitoring requirement can be met, and the precision is high.

Description

Technical Field

[0001] This invention belongs to the field of process control and fault diagnosis technology, and in particular relates to a method and system for detecting faults in chemical processes with missing data. Background Technology

[0002] Missing process historical data is usually caused by data acquisition failures or the excessive cost of collecting complete data. It is worth noting that missing values ​​degrade the quality of process historical data and the performance of process monitoring. Methods such as PCA, CCA, ICA, and PLS are highly sensitive to outliers, and the aforementioned methods are not ideal for monitoring missing data.

[0003] Currently, a typical approach is to use a PCA model trained on complete data to estimate missing values ​​in new data. When the training data is incomplete, low-rank matrix completion (LRMC) is used to estimate missing values. However, PCA and LRMC are linear methods that assume the data matrix is ​​low-rank or approximately low-rank. In reality, it is difficult for data matrices to satisfy the low-rank assumption, so using low-rank matrices to approximate the data matrix still has certain shortcomings.

[0004] In the existing technology, the publicly available process fault detection methods can save computing resources, but the missing values ​​are only nonlinear predictions of the data and cannot take into account the time delay of the data. The linear methods used for fault detection are not effective for nonlinear process fault detection.

[0005] Some techniques determine the optimal solution for the training data and the complete data after imputation by minimizing the detection index. Although this effectively reduces the false alarm rate when handling missing data, it only considers the global optimal solution of the two-dimensional matrix and does not involve the optimization of missing values ​​in the three-dimensional matrix. Fault detection still has a certain time lag. For linear methods used in fault detection, the effect of detection on nonlinear processes is also poor.

[0006] Based on the above analysis, existing technologies still have certain limitations in fault detection of chemical processes with missing nonlinear data, and more advanced methods need to be developed to overcome the time delay and nonlinearity problems in fault detection. Summary of the Invention

[0007] The problem to be solved by the present invention is to provide a method and system for fault detection in chemical processes with missing data. The method uses a stacked autoencoder to learn a nonlinear representation of smooth CP decomposition and extracts potential reconstruction features of the data by reconstructing the feature matrix, thereby improving the fault detection rate of chemical processes with missing data.

[0008] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for detecting faults in a chemical process with missing data, comprising the following steps: S1: Collect raw data X0 of the chemical process under normal operating conditions, and standardize the raw data X0 to obtain a two-dimensional data matrix. ; S2: Employing a multi-directional delayed embedding transformation to transform the two-dimensional data matrix X N Transformed into three-dimensional tensor data Singular value decomposition is performed on each two-dimensional data in the three-dimensional tensor data X to obtain the first eigenvalue matrix E; simultaneously, smoothing CP decomposition is performed on the three-dimensional tensor data X to obtain the completed three-dimensional tensor data. The completed three-dimensional tensor data X' is subjected to singular value decomposition to obtain the second eigenvalue matrix. And retain the unitary matrices U' and V'; S3: Using the first eigenvalue matrix E as the training data for CP-SAE and the second eigenvalue matrix E' as the reference data for CP-SAE, the latent representation of smooth CP decomposition is learned using the CP-SAE method to obtain the reconstructed eigenvalue matrix E'' and feature space H; S4: Multiply the reconstructed eigenvalue matrix E'' with the unitary matrices U' and V' to obtain the reconstructed three-dimensional tensor data X''. Perform an inverse multi-directional delayed embedding transformation on the reconstructed three-dimensional tensor data X'' to obtain the reconstructed two-dimensional process data X. N '; S5: Based on the reconstructed eigenvalue matrix E'', the reconstructed three-dimensional tensor data X'', and the feature space H, construct the statistic E. 2 D 2 T 2 and determine control limit E 2 lim D 2 lim T 2 lim The process is monitored in real time.

[0009] Furthermore, in S1, the raw data of the chemical process X0 = [x 1,... ,x N ]∈R L×N , Where L represents the number of process variables and N represents the number of data sampling points; The missing values ​​in the data are filled with 0, and the two-dimensional data matrix X is... N The standardized calculation method is as follows: .

