A fault detection method in chemical production process based on improved LDA

Abstract

The present invention discloses a fault detection method in a chemical production process based on an improved LDA. The method includes the following steps: collecting a data set containing time information and constructing a data set containing outliers; expanding the data set containing time information into a two-dimensional data matrix through a time lag window; constructing a fault diagnosis model based on the LDA function, using the F-norm as a metric standard, and introducing a non-dimensionality reduction projection matrix and soft constraints; updating the parameters in the fault diagnosis model using gradient descent and alternating minimization methods; using the T<supgt;2< / supgt> statistic to measure the differences between samples and using the kernel density estimation method to calculate the control limit of T<supgt;2< / supgt>, thereby realizing fault detection. The present invention uses the F-norm as a metric standard, enhancing the robustness of the algorithm. At the same time, a non-dimensionality reduction projection matrix and soft constraints are introduced to construct a fault diagnosis model, enabling the model to have a high fault detection accuracy.

Description

Technical Field

[0001] The invention relates to an industrial process control and fault diagnosis method, and in particular to a fault detection method in a chemical production process based on an improved LDA. Background Art

[0002] The chemical production process is a complex system that contains a large number of sensors and various data monitored by measuring equipment. These data reflect the status of the production process, which is essential to ensure the normal operation of the equipment and improve production efficiency. However, in the data monitoring process of the chemical process, due to factors such as equipment aging, equipment failure and environmental changes, the measuring equipment may generate fault data. This will lead to instability in the production process, increase operational risks, and reduce production efficiency. Therefore, in-depth research on fault detection in chemical production processes has become a vital task.

[0003] There is a large amount of data in the chemical production process. In order to effectively diagnose potential faults, scientists at home and abroad have proposed a variety of feature extraction techniques, including principal component analysis (PCA), kernel principal component analysis (KPCA) and linear discriminant analysis (LDA). However, these methods have some limitations. PCA is sensitive to outliers and is easily affected by extreme values. The improved PCA enhances robustness, but also ignores the authenticity of the data and usually does not pay attention to category information. In the chemical production process, people pay more attention to the difference between normal and abnormal processes.

[0004] To address this problem, LDA demonstrates its advantages. LDA is a supervised learning algorithm that can effectively utilize the category information in normal and abnormal process data. However, traditional LDA has certain limitations in data processing, including:

[0005] (1) LDA is sensitive to outliers, which limits its application in chemical processes.

[0006] (2) LDA does not consider dynamic characteristics during the modeling process and ignores the correlation in the time axis direction.

[0007] (3) The hard constraints of LDA may lead to unstable performance in the presence of outliers. Summary of the invention

[0008] Purpose of the invention: The purpose of the present invention is to provide a fault detection method in a chemical production process based on an improved LDA to solve the problems of low accuracy and robustness in traditional LDA fault detection.

[0009] Technical solution: The present invention discloses a method for detecting faults in a chemical production process based on an improved LDA, comprising the following steps:

[0010] Collect data sets containing time information and construct data sets containing outliers;

[0011] The dataset containing time information is expanded into a two-dimensional data matrix through a time lag window;

[0012] Based on the LDA function, the F-norm is used as the metric, and the non-dimensionality reduction projection matrix and soft constraints are introduced to build a fault diagnosis model.

[0013] The parameters in the fault diagnosis model are updated using gradient descent and alternating minimization methods;

[0014] Using T 2 The statistic measures the difference between samples and is calculated using the kernel density estimation method. 2 control limits, thereby enabling fault detection.

[0015] Preferably, the data set containing time information is the Tennessee Eastman data set.

[0016] Preferably, the step of expanding the data set containing time information into a two-dimensional data matrix by using a time lag window is as follows: for each batch of data containing time information in the database, the data is expanded into a two-dimensional data matrix by using a time lag window, which is expressed as:

[0017]

[0018] Where K represents the batch length, u represents the lag order, and i represents the i-th batch. This step expands the data matrix by augmenting the time series variables, thereby eliminating the impact of dynamics on model performance.

