A method for early fault detection for dynamic industrial processes

Abstract

The application discloses a kind of early fault detection methods for dynamic industrial process, belong to industrial process monitoring and fault diagnosis field, this method includes: two groups of independent measurement data under normal working condition are collected as training data, and autoregressive model with external input is constructed;Solving optimization problem obtains the time delay of industrial process, autoregressive coefficient and time-independent component;For each sample of time-independent component, the optimal principal component of each sample is selected by maximizing detection performance index;According to optimal principal component, the statistics of training data is constructed, and its control limit is determined;Collect industrial process real-time data as test sample, and the time-independent component of test sample is calculated using autoregressive coefficient;The optimal principal component of test sample is calculated by maximizing detection performance index;Calculate statistics and optimize, compare with control limit to realize fault detection.The application does not need the accurate mathematical model of process and fault data, and can realize the efficient detection of early fault.

Description

Technical Field

[0001] This invention belongs to the field of industrial process monitoring and fault diagnosis, and specifically relates to a method for detecting early faults in dynamic industrial processes. Background Technology

[0002] In modern industrial production, the demand for safer and more reliable systems has driven the rapid development of industrial process fault detection technology. Fault detection technology can promptly detect abnormal events such as process disturbances and equipment failures, playing a crucial role not only in ensuring production safety but also in improving industrial production efficiency. With the automatic measurement and storage of large numbers of variables in distributed control systems, multivariate statistical process monitoring methods have been successfully applied to the online monitoring of various industrial processes. For example, methods such as principal component analysis (PCA) and partial least squares have made significant progress over the past two decades.

[0003] However, the methods described above only consider the static characteristics of the measurement data. Generally, industrial production process measurement data contain dynamic characteristics. For industrial process monitoring problems involving dynamic characteristics, a common strategy is to use augmented matrices to incorporate the autocorrelation sequence of the sample data. This has led to the development of numerous dynamic process monitoring methods, such as dynamic principal component analysis (DPCA). However, this method does not consider the actual physical variable relationships during data augmentation, resulting in inaccurate monitoring results and poor interpretability.

[0004] On the other hand, more serious failures often evolve from early-stage failures, and many major catastrophic accidents in history have been caused by the failure to detect and resolve minor anomalies in the system in a timely manner. Therefore, the dangers of early-stage failures cannot be ignored, and timely detection of early-stage failures and the implementation of effective protective measures are of great significance for ensuring the safe and efficient operation of industrial processes. Summary of the Invention

[0005] In view of the above-mentioned technical problems in the prior art, the present invention proposes an early fault detection method for dynamic industrial processes. The method is reasonably designed, overcomes the shortcomings of the prior art, and has good results.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] An early fault detection method for dynamic industrial processes includes an offline modeling stage and an online detection stage; wherein:

[0008] The offline modeling phase includes the following steps:

[0009] Step S1: Collect two sets of independent sensor measurement data under normal operating conditions of the industrial process as training datasets, and construct an autoregressive model with external input;

[0010] Step S2: Temporarily determine the lag parameter value, estimate the autoregressive coefficients using least squares, and then obtain the time-independent components. Based on the time-independent components, solve the time lag of the industrial process using the optimization problem, thereby obtaining the determined autoregressive coefficients and time-independent components.

[0011] Step S3: For each sample of time-independent components, calculate the optimal principal component for each sample by maximizing the detection performance index;

[0012] Step S4: Construct statistics for the training data based on the determined optimal principal components, and determine the control limits using kernel density estimation.

[0013] The online testing phase includes the following steps:

[0014] Step S5: Collect real-time sensor data of the industrial process as test samples, and calculate the time-independent components of the test samples based on the autoregressive coefficients in step S2.

[0015] Step S6: For the time-independent components in step S5, calculate the optimal principal components of the test samples by maximizing the detection performance index;

[0016] Step S7: Calculate the statistics of the test samples, perform optimization processing, and then compare them with the control limits in step S4 to determine whether a fault has occurred in the industrial process.

