Method for micro-fault detection based on dynamic covariance mahalanobis kernel ocsvm

Abstract

The application provides a kind of dynamic covariance Markov kernel OCSVM-based micro-fault detection method, belongs to the technical field of industrial process fault detection.The technical problem that traditional data-driven method is difficult to effectively detect the micro-fault of complex nonlinear industrial process is solved.The technical scheme is: S1: standardization processing to training data;S2: calculate the global covariance of training data;S3: construct hybrid covariance matrix;S4: build dynamic Markov kernel function;S5: train one-class support vector machine;S6: calculate dynamic threshold;S7: standardization to test data;S8: test data is substituted into the OCSVM model trained in step S5 to calculate abnormal score;S9: compare abnormal score with dynamic threshold, judge whether fault occurs or not.The beneficial effects of the application are: dynamic covariance adjustment mechanism is combined with Markov kernel one-class support vector machine OCSVM.

Description

Technical Field

[0001] This invention relates to the field of technology, and in particular to a method for detecting minute faults based on dynamic covariance Markov kernel OCSVM. Background Technology

[0002] Since the beginning of the 21st century, global market competition has intensified, and product quality assurance, production process safety requirements, and increasingly stringent environmental and safety regulations have collectively constituted core challenges for enterprise development. Modern process industries rely on automation, information, and computer technologies as their core support, integrating control, scheduling, management, and decision-making into comprehensive enterprise automation systems. This trend has driven the continuous expansion of industrial production scale and a significant increase in system complexity. However, in large-scale, highly complex industrial processes, minor faults such as sensor drift, pipeline leaks, and component aging caused by long-term equipment operation are unavoidable. If these faults are not detected and eliminated in a timely manner, they will directly undermine the stability of the control system, leading to performance degradation or even system failure, thereby causing risks such as decreased product quality and production interruptions. More seriously, such faults may escalate into safety accidents, threatening personnel lives and causing incalculable economic losses. Therefore, how to accurately and effectively detect minor faults in chemical processes has become one of the hot and challenging issues in the field.

[0003] Traditional data-driven fault detection methods, such as Principal Component Analysis (PCA), Slow Feature Analysis (SFA), and Canonical Variate Analysis (CVA), are not very effective at detecting potential minor faults in chemical processes. These methods extract low-dimensional features through linear projection, but they are essentially still shallow feature models, and their ability to capture small-amplitude, minor fault features is limited.

[0004] Patent CN108716398B proposes a method and device for fault detection in controlled-pressure drilling processes based on slow feature analysis (SFA). Utilizing SFA technology, it establishes a detection model offline (calculating the transformation matrix, constructing statistics, and calculating control limits for the statistics). The detection model is then used to calculate statistics on real-time controlled-pressure drilling data, and the statistics are compared with the control limits, effectively improving the accuracy of fault detection and reducing the false alarm rate. While SFA can extract slowly varying components, its detection performance is poor for minor faults with insignificant variance changes. Patent CN108376266A proposes a single-class support vector machine kernel parameter optimization method based on points within sample edge points. This method automatically optimizes parameters by analyzing the geometric relationships of sample points. However, for minor faults with low amplitude and susceptibility to noise interference, the nearest neighbor mechanism based on Euclidean distance has limitations and cannot effectively detect the edge points of minor faults.

[0005] Therefore, how to deeply mine effective micro-fault features from complex nonlinear industrial process data and achieve timely detection is a major and challenging problem in the field of fault detection research. Summary of the Invention

[0006] To address the technical challenge of effectively detecting minute faults in complex nonlinear industrial processes using traditional data-driven methods, a minute fault detection method based on Dynamic Covariance Markov Kernel OCSVM is proposed. This method combines the dynamic covariance adjustment mechanism with Markov kernel single-class support vector machine OCSVM, and proposes an online framework for minute fault detection in complex industrial processes.

