A method for detecting faults of related and independent chemical processes based on SDAE-LSVDD

Abstract

This invention designs a fault detection method for chemical processes based on SDAE-LSVDD with correlated and independent variables. The method includes: collecting chemical process data X0 under normal operating conditions and standardizing the data to obtain data X. N The mutual information p between each data point is calculated. i And the mutual information q between each data point and the random Gaussian distribution. i X N Divided into the relevant variable space X NR and the space of independent variables X NI Using relevant variable spatial data X NR Train the SDAE and find its optimal parameter set θ; use data X from the independent variable space. NI Train the LSVDD and calculate its radius R; use SDAE to calculate the characteristic space H and residual space R of the relevant variable space, and calculate T. 2 The sum and Q statistic are obtained using kernel density estimation. lim ; Use SDAE to calculate the relevant variable space X MR The feature space and residual space are calculated, and T is calculated. 2 The Q statistic and the Q statistic are used to calculate the independent variable space X. MI The distance D from the data point to the center of the LSVDD circle is calculated; the statistical value is compared with the control limit, and the distance from the data point to the center of the circle is compared with the radius to achieve online real-time monitoring.

Description

Technical Field

[0001] This invention relates to the field of chemical production process monitoring, and in particular to a method for detecting faults in chemical processes based on SDAE-LSVDD with both correlated and independent variables. Background Technology

[0002] With the continuous expansion of modern industry, monitoring industrial processes plays a crucial role in ensuring safe production and product quality. To improve system reliability and stability, a new, efficient algorithm for control systems is needed for fault detection and diagnosis. In modern industry, vast amounts of data are collected and stored as a tool, representing the results of distributed control systems and computer science applications. The relationships between variables in actual industrial processes are complex. Some variables are linearly correlated, while others are non-linearly correlated, and some are independent. Existing research on multi-block or multi-space process monitoring rarely emphasizes the independence and correlation of variables. However, many variables are independent of other variables. Therefore, variables should be categorized into independent and correlated variables for independent monitoring.

[0003] The Stacked Denoising Autoencoder (SDAE) possesses strong data reconstruction capabilities. During data reconstruction, it effectively extracts data features, demonstrating excellent performance in anomaly detection tasks. It can effectively extract features from nonlinear data and realize the extraction of latent features from related variables, thereby achieving fault detection. The Support Vector Data Description (SVDD) algorithm has good fault detection capabilities for independent data, while the Lagrange Support Vector Data Description (LSVDD) algorithm is an improved version of SVDD. It has lower complexity, faster solution speed, higher accuracy, and is more suitable for practical industrial situations. Therefore, this invention proposes a fault detection method for chemical processes based on SDAE-LSVDD for related and independent variables. Summary of the Invention

[0004] The purpose of this invention is to overcome the influence of independent and correlated variables and to use a more advanced method to monitor the space of correlated and independent variables, thereby proposing a chemical process fault detection method based on SDAE-LSVDD for correlated and independent variables.

[0005] The objective of this invention can be achieved through the following solutions:

[0006] A fault detection method for chemical processes based on SDAE-LSVDD with correlated and independent variables, comprising the following steps:

[0007] Step S1: Collect chemical process data X0 under normal operating conditions and standardize it to obtain data X. N ;

[0008] Step S2: Calculate the mutual information p between each data point. i And the mutual information q between each data point and the random Gaussian distribution. i X N Divided into the relevant variable space X NR and the space of independent variables X NI ;

[0009] Step S3: Use the relevant variable space data X NR Train the SDAE and find the optimal set of parameters θ for the SDAE;

[0010] Step S4: Use data X from the independent variable space NI Train the LSVDD and calculate its radius R.

[0011] Step S5: Use SDAE to obtain the characteristic space H and residual space R of the relevant variable space, and calculate T. 2 The Q statistic is obtained using kernel density estimation. and Q lim ;

[0012] Step S6: Collect online data and standardize it to obtain data X. M ;

[0013] Step S7: According to the relevant variable space X in step S2 NR and the space of independent variables X NI The same variable, X M Divided into the relevant variable space X MR and the space of independent variables X MI ;

[0014] Step S8: Calculate the relevant variable space X using SDAE MR The feature space and residual space are calculated, and T is calculated. 2 The Q statistic and the Q statistic are used to calculate the independent variable space X. MI The distance D from the data in the data to the center of the LSVDD circle;

[0015] Step S9: Compare the statistic with the control limit, and the distance from the data point to the center of the circle with the radius, to achieve online real-time monitoring.

