A dynamic process monitoring method based on fault correlation feature analysis

Abstract

This invention discloses a dynamic process monitoring method based on fault correlation feature analysis, belonging to the field of industrial process monitoring and fault diagnosis. The method includes: collecting sensor measurement data under normal and fault conditions of an industrial process as normal training data and fault training data, respectively; constructing augmented matrices for the two sets of training data; establishing a fault correlation feature analysis model to determine fault-related and fault-independent subspaces; calculating the statistic for each sample based on the constructed augmented matrix of the normal training data, and determining control limits using kernel density estimation; collecting real-time sensor measurements as test data, augmenting them, and calculating the statistic of the augmented data; comparing the statistic with the corresponding control limits to determine whether a fault has occurred and whether the process monitoring model is applicable. Compared with existing technologies, this invention achieves effective monitoring of dynamic processes without requiring a process mathematical model.

Description

Technical Field

[0001] This invention belongs to the field of industrial process monitoring and fault diagnosis, and specifically relates to a dynamic process monitoring method based on fault-related feature analysis. Background Technology

[0002] Over the past few decades, data-driven fault diagnosis technology has developed rapidly, ensuring the safe and reliable operation of industrial processes. This progress stems primarily from two factors: First, compared to model-based and knowledge-based technologies, data-driven fault diagnosis does not require the establishment of accurate mathematical models of industrial processes; second, the rapid development of technologies such as sensors and databases has enabled the collection and storage of vast amounts of industrial process data, providing ample data support for the application of data-driven fault diagnosis technology. Multivariate statistical process monitoring, as an important branch of data-driven fault diagnosis, has received widespread attention from academia and industry. Representative methods include principal component analysis, partial least squares, and canonical correlation analysis.

[0003] Modern industrial processes typically exhibit a degree of dynamism, meaning that measured samples possess temporal correlations. Traditional multivariate statistical process monitoring methods struggle to extract these temporal correlations from the data, leading to inaccurate process monitoring models. Furthermore, traditional methods often analyze data collected under normal operating conditions, meaning the resulting process monitoring models cannot guarantee strong sensitivity to faults. In fact, timely and accurate monitoring of common, specific faults in industrial processes remains a challenging problem. Therefore, a fault-related dynamic process monitoring method is urgently needed to address certain common, specific faults in industrial processes. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a dynamic process monitoring method based on fault-related feature analysis. The method is rationally designed, overcomes the deficiencies of existing technologies, and has good performance.

[0005] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0006] A dynamic process monitoring method based on fault-related feature analysis includes two stages: offline modeling and online monitoring.

[0007] The offline modeling stage specifically includes the following steps:

[0008] Step S1: Collect sensor measurement data for a period of time under normal and fault conditions of the industrial process, respectively, as normal training data and fault training data.

[0009] Step S2: Construct augmented matrices for normal training data and faulty training data respectively;

[0010] Step S3: Based on the augmented matrices of the normal training data and fault training data constructed in step S2, establish a fault-related feature analysis model to obtain the fault-related subspace and the fault-independent subspace.

[0011] Step S4: Based on the augmented matrix of the normal training data constructed in step S2, calculate the statistic for each sample and use the kernel density estimation method to determine the control limits.

[0012] The online monitoring phase includes the following steps:

[0013] Step S5: Collect real-time sensor measurements as test data, perform augmentation processing on the data, and calculate the statistics of the standardized data.

[0014] Step S6: Compare the calculated statistics with the control limits obtained in step S4 to determine whether a fault has occurred and whether the process monitoring model is applicable.

[0015] Further, step S1 specifically involves: collecting sensor measurement data over a period of time under normal and fault conditions in the industrial process as normal training data and fault training data, respectively denoted as X0∈R. N×m and X f,0 ∈R Nf×m Each row represents a sample, and each column represents a sensor variable.

[0016] Furthermore, step S2 specifically involves: for X0 and X... f,0 After augmentation, incorporating the measurements from the first q time steps, the augmented matrix expression is as follows:

[0017]

[0018]

[0019] Where, x 0,i ∈R m Let x represent the normal training sample at time i. f,0,i ∈R m Let represent the fault training sample at time i.