[0007] To achieve the above-mentioned objectives, the present invention employs the following technical solution: a method for detecting minute faults based on Dynamic Covariance Markov Kernel OCSVM, comprising the following steps:

[0008] Step S1: Obtain normal operating condition data X0 from the historical database, and use its mean (mean(X0)) and standard deviation (std(X0)) to analyze the historical data X. old Standardization, to obtain standardized training data X train ;

[0009] Step S2: Calculate the training data X after adding a regularization term. train Global covariance Σ global ;

[0010] Step S3: Calculate the local covariance Σ using a sliding window SW1. local By dynamically fusing local and global covariances through sliding window size and attenuation coefficient, a hybrid covariance matrix Σ is constructed. hd ;

[0011] Step S4: Based on mixed covariance Σ hd Construct a dynamic Markov kernel function;

[0012] Step S5: Extract training data X using the sliding window SW2. tri For each window, a single-class support vector machine (OCSVM) model is trained. i ;

[0013] Step S6: Based on the training data for each X tri The abnormal score is used to calculate the corresponding dynamic threshold;

[0014] Step S7: Collect data from the industrial production process and process the data using the same method as in Step S1 to obtain the test dataset X. test ;

[0015] Step S8: For X test The test data X is captured using a sliding window, similar to step S5. tsi Using the OCSVM model trained in S5 i Calculate the anomaly score for the corresponding test data;

[0016] Step S9: Compare the abnormal score of the obtained test data with the corresponding dynamic threshold. If the abnormal score is greater than the dynamic threshold, a fault has occurred; otherwise, no fault has occurred.

[0017] Further, in step S1, normal operating condition data X0 is obtained from the historical database, and its mean (mean(X0)) and standard deviation (std(X0)) are used to analyze the historical data X. old Standardization, resulting in standardized training data Σ global The specific steps are as follows:

[0018]

[0019] In the formula, n is the number of samples, and m is the number of variables.

[0020] Further, in step S2, the training data X is calculated after adding a regularization term. train Global covariance Σ global The specific steps are as follows:

[0021] Σ global =cov(X train )+εI (25)

[0022] In the formula, ε is a small constant (e.g., 10). -6 ), where I is the identity matrix.

[0023] Adding a regularization term can avoid the singularity problem, ensure that the matrix is ​​positive definite and invertible, and improve the robustness of the algorithm.

[0024] Furthermore, in step S3, the local covariance Σ is calculated using a sliding window SW1. local By dynamically fusing local and global covariances through sliding window size and attenuation coefficient, a hybrid covariance matrix Σ is constructed. hd The specific steps are as follows:

[0025] The parameters of the sliding window SW1 are set as follows: window width is set to H, step size is set to 1, it moves backward once at each sampling time, the number of data samples is n, and the total number of samples is N. W1 = n-H+1 sampling times; for the k-th sampling time:

[0026]

[0027] In the formula,

[0028] The fusion ratio of global and local covariance is controlled by the attenuation coefficient τ.

[0029]

[0030] H represents the width of the sliding window SW1.

[0031] Constructed covariance matrix Σ hd The calculation is as follows:

[0032]

[0033] When the set sliding window width H is large, λ k Rapid decay, local covariance weight (1-λ) k The improvement is significant, and the model can better capture local features; conversely, when the sliding window width H is set small, λ... k Slow decay, global covariance weight λ k Dominant, which can effectively avoid estimation bias under small sample conditions.

[0034] In summary, by combining the dynamic fusion mechanism, the statistical characteristics of historical data are preserved while real-time changes are captured.

[0035] Further, in step S4, based on the mixed covariance Σ hd The specific steps for constructing a dynamic Markov kernel function are as follows:

[0036] For the sample Its dynamic Mahalanobis distance is:

[0037]

[0038] Dynamic Markov kernel function based on mixed covariance matrix Mahalanobis distance is used to measure the similarity between samples, and its mathematical form is:

[0039]

[0040] In the formula, γ is greater than 0 and is the scaling parameter of the kernel function. Let be the mixture covariance matrix at the k-th sampling time.

[0041] The smaller the γ value, the less sensitive the kernel function is to changes in distance, and the smoother the decision boundary, making it suitable for processing noisy data; conversely, the larger the γ value, the more sensitive it is to changes in distance, making it suitable for capturing the characteristics of minor faults.

[0042] Kernel function rationality judgment:

[0043] In machine learning, kernel functions must satisfy the Mercer condition (i.e., the positive definite kernel condition) to ensure the existence of their corresponding reproducing kernel Hilbert space (RKHS), thereby supporting the mathematical validity of algorithms (such as support vector machines).

[0044] Symmetry: by Mahalanobis distance satisfies symmetry; exp(-a)=exp(-a), the exponential function also satisfies symmetry, that is, the dynamic Mahalanobis kernel function naturally satisfies symmetry.