[0017] Preferably, step S1 is specifically performed as follows:

[0018] Two independent sets of sensor measurement data under normal operating conditions of the industrial process are collected as the training dataset, denoted as X1∈R. N×m and X2∈R N×m Each row represents a sample, and each column represents a sensor variable. Autoregressive models with external inputs are then built for each of these variables.

[0019]

[0020]

[0021] Where x1(k) and x2(k) represent the samples of X1 and X2 at the k-th sampling time, respectively, and A i ∈R m×mLet represent the autoregressive coefficients, q represent the time delay, and u1(k) and u2(k) represent the external inputs to x1(k) and x2(k), respectively; noise is contained within u1(k) and u2(k), and u1(k) and u2(k) follow a Gaussian distribution; furthermore,

[0022] Preferably, step S2 is performed as follows:

[0023] Subtracting the autoregressive models with external inputs from those in step S1, we get:

[0024]

[0025] It can be written in matrix form as follows:

[0026]

[0027] in,

[0028] ΔX=[Δx(q+1) Δx(q+2) … Δx(N)] T ∈R (N-q)×m ,

[0029]

[0030] ΔU0=[Δu0(q+1) Δu0(q+2) … Δu0(N)] T ∈R (N-q)×m ,

[0031]

[0032] The estimated values ​​of the autoregressive coefficients obtained using the least squares estimation method are as follows:

[0033]

[0034] Calculation of time-independent components As shown in formula (6):

[0035]

[0036] in, It is the matrix formed by rows q+1 to N of X1; the time delay of the industrial process is determined according to equation (7):

[0037]

[0038] in, For the estimated time-independent components The element in the i-th column;

[0039] Finally, the time delay q is obtained according to equation (7). * The determined autoregressive coefficients and time-independent components are recalculated using formulas (3), (4), (5), and (6), and are denoted as A. * and U * .

[0040] Preferably, step S3 is performed as follows:

[0041] First, for the time-independent component U * =[u * (1) u * (2) … u * (Nq)] T ∈R (N-q)×m Perform zero-mean normalization, i.e., u(k) = u * (k)-μ U , where u * (k) is U * The k-th row, μ U For U * Let U be the sample mean, and denote the zero-mean data matrix as U.

[0042] Find the covariance matrix S of U, and perform its eigenvalue decomposition as shown in Equation (8):

[0043]

[0044] Among them, U=[u(1) u(2) … u(Nq)] T ∈R (N-q)×m P is the load matrix, and PP T =P T P = I m Λ=diag(λ1 λ2 … λ m It contains all the eigenvalues ​​arranged in descending order;

[0045] According to formula (9), obtain all principal components for each sample:

[0046] t(k)=P T u(k) (9);

[0047] Secondly, the detection performance indicators to be optimized are defined as follows:

[0048]

[0049] Where W = [w1 w2 … w d ]∈{0,1} m×d The selection matrix is ​​determined by the identity matrix I. mThe d column vectors are used to select the principal component, and Ξf represents the fault information. Let represent the critical value of a chi-square distribution with degrees of freedom d and a significance level of α; for each sample u(k), maximize the detection performance index. The solution for the optimal number of principal components d is shown in equation (11):

[0050]

[0051] First, σ is defined. i =(t i ) 2 / λ i , t i Let λ be the i-th element of t(k). i Let be the i-th element of the diagonal of Λ; for all calculated {σ i Sort the integers i = 1, 2, ..., m in descending order and assign them to σ in turn. [i] , i.e. σ [1] >σ [2] >…>σ [m] The solution to the optimization problem shown in equation (11), i.e., selecting the first d * σ [i] As the optimal principal component.