[0020] Furthermore, the specific process of step S3 is as follows:

[0021] Based on the construction in step S2 and ,right Standardization will be carried out, that is... Each column of data is converted to a zero-mean, one-standard-deviation dataset, and the standardized normal training data is denoted as X. Using... The mean and standard deviation of Perform standardization processing, and denote the standardized fault training data as X. f ;

[0022] Obtain X and X f Then, a fault-related feature analysis model is established based on formula (3):

[0023]

[0024] Where, a∈R (q+1)m Indicating the projection direction, we optimize equation (3) to obtain:

[0025]

[0026] because ||Xa|| 2 =a T X T Xa, Formula (4) can be rewritten as:

[0027]

[0028] Let a = Φ -1 / 2 v, Φ = X T X, Formula (5) can be rewritten as:

[0029]

[0030] Where v represents the vector to be optimized; constructing the Lagrange multiplier method for v in formula (6), we get:

[0031]

[0032] Where λ represents a constant; taking the derivative of v in formula (7) and setting the derivative to 0, we get:

[0033]

[0034]

[0035] By analyzing the matrix Eigenvalue decomposition yields v j Then, according to a = Φ -1 / 2 v obtains a j Where j = 1, 2, ..., (q+1)m, then the ratio D of the average deviation of fault data and normal data in the same mapping direction is calculated. j Determine whether this direction is sensitive to faults, D j The expression is:

[0036]

[0037] Where N represents the number of normal training data samples, N f The number of training data samples for the fault; select D. j Mapping directions greater than 1 form the fault-related subspace W, used to monitor whether the process is operating normally; select D. j Mapping directions ≤1 form a fault-independent subspace. Used to monitor whether the model is suitable.

[0038] After obtaining the fault-related subspace and the fault-independent subspace, the following statistics are constructed in the corresponding subspaces using statistical analysis methods and the process is monitored. The expressions for the statistics are as follows:

[0039]

[0040]

[0041] Where Q1 is the statistic constructed in the fault-related subspace, and Q2 is the statistic constructed in the fault-independent subspace.

[0042] Beneficial technical effects:

[0043] Before modeling, the present invention considers the temporal correlation of industrial process data and therefore performs augmentation processing on the data. A fault-related feature analysis model is established on the augmented data, which yields a process monitoring model that is highly sensitive to specific faults. This method can achieve effective monitoring of dynamic processes without the need for an accurate process mathematical model, making it convenient for practical applications. Attached Figure Description

[0044] Figure 1 This is a flowchart of the dynamic process monitoring method based on fault-related feature analysis in this invention;

[0045] Figure 2 This is a schematic diagram of the process monitoring results for a specific fault 1 in an embodiment of the present invention;

[0046] Among them, (a) is a graph showing the changes in statistic Q1 and control limits; (b) is a graph showing the changes in statistic Q2 and control limits.

[0047] Figure 3 This is a schematic diagram of the process monitoring results for a specific fault 2 in an embodiment of the present invention;

[0048] Among them, (a) is a graph showing the changes in statistic Q1 and control limits; (b) is a graph showing the changes in statistic Q2 and control limits. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. The examples described below with reference to the accompanying drawings are exemplary and should not be considered as limitations on the invention. It should be understood that in the description of this invention, the orientations or positional relationships indicated by terms such as top, bottom, upper, lower, left, and right are based on the orientations or positional relationships shown in the accompanying drawings and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation; therefore, they should not be construed as limitations on the invention.

[0050] To further illustrate the technical solution of the present invention, a detailed description will be provided below through specific embodiments.

[0051] A dynamic process monitoring method based on fault-related feature analysis, such as Figure 1 As shown, it includes two stages: offline modeling and online monitoring;

[0052] The offline modeling phase includes the following steps:

[0053] Step S1: Collect sensor measurement data for a period of time under normal and fault conditions of the industrial process, respectively, as normal training data and fault training data.

[0054] Sensor measurement data collected over a period of time under normal and fault conditions in the industrial process are used as normal training data and fault training data, respectively denoted as X0∈R. N×m and Each row represents a sample, and each column represents a sensor variable.

[0055] Step S2: Construct augmented matrices for normal training data and faulty training data respectively;

[0056] For X0 and X f,0 After augmentation, incorporating the measurements from the first q time steps, the augmented matrix expression is as follows:

[0057]

[0058]

[0059] Where, x 0,i ∈R m Let x represent the normal training sample at time i. f,0,i ∈R m This represents the fault training sample at time i.

[0060] Step S3: Based on the augmented matrices of the normal training data and fault training data constructed in step S2, establish a fault-related feature analysis model to obtain the fault-related subspace and the fault-independent subspace.