[0010] Furthermore, in S2, the multi-directional delay embedding transform converts the sampling point sequence Transformed into the following Hankel matrix H r (v), Where L is the sequence length, The number of iterations of the transformation. The forward representation of MDT is: Includes copy and fold operations. MDT is specifically represented as: , assuming The input data consists of multiple sequences. " " "" indicates a matrix multiplication operation on the Nth dimension.

[0011] Furthermore, in S2, the smooth CP decomposition is achieved by minimizing the following objective function: Where X is the input tensor; X' is the CP tensor with data completion; The coordinates representing the non-missing values ​​of T; The coordinates representing the missing values ​​of T; L represents the smoothing parameter. (n) The matrix represents the smoothing constraint matrix; p represents the normal form type; F represents the normal form type. Represents the cross product of vectors; g r R is an adjustable parameter; R is the rank of the CP decomposition tensor X, and N is the ordinal number of tensor X. r Let be the factor matrix of the smooth BS decomposition; the first term in the above equation is the CP decomposition reconstruction error, and the second term is the smooth decomposition constraint matrix.

[0012] Furthermore, step S3 includes the following steps: S31: E is projected onto H through a nonlinear transformation f, where f is a Selu function, as shown in the following formula: Where W and b are the encoder's weights and biases; The autoencoder AE reconstructs E into E''; Where W' and b' are the weights and biases of the decoder; S32: The objective function of AE1 in CP-SAE is: To learn the nonlinear representation of the BS-CP tensor decomposition algorithm; S33: Solving for the optimal parameters of AE1 using the AutoBP algorithm. The parameter update method is as follows: Where s is the number of iterations; S34: Using the hidden representation H1 of AE1 as the input to AE2, train AE2 according to the training method of AE1 described above, and obtain... Using the hidden representation H2 of AE2 as the input to AE3, the pre-training of AE1-AEn is completed sequentially according to the method described for AE1, resulting in... ; S35: DAE1-DAE n The stack connections constitute the entire CP-SAE, As the initialization parameter for each layer of CP-SAE, calculate H n For the feature space H of CP-SAE: ; S36: Calculate the reconstructed output E'' of AE: ; S37: Using the AutoBP algorithm, fine-tune the parameters of CP-SAE. When CP-SAE reaches the preset maximum number of iterations or the reconstruction error is less than the minimum set value, return the optimal parameter set. .

[0013] Furthermore, S4 includes the following steps: S41: Reconstruct the i-th element X of the three-dimensional tensor data X'' i The formula for calculating '' is: Among them, U i ', V i ',e i '' are U' and V' respectively Find the i-th element of E'', and then find the N elements of X'' in sequence, and concatenate them to form X''; S42: Inverse MDT Transform. The inverse MDT transform includes vectorization operations and the Moore-Penrose pseudo-inverse. .

[0014] for Moore-Penrose pseudo-rebellion, " " "" indicates a matrix multiplication operation on the Nth dimension.

[0015] Furthermore, in S5, the constructed statistics include: Reconstruction error statistics based on eigenvalue matrices ; Reconstruction error statistics based on 3D tensor data ; Hotelling's T based on feature space H 2 Statistic ,in, Let denoted as the mean and Φ as the covariance matrix.

[0016] Furthermore, the present invention also provides a chemical data missing process fault detection system, which runs the above-described chemical data missing process fault detection method.

[0017] Furthermore, the present invention also provides a computer device, including a memory, a processor, and an algorithm stored in the memory and executable on the processor, wherein the processor implements the above-described data processing method when executing the computer program.

[0018] Furthermore, the present invention also provides a computer-readable storage medium storing a computer algorithm, which, when executed by a processor, performs the above-described data processing.

[0019] The advantages and positive effects of this invention are: 1. This invention performs MDT transformation on the data and then considers using linear smoothing CP decomposition to supplement missing values. Addressing the issue of data nonlinearity, it combines linear smoothing CP decomposition with SAE, constructing a CP-SAE by approximating the result of the smoothing CP decomposition using SAE. The smoothing CP-SAE then generates missing value prediction data. While learning the smoothing CP decomposition, CP-SAE can extract latent features from the data. This method is equally effective for processes with both linear and nonlinear missing data, thereby improving the fault detection rate of data-incomplete chemical processes.