[0052] Preferably, step S4 is performed as follows:

[0053] First, calculate the statistic for the corresponding sample according to formula (12):

[0054]

[0055] The statistics for all samples are obtained using equation (12), and are composed of D = [D(1) D(2) … D(Nq)] T ;

[0056] Then, the control limits D for all sample statistics were determined using kernel density estimation. limit .

[0057] Preferably, step S7 is specifically performed as follows:

[0058] According to formula (12), the statistic of the test sample is calculated and denoted as D(t);

[0059] Then, the statistic is optimized: D(t) is compared with the control limit D. limit For comparison, if D(t) < D limit Then D * (t) = D(t) - c, otherwise D * (t) = D(t) + h, where c and h are both positive numbers;

[0060] Using equation (13), the new test sample statistic D is obtained. new (t):

[0061]

[0062] D new (t) and D limit Comparison, if D new (t)>D limit If the process fails, a malfunction has occurred; otherwise, it is in a normal state.

[0063] The beneficial technical effects of this invention are as follows:

[0064] The method of this invention eliminates the dynamic characteristics of the original data by using a time series model, then selects the optimal number of principal components based on the principle of maximizing detection performance indicators, and optimizes the statistics to increase the distinguishability between fault data and normal data, thus realizing early fault detection in dynamic industrial processes. This method does not require a precise mathematical model or data under fault conditions in industrial processes, making it convenient for practical applications. Attached Figure Description

[0065] Figure 1 This is a flowchart of the method for detecting early faults in dynamic industrial processes according to the present invention;

[0066] Figure 2 This is a flowchart of the offline modeling process of this invention;

[0067] Figure 3 This is a flowchart of the online detection process of the present invention;

[0068] Figure 4 This is a schematic diagram illustrating the detection results of sensor deviation faults based on the method proposed in this invention, as an example of the present invention.

[0069] Figure 5 This is a schematic diagram illustrating the detection results of sensor accuracy degradation faults based on the method proposed in this invention, as an example of the present invention. Detailed Implementation

[0070] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0071] Reference Figure 1 The overall process of this method is explained.

[0072] First, offline modeling is performed; the specific process is as follows:

[0073] Step S110: Collect two sets of independent sensor measurement data under normal operating conditions of the industrial process as training datasets, and construct an autoregressive (ARX) model with external input.

[0074] Step S120: Temporarily determine the time delay parameter value, estimate the autoregressive coefficients using least squares, and then obtain the time-independent components. Based on the time-independent components, solve the time delay of the industrial process using the optimization problem, thereby obtaining the determined autoregressive coefficients and time-independent components.

[0075] Step S130: For each sample of time-independent components, calculate the optimal principal component for each sample by maximizing the detection performance index;

[0076] Step S140: Construct statistics for the training data based on the determined optimal principal components, and determine the control limits using kernel density estimation.

[0077] Then comes the online testing; the specific process is as follows:

[0078] Step S150: Collect real-time sensor data of the industrial process as test samples, and calculate the time-independent components of the test samples based on the autoregressive coefficients in step S120.

[0079] Step S160: For the time-independent components in step S150, the optimal principal component of the test sample is calculated by maximizing the detection performance index;

[0080] Step S170: Calculate the statistics of the test samples, perform optimization processing, and then compare them with the control limits in step S140 to determine whether a fault has occurred in the industrial process.

[0081] Figure 2 The detailed flowchart of the offline modeling process is as follows.

[0082] Step S210: Collect two sets of independent sensor measurement data under normal industrial process conditions as training datasets, and construct an autoregressive model with external input. Specifically, collect two sets of independent sensor measurement data under normal industrial process conditions as training datasets, denoted as X1∈R. N×m ,X2∈R N×m Each row represents a sample, and each column represents a sensor variable. The data matrix contains N samples and m variables, and an autoregressive (ARX) model with external input is built for each of them.

