Process monitoring method based on space-time fusion preserving embedding

Abstract

The invention provides a process monitoring method based on space-time fusion preserving embedding, relates to the technical field of industrial process monitoring, and aims to extract and store local and global space structures of a data set by learning density information of samples. Meanwhile, local and global features are extracted on a time sequence to retain dynamic features of the data set, and the original distribution relation of the data set after dimension reduction is more fully maintained. Dynamic features of a time sequence of a data set are fully mined, the influence of local time neighbor samples of samples is maximized, and meanwhile, the correlation of global non-time neighbor samples is reduced. Dimension reduction projection is carried out based on the information, abnormal working conditions are detected, and the process monitoring accuracy is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of industrial process monitoring, and in particular to a process monitoring method based on time-space fusion and embedded maintenance. Background Art

[0002] Modern industrial processes are becoming increasingly complex, characterized by larger scale, more processing variables, and greater uncertainty and variability in production. The data sets generated by these complex industrial processes are characterized by large data volume, diversity, and multi-dimensional correlation. Therefore, effective monitoring of industrial processes is particularly important. Reliable monitoring systems can ensure employee safety, support preventive maintenance measures, minimize economic losses, and improve product quality. Under this trend, the demand for monitoring complex industrial processes continues to increase, and establishing efficient process monitoring methods to detect abnormal events and prevent failures has become an urgent need in today's era.

[0003] The data-driven method is the most commonly used industrial process monitoring method. It regards the industrial process as a black box and only requires sufficient and accurate process data without additional system theory or strict process modeling technology. It can easily monitor various complex production processes. Scholars have conducted extensive exploration and research on data-driven process monitoring methods, among which multivariate statistical process monitoring (MSPM) has received widespread attention and application due to its moderate modeling cost. Common MSPM methods include principal component analysis and independent component analysis. These methods use multivariate projection to convert the high-dimensional process variable set in the industrial process into a low-dimensional subspace, extract the key feature information in the original data set, and perform real-time statistical analysis to detect abnormal conditions.

[0004] Although previous studies have shown promising results, these methods still have the problem of insufficient mining of the original spatial structure of the data in the learning of subspaces, and do not effectively preserve the complete temporal dynamics and spatial structure. These studies often ignore certain aspects, such as the density information of the original data during the projection process, resulting in the inability to fully capture the essential characteristics of the original data. Specific abnormal information may be lost, reducing the accuracy of the model. In view of the above dilemma, it is urgent to develop a new process monitoring method to cope with the task of detecting abnormal events in complex industrial processes. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention provides a process monitoring method based on spatiotemporal fusion and embedding preservation to complete the task of detecting abnormal events in complex industrial processes. By learning the density information of the samples, the local and global spatial structures of the data set are extracted and preserved. At the same time, local and global features are extracted on the time series to retain the dynamic features of the data set, and the original distribution relationship of the data set after dimensionality reduction is more fully maintained.

[0006] The technical solution adopted by the present invention is:

[0007] A process monitoring method based on spatiotemporal fusion and embedding preservation includes the following steps:

[0008] Step 1: Collect the data of the industrial process under normal working conditions and perform standardization to obtain the offline training data set X = (x1, x2, ..., x n ), where X∈R m×n Indicates that the data set contains n samples, m represents the feature dimension of the original sample space, R m×n represents an m×n dimensional real matrix, x i ∈R m represents the i-th sample, R m represents an m-dimensional real vector;

[0009] Step 2: Based on the offline training dataset X obtained in step 1, learn and maintain the spatial distribution of samples for dimensionality reduction projection; learn the projection matrix P, P∈R m×d , where d represents the feature dimension of the latent subspace mapped to; learn the dense or sparse sample distribution density relationship around X; first use local preservation projection to capture the local structure, and use the k-nearest neighbor algorithm to obtain the neighborhood of the sample, calculate the distance between the sample neighborhood and the cluster center, and establish the local density coefficient matrix of the data set to describe the distribution of each sample neighborhood;

[0010] Step 2 is as follows:

[0011] Define each sample point x in the industrial process data set i There exists a neighborhood Ne(x i ), sample point x j ∈Ne(x i ) is the sample point x i Neighboring points; judge each neighboring point x j Impact: Define k as the number of neighbors of the sample and calculate the sample point x i The center of the neighborhood x i-core ,have Calculate x i Samples in the neighborhood to the center x i-core The average distance R i ,have Calculate from the neighborhood Ne(x i ) to remove the sample point x j The average distance Rout from the remaining neighboring points to the new center ij , for each sample x i and its nearest neighbors x j , define the local density coefficient matrix ρ, ρ∈Rn×n , where the element ρ ij is represented as:

[0012]

[0013] According to the local preservation projection algorithm, the adjacency matrix W of the data sample is obtained, and the local density coefficient matrix ρ is used to update the adjacency matrix W, and the local density coefficient adjacency matrix W is defined * , the element W in the matrix * ij =ρ ij ×W ij ; The optimization problem of sample potential subspace projection is as follows:

[0014]

[0015] Where T is the matrix transpose, construct the diagonal matrix D∈R n×n , let the diagonal elements D ii =Σ j W * ij , then construct the Laplace matrix L = DW * ,The optimization problem of formula (2) is transformed into the objective function:

[0016]

[0017] where tr() is the matrix trace.

[0018] Step 3: Explore the influence of non-neighboring points, save and extract the global geometric space structure of the sample;

[0019] The details are as follows:

[0020] Define each sample point x in the offline training dataset i There exists a neighborhood Ne(x i ), sample point x k is the sample point x i Non-neighboring points, sample points x k There exists a neighborhood Ne(x k ); define the center of the union of the two sets of neighborhoods as x i,k-core , where n ij Represents the number of samples in the union; define Rn ik Represents the union of two sets of neighborhoods to their center x i,k-core The average distance Define the center of all sample points as x core , all samples to x core The average distance is For each sample x i and its non-neighbors xk , define the global density coefficient matrix ρglobal, ρglobal∈R n×n , where the element ρglobal ik is represented as:

[0021]

[0022] The optimization problem of sample latent subspace projection is formulated as:

[0023]

[0024] Construct a diagonal matrix E∈R n×n , whose diagonal elements E ii =Σ j ρglobal ik , then let V = E-ρglobal, the objective function of the optimization problem of formula (5) is as follows:

[0025]

[0026] Step 4: Define the local time correlation as the correlation between the sample point and its neighboring points in the time series, and define the global time correlation as the correlation between the sample and its non-neighboring points in the time series; specify the local time neighbor range, select the a samples closest to the sample in the time series as the time neighbors of the sample point, and construct the local time relationship matrix A∈R accordingly. n×n , any element A in the matrix ij It is expressed as:

[0027]

[0028] The objective function of the latent subspace projection is established to maximize the local temporal correlation:

[0029]

[0030] Define the identity matrix I∈R n×n , let the matrix Formula (7) is rearranged into the objective function:

[0031]

[0032] Select the non-temporal neighbors of the sample to construct the global temporal relationship matrix B∈R n×n , any element B in the matrix ij It is expressed as:

[0033]

[0034] The objective function of the latent subspace projection is established to minimize the global temporal correlation:

[0035]

[0036] Let the matrix The objective function (10) can be rearranged as:

[0037]

[0038] Step 5: Combine the objective functions (3), (5), (8), and (11) of steps 2, 3, and 4 to form a unified joint objective function of the spatiotemporal fusion preserving embedding method as follows:

[0039]

[0040] The latent subspace projection matrix P = [p1, p2, ..., p d ], p∈R m×1 represents the projection vector in the projection matrix P; the joint objective function of equation (12) is transformed into the following optimization problem to solve the projection vector p:

[0041]

[0042] Using the Lagrange multiplier method, the projection vector p is obtained by calculating the eigenvector of the following formula:

[0043]

[0044] At this point, the latent subspace projection matrix P consists of the eigenvectors corresponding to the first d largest eigenvalues;

[0045] Step 6: Project the training data set X into the feature space and residual space through the projection matrix P obtained in step 5, and then establish the detection statistic T in the two spaces respectively. 2 , SPE, and then get the joint detection statistic And the control limit of the joint detection statistic is obtained according to the kernel density method for anomaly detection; when a sample x is given * When , its combined monitoring indicators are:

[0046]

[0047] Where P * =P(P T P) -1 ,Σ=P *T XX T P * / (n-1) is the covariance matrix of the latent subspace from the offline training dataset. T 2 α and SPE αHotelling T is one of the two commonly used monitoring indicators in process monitoring. 2 The control limits of the sum squared prediction error SPE are determined by the kernel density estimation method, and α is the significance level;

[0048] Step 7: The joint detection statistic obtained by step 6 (15) Determining control limits by kernel density estimation Use Control Limits To determine whether an exception occurs at the current moment, the specific method is:

[0049] Given an online detection sample x new , and standardize it; use the projection matrix P obtained in step 5, and then new Substitute into equation (15) in step 6 to calculate x new The joint detection statistic if If an abnormal event occurs in the industrial process at the current moment, it is determined that the industrial process is in normal operation.