[0020] 2. This invention uses MDT transformation and smooth CP decomposition to solve the problems of missing data and time delay in data sample sampling, and has strong timeliness.

[0021] 3. The CP-SAE feature extraction method of this invention is robust, has higher accuracy and faster response speed than conventional linear methods.

[0022] 4. Compared with other methods, this invention is simple to operate, does not require repeated operations, and only needs to be operated on the incomplete dataset to extract the key features of the data while reconstructing the complete dataset. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the overall process of an embodiment of the present invention.

[0024] Figure 2 This is a framework diagram of the present invention based on BS-CP decomposition and CP-SAE for missing data prediction and data feature learning.

[0025] Figure 3 This is a structural schematic diagram of an embodiment of the system of the present invention. Detailed Implementation

[0026] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] The embodiments of the present invention will be further described below with reference to the accompanying drawings: like Figure 1 As shown, a method for detecting process faults with missing chemical data includes the following steps: S1: Collect chemical process data X0 under normal operating conditions and standardize the data to obtain the final data. .

[0028] Specifically, assume that the samples collected during the normal process contain missing values ​​x. N21 x N 42 , ..., x N3T The normal sample X0 is specifically represented as follows: nan in the above formula 21 For example, this indicates that the data of the first sampling point at the second sampling time is missing.

[0029] To ensure that the distribution of sample points in the original dataset remains unchanged, missing samples are ignored when calculating the sample variance and mean. Let X... N Taking the first variable as an example, The original chemical process data X0 is a single-modal missing chemical process data. The original chemical process data X0=[x1,...,x N ]∈RL×N Where L represents the number of process variables and N represents the number of data sampling points; missing values ​​in the data are padded with 0, X N The calculation method is as follows: .

[0030] S2: Employing Multi-directional Delayed Embedding Transform (MDT) to transform the two-dimensional data matrix X N Transformed into three-dimensional tensor data The singular value decomposition (SVD) is performed on each two-dimensional data point in the three-dimensional tensor data X to obtain the first eigenvalue matrix E; simultaneously, the smoothed CP decomposition is performed on the three-dimensional tensor data X to obtain the completed three-dimensional tensor data. The second eigenvalue matrix is ​​obtained by performing SVD decomposition on the completed 3D tensor data X'. And retain the unitary matrices U' and V'. Specifically, S2 includes the following steps.

[0031] S21: Input data X N The MDT forward transformation, specifically, Assume data X N A sampling point sequence is MDT can transform v The Hankel matrix is ​​as follows: in, Let L be the number of iterations in the MDT, and L be the sampling point length. The forward MDT is represented as: This includes copy and fold operations.

[0032] MDT is specifically represented as: T represents the input data, which consists of multiple sequences. This represents the matrix multiplication operation on the Nth dimension.

[0033] S22: Transfer three-dimensional tensor data Each two-dimensional tensor in the data undergoes SVD decomposition; the i-th element of the three-dimensional tensor data... Decomposed in the following way. in, Both sides ride on V i T The singular value decomposition of the matrix can be obtained: U can be obtained through decomposition. i V i , The SVD decomposition matrix of the N elements of X can be obtained sequentially.

[0034] S23: Characteristic matrix E=[e1,…,e N The method for finding ]: With e N For example, ,in It is a column vector consisting entirely of 1s. e1 to e2 can be obtained sequentially. N And thus E is obtained.

[0035] S24: Smooth CP decomposition (BS-CP) predicts missing values, employing a hierarchical alternating least squares approach, using the Hankel matrix of a single element as the factor matrix unit, and sequentially updating the normal form of each factor matrix: Where X is the input tensor; X' is the CP tensor with data completion; The coordinates representing the non-missing values ​​of T; The coordinates representing the missing values ​​of T; L represents the smoothing parameter. (n) The matrix represents the smoothing constraint matrix; p represents the normal form type; F is the normal form type. Represents the cross product of vectors; g r R is an adjustable parameter; R is the rank of the CP decomposition tensor X, and N is the ordinal number of tensor X. r Let be the factor matrix of the smooth BS decomposition; the first term in the above equation is the CP decomposition reconstruction error, and the second term is the smooth decomposition constraint matrix.