[0083]

[0084]

[0085] Step S220: Temporarily determine the time lag parameter values, estimate the autoregressive coefficients using least squares, and then obtain the time-independent components. Based on the time-independent components, solve the time lag of the industrial process using an optimization problem to obtain the determined autoregressive coefficients and time-independent components. Specifically, subtract the ARX models of the two sets of data from step S120, and then use the least squares estimation method to obtain the estimated values ​​of the autoregressive coefficients. Then, the time-independent component is obtained using equation (5), and the time delay q of the industrial process is determined using equation (6). * The determined autoregressive coefficients and time-independent components are recalculated using formulas (3), (4), and (5), and are denoted as A. * and U * .

[0086]

[0087]

[0088]

[0089]

[0090] Step S230: For each sample of the time-independent components, calculate the optimal principal component for each sample by maximizing the detection performance index. Specifically, first, the time-independent components are zero-mean processed, and the covariance matrix is ​​calculated. Then, the covariance matrix is ​​eigenvalued, and d is selected using the following formula. * One principal element:

[0091]

[0092] Step S240: Construct the statistics of the training data based on the determined optimal principal components, and determine the control limits using the kernel density estimation method. Specifically, use equation (8) to obtain the statistics of the corresponding training samples, and use the kernel density estimation algorithm to obtain the control limits D of the training samples. limit .

[0093]

[0094] Figure 3 This is a detailed flowchart of the online detection process. The specific implementation process is as follows:

[0095] Step S310: Collect real-time sensor data of the industrial process as test samples, and calculate the time-independent component of the test samples based on the autoregressive coefficients obtained in step S220. Specifically, collect real-time data and use the A obtained in step S220... *Calculate the time-independent components of the test samples.

[0096] Step S320: For the time-independent components in step S310, the optimal principal components of the test samples are calculated by maximizing the detection performance index. Specifically, the time-independent components of the test samples are first zero-mean normalized, and then the corresponding principal components are obtained by solving the problem of maximizing the detection performance index.

[0097] Step S330: Calculate the test sample statistic and optimize it to obtain a new test sample statistic. Specifically, first calculate the test sample statistic, denoted as D(t). Then optimize the statistic by comparing it with the control limit D determined in step S240. limit First, make a comparison; if D(t) < D limit Then D * (t) = D(t) - c, otherwise D * (t)=D(t)+h.

[0098] Where c and h are both positive numbers. Then we use equation (9) to calculate the new test sample statistic D. new (t):

[0099]

[0100] Step S340: Compare the new statistic with the control limit in step S240 to determine whether the industrial process has malfunctioned. If it is greater than the control limit, the industrial process is considered to have malfunctioned; otherwise, it is in a normal state.

[0101] Example

[0102] To demonstrate the effectiveness of detecting early-stage faults in dynamic industrial processes, an example is provided below. This example, based on Matlab, uses an industrial case study of a continuous stirred tank reactor (CSTR) to illustrate the present invention, and the effects of the present invention are shown in conjunction with the accompanying drawings.

[0103] (1) Generate a training dataset and establish a statistical process monitoring model for the training dataset.

[0104] This application uses the CSTR industrial process to generate two sets of training data, each with 1500 normal samples. Temporary time delay parameter values ​​are used, and the autoregressive coefficients are estimated using least squares. Then, the time-independent components are obtained, and the time delays of the industrial process are solved using an optimization problem based on these components. After testing, q... * =4, thus obtaining the definite autoregressive coefficient and time-independent component, denoted as A, respectively. * and U *The time-independent components were subjected to zero-mean processing, and the principal components were obtained using formula (7). Then, a statistic was established using (8), and the control limit D was obtained by kernel density estimation. limit The significance level in this example is 0.01.

[0105] (2) Generate test samples and apply faults.

[0106] In this example, we consider two types of sensor faults: sensor deviation fault, expressed as x = x * +f; Measurement accuracy degradation fault, expressed in the form x=x * +e. Based on the above expression, two sets of test samples were generated, each containing 3000 samples. The fault was applied starting from the 1001st sample and continuing until the 3000th sample. Type I fault was applied to sensor 2 with an amplitude of 0.3; Type II fault was applied to sensor 2 with zero-mean white noise e having a standard deviation of 0.5.