[0050] The beneficial effects of adopting the above technical solution are:

[0051] The present invention provides a process monitoring method based on time-space fusion and embedded preservation. In the study, the local and global structures in the time series and spatial structure of the data set are fully extracted for dimensionality reduction projection. More original data information is retained to improve monitoring performance. Density information is used to capture the geometric spatial structure of the data set. In process monitoring, the data distribution under normal conditions is relatively concentrated and dense, while the distribution of abnormal data is far from normal data and is relatively sparse. This density relationship is used to fully retain the local-global structure in the sample geometric space, so that the mapped subspace is closer to the original distribution of the data. The dynamic characteristics of the time series of the data set are fully explored, the influence of the local time neighbor samples of the sample is maximized, and the correlation of the global non-time neighbor samples is reduced. Based on the above information, dimensionality reduction projection is performed, and abnormal conditions are detected to improve the accuracy of process monitoring. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 A process flow chart of the Tennessee Eastman process provided for an embodiment of the present invention;

[0053] Figure 2 A flow chart of a process monitoring method based on spatiotemporal fusion and embedding maintenance provided by an embodiment of the present invention;

[0054] Figure 3 The abnormal detection result of the specific fault 10 provided by the embodiment of the present invention;

[0055] Figure 4The abnormal detection result of the specific fault 16 provided by the embodiment of the present invention;

[0056] Figure 5 The abnormal detection result of the specific fault 17 provided by the embodiment of the present invention;

[0057] Figure 6 The abnormal detection result of the specific fault 20 provided by the embodiment of the present invention. DETAILED DESCRIPTION

[0058] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0059] A process monitoring method based on spatiotemporal fusion to maintain embedding, such as Figure 2 As shown, the following steps are included:

[0060] Step 1: Collect the data of the industrial process under normal working conditions and perform standardization to obtain the offline training data set X = (x1, x2, ..., x n ), where X∈R m×n Indicates that the data set contains n samples, m represents the feature dimension of the original sample space, R m×n represents an m×n dimensional real matrix, x i ∈R m represents the i-th sample, R m represents an m-dimensional real vector;

[0061] This embodiment is based on Matlab tools, using Figure 1 The Tennessee Eastman process shown is used to illustrate the method of the present invention. 33 variables in the Tennessee Eastman process are selected, including 22 process variables and 11 operating variables, and the effect of the method of the present invention is demonstrated in conjunction with the accompanying drawings.

[0062] In this embodiment, X∈R 33×500 , that is, there are 500 samples in X, and the dimension of each sample is 33 dimensions.

[0063] Step 2: Based on the offline training dataset X obtained in step 1, learn and maintain the spatial distribution of samples for dimensionality reduction projection; learn the projection matrix P, P∈R m×d , where d represents the feature dimension of the latent subspace mapped to; learn the dense or sparse sample distribution density relationship around X; first use local preservation projection to capture the local structure, and use the k-nearest neighbor algorithm to obtain the neighborhood of the sample, calculate the distance between the sample neighborhood and the cluster center, and establish the local density coefficient matrix of the data set to describe the distribution of each sample neighborhood;

[0064] Step 2 is as follows:

[0065] Define each sample point x in the industrial process data set i There exists a neighborhood Ne(x i ), the industrial process data set contains industrial process data, sample point x j ∈Ne(x i ) is the sample point x i The neighboring points of x are determined from the density perspective. j Impact: Define k as the number of neighbors of the sample and calculate the sample point x i The center of the neighborhood x i-core ,have Calculate x i Samples in the neighborhood to the center x i-core The average distance R i ,have Calculate from the neighborhood Ne(x i ) to remove the sample point x j The average distance Rout from the remaining neighboring points to the new center ij , for each sample x i and its nearest neighbors x j , define the local density coefficient matrix ρ, ρ∈R n×n , where the element ρ ij is represented as:

[0066]

[0067] According to the local preservation projection algorithm, the adjacency matrix W of the data sample is obtained, and the local density coefficient matrix ρ is used to update the adjacency matrix W, and the local density coefficient adjacency matrix W is defined * , the element W in the matrix * ij =ρ ij ×W ij ; The optimization problem of sample potential subspace projection is as follows:

[0068]

[0069] Where T is the matrix transpose, construct the diagonal matrix D∈R n×n , let the diagonal elements D ii =Σ j W * ij , then construct the Laplace matrix L = DW * ,The optimization problem of formula (2) is transformed into the objective function:

[0070]

[0071] Where tr() is the matrix trace. In this embodiment, the number of nearest neighbors k of the sample is set to 30.