[0016] The raw data for the chemical process is single-modal chemical data, wherein the raw data X0 = [x1, ..., x S ]∈R V×S Where V represents the number of process variables, and S represents the number of data sampling points; the X N The calculation method is as follows:

[0017]

[0018] Preferably, step S2 specifically involves x i and x j For data X N Two data points in the dataset.

[0019] Step S201: Calculate the mutual information p between data points i ;

[0020] Assume variable x i ∈R 1×S and x j ∈R 1×S The joint probability density p(x) i ,x j ),variable x i and x j The marginal distribution law can be expressed as p(x) i )=∫p(x i ,x j )dx j and p(x) i )=∫p(x i ,x j )dx j Mutual information p ij It can be represented as:

[0021]

[0022] Then x i The mutual information with S-1 samples is p i =[p i1 ,p2,…,p iS-1 ].

[0023] Step S202: Calculate the mutual information between the data points and the random Gaussian distribution;

[0024] Suppose a random Gaussian variable X g ∈R V-1×S , where X g All sample points in the dataset follow a Gaussian distribution.

[0025] x i and x g The joint probability density p(x) i ,x g ), mutual information q ij for:

[0026]

[0027] Then x i The mutual information with S-1 Gaussian samples is q i =[qi1 ,q2,…,q iS-1 ].

[0028] In steps S201 and S202, the conditions for determining whether a variable is a correlated variable or an independent variable are as follows: Then x i If they are related variables, then they are independent variables.

[0029] Preferably, in step S3, relevant variable space data X is used. NR Training the SDAE and obtaining its optimal parameter set θ involves the following steps:

[0030] Step S301: Project q D X NR Partial damage is Right now

[0031] Step S302: After a nonlinear transformation f is projected onto the implicit representation h, f is chosen as a tanh function.

[0032]

[0033] Where W and b are the weights and biases of the encoding process.

[0034] Step S303: Reconstruct h1 into r using a similar nonlinear transformation.

[0035] r=f(W'h1+b') (5)

[0036] Where W' and b' are the weights and biases of the decoding process.

[0037] Step S304: Train DAE1 with the goal of minimizing the reconstruction error:

[0038]

[0039] Step S305: Using the gradient descent algorithm, solve for the optimal parameters θ = {W, b, W', b'} of DAE1, where the parameter update method is as follows:

[0040]

[0041] Where t is the number of iterations.

[0042] Step S305: Use the hidden representation h1 of DAE1 as the input of DAE2, and complete the training of DAE2 according to the training method of DAE1 to obtain θ2. Use the hidden representation h2 of DAE2 as the input of DAE3, and complete the pre-training of DAE1-DAEn sequentially according to the method of DAE1 to obtain θ1~θ n .

[0043] Step S306: Connect DAE1-DAEn layer by layer to form the entire SDAE, and connect θ1 to θ n As the initialization parameter for each layer of SDAE, h is calculated. n For the feature space h of SDAE:

[0044] h = h n =f(W n-1 h n-1 +b n-1 (6);

[0045] Step S307: Calculate the reconstructed output r of the DAE:

[0046]

[0047] Step S308: Use the gradient descent algorithm to fine-tune the parameters of SDAE. When SDAE reaches the set number of iterations or the error is less than the set value of 0.001, the optimal parameter set θ is obtained.

[0048] Preferably, in step S4, data X from the independent variable space is used. NI The specific steps for training an LSVDD and calculating its radius R are as follows:

[0049] Step S401: Project the original data into a high-dimensional feature space through a nonlinear transformation, i.e., Φ:x→F.

[0050] The inner product in the feature space is K(x,y)=Φ(x). T Φ(y)=exp(-||xy|| 2 The problem of LSVDD is to find a minimal hypersphere that encloses all the data.