[0045] Positive definiteness: Construction of mixed covariance It ensures strict positive definiteness:

[0046]

[0047] A convex combination of positive definite functions is still positive definite (λ∈[0,1]), and has positive definite covariance. inverse matrix It also satisfies positive definiteness. Dynamic covariance matrix It varies with sampling time k, but at each time Since they independently satisfy positive definiteness, the kernel function K at each time step... t All meet the Mercer condition.

[0048] Furthermore, in step S5, training data X is extracted using a sliding window SW2. tri For each window, a single-class support vector machine (OCSVM) model is trained. i The specific steps are as follows:

[0049] S5.1: Training process of OCSVM model:

[0050] The optimization problem of OCSVM is:

[0051] Given a training dataset Given from A nonlinear mapping Φ to a certain high-dimensional feature space χ, such that Φ(x) i For each x ∈ χ, a hyperplane ω·Φ(x)-ρ=0 is constructed in the high-dimensional space to separate the mapped samples from the origin by an interval ρ, where ω is the normal vector of the hyperplane and ρ is the intercept of the hyperplane. The goal is to maximize the Euclidean distance between the origin and the target data in order to make the hyperplane as far away from the origin as possible. The goal is to find the optimal hyperplane. The optimal hyperplane found by OCSVM in two-dimensional space after mapping is described.

[0052] To make the algorithm more robust, a relaxation factor ξ is introduced. i ≥0, in this case, the optimization problem of OCSVM is:

[0053]

[0054] Where ω∈ξ and Let v be the hyperplane parameters. v∈(0,1] is a predefined percentage parameter estimate, n is the total number of samples, and vn has a similar function to the penalty coefficient C in the standard support vector machine, representing the upper bound of the boundary support vector rate (classification error rate) and the lower bound of the overall support vector rate. To solve the quadratic programming problem, the Lagrange function is introduced:

[0055]

[0056] Minimize ω and ξ respectively i And ρ, we get:

[0057]

[0058] Substituting the above three formulas into (10), and simultaneously using the Mercer kernel function to replace the inner product on space χ, i.e., K(x i ,x j )=φ(x i )·φ(x j The dual problem can then be derived:

[0059]

[0060] And it satisfies the Caro-Kun-Tucker condition (KKT)ξ i β i =0 and (ω·φ(x) i )-ρ+ξ i )α i =0.

[0061] The parameter ρ in formula (10) can be obtained from any equation that satisfies The sample is obtained, that is The decision function can then be written as:

[0062]

[0063] S5.2: In this method, the parameters of the sliding window SW2 are set as follows: window width is set to W, step size is set to 1, it moves backward once at each sampling time, the number of data samples is N, and the total number of windows is N. W2 = N-W+1, corresponding to N-W+1 sampling times. For the i-th sampling time:

[0064] Training data X train The extracted data is:

[0065]

[0066] Among them, start i =max(i,N-W+1), end i = i, i∈[1,N]

[0067] That is, the data of the i-th sliding window is Mixed covariance within the current window Generated by step S3. That is, the calculation of the kernel matrix:

[0068]

[0069] in:

[0070]

[0071] S5.3: Substitute the kernel matrix above into the OCSVM training process described above, that is, train an OCSVM model for each window, denoted as model. i The training score S for each window i

[0072] S i =α i K i -ρ (42)

[0073] Further, in step S6, based on the training data X tri The specific steps for calculating the dynamic threshold corresponding to the abnormal score are as follows:

[0074] From the above steps, we can see that for each time i, a corresponding model has been trained. i The model, according to Equation 19, yields the training score S at the i-th sampling time. i A window contains k time points, meaning there are a total of S time points within that window.k Training scores:

[0075]

[0076] Calculate S k mean(S) k ) and standard deviation std(S k Based on the empirical distribution law, the dynamic threshold can be obtained. i :

[0077] threshold i =mean(S) k )+δ·std(S k (44)

[0078] Where δ is set to 3.

[0079] Furthermore, in step S7, data from the industrial production process is collected and processed in the same way as in step S1 to obtain the test dataset X. test The specific steps are as follows:

[0080]

[0081] In the formula, n is the number of samples, and m is the number of variables.