[0019] Preferably, the LDA function is:

[0020]

[0021] In the formula, ||·|| F represents the F norm of the matrix. Assuming that the data has c categories, M i represents the number of samples in the cth class, W∈R m×k represents the projection matrix, represents the mean value of the i-th group, represents the average value of all samples, represents the jth sample of the i-th group, represents the mean of the cth class.

[0022] Preferably, the F-norm is used as a metric:

[0023] In order to minimize the negative impact of outliers on classification results, the square term in the LDA function is replaced by a linear term, and the F norm is used to measure the intra-class and inter-class scatter matrices of the objective function. The improved objective function is expressed as:

[0024]

[0025] Furthermore, a non-dimensionality reduction projection matrix is ​​introduced. The improved objective function is expressed as:

[0026]

[0027] Where Q∈R m×m represents the non-dimensionality reduction projection matrix, and n represents the number of samples.

[0028] The specific introduction of soft constraints is:

[0029] Introducing the Matrix This matrix contains the j For other eigenvectors other than j It can be expressed as follows:

[0030]

[0031] Among them, d j represents the parameters of the eigenvector, and then minimizes w j and The correlation between them is then defined as follows:

[0032]

[0033] in, r<a,b> It can be expressed as follows:

[0034]

[0035] In the formula, and They are respectively a i and b i The mean value, σ a and σ b Represents the standard deviation, and the final simplified expression is as follows:

[0036]

[0037] After adding the above soft constraints, the final objective function, that is, the fault diagnosis model is obtained:

[0038]

[0039] Where λ, η, μ1 and μ2 represent equilibrium parameters.

[0040] Preferably, the updating of the parameters in the fault diagnosis model using the gradient descent and alternating minimization method is specifically as follows:

[0041] First fix Q, then update W. The update formula is as follows:

[0042]

[0043] The above formula can be expressed as:

[0044]

[0045] make The formula can be expressed as:

[0046]

[0047] You can get:

[0048]

[0049] Then take the derivative of W and get:

[0050]

[0051] The final calculation W is:

[0052]

[0053] First fix W, then update Q. The update formula is as follows:

[0054]

[0055] The above formula can be expressed as:

[0056]

[0057] make The formula can be expressed as:

[0058]

[0059] Then, taking the derivative of Q, we get:

[0060]

[0061] Using the gradient descent method to solve it, we can get:

[0062] Q t+1 =Q t +δ△.

[0063] Based on the above method, the present invention further provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor implements the above method when executing the computer program.

[0064] Based on the above method, the present invention further provides a computer storage medium, wherein the computer storage medium stores instructions, and when the instructions are executed on a computer, the computer executes the above method.

[0065] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0066] 1. In order to better preserve the characteristics of data changes, the matrix is ​​used as a sample, and the dynamic characteristics of the data are extracted through a sliding window. At the same time, in order to enhance the robustness of the algorithm, the F-norm is used instead of the square of the F-norm as a metric, so as to more accurately measure the relationship between dimensions.

[0067] 2. In order to make the characteristics of the training data more obvious, a non-dimensionality reduction projection matrix is ​​introduced to further sparsely process the data. The traditional hard constraints are replaced by soft constraints to better adapt to changes in the data. Soft constraints help balance the outliers and normal values ​​in the data, making the model more robust when processing complex data. The proposed algorithm has high fault detection accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 is a flow chart of the present invention;

[0069] Figure 2 A scatter plot with outliers added to the data set of an embodiment of the present invention;

[0070] Figure 3 is the detection result of fault 11 in the data set without outliers according to an embodiment of the present invention;

[0071] Figure 4 This is the detection result of fault 11 in the data set with outliers added in the embodiment of the present invention. DETAILED DESCRIPTION

[0072] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0073] Embodiment: A fault detection method in a chemical production process based on an improved LDA, such as Figure 1 As shown, the following steps are included:

[0074] (1) Figure 2 As shown, a data set containing time information (Tennessee Eastman data set) is collected, and a data set containing outliers is constructed; 10 outliers are added to the Tennessee Eastman data set to verify the robustness of the proposed method.