[0051]

[0052] Where a and R are the center and radius of the hypersphere, respectively. Parameter C controls the volume and tolerance for error of the hypersphere. ξ i As a slack variable, it allows some data to extend beyond the hypersphere.

[0053] Step S402: The dual problem of this problem can be transformed into:

[0054]

[0055]

[0056] Where α i It is a Lagrange multiplier. 0≤α i The samples corresponding to ≤C are support vectors (SVs). Then...

[0057] Step S403: x0∈SVs, the radius R of the hypersphere is calculated as follows:

[0058]

[0059] Preferably, in step S5, the characteristic space H and residual space R of the relevant variable space are obtained using SDAE, and T is calculated. 2 The Q statistic is obtained using kernel density estimation. and Q lim The characteristic space is H = h = h n The residual space R = (X NR -r), the confidence level of the kernel density estimation KDE is 0.99.

[0060] T based on the feature space and residual space of SDAE 2 The calculation methods for the statistical statistic and Q-statistic are as follows:

[0061]

[0062] Preferably, step S7 is performed according to the relevant variable space X in step S2. NR and the space of independent variables X NI The same variable, X M Divided into the relevant variable space X MR and the space of independent variables X MI The method is as follows:

[0063] Suppose X N It consists of 5 variables, where X NR =[x N1 ,x N3 ,x N5 ], X NI =[x N2 ,x N4 ];

[0064] Then X M =[X MR ,X MI ], where X MR =[x M1 ,x M3 ,x M5 ], X MI=[x M2 ,x M4 ].

[0065] Preferably, step S8 involves calculating the independent variable space X. MI The distance D from the data in the diagram to the center of the LSVDD circle. The method for calculating distance D is as follows:

[0066]

[0067] Preferably, according to step S9, the monitoring method is as follows: Q≤Q lim A process where D ≤ R is in a normal state, and vice versa is in a fault state.

[0068] Compared with existing process fault detection methods, the present invention has the following advantages:

[0069] 1) Dividing variables into independent variable space and related variable space can eliminate the influence between the two. Establishing monitoring models in independent variable space and related variable space respectively can increase the fault sensitivity of fault detection system.

[0070] 2) The SDAE algorithm is used to monitor the space of related variables, and LSVDD is used to monitor the space of independent variables. SDAE can extract key features from the space of related variables to construct statistics, which is superior to traditional linear methods. The LSVDD algorithm inherits the advantages of the SVDD algorithm and can effectively detect faults in independent variables. Compared with the existing SVDD algorithm, the complexity of LSVDD is O(n^2). 2 The value of o(n) is much smaller than that of SVDD. 3 This can significantly improve training speed and save time.

[0071] 3) Compared with the prior art, the present invention can effectively overcome the interference of independent related variables, meet the needs of process monitoring, and has high accuracy. Attached Figure Description

[0072] Figure 1 This is a flowchart of a chemical process fault detection method based on SDAE-LSVDD with correlations and independent variables.

[0073] Figure 2 It is an SDAE pre-training method for fault detection in chemical processes based on SDAE-LSVDD with correlation and independent variables.

[0074] Figure 3 This is a fine-tuning of SDAE parameters for a chemical process fault detection method based on SDAE-LSVDD with correlations and independent variables. Detailed Implementation

[0075] To better implement the contents of this patent, a detailed description is provided with reference to the accompanying drawings and the technical solutions in the examples. Obviously, the specific embodiments described below represent only a portion of the embodiments of this invention, and not all examples. These examples are general in nature and all other examples obtained by those skilled in the art without inventive effort upon referring to these examples should fall within the scope of these examples and be protected by this invention.

[0076] like Figure 1-3 As shown, this invention provides a method for detecting faults in chemical processes based on SDAE-LSVDD with both correlated and independent variables. This method includes the following steps:

[0077] Step S1: Collect chemical process data X0 under normal operating conditions and standardize it to obtain data X. N ;

[0078] Step S2: Calculate the mutual information p between each data point. i And the mutual information q between each data point and the random Gaussian distribution. i X N Divided into the relevant variable space X NR and the space of independent variables X NI ;

[0079] Step S3: Use the relevant variable space data X NR Train the SDAE and find the optimal set of parameters θ for the SDAE;

[0080] Step S4: Use data X from the independent variable space NI Train the LSVDD and calculate its radius R.