[0082] Further, in step S8, for X test The test data X is captured using a sliding window, similar to step S5. tsi Using the OCSVM model trained in S5 i The specific steps for calculating the anomaly score for the corresponding test data are as follows:

[0083] S ti =α k K i -ρ (46)

[0084] Further, in step S9, the abnormal score of the obtained test data is compared with the corresponding dynamic threshold. If the abnormal score is greater than the dynamic threshold, a fault has occurred; otherwise, no fault has occurred. The specific steps are as follows:

[0085] In step S8, X has been... test Corresponding anomaly score S ti All have been calculated, and the dynamic threshold has been determined. i By comparison, we can obtain f(X) tis ):

[0086]

[0087] The online testing process can then be completed.

[0088] Compared with the prior art, the beneficial results of the present invention are as follows:

[0089] 1. This invention proposes a kernel function OCSVM based on Mahalanobis distance, which changes the distance measurement method in the feature space. This method abandons the implicit assumptions of Euclidean distance regarding feature scale and correlation, dynamically adapts to the non-uniform distribution of features, and thus characterizes the essential differences between minute fault points and normal samples in local regions, improving the model's ability to distinguish fault-sensitive edge points, and is particularly good at capturing weak and minute fault signals.

[0090] 2. This invention overcomes the shortcomings of fixed covariance matrices in adapting to dynamic scenarios by designing a dynamic exponential decay fusion strategy of local covariance (sliding window calculation) and global covariance (historical data statistics), which adapts in real time to minor problems such as data distribution drift in non-steady-state industrial processes.

[0091] 3. This invention proposes a new dynamic threshold method that can update the threshold size in real time, avoiding the risk of increased false alarm rate or missed detection caused by data drift in traditional fixed thresholds, and further enhancing the ability to capture minor fault data. Attached Figure Description

[0092] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0093] Figure 1 This is a flowchart illustrating the overall process of detecting minor faults using the method of the present invention.

[0094] Figure 2 In Embodiment 1 of the present invention, T in PCA is used 2 The statistics and SPE statistics are used to analyze the fault detection map of Fault 3.

[0095] Figure 3 The fault detection diagram for fault 3 is shown in Embodiment 1 of the present invention using the MKOCSVM detection method.

[0096] Figure 4 The fault detection diagram for fault 3 is shown in Embodiment 1 of the present invention, which uses the DCMKOCSVM detection method of the present invention.

[0097] Figure 5 In Embodiment 1 of the present invention, T in PCA is used 2 The statistics and SPE statistics are used to detect faults in Fault 9.

[0098] Figure 6The fault detection diagram for fault 9 is shown in Embodiment 1 of the present invention using the MKOCSVM detection method.

[0099] Figure 7 The fault detection diagram for fault 9 is shown in Embodiment 1 of the present invention, which uses the DCMKOCSVM detection method of the present invention.

[0100] Figure 8 In Embodiment 1 of the present invention, T in PCA is used 2 The statistics and SPE statistics are used to detect faults in Fault 15.

[0101] Figure 9 The fault detection diagram for fault 15 is shown in Embodiment 1 of the present invention using the MKOCSVM detection method.

[0102] Figure 10 The fault detection diagram for fault 15 is shown in Embodiment 1 of the present invention, which uses the DCMKOCSVM detection method of the present invention.

[0103] Figure 11 In Embodiment 2 of the present invention, T in PCA is used 2 The statistical measures and SPE statistics are used to detect deviation faults in the fault detection graph.

[0104] Figure 12 The OCSVM detection method is used to detect deviation faults in Embodiment 2 of the present invention.

[0105] Figure 13 Example 2 of this invention uses the DCMKOCSVM detection method of this invention to detect deviation faults.

[0106] Figure 14 In Embodiment 2 of the present invention, T in PCA is used 2 The accuracy of fault detection maps is reduced by the statistic and SPE statistic.

[0107] Figure 15 This is a fault detection diagram of accuracy degradation using the OCSVM detection method in Embodiment 2 of the present invention.

[0108] Figure 16 Example 2 of this invention uses the DCMKOCSVM detection method of this invention to detect faults with decreased accuracy.

[0109] Figure 17 In Embodiment 2 of the present invention, T in PCA is used 2 Statistics and SPE statistics for drift fault detection maps.

[0110] Figure 18 This is a drift fault detection diagram using the OCSVM detection method in Embodiment 2 of the present invention.