[0072] Step 3: Explore the influence of non-neighboring points, save and extract the global geometric space structure of the sample;

[0073] The details are as follows:

[0074] Define each sample point x in the offline training dataset i There exists a neighborhood Ne(x i ), sample point x k is the sample point x i Non-neighboring points, sample points x k There exists a neighborhood Ne(x k ); define the center of the union of the two sets of neighborhoods as x i,k-core , where n ij Represents the number of samples in the union; define Rn ik Represents the union of two sets of neighborhoods to their center x i,k-core The average distance Define the center of all sample points as x core , all samples to x core The average distance is For each sample x i and its non-neighbors x k , define the global density coefficient matrix ρglobal, ρglobal∈R n×n , where the element ρglobal ik is represented as:

[0075]

[0076] The optimization problem of sample latent subspace projection is formulated as:

[0077]

[0078] Construct a diagonal matrix E∈R n×n , whose diagonal elements E ii =Σ j ρglobal ik , then let V = E-ρglobal, the objective function of the optimization problem of formula (5) is as follows:

[0079]

[0080] Step 4: Define the local time correlation as the correlation between the sample point and its neighboring points in the time series, and define the global time correlation as the correlation between the sample and its non-neighboring points in the time series; specify the local time neighbor range, select the a samples closest to the sample in the time series as the time neighbors of the sample point, and construct the local time relationship matrix A∈R accordingly. n×n , any element A in the matrix ij It is expressed as:

[0081]

[0082] The objective function of the latent subspace projection is established to maximize the local temporal correlation:

[0083]

[0084] Define the identity matrix I∈R n×n , let the matrix Formula (7) is rearranged into the objective function:

[0085]

[0086] Select the non-temporal neighbors of the sample to construct the global temporal relationship matrix B∈R n×n , any element B in the matrix ij It is expressed as:

[0087]

[0088] The objective function of the latent subspace projection is established to minimize the global temporal correlation:

[0089]

[0090] Let the matrix The objective function (10) can be rearranged as:

[0091]

[0092] In this embodiment, the number a of time neighbor points of the sample is set to 12.

[0093] Step 5: In order to fully extract the local and global structural information in the time series and spatial structure of the dataset, it is necessary to combine the objective functions (3), (5), (8), and (11) of steps 2, 3, and 4 to form a unified joint objective function of the spatiotemporal fusion preserving embedding method as follows:

[0094]

[0095] The latent subspace projection matrix P = [p1, p2, ..., p d ], p∈Rm×1 represents the projection vector in the projection matrix P; the joint objective function of equation (12) is transformed into the following optimization problem to solve the projection vector p:

[0096]

[0097] Using the Lagrange multiplier method, the projection vector p is obtained by calculating the eigenvector of the following formula:

[0098]

[0099] At this point, the latent subspace projection matrix P consists of the eigenvectors corresponding to the first d largest eigenvalues;

[0100] In this embodiment, the dimension d of the potential subspace projection matrix P is set to 31.

[0101] Step 6: Project the training data set X into the feature space and residual space through the projection matrix P obtained in step 5, and then establish the detection statistic T in the two spaces respectively. 2 , SPE, and then get the joint detection statistic And the control limit of the joint detection statistic is obtained according to the kernel density method for anomaly detection; when a sample x is given * When , its combined monitoring indicators are:

[0102]

[0103] Where P * =P(P T P) -1 ,Σ=P *T XX T P * / (n-1) is the covariance matrix of the latent subspace from the offline training dataset. T 2 α and SPE α Hotelling T is one of the two commonly used monitoring indicators in process monitoring. 2 The control limits of the sum squared prediction error SPE are determined by the kernel density estimation method, where α is the significance level; in this embodiment, α = 99%; the control limits of the joint test statistic are obtained according to the kernel density method

[0104] Step 7: After the offline training is completed, the online detection phase is carried out; in this phase, industrial process data is collected in real time, and the joint detection statistic obtained by step 6 (15) is Determining control limits by kernel density estimation Use Control Limits To determine whether an exception occurs at the current moment, the specific method is:

[0105] Given an online detection sample x new , and standardize it; use the projection matrix P obtained in step 5, and then new Substitute into equation (15) in step 6 to calculate x new The joint detection statistic if If an abnormal event occurs in the industrial process at the current moment, it is determined that the industrial process is in normal operation.