[0081] Step S5: Use SDAE to obtain the characteristic space H and residual space R of the relevant variable space, and calculate T. 2 The Q statistic is obtained using kernel density estimation. and Q lim ;

[0082] Step S6: Collect online data and standardize it to obtain data X. M ;

[0083] Step S7: According to the relevant variable space X in step S2 NR and the space of independent variables X NI The same variable, X M Divided into the relevant variable space X MR and the space of independent variables X MI ;

[0084] Step S8: Calculate the relevant variable space X using SDAE MR The feature space and residual space are calculated, and T is calculated. 2 The Q statistic and the Q statistic are used to calculate the independent variable space X. MI The distance D from the data in the data to the center of the LSVDD circle;

[0085] Step S9: Compare the statistic with the control limit, and the distance from the data point to the center of the circle with the radius, to achieve online real-time monitoring.

[0086] In step S1, the raw chemical process data is single-modal chemical process data, wherein the raw data X0 = [x1, ..., x S ]∈R V×S Where V represents the number of process variables, and S represents the number of data sampling points; the X N The calculation method is as follows:

[0087]

[0088] Step S2, specifically x i and x j For data X N Two data points in the dataset.

[0089] Specifically:

[0090] (1) Calculate the mutual information p between data points i ;

[0091] Assume variable x i ∈R 1×s and x j ∈R 1×s The joint probability density p(x) i ,x j ),variable x i and x j The marginal distribution law can be expressed as p(x) i )=∫p(x i ,x j )dx j and p(x) i )=∫p(x i ,x j )dx j Mutual information p ij It can be represented as:

[0092]

[0093] Then x i The mutual information with S-1 samples is p i =[p i1 ,p2,…,piS-1 ].

[0094] (2) Calculate the mutual information between the data points and the random Gaussian distribution;

[0095] Suppose a random Gaussian variable X g ∈R V-1×S , where X g All sample points in x follow a Gaussian distribution. i and x g The joint probability density p(x) i ,x g ), mutual information q ij for:

[0096]

[0097] Then x i The mutual information with S-1 Gaussian samples is q i =[q i1 ,q2,…,q iS-1 ].

[0098] The conditions for determining whether a variable is a correlated variable or an independent variable are as follows: Then x i λ is considered a related variable, otherwise it is considered an independent variable. In this invention, the value of λ is 1.1, and the range of λ is generally 1.05 to 1.3.

[0099] Step S3, using the relevant variable space data X NR Training the SDAE and obtaining its optimal parameter set θ involves the following steps:

[0100] (1): Projection q D X NR Partial damage is Right now

[0101] (2): After a nonlinear transformation f is projected onto the implicit representation h, f is chosen as a tanh function.

[0102]

[0103] Where W and b are the weights and biases of the encoding process.

[0104] (3): h1 is reconstructed into r by using a similar nonlinear transformation.

[0105] r=f(W'h1+b') (5)

[0106] Where W' and b' are the weights and biases of the decoding process.

[0107] (4): Train DAE1 with the goal of minimizing the reconstruction error:

[0108]

[0109] (5): Use the gradient descent algorithm to solve for the optimal parameters θ = {W, b, W', b'} of DAE1, where the parameter update method is as follows:

[0110]

[0111] where t is the number of iterations.

[0112] (6): Take the hidden representation h1 of DAE1 as the input of DAE2, and complete the training of DAE2 according to the above training method of DAE1 to obtain θ2. Take the hidden representation h2 of DAE2 as the input of DAE3, and the pre-training of DAE1 - DAEn can be completed in sequence according to the method of DAE1 above to obtain θ1 ~ θ n .