[0061] Based on the construction in step S2 and right Standardization will be carried out, that is... Each column of data is converted to a zero-mean, one-standard-deviation dataset, and the standardized normal training data is denoted as X. Using... The mean and standard deviation of Perform standardization processing, and denote the standardized fault training data as X. f ;

[0062] Obtain X and X f Then, a fault-related feature analysis model is established based on formula (3):

[0063]

[0064] Where, a∈R (q+1)m Indicating the projection direction, we optimize equation (3) to obtain:

[0065]

[0066] because ||Xa|| 2 =a T X T Xa, Formula (4) can be rewritten as:

[0067]

[0068] Let a = Φ -1 / 2 v, Φ = X T X, Formula (5) can be rewritten as:

[0069]

[0070] Where v is the vector to be optimized; constructing the Lagrange multiplier method for v in formula (6), we get:

[0071]

[0072] Where λ represents a constant; taking the derivative of v in formula (7) and setting the derivative to 0, we get:

[0073]

[0074]

[0075] By analyzing the matrix Eigenvalue decomposition yields v j Then, according to a = Φ -1 / 2 v obtains a j Where j = 1, 2, ..., (q+1)m, then the ratio D of the average deviation of fault data and normal data in the same mapping direction is calculated. j Determine whether this direction is sensitive to faults, D j The expression is:

[0076]

[0077] Where N represents the number of normal training data samples, N f The number of training data samples for the fault; select D. j Mapping directions greater than 1 form the fault-related subspace W, used to monitor whether the process is operating normally; select D. j Mapping directions ≤1 form a fault-independent subspace. Used to monitor whether the model is suitable.

[0078] After obtaining the fault-related subspace and the fault-independent subspace, the following statistics are constructed in the corresponding subspaces using statistical analysis methods and the process is monitored. The expressions for the statistics are as follows:

[0079]

[0080]

[0081] Where Q1 is the statistic constructed in the fault-related subspace, and Q2 is the statistic constructed in the fault-independent subspace.

[0082] Step S4: Based on the augmented matrix of the normal training data constructed in step S2, calculate the statistic for each sample, and determine the control limit Q using the kernel density estimation method. 1,lim and Q 2,lim ;

[0083] The online monitoring phase includes the following steps:

[0084] Step S5: Collect real-time sensor measurements as test data, denoted as x. t,0 After augmentation, it is obtained Use step 3 The mean and standard deviation of Perform standardization processing, and denote the standardized test data as x. t Calculate x according to formulas (11) and (12) t Statistic Q 1,t and Q 2,t ;

[0085] Step S6: Based on the statistic Q obtained in step S5 1,t and Q 2,t The control limit Q obtained in step S4 1,lim and Q 2,lim Comparison, if Q 1,t Q 1,lim If the Q2 statistic is greater than Q at time t, then a fault occurs. Otherwise, the process runs normally at time t; if a large number or consecutive Q2 statistic values ​​are greater than Q, then a fault occurs. 2,lim If the situation is as described, it indicates that the process monitoring model is no longer applicable.

[0086] To demonstrate the effectiveness of monitoring dynamic processes, an example is described below:

[0087] This embodiment is based on the Matlab tool and uses a numerical ion from existing literature (Li Qin, et al., Control Engineering Practice, 2021, 115:104889) to illustrate the present invention, and the effects of the present invention are shown in conjunction with the accompanying drawings.

[0088] (1) Generate training data and establish a process monitoring model;

[0089] This embodiment uses the following discrete state-space model to generate samples of normal operating conditions:

[0090]

[0091]

[0092] Where z(t)∈R 3 Let represent the state vector, y(t) represent the output vector, and e(t) and v(t) represent white noise following a Gaussian distribution with a mean of 0 and standard deviations of 0.2 and 0.5, respectively. The input vector u(t) ∈ R 2 The following was generated:

[0093]

[0094] Where, element w(t)∈R 2 It follows a uniform distribution in (-2, 2). Assuming the input and output variables of the discrete dynamic system can be measured, then the sampled value at time t is x(t) = [u(t)]. T ,y(t) T ] T ∈R 7 The model was used to generate 5000 samples to form normal training data X0;

[0095] In formula (13), the coefficient matrix The element at position is replaced with 0 to simulate the occurrence of fault 1; in formula (15), the coefficient matrix Replace the element at position 0 to simulate the occurrence of fault 2.

[0096] Using the Fault 1 model, generate fault training data X consisting of 1000 samples. f,0 Obtain X0 and X f,0 Then, it is first augmented to obtain the following results: and Secondly, for and Perform standardization processing, and denote the standardized data as X and X'. f Again, use X and X f A fault-related feature analysis model is established to obtain the mapping space A. Based on the strategy of formula (10), the fault-related subspace W and the fault-independent subspace are determined. Finally, calculate the statistic Q of X in the corresponding subspace. 1,t and Q 2,t The control limit Q was determined using the kernel density estimation method. 1,lim and Q 2,lim In this way, a process monitoring model can be established for specific fault 1. In this embodiment, the significance level is 0.01.