[0111] Figure 19Example 2 of this invention uses the DCMKOCSVM detection method of this invention to detect drift faults. Detailed Implementation

[0112] 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. Of course, the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0113] Example 1

[0114] See Figure 1 and Figure 10 This embodiment is based on the Tennessee-Eastman (TE) process, a typical nonlinear industrial process derived from an actual industrial process at Tennessee Eastman Chemical Company in the United States. The TE process experimental platform simulates an actual chemical complex reaction process at Tennessee Eastman Chemical Company. This platform is an open and highly challenging chemical model testing platform, mainly composed of multiple operating units such as a continuous stirred reactor, condenser, gas-liquid separator, stripping tower, reboiler, and centrifugal compressor. Its process flow diagram is shown below. Figure 2 As shown. Three gaseous reactants A, D, and E directly enter the reactor. Feed C and a certain amount of feed A enter the process through the condenser. The TE process has a total of 11 operating variables and 41 process variables. When determining the process monitoring variables, several commonly used process variables closely related to the process operation status are selected. Among them, 11 operating variables XMV(1)~XMV(11) are used as inputs, namely material D (flow rate 2), material E (flow rate 3), material A (flow rate 1), material A and C (flow rate 4), compressor circulation valve, air release valve, separator liquid flow rate, desorption tower steam valve, reactor cold water flow rate, and condenser cold water flow rate. Components F, G, and H are used as output variables.

[0115] The TE process is configured with 21 fault types, categorized into step, unknown, and other fault types. Among these faults, faults 3, 9, and 15 are particularly noteworthy, as they are minor faults that are difficult to detect and are the focus of this invention. The causes and types of these three minor faults are shown in Table 1.

[0116] Table 1. Causes and Types of Minor Faults in the TE Process

[0117] Fault 3 D Feed temperature change Step micro-fault Fault 9 D Feed temperature change Random minor faults Fault 15 Condenser cooling water valve stuck Viscous Minor Faults

[0118] This invention uses the Fault Detection Rate (FDR) and Fault False Alarm Rate (FAR) to quantitatively evaluate the performance of all fault detection methods, with the specific formulas as follows:

[0119]

[0120] Where, N p N represents the number of normal samples that were falsely detected as faulty. t N represents the total number of normal samples. v N represents the number of fault samples detected. n This represents the total number of faulty samples.

[0121] Minor fault 3:

[0122] To address minor fault 3 in the Tennessee Eastman process, a small step fault is introduced into the feed temperature of gaseous reactant D. Because minor fault 3 has a negligible impact on the Tennessee Eastman process, with almost no change in the mean and variance of the fault data, traditional data-driven methods cannot detect minor fault 3.

[0123] S1: For the TE process fault 3 dataset, the normal operating condition data in the historical database. Where n is 960 and m is 52. The historical data is standardized according to formula (1) to obtain X. train ;

[0124] S2: Calculate X using formula (2) train Global covariance Σ global ;

[0125] S3: Here, the window width of the sliding window SW1 is set to H = 50. For X train In other words, the data within the window at the k-th sampling time... We can calculate using formula (3) Taking the attenuation coefficient τ = 70, the fusion ratio λ of the global and local covariances is calculated using formula (4). k Then, using formula (5) to calculate

[0126] S4: Will Substituting into formula (6) yields the following results: Then, the dynamic Markov kernel function K is obtained using formula (7). M (X,Y);

[0127] S5.1: The OCSVM model training process is introduced, namely, solving the optimization problem shown in formula (9), using formula (10) to introduce the Lagrangian function to solve it, and the solution results are formulas (11), (12), and (13). Then, the above three solution results are substituted into formula (10), and the Mercer kernel function is used to replace the inner product of χ in the space to obtain the dual problem (14), and then the decision function (15) is obtained.

[0128] S5.2: Here, the window width of the sliding window SW2 is set to W = 100. For X train In other words, the data within the window corresponding to the i-th sampling time. And the mixed covariance within the current window The kernel function matrix required for model training is determined in step S3 and in step S4.

[0129] S5.3 Then, using step S5.1, the corresponding OCSVM model is trained. i Calculate α based on KKT conditions i ρ is calculated using formula (10), and then the symbolic function f(x) is obtained using formula (15).

[0130] S6: Calculate the training score S at each sampling time i using formula (19). i The dynamic threshold can be calculated using formula (21). i ;

[0131] S7: Collect data from the industrial production process, process the data using the same method as in step S1, and obtain test data X. test In this example, n is 960, m is 52;

[0132] S8: Extract test data X using the same sliding window method as S5. tsi According to formula (23), the corresponding model is used i Calculate the anomaly score S for the corresponding test data. ti ;

[0133] S9: Use formula (24) to obtain the anomaly score S ti With dynamic threshold i By comparing the results, it can be determined whether a fault has occurred at this sampling point, thus completing the online detection process.