[0113] (7): Connect DAE1 - DAEn layer by layer to form the entire SDAE, and take θ1 ~ θ n as the initialization parameters of each layer of the SDAE, and calculate h n as the feature space h of the SDAE:

[0114] h = h n = f(W n-1 h n-1 + b n-1 ) (8);

[0115] Step S307: Calculate the reconstruction output r of the DAE:

[0116]

[0117] (8): Use the gradient descent algorithm to fine-tune the parameters of the SDAE. When the SDAE reaches the set number of iterations 1000 or the error is less than the set value 0.001, obtain the optimal parameter set θ. Generally, the selected SDAE is a deep autoencoder structure composed of three DAEs, S - 2048 - 1024 - K - 1024 - 2048 - S, where S is the dimension of the data sample and the dimension of the reconstruction space, and K (K < S) is the dimension of the hidden variable, that is, the dimension of the low-dimensional feature space.

[0118] Step S4, use the data X in the independent variable space NI to train LSVDD and obtain the radius R of LSVDD. The specific steps are as follows:

[0119] (1): Project the original data into the high-dimensional feature space through a non-linear transformation, that is, Φ: x → F.

[0120] The inner product in the feature space is K(x,y)=Φ(x). T Φ(y)=exp(-||xy|| 2 The problem of LSVDD is to find a minimal hypersphere that encloses all the data.

[0121]

[0122] Where a and R are the center and radius of the hypersphere, respectively. Parameter C controls the volume and tolerance for error of the hypersphere. ξ i As a slack variable, it allows some data to extend beyond the hypersphere.

[0123] (2) Introducing inner product operations, the problem can be transformed into:

[0124]

[0125] Where α i It is a Lagrange multiplier.

[0126] (3) Using the Lagrange multiplier method, let the partial derivative of the above equation be zero, then we have:

[0127]

[0128] (4): The dual problem of this problem can be transformed into:

[0129]

[0130] α can be solved based on the dual problem. i 0≤α i The samples corresponding to ≤C are support vectors (SVs). Then...

[0131] (5): x0∈SVs, the radius R of the hypersphere is calculated as follows:

[0132]

[0133] Step S5: Use SDAE to obtain the characteristic space H and residual space R of the relevant variable space, and calculate T. 2 The Q statistic is obtained using kernel density estimation. and Q lim The characteristic space is H = h = h n The residual space R = (X NR -r), the confidence level of the kernel density estimation KDE is 0.99.

[0134] T based on the feature space and residual space of SDAE 2 The calculation methods for the statistical statistic and Q-statistic are as follows:

[0135]

[0136] Kernel density estimation (KDE) determines the control limits of a statistic for a given sample x. i ∈X, suppose x i If the probability density function is f(x), then the following integration condition is satisfied:

[0137]

[0138] The Gaussian kernel function is chosen as the kernel function of the KDE.

[0139] Where K(·) is the kernel function, satisfying K(x)>0 and h > 0 is the smoothing parameter, also known as the bandwidth.

[0140] Step S6, Online Data X M0 ∈R V×H X is obtained by standardization according to step 1. M .

[0141] Step S7, according to the relevant variable space X in step S2 NR and the space of independent variables X NI The same variable, X M Divided into the relevant variable space X MR and the space of independent variables X MI The method is as follows:

[0142] Suppose X N It consists of 5 variables, where X NR =[x N1 ,x N3 ,x N5 ], X NI =[x N2 ,x N4 ];

[0143] Then X M =[X MR ,X MI ], where X MR =[x M1 ,x M3 ,x M5 ], X MI =[x M2 ,x M4 ].

[0144] Step S8: Calculate the independent variable space X MI The distance D from the data in the diagram to the center of the LSVDD circle. The method for calculating distance D is as follows:

[0145]

[0146] Step S9, the monitoring method is as follows: Q≤Q lim A process where D ≤ R is in a normal state, and vice versa is in a fault state.