[0097] (2) Production test data, and online monitoring;

[0098] For specific fault 1, real-time sensor measurements are collected as test data. Assume the fault occurs at the 201st sample time, and a total of 1000 samples are collected. The collected test data is x. t,0 Then, it is first augmented to obtain the augmented vector. Secondly, use The mean and standard deviation of Perform standardization processing, and denote the standardized fault training data as x. t Finally, calculate x. t Q 1,t and Q 2,t The statistical value is calculated and compared with the corresponding control limit. Similarly, by using a process monitoring model for a specific fault 2, effective monitoring of that specific fault 2 can be achieved.

[0099] Figure 2 and Figure 3 The process monitoring results of the proposed method for specific fault 1 and specific fault 2 are shown respectively. The method of the present invention can effectively detect faults with high fault detection rates (92% and 82.63% respectively) and low false alarm rates (0% and 1% respectively).

[0100] To demonstrate the effectiveness of the method of this invention in monitoring specific faults in dynamic industrial processes, comparative simulations were conducted, showcasing the fault monitoring performance of several traditional methods in this embodiment. These traditional methods include dynamic principal component analysis, fault-related principal component analysis, and dynamic internal principal component analysis. The fault detection rates (false alarm rates) of the traditional methods are shown in Table 1. The comparison clearly shows that the method of this invention exhibits the best performance.

[0101] Table 1 shows the fault detection rate (false alarm rate) of the traditional method in the examples.

[0102] method Dynamic principal component analysis Fault-related principal component analysis Dynamic internal principal component analysis Fault 1 11.5(0) 60.13(2) 61.38(2.5) Fault 2 0.25(0) 0(0) 33(2.5)

[0103] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A dynamic process monitoring method based on fault correlation feature analysis, characterized in that, It includes two stages: offline modeling and online monitoring; The offline modeling stage specifically includes the following steps: Step S1: Collect sensor measurement data for a period of time under normal and fault conditions of the industrial process, respectively, as normal training data and fault training data. Step S2: Construct augmented matrices for normal training data and faulty training data respectively; Step S3: Based on the augmented matrices of the normal training data and fault training data constructed in step S2, establish a fault-related feature analysis model to obtain the fault-related subspace and the fault-independent subspace. Step S4: Based on the augmented matrix of the normal training data constructed in step S2, calculate the statistic for each sample and use the kernel density estimation method to determine the control limits. The online monitoring phase includes the following steps: Step S5: Collect real-time sensor measurements as test data, perform augmentation processing on the data, and calculate the statistics of the standardized data. Step S6: Compare the calculated statistics with the control limits obtained in step S4 to determine whether a fault has occurred and whether the process monitoring model is applicable. The specific process of step S2 is as follows: For and Perform augmentation processing, introducing the pre- The measured values ​​at each time point, after augmentation, are expressed as the matrix: ；(1) ；(2) in, Indicates the first Normal training samples at any given time. Indicates the first Each moment of fault training sample; The specific process of step S3 is as follows: Based on the construction in step S2 and ,right Standardization will be carried out, that is... Each column of data is converted to a data set with zero mean and unit standard deviation. Let the standardized normal training data be denoted as [data type]. ;use The mean and standard deviation of Perform standardization processing, and denote the standardized fault training data as follows: ; get and Then, a fault-related feature analysis model is established based on formula (3): ；(3) in, Indicating the projection direction, we optimize equation (3) to obtain: ；(4) because , Formula (4) can be rewritten as: ；(5) make , Formula (5) can be rewritten as: ；(6) in, Represents the vector to be optimized; for formula (6) By constructing the Lagrange multiplier method, we obtain: ；(7) in, Represents a constant; for formula (7) Taking the derivative and setting it to 0, we get: ；(8) ；(9) By analyzing the matrix Eigenvalue decomposition yields And then according to get ,in Then, the ratio of the average deviation of fault data and normal data in the same mapping direction is calculated. Determine whether this direction is sensitive to faults. The expression is: ；(10) in, This represents the number of normal training data samples. The number of training data samples for fault diagnosis; select The mapping directions form the fault-related subspace. Used to monitor whether the process is operating normally; select The mapping direction forms a fault-independent subspace. This is used to monitor whether the model is suitable; After obtaining the fault-related subspace and the fault-independent subspace, the following statistics are constructed in the corresponding subspaces using statistical analysis methods and the process is monitored. The expressions for the statistics are as follows: ；(11) ；(12) in, This represents the statistics constructed in the fault-related subspace. This represents the statistics constructed in the fault-independent subspace.

2. The dynamic process monitoring method based on fault correlation feature analysis according to claim 1, characterized in that, Step S1 specifically involves: collecting sensor measurement data over a period of time under normal and fault conditions in the industrial process as normal training data and fault training data, respectively denoted as... and Each row represents a sample, and each column represents a sensor variable.

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