[0107] (3) Perform online testing on the test samples.

[0108] Based on the autoregressive coefficients A of the training data in step (1) of this example * To obtain the time-independent components of the test data, and after zero-mean processing, the principal component is selected using formula (7), and the statistic of the test sample is obtained, denoted as D(t). Next, the statistic is optimized: it is compared with the control limit D... limit First, make a comparison; if D(t) < D limit Then D * (t) = D(t) - c, otherwise D * (t)=D(t)+h, in this verification let c=D limit / 10, h=4c, n=10, and then use equation (9) to obtain the new test sample statistic D. new (t), and then compare the new statistic with the control limit. If it is greater than the control limit, the industrial process is considered to have malfunctioned; otherwise, it is in a normal state.

[0109] Figure 4 , Figure 5 The detection results of the proposed method for the two types of sensor faults are shown respectively. It can be seen that after a fault occurs, the proposed method can detect the fault very well, with high fault detection rates (99.95% and 97.85%, respectively), and low false alarm rates (0% and 0.40%, respectively). It is worth noting that because the statistics were processed in step (3) of this example, a very small number of test samples will have slightly negative values ​​of statistics less than zero. For clarity, and without affecting the detection performance, the results will be... Figure 4 and Figure 5The negative statistics in the table are displayed after being set to zero.

[0110] To illustrate the effectiveness of the proposed method for early fault detection in dynamic industrial processes, comparative experiments were conducted, demonstrating the fault detection performance of several traditional methods in this example. These traditional methods include dynamic principal component analysis, two-step principal component analysis, and principal component analysis based on detection performance indicators. The false alarm rate and fault detection rate of the traditional methods are shown in Tables 1 and 2, respectively. The comparison shows that the method of the present invention exhibits the best performance.

[0111] Table 1 shows the false alarm rate of the traditional method in the examples.

[0112]

[0113] Table 2 shows the fault detection rate of the traditional method in the examples.

[0114]

[0115] 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. An early fault detection method for dynamic industrial processes, characterized in that: It includes an offline modeling phase and an online detection phase; among which: The offline modeling phase includes the following steps: Step S1: Collect two sets of independent sensor measurement data under normal operating conditions of the industrial process as training datasets, and construct an autoregressive model with external input; Step S2: Temporarily determine the lag parameter value, estimate the autoregressive coefficients using least squares, and then obtain the time-independent components. Based on the time-independent components, solve the time lag of the industrial process using the optimization problem, thereby obtaining the determined autoregressive coefficients and time-independent components. Step S3: For each sample of time-independent components, calculate the optimal principal component for each sample by maximizing the detection performance index; Step S4: Construct statistics for the training data based on the determined optimal principal components, and determine the control limits using kernel density estimation. The online testing phase includes the following steps: Step S5: Collect real-time sensor data of the industrial process as test samples, and calculate the time-independent components of the test samples based on the autoregressive coefficients in step S2. Step S6: For the time-independent components in step S5, calculate the optimal principal components of the test samples by maximizing the detection performance index; Step S7: Calculate the statistics of the test samples, perform optimization processing, and then compare them with the control limits in step S4 to determine whether a fault has occurred in the industrial process.