[0075] (2) By augmenting the time series variables to expand the data matrix, the impact of dynamics on model performance is eliminated. Each batch of data in the database is expanded into a two-dimensional data matrix using a time lag window, which can be expressed as:

[0076]

[0077] Among them, K represents the batch length, u represents the lag order, and i represents the i-th batch.

[0078] (3) Based on the LDA function, the F-norm is used as a metric, a non-dimensionality reduction projection matrix and soft constraints are introduced to construct a fault diagnosis model, which specifically includes the following steps:

[0079] 3-1) Construct LDA function. Assume that the data has c categories, M i represents the number of samples in the cth class, W∈R m×k represents the projection matrix, represents the mean value of the i-th group, represents the average value of all samples, represents the jth sample of the i-th group, represents the mean of the cth class. The LDA function can be expressed as:

[0080]

[0081] In the formula, ||·|| F Represents the F-norm of the matrix.

[0082] 3-2) Use F-norm as the metric. In order to minimize the negative impact of outliers on the classification effect, the square term in the LDA function is replaced by a linear term. Therefore, the F-norm is used to measure the intra-class and inter-class scattering matrices of the objective function. The improved objective function is expressed as:

[0083]

[0084] 3-3) Introduce the non-dimensionality reduction projection matrix. The improved objective function is expressed as:

[0085]

[0086] Where Q∈R m×m represents the non-dimensionality reduction projection matrix, and n represents the number of samples.

[0087] 3-4) Introduce soft constraints.

[0088] Here we introduce a new matrix This matrix contains the j Other eigenvectors than . Assume that wj It can be expressed as follows:

[0089]

[0090] Among them, d j represents the parameters of the eigenvector. Then minimize w j and The correlation between them is then defined as follows:

[0091]

[0092] in, r<a,b> It can be expressed as follows:

[0093]

[0094] here, and They are respectively a i and b i The mean value, σ a and σ b Represents the standard deviation. The final simplified expression is as follows:

[0095]

[0096] After adding the above soft constraints, the final objective function is expressed as follows:

[0097]

[0098] Where λ, η, μ1 and μ2 represent equilibrium parameters.

[0099] (4) Use gradient descent and alternating minimization method to update the parameters in the fault diagnosis model. The specific steps are as follows:

[0100] 4-1) First fix Q, then update W. The update formula is as follows:

[0101]

[0102] The above formula can be transformed into:

[0103]

[0104] make The formula can be expressed as:

[0105]

[0106] You can get:

[0107]

[0108] Then take the derivative of W and get:

[0109]

[0110] The final calculation W is:

[0111]

[0112] 4-2) First fix W, then update Q. The update formula is as follows:

[0113]

[0114] The above formula can be transformed into:

[0115]

[0116] make The formula can be expressed as:

[0117]

[0118] Then, taking the derivative of Q, we get:

[0119]

[0120] Using the gradient descent method to solve it, we can get:

[0121] Q t+1 =Q t +δ△

[0122] (5) Use T 2 The statistic measures the difference between samples and is calculated using the kernel density estimation method. 2 The control limit of the fault is thus realized. Figure 3 The following are the detection results of the four algorithms for fault 11 in the Tennessee Eastman dataset without outliers. Figure 4 The figure shows the detection results of fault 11 of four algorithms in the Tennessee Eastman dataset with 10 outliers added, where Ours is a soft LDA algorithm based on the F norm. The parameters λ, η, μ1, and μ2 are set to 30, 10, 30, and 1, respectively. Experimental verification shows that the fault diagnosis rate of the method proposed in the present invention is 98.0% in the Tennessee Eastman dataset, and the fault diagnosis rate is 98.2% in the Tennessee Eastman dataset with 10 outliers added. This proves that the method proposed in the present invention has good robustness in dealing with outliers. The presence of outliers usually has a negative impact on the test results of the model. However, after many experiments, it was found that these 10 outliers did not significantly interfere with the performance of the model. This is because the method of the present invention has good robustness and can effectively deal with these outliers.