[0106] In this embodiment, specific faults 10, 16, 17 and 20 are used as test data respectively. Each test data contains 960 samples, and an abnormality occurs at the 161st sample moment. Figure 3 to Figure 6 The anomaly detection results of the method of the present invention for specific fault 10, specific fault 16, specific fault 17 and specific fault 20 are respectively shown; it can be seen that the method of the present invention can effectively detect anomalies and has the highest anomaly detection rate (86.00%, 87.88%, 95.63% and 89.25% respectively).

[0107] In order to verify the anomaly detection effect of the method of the present invention, this embodiment also compares the method of the present invention with several typical process monitoring methods. Specifically, the local preservation projection method and the kernel independent element analysis method are selected as comparison methods and compared in the same industrial process monitoring case. Figure 3 The abnormal detection result of fault 10 is shown in FIG. Figure 4 The abnormal detection result of fault 16 is shown in FIG. Figure 5 The following is the abnormal detection result of fault 17; Figure 6 The abnormal detection result of fault 20 is shown.

[0108] The comparison results of anomaly detection rates are shown in Table 1. It can be seen from the comparison that the method of the present invention has the best performance.

[0109] Table 1 Anomaly detection rate of several fault methods (%)

[0110] Locality Preserving Projection Nuclear-independent meta-analysis Spatiotemporal fusion maintains embedding Fault 10 58.25 56.63 86.00 Fault 16 47.50 45.00 87.88 Fault 17 8.75 22.00 95.63 Fault 20 59.00 61.00 89.25

[0111] The above description is only a preferred embodiment of the present disclosure and an explanation of the technical principles used. Those skilled in the art should understand that the scope of the invention involved in the embodiments of the present disclosure is not limited to the technical solutions formed by a specific combination of the above-mentioned technical features, but should also cover other technical solutions formed by any combination of the above-mentioned technical features or their equivalent features without departing from the above-mentioned inventive concept. For example, the above-mentioned features are replaced with the technical features with similar functions disclosed in the embodiments of the present disclosure (but not limited to) to form a technical solution.

Claims

1. A process monitoring method based on spatiotemporal fusion and embedding preservation, characterized in that: The following steps are involved: Step 1: Collect the data of the industrial process under normal working conditions and perform standardization to obtain the offline training data set X = (x1, x2, ..., x n ), where X∈R m×n Indicates that the data set contains n samples, m represents the feature dimension of the original sample space, R m×n represents an m×n dimensional real matrix, x i ∈R m represents the i-th sample, R m represents an m-dimensional real vector; Step 2: Based on the offline training dataset X obtained in step 1, learn and maintain the spatial distribution of samples for dimensionality reduction projection; learn the projection matrix P, P∈R m×d , where d represents the feature dimension of the latent subspace mapped to; learn the dense or sparse sample distribution density relationship around X; first use local preservation projection to capture the local structure, and use the k-nearest neighbor algorithm to obtain the neighborhood of the sample, calculate the distance between the sample neighborhood and the cluster center, and establish the local density coefficient matrix of the data set to describe the distribution of each sample neighborhood; Step 3: Explore the influence of non-neighboring points, save and extract the global geometric space structure of the sample; Step 4: Define the local time correlation as the correlation between the sample point and its neighboring points in the time series, and define the global time correlation as the correlation between the sample and its non-neighboring points in the time series; specify the local time neighbor range, select the a samples closest to the sample in the time series as the time neighbors of the sample point, and construct the local time relationship matrix A∈R accordingly. n×n ; Step 5: Construct the joint objective function of the spatiotemporal fusion embedding preservation method; Step 6: Project the training data set X into the feature space and residual space through the projection matrix P, and then establish the detection statistic T in the two spaces respectively. 2 , SPE, and then get the joint detection statistic And the control limits of the joint detection statistics are obtained according to the kernel density method for anomaly detection; Step 7: The joint detection statistic obtained in step 6 Determining control limits by kernel density estimation Use Control Limits To determine whether an exception occurs at the current moment.