2. The early fault detection method for dynamic industrial processes according to claim 1, characterized in that: The specific process of step S1 is as follows: Two independent sets of sensor measurement data under normal operating conditions of the industrial process are collected as the training dataset, denoted as X1∈R. N ×m and X2∈R N×m Each row represents a sample, and each column represents a sensor variable. Autoregressive models with external inputs are then built for each of these variables. Where x1(k) and x2(k) represent the samples of X1 and X2 at the k-th sampling time, respectively, and A i ∈R m×m Let represent the autoregressive coefficients, q represent the time delay, and u1(k) and u2(k) represent the external inputs to x1(k) and x2(k), respectively; noise is contained within u1(k) and u2(k), and u1(k) and u2(k) follow a Gaussian distribution; furthermore, 3. The early fault detection method for dynamic industrial processes according to claim 2, characterized in that: The specific process of step S2 is as follows: Subtracting the autoregressive models with external inputs from those in step S1, we get: It can be written in matrix form as follows: in, ΔX=[Δx(q+1) Δx(q+2) … Δx(N)] T ∈R (N-q)×m , ΔU0=[Δu0(q+1) Δu0(q+2) … Δu0(N)] T ∈R (N-q)×m , The estimated values ​​of the autoregressive coefficients obtained using the least squares estimation method are as follows: Calculation of time-independent components As shown in formula (6): in, It is the matrix formed by rows q+1 to N of X1; the time delay of the industrial process is determined according to equation (7): in, For the estimated time-independent components The element in the i-th column; Finally, the time delay q is obtained according to equation (7). * The determined autoregressive coefficients and time-independent components are recalculated using formulas (3), (4), (5), and (6), and are denoted as A. * and U * .

4. The early fault detection method for dynamic industrial processes according to claim 3, characterized in that: The specific process of step S3 is as follows: First, for the time-independent component U * =[u * (1) u * (2) … u * (Nq)] T ∈R (N-q)×m Perform zero-mean normalization, i.e., u(k) = u * (k)-μ U , where u * (k) is U * The k-th row, μ U For U * Let U be the sample mean, and denote the zero-mean data matrix as U; Find the covariance matrix S of U, and perform its eigenvalue decomposition as shown in Equation (8): Among them, U=[u(1) u(2) … u(Nq)] T ∈R (N-q)×m P is the load matrix, and PP T =P T P = I m Λ=diag(λ1 λ2 … λ m It contains all the eigenvalues ​​arranged in descending order; According to formula (9), obtain all principal components for each sample: t(k)=P T u(k) (9); Secondly, the detection performance indicators to be optimized are defined as follows: Where W = [w1 w2 … w d ]∈{0,1} m×d The selection matrix is ​​determined by the identity matrix I. m The d column vectors are used to select the principal component, and Ξf represents the fault information. Let represent the critical value of a chi-square distribution with degrees of freedom d and a significance level of α; for each sample u(k), maximize the detection performance index. The solution for the optimal number of principal components d is shown in equation (11): First, σ is defined. i =(t i ) 2 / λ i , t i Let λ be the i-th element of t(k). i Let be the i-th element of the diagonal of Λ; for all calculated {σ i Sort the integers i = 1, 2, ..., m in descending order and assign them to σ in turn. [i] , i.e. σ [1] >σ [2] >…>σ [m] The solution to the optimization problem shown in equation (11), i.e., selecting the first d * σ [i] As the optimal principal component.

5. The early fault detection method for dynamic industrial processes according to claim 4, characterized in that: The specific process of step S4 is as follows: First, calculate the statistic for the corresponding sample according to formula (12): The statistics for all samples are obtained using equation (12), and are composed of D = [D(1)D(2)…D(Nq)] T ; Then, the control limits Di of all sample statistics Di are determined using kernel density estimation. limit .

6. The early fault detection method for dynamic industrial processes according to claim 5, characterized in that: The specific process of step S7 is as follows: According to formula (12), the statistic of the test sample is calculated and denoted as D(t); Then, the statistic is optimized: D(t) is compared with the control limit D. limit For comparison, if D(t) < D limit Then D * (t) = D(t) - c, otherwise D * (t) = D(t) + h, where c and h are both positive numbers; Using equation (13), the new test sample statistic D is obtained. new (t): D new (t) and D limit Comparison, if D new (t)>D limit If the process fails, a malfunction has occurred; otherwise, it is in a normal state.

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