[0036] Specifically, In the above formula, Among them, X r Let X be the r-th component of the input tensor X. r 'The r-th component of the CP tensor X' is the data completion tensor.

[0037] To obtain the optimal solution of CP decomposition, u r (1) ur (2) ,…,u r (r) Update in the following manner: in, For all n and r, we have: with u k and v k Let u represent the value of the k-th update. r (n) and , The gradient of the objective function. k+1 The update method is as follows: In the formula, The step size parameter, and The iteration continues until convergence.

[0038] F p （r,n） It can be simplified to: In the above formula, , The gradient of the objective function is as follows: SGN can be defined as: For any have: The objective function can be simplified to: g r The update rules are as follows: SVD decomposition of X' yields E'. Specifically, repeating the above operation on X' yields... And retain the unitary matrices U' and V'.

[0039] S3: Using E as the training data for CP-SAE and E' as the reference data for the reconstructed data E'' in CP-SAE, learn the latent representation of smooth CP decomposition using the CP-SAE method. Specifically, S3 includes the following steps: S31: E is projected onto H through a nonlinear transformation f, where f is a Selu function, as shown in the following formula: Where W and b are the encoder's weights and biases; The autoencoder AE reconstructs E into E''; Where W' and b' are the weights and biases of the decoder.

[0040] S32: The objective function of AE1 in CP-SAE is: To learn the nonlinear representation of the BS-CP tensor decomposition algorithm.

[0041] S33: Solving for the optimal parameters of AE1 using the AutoBP algorithm. The parameter update method is as follows: Where s is the number of iterations.

[0042] S34: Using the hidden representation H1 of AE1 as the input to AE2, train AE2 according to the training method of AE1 described above, and obtain... Using the hidden representation H2 of AE2 as the input to AE3, the pre-training of AE1-AEn can be completed sequentially according to the method described for AE1, resulting in... .

[0043] S35: Connect the DAE1-DAEn stacks to form the entire CP-SAE. As the initialization parameter for each layer of CP-SAE, calculate H n For the feature space H of CP-SAE: .

[0044] S36: Calculate the reconstructed output E'' of AE: .

[0045] S37: Using the AutoBP algorithm, fine-tune the parameters of CP-SAE. When CP-SAE reaches the preset maximum number of iterations or the reconstruction error is less than the minimum set value, return the optimal parameter set. .

[0046] S4: Multiply E'' with unitary matrices U' and V' to obtain X'', and perform inverse MDT to obtain x'. N Specifically, S4 includes the following steps: S41: Reconstruct the i-th element X of the three-dimensional tensor data X'' i The formula for calculating '' is: Among them, U i ', V i ',e i '' are U' and V' respectively Find the i-th element of E'', and then find the N elements of X'' in sequence, and concatenate them to form X''.

[0047] S42: Inverse MDT Transform. The inverse MDT transform includes vectorization operations and the Moore-Penrose pseudo-inverse. .

[0048] S5: Constructing the statistic E 2 D 2 T 2 and determine control limit E 2 lim D 2 lim T 2 lim The process is monitored in real time. Specifically, in S5, the statistics constructed include: Reconstruction error statistics based on eigenvalue matrices ; Reconstruction error statistics based on 3D tensor data ; Hotelling's T based on feature space H 2 Statistic ,in, Let denoted as the mean and Φ as the covariance matrix.

[0049] The specific method for controlling limits is as follows: For offline data X N Construct E respectively 2 D 2 T 2 The statistic was used, and the control limit E was calculated using kernel density estimation. 2 lim D 2 lim T 2 lim .

[0050] The specific steps for online monitoring are as follows: standardize the sampled online data to X. M0 .

[0051] , , The process is considered normal if it is not in a normal state, and otherwise it is considered a fault state.