[0134] Following the steps above, a Markov kernel-based single-class support vector machine (MKOCSVM) model is trained. Test data is then fed into the trained model to obtain the score matrix. Fault detection is then performed by comparing this score matrix with a dynamic threshold. The fault detection performance of Principal Component Analysis (PCA)-based fault detection methods, Markov kernel-based single-class support vector machine (MKOCSVM), and the fault detection method of this invention are compared. Experimental results show that the fault detection method of this invention is more sensitive to detecting minute faults in complex industrial systems, has higher accuracy, and achieves the highest fault detection rate.

[0135] Simulation results show that: T based on the Principal Component Analysis (PCA) fault detection method 2The fault detection rates for the statistical test and the SPE statistical test were 1.88% and 2.88%, respectively, and the false alarm rates were 0.00% and 3.75%, respectively. Figure 2 As shown in the figure, principal component analysis is ineffective for minor faults with small changes in mean and variance, regardless of T. 2 Both the statistical measure and the SPE statistic show that the number of detected cases is only in the single digits; the fault detection rate based on the Markov kernel single-class support vector machine (MKOCSVM) is 98.38%, and the false alarm rate is 68.12%. Figure 3 As shown in the figure, after replacing the kernel function of OCSVM with the Markov kernel, the detection rate was significantly improved, but the false alarm rate also increased considerably, reaching 68.12%. The fault detection method based on dynamic covariance Markov kernel single-class support vector machine (DCMKOCSVM) achieved a fault detection rate of 98.00% and a false alarm rate of 5.62%. Figure 4 As shown in the figure; it is clearly visible that the fault detection method based on dynamic covariance Markov kernel single-class support vector machine (DCMKOCSVM) proposed in this invention has the highest fault detection rate for the minor fault 3 in the TE process, and compared with the Markov kernel single-class support vector machine (MKOCSVM) fault detection method, the false alarm rate of this method is significantly reduced, and the detection effect is the best.

[0136] Minor Fault 9:

[0137] To address the minor fault 9 in the Tennessee Eastman process, a random minor fault is introduced into the feed temperature of gaseous reactant D. Because a random minor fault is introduced, the fault data exhibits almost no fluctuation in mean and variance, making it virtually impossible for traditional data-driven methods to detect minor fault 9.

[0138] Following the same steps as for fault 3, a Markov kernel-based single-class support vector machine model with dynamic covariance is trained. Test data is then fed into the trained model to obtain the score matrix. This score matrix is ​​compared with a dynamic threshold to complete fault detection. The fault detection performance of principal component analysis (PCA)-based fault detection methods, Markov kernel-based single-class support vector machine (MKOCSVM)-based fault detection methods, and the fault detection method of this invention is compared to demonstrate the superiority of this invention.

[0139] Simulation results show that: T based on the Principal Component Analysis (PCA) fault detection method 2 The fault detection rates for the statistical test and the SPE statistical test were 1.25% and 1.75%, respectively, and the false alarm rates were 2.50% and 4.38%, respectively. Figure 5 As shown in the figure); the fault detection method based on Markov kernel single-class support vector machine (MKOCSVM) has a fault detection rate of 98.62% and a false alarm rate of 65.00%. Figure 6As shown in the figure); the fault detection method based on Dynamic Covariance Markov Kernel Single-Class Support Vector Machine (DCMKOCSVM) has a fault detection rate of 92.50% and a false alarm rate of 13.12%. Figure 7 As shown in the figure); it can be seen that for minor faults 9, the fault detection method based on dynamic covariance Markov kernel single-class support vector machine (DCMKOCSVM) proposed in this invention has a high fault detection rate, a low false alarm rate, and the best detection effect.

[0140] Minor Fault 15:

[0141] To address minor fault 15 in the Tennessee Eastman process, a viscous minor fault caused by a stuck condenser cooling water valve was introduced. Because a viscous minor fault was introduced, the fault data still showed almost no fluctuation in mean and variance, making fault detection quite difficult.

[0142] Following the same steps as for fault 3, a Markov kernel-based single-class support vector machine model with dynamic covariance is trained. Test data is then fed into the trained model to obtain the score matrix. This score matrix is ​​compared with a dynamic threshold to complete fault detection. The fault detection performance of principal component analysis (PCA)-based fault detection methods, Markov kernel-based single-class support vector machine (MKOCSVM)-based fault detection methods, and the fault detection method of this invention is compared to demonstrate the superiority of this invention.