Claims

1. A fault detection method in a chemical production process based on an improved LDA, characterized in that: The steps include: Collect data sets containing time information and construct data sets containing outliers; The dataset containing time information is expanded into a two-dimensional data matrix through a time lag window; Based on the LDA function, the F-norm is used as the metric, and the non-dimensionality reduction projection matrix and soft constraints are introduced to build a fault diagnosis model. The parameters in the fault diagnosis model are updated using gradient descent and alternating minimization methods; Using T 2 The statistic measures the difference between samples and is calculated using the kernel density estimation method. 2 control limits to achieve fault detection; The LDA function is: In the formula, ||·|| F represents the F norm of the matrix. Assuming that the data has c categories, i represents the category index, j represents the sample index in the i-th category, and M i Represents the number of samples in the i-th category, W∈R m×k represents the projection matrix, m is the number of rows of matrix W, k is the number of columns of matrix W, represents the average value of the i-th category, represents the average value of all samples, represents the jth sample of the i-th class; The use of the F norm as a metric is specifically: Replace the square term in the LDA function with a linear term, and the improved objective function is expressed as: The F-norm is used to measure the intra-class and inter-class scatter matrices of the objective function; The objective function after introducing the non-dimensionality reduction projection matrix is ​​expressed as: Where Q∈R m×m represents the non-reduced projection matrix, x i represents the feature vector of the i-th sample, ||·|| 21 Indicates L 21 norm; n represents the number of samples; The specific soft constraints introduced are: Introducing the Matrix The number of rows in the matrix is ​​m, the number of columns is k-1, and the matrix contains all the numbers except w. j′ For other eigenvectors other than j′ It is expressed as follows: Among them, d j′ represents the parameter of the feature vector, j′ represents the index of the feature, and then minimizes w j′ and The correlation between them is then defined as follows: Where t is a scalar, d j′(k-1) represents the feature quantity of the k-1th feature, r<a,b> It is expressed as follows: In the formula, a and b represent two vectors, and They are respectively a i and b i The mean value of i and b i are the i-th element of vectors a and b, σ a and σ b Represents the standard deviation of vectors a and b. The simplified expression is as follows: The fault diagnosis model is: Where λ, η, μ1 and μ2 represent equilibrium parameters.

2. The fault detection method in the chemical production process based on the improved LDA according to claim 1 is characterized in that: The data set containing time information is the Tennessee Eastman data set.

3. The fault detection method in the chemical production process based on the improved LDA according to claim 1 is characterized in that: The method of expanding the data set containing time information into a two-dimensional data matrix by using a time lag window is as follows: for each batch of data containing time information in the database, the data is expanded into a two-dimensional data matrix by using a time lag window. It is expressed as: Where K represents the batch length, u represents the time lag order, i represents the i-th batch, and x i Represents the time series data corresponding to the i-th batch in the database.

4. The fault detection method in a chemical production process based on improved LDA according to claim 1 is characterized in that: The parameters in the fault diagnosis model are updated by using the gradient descent and alternating minimization method, specifically: First fix Q, then update W. The update formula is as follows: The above formula is expressed as: make The formula is: get: Then take the derivative with respect to W and we get: The final calculation W is: First fix W, then update Q. The update formula is as follows: The above formula is expressed as: make The formula is: Then take the derivative with respect to Q and we get: Using the gradient descent method, we can get: Q t+1 =Q t +ddD Among them, δ represents the update step size.

5. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the method according to any one of claims 1 to 4 is implemented.

6. A computer storage medium, characterized in that: The computer storage medium stores instructions, and when the instructions are executed on a computer, the computer is caused to perform the method according to any one of claims 1 to 4.

Images