[0052] Incomplete chemical process data can be caused by sensor malfunctions, acquisition system failures, human error, discontinuous measurement intervals, and data transmission errors. This invention provides a method for detecting chemical process faults in cases of incomplete data. It converts two-dimensional data into a three-dimensional tensor using Multidimensional Decomposition (MDT). Linear smoothing CP and CP-SAE are used to perform linear and nonlinear predictions of the missing values, respectively, as well as to reconstruct the normal data. CP-SAE extracts the residuals and feature space of the missing process data. Combining the features extracted by smoothing CP-decomposition and CP-SAE, three statistical measures are established to achieve fault detection. Compared with existing technologies, this invention can effectively supplement missing data, meet the needs of process monitoring, and achieve high accuracy.

[0053] This invention also provides a data missing process fault detection system for chemical processes using tensor decomposition and stack autoencoder, such as... Figure 3 As shown, the system includes a processor, a computer-readable storage medium, and a computer program stored in the computer-readable storage medium and executable on the processor. When the processor executes the computer program, it implements the data missing process fault detection method for tensor decomposition and stack autoencoder as described in the above embodiments. The system is implemented by a fault detection device, which may be, but is not limited to, the following: DCS-specific software packages and hardware modules in a distributed control system (DCS); fault detection software and hardware modules in a standalone condition monitoring system integrated with the DCS via a standard interface; and servers and software for the upper-level platform.

[0054] The advantages and positive effects of this invention are: 1. This invention performs MDT transformation on the data and then considers using linear smoothing CP decomposition to supplement missing values. Addressing the issue of data nonlinearity, it combines linear smoothing CP decomposition with SAE, constructing a CP-SAE by approximating the result of the smoothing CP decomposition using SAE. The smoothing CP-SAE then generates missing value prediction data. While learning the smoothing CP decomposition, CP-SAE can extract latent features from the data. This method is equally effective for processes with both linear and nonlinear missing data, thereby improving the fault detection rate of data-incomplete chemical processes.

[0055] 2. This invention uses MDT transformation and smooth CP decomposition to solve the problems of missing data and time delay in data sample sampling, and has strong timeliness.

[0056] 3. The CP-SAE feature extraction method of this invention is robust, has higher accuracy and faster response speed than conventional linear methods.

[0057] 4. Compared with other methods, this invention is simple to operate, does not require repeated operations, and only needs to be operated on the incomplete dataset to extract the key features of the data while reconstructing the complete dataset.

[0058] The foregoing has provided a detailed description of one embodiment of the present invention, but this description is merely a preferred embodiment and should not be construed as limiting the scope of the invention. All equivalent variations and modifications made within the scope of the claims of this invention should still fall within the patent coverage of this invention.

Claims

1. A method for chemical data missing process fault detection, characterized in that: Includes the following steps, S1: Collect chemical process data under normal operating conditions. The data was obtained through standardization. ; S2: Employing a multi-directional delayed embedding transformation to transform the two-dimensional data matrix Transformed into three-dimensional tensor data Singular value decomposition is performed on each two-dimensional data in the three-dimensional tensor data X to obtain the first eigenvalue matrix E; simultaneously, smoothing CP decomposition is performed on the three-dimensional tensor data X to obtain the completed three-dimensional tensor data. The completed three-dimensional tensor data X' is subjected to singular value decomposition to obtain the second eigenvalue matrix. And retain the unitary matrix , ; S3: Using the first eigenvalue matrix E as the training data for CP-SAE, the second eigenvalue matrix... Using CP-SAE as reference data, the latent representation of smooth CP decomposition is learned using the CP-SAE method, and the reconstructed eigenvalue matrix E'' and feature space H are obtained; S4: multiplying the reconstructed eigenvalue matrix E" with the unitary matrices U', V' to obtain reconstructed three-dimensional tensor data X", performing inverse multidirectional delay embedding transformation on the reconstructed three-dimensional tensor data X" to obtain reconstructed two-dimensional process data X N ' S5: based on the reconstructed eigenvalue matrix E", the reconstructed three-dimensional tensor data X" and the feature space H, construct a statistic E 2 , D 2 , T 2 , and determine the control limit E 2 lim , D 2 lim , T 2 lim Real-time monitoring of the process.