2. A process monitoring method based on spatiotemporal fusion and embedding according to claim 1, characterized in that: The step 2 is specifically as follows: Define each sample point x in the industrial process data set i There exists a neighborhood Ne(x i ), sample point x j ∈Ne(x i ) is the sample point x i Neighboring points; judge each neighboring point x j Impact: Define k as the number of neighbors of the sample and calculate the sample point x i The center of the neighborhood x i-core ,have Calculate x i Samples in the neighborhood to the center x i-core The average distance R i ,have Calculate from the neighborhood Ne(x i ) to remove the sample point x j The average distance Rout from the remaining neighboring points to the new center ij , for each sample x i and its nearest neighbors x j , define the local density coefficient matrix ρ, ρ∈R n×n , where the element ρ ij is represented as: According to the local preservation projection algorithm, the adjacency matrix W of the data sample is obtained, and the local density coefficient matrix ρ is used to update the adjacency matrix W, and the local density coefficient adjacency matrix W is defined * , the element W in the matrix * ij =ρ ij ×W ij ; The optimization problem of sample potential subspace projection is as follows: Where T is the matrix transpose, construct the diagonal matrix D∈R n×n , let the diagonal elements D ii =Σ j W * ij , then construct the Laplace matrix L = DW * ,The optimization problem of formula (2) is transformed into the objective function: where tr() is the matrix trace.

3. The process monitoring method based on spatiotemporal fusion and embedding according to claim 2 is characterized in that: The step 3 is as follows: Define each sample point x in the offline training dataset i There exists a neighborhood Ne(x i ), sample point x k is the sample point x i Non-neighboring points, sample points x k There exists a neighborhood Ne(x k ); define the center of the union of the two sets of neighborhoods as x i,k-core , where n ij Represents the number of samples in the union; define Rn ik Represents the union of two sets of neighborhoods to their center x i,k-core The average distance Define the center of all sample points as x core , all samples to x core The average distance is For each sample x i and its non-neighbors x k , define the global density coefficient matrix ρglobal, ρglobal∈R n×n , where the element ρglobal ik is represented as: The optimization problem of sample latent subspace projection is formulated as: Construct a diagonal matrix E∈R n×n , whose diagonal elements E ii =Σ j ρglobal ik , then let V = E-ρglobal, the objective function of the optimization problem of formula (5) is as follows:

4. The process monitoring method based on spatiotemporal fusion and embedding according to claim 3 is characterized in that: Any element A in the local time relationship matrix described in step 4 ij It is expressed as: The objective function of the latent subspace projection is established to maximize the local temporal correlation: Define the identity matrix I∈R n×n , let the matrix Formula (7) is rearranged into the objective function: Select the non-temporal neighbors of the sample to construct the global temporal relationship matrix B∈R n×n , any element B in the matrix ij It is expressed as: The objective function of the latent subspace projection is established to minimize the global temporal correlation: Let the matrix The objective function (10) can be rearranged as:

5. The process monitoring method based on spatiotemporal fusion and embedding preservation according to claim 4 is characterized in that: The step 5 is specifically: combining the objective functions (3), (5), (8), and (11) of steps 2, 3, and 4 to form a unified joint objective function of the spatiotemporal fusion preserving embedding method as follows: The latent subspace projection matrix P = [p1, p2, ..., p d ], p∈R m×1 represents the projection vector in the projection matrix P; the joint objective function of equation (12) is transformed into the following optimization problem to solve the projection vector p: Using the Lagrange multiplier method, the projection vector p is obtained by calculating the eigenvector of the following formula: At this point, the potential subspace projection matrix P consists of the eigenvectors corresponding to the first d largest eigenvalues.

6. A process monitoring method based on spatiotemporal fusion and embedding according to claim 5, characterized in that: The specific step 6 is: when a sample x is given * When , its combined monitoring indicators are: Where P * =P(P T P) -1 ,Σ=P *T XX T P * / (n-1) is the covariance matrix of the latent subspace from the offline training dataset; T 2 α and SPE α Hotelling T is one of the two commonly used monitoring indicators in process monitoring. 2 The control limits of the sum squared prediction error SPE are determined by the kernel density estimation method, and α is the significance level.

7. A process monitoring method based on spatiotemporal fusion and embedding preservation according to claim 6, characterized in that: The step 7 is specifically as follows: Given an online detection sample x new , and standardize it; use the projection matrix P obtained in step 5, and then new Substitute into equation (15) in step 6 to calculate x new The joint detection statistic if If an abnormal event occurs in the industrial process at the current moment, it is determined that the industrial process is in a normal operating state.

Images