[0147] Working principle and usage of this invention:

[0148] During use, chemical process data X0 under normal operating conditions is collected and standardized to obtain data X. N The mutual information p between each data point is calculated. i And the mutual information q between each data point and the random Gaussian distribution. i X N Divided into the relevant variable space X NR and the space of independent variables X NI Using relevant variable spatial data X NR Train the SDAE and find its optimal parameter set θ; use data X from the independent variable space. NI Train the LSVDD and calculate its radius R; use SDAE to calculate the characteristic space H and residual space R of the relevant variable space, and calculate T. 2 The Q statistic is obtained using kernel density estimation. and Q lim Collect online data and standardize it to obtain data X. M According to the relevant variable space X in step S2 NR and the space of independent variables X NI The same variable, X M Divided into the relevant variable space X MR and the space of independent variables X MI ; Use SDAE to calculate the relevant variable space X MR The feature space and residual space are calculated, and T is calculated. 2 The Q statistic and the Q statistic are used to calculate the independent variable space X. MI The distance D from the data point to the center of the LSVDD circle is calculated; the statistical value is compared with the control limit, and the distance from the data point to the center of the circle is compared with the radius to achieve online real-time monitoring;

[0149] Dividing variables into independent and correlated variable spaces can eliminate the influence between them. Establishing monitoring models in both independent and correlated variable spaces increases the fault sensitivity of the fault detection system. The SDAE algorithm is used to monitor the correlated variable space, and LSVDD is used to monitor the independent variable space. SDAE can extract key features from the correlated variable space for constructing statistics, which is superior to traditional linear methods. The LSVDD algorithm inherits the advantages of the SVDD algorithm and can effectively address fault detection of independent variables. Compared with existing SVDD algorithms, the complexity of LSVDD is O(n^2). 2 The value of o(n) is much smaller than that of SVDD. 3 This invention can significantly improve training speed and save time costs. Compared with existing technologies, this invention can effectively overcome the interference of independent related variables, meet the needs of process monitoring, and has high accuracy.

[0150] The above description is an embodiment of the present invention. The embodiments of the present invention include, but are not limited to, these embodiments. Any person skilled in the art is within the scope of the disclosure of the present invention, and any simple modifications or substitutions should be covered within the protection scope of the present invention.

Claims

1. A method for detecting faults in chemical processes based on SDAE-LSVDD with correlated and independent variables, characterized in that, The method includes the following steps: Step S1: Collect chemical process data under normal operating conditions The data was obtained through standardization. ; Step S2: Calculate the mutual information between each data point. And the mutual information between each data point and the random Gaussian distribution. ,Will Divided into relevant variable space and independent variable space ; Step S3: Use relevant variable space data Train the SDAE and find its optimal parameter set. ; Step S4: Use data from the independent variable space Train an LSVDD and calculate its radius. ; Step S5: Use SDAE to obtain the feature space of the relevant variable space. and residual space And seek and The statistic is obtained using kernel density estimation. and ; Step S6: Collect online data and standardize it to obtain data. ; Step S7: According to the relevant variable space in step S2 and independent variable space The same variable will Divided into relevant variable space and independent variable space ; Step S8: Calculate the relevant variable space using SDAE The feature space and residual space are calculated, and the calculation is performed. Statistics and Statistics, used to calculate the space of independent variables Distance from the data in the LSVDD circle ; Step S9: Compare the statistic with the control limit, and the distance from the data point to the center of the circle with the radius, to achieve online real-time monitoring.

2. The method for detecting faults in chemical processes based on SDAE-LSVDD with correlations and independent variables according to claim 1, characterized in that, In step S1, the raw chemical process data is single-modal chemical process data. Where V represents the number of process variables and S represents the number of data sampling points; The calculation method is as follows: (1)。 3. The method for detecting faults in chemical processes based on SDAE-LSVDD with correlations and independent variables according to claim 2, characterized in that, In step S2, specifically: and For data Two data points in the middle; Step S201: Calculate the mutual information between data points ; Hypothetical variables and There is a joint probability density ,variable and The marginal distribution laws can be expressed as follows: and mutual information It can be represented as: (2)； but The mutual information with S-1 samples is ; Step S202: Calculate the mutual information between the data points and the random Gaussian distribution; Assume random Gaussian variables ,in All sample points in the dataset follow a Gaussian distribution; and There is a joint probability density mutual information for: (3)； but The mutual information with S-1 Gaussian samples is .

4. The method for detecting faults in chemical processes based on SDAE-LSVDD with correlations and independent variables according to claim 3, characterized in that, In steps S201 and S202, the conditions for determining whether a variable is a related variable or an independent variable are as follows: ,but If they are related variables, then they are independent variables.

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