2. The method for detecting missing data in a chemical process according to claim 1, characterized in that: In the S1, the chemical process original data X0= [x1,..., x N ]∈R L×N , Where L represents the number of process variables and N represents the number of data sampling points; The missing value position in the data is supplemented as 0, and the two-dimensional data matrix X N The standardization calculation method is as follows: 。 3. A method for detecting faults in a chemical process with missing data according to claim 1 or 2, characterized in that: In S2, the multi-directional delay embedding transform sampling point sequence is: MDT will Transform into The matrix is: Where L is the sequence length, Let be the number of iterations of the transformation. The forward representation of the MDT is: Includes copy and fold operations. MDT is specifically represented as: , assuming The input data consists of multiple sequences. "," "," "" indicates a matrix multiplication operation on the Nth dimension.

4. A method for detecting faults in a chemical process with missing data according to claim 1 or 2, characterized in that: In S2, the smooth CP decomposition is achieved by minimizing the following objective function: Where X is the input tensor; X' is the CP tensor for data completion; and T represents the observation tensor. The coordinates representing the non-missing values ​​of T; The coordinates representing the missing values ​​of T; L represents the smoothing parameter. (n) The matrix represents the smoothing constraint matrix; p represents the normal form type; F is the normal form type. Represents the cross product of vectors; g r R is an adjustable parameter; R is the rank of the CP decomposition tensor X, and N is the ordinal number of tensor X. r Let be the factor matrix of the smooth BS decomposition; the first term in the above equation is the CP decomposition reconstruction error, and the second term is the smooth decomposition constraint matrix.

5. A method for detecting faults in a chemical process with missing data according to claim 1 or 2, characterized in that: S3 includes the following steps: S31: E is projected onto H through a nonlinear transformation f, where f is a Selu function, as shown in the following formula: Where W and b are the encoder's weights and biases; The autoencoder AE reconstructs E into E''; Where W' and b' are the weights and biases of the decoder; S32: The objective function of AE1 in CP-SAE is: To learn the nonlinear representation of the BS-CP tensor decomposition algorithm; S33: Solving for the optimal parameters of AE1 using the AutoBP algorithm. The parameter update method is as follows: Where s is the number of iterations; S34: Using the hidden representation H1 of AE1 as the input to AE2, train AE2 according to the training method of AE1 described above, and obtain... Using the hidden representation H2 of AE2 as the input to AE3, the pre-training of AE1-AEn is completed sequentially according to the method described for AE1, resulting in... ; S35: Connect the DAE1-DAEn stacks to form the entire CP-SAE. As the initialization parameter for each layer of CP-SAE, calculate H n For the feature space H of CP-SAE: ； S36: Calculate the reconstructed output E'' of AE: ； S37: Using the AutoBP algorithm, fine-tune the parameters of CP-SAE. When CP-SAE reaches the preset maximum number of iterations or the reconstruction error is less than the minimum set value, return the optimal parameter set. .

6. A method for detecting faults in a chemical process with missing data according to claim 1 or 2, characterized in that: S4 includes the following steps: S41: reconstructing an i-th element X of the three-dimensional tensor data X" i The calculation formula of X is: wherein U i ', V i ', e i are the i-th elements of U', V', E'', respectively, and the N elements of X'' are obtained successively, concatenated into X''. S42: Inverse MDT Transform. The inverse MDT transform includes vectorization operations and the Moore-Penrose pseudo-inverse. ； for Moore-Penrose pseudo-reversal, "," "," "" indicates a matrix multiplication operation on the Nth dimension.

7. A method for detecting faults in a chemical process with missing data according to claim 1 or 2, characterized in that: In S5, the constructed statistics include: Reconstruction error statistics based on eigenvalue matrices ; Reconstruction error statistics based on 3D tensor data ; Hotelling's T based on feature space H 2 Statistic ,in, Let denoted as the mean and Φ as the covariance matrix.

8. A fault detection system for missing chemical data processes, characterized in that: The chemical data missing process fault detection method according to any one of claims 1 to 7 is implemented.

9. A computer device comprising a memory, a processor, and an algorithm stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, it implements the data processing method as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer algorithm, characterized in that, When the computer algorithm is executed by the processor, it performs the data processing as described in any one of claims 1 to 7.

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