[0143] Simulation results show that: T based on the Principal Component Analysis (PCA) fault detection method 2 The fault detection rates for the statistical test and the SPE statistical test were 2.38% and 2.88%, respectively, and the false alarm rates were 1.25% and 1.25%, respectively. Figure 8 (As shown); the fault detection method based on Markov kernel single-class support vector machine (MKOCSVM) has a fault detection rate of 99.25% and a false alarm rate of 67.50%. Figure 9 As shown, the fault detection method based on Dynamic Covariance Markov Kernel Single-Class Support Vector Machine (DCMKOCSVM) has a fault detection rate of 95.62% and a false alarm rate of 10.00%. Figure 10 As shown, for viscous faults, the Markov kernel single-class support vector machine (MKOCSVM) has the highest detection rate, but its false alarm rate is also very high, reaching 67.50%. The fault detection method based on dynamic covariance Markov kernel single-class support vector machine (DCMKOCSVM) proposed in this invention reduces the false alarm rate to 10%, while the fault detection rate is still above 95%. Therefore, this method has the best detection effect.

[0144] Example 2

[0145] This embodiment is based on the Continuous Stirred Tank Heater Process Dataset, abbreviated as CSTH process, which is also a typical nonlinear industrial process, derived from the experimental platform developed by the University of Alberta laboratory.

[0146] In the CSTH process, cold water and hot water are mixed in a mixing vessel. This mixture is further heated by steam passing through a heating coil and then discharged from the bottom of the vessel through a long pipe. The process involves a total of three sensor measurements: cold water flow rate F, tank level L, and outlet water temperature T. These three sensors include three PI controllers and two closed-loop control loops, with the two closed-loop control loops closely related to each other. For example, the output of the PI controller for the level is used as an input to the flow controller, which is used as the closed-loop control loop. Therefore, together with the three PI controllers monitoring the output variables, there are six monitored measurements, denoted as X = [L, F, T, C]. L C F C T ] T Table 2 briefly describes the three initial faults (sensor bias, sensor accuracy degradation, and sensor drift) in the CSTH process of the case study. The training dataset contains 500 samples collected under normal operating conditions. Each test dataset contains 500 samples with the initial faults introduced since the 201st sampling time.

[0147] Table 2. Causes and Types of Minor Faults in the CSTH Process

[0148] biasfault Sensor deviation fault 201 degrafault Sensor accuracy degradation fault 201 driftfault Sensor drift fault 201

[0149] This invention uses Fault Detection Rate (FDR) and Fault False Alarm Rate (FAR) to quantitatively evaluate the performance of all fault detection methods, and the calculation formula is referenced in formula (25).

[0150] Sensor deviation fault:

[0151] This addresses sensor bias faults that occur during the CSTH process. Because sensor bias faults have a minimal impact on the CSTH process, with almost no change in the mean and variance of the fault data, traditional data-driven methods cannot detect them.

[0152] S1: For the CSTH deviation fault dataset, the normal operating condition data in the historical database. Where n is 500 and m is 7. The historical data is standardized according to formula (1) to obtain X. train ;

[0153] S2: Calculate X using formula (2) train Global covariance Σ global ;

[0154] S3: Here, the window width of the sliding window SW1 is set to H=15. For X train In other words, the data within the window at the k-th sampling time... We can calculate using formula (3) Taking the attenuation coefficient τ = 70, the fusion ratio λ of the global and local covariances is calculated using formula (4). k Then, using formula (5) to calculate

[0155] S4: Will Substituting into formula (6) yields the following results: Then, the dynamic Markov kernel function K is obtained using formula (7). M (X,Y);

[0156] S5.1: The OCSVM model training process is introduced, namely, solving the optimization problem shown in formula (9), using formula (10) to introduce the Lagrangian function to solve it, and the solution results are formulas (11), (12), and (13). Then, the above three solution results are substituted into formula (10), and the Mercer kernel function is used to replace the inner product of χ in the space to obtain the dual problem (14), and then the decision function (15) is obtained.

[0157] S5.2: Here, the window width of the sliding window SW2 is set to W = 30. For X train In other words, the data within the window corresponding to the i-th sampling time. And the mixed covariance within the current window The kernel function matrix required for model training is determined in step S3 and in step S4.

[0158] S5.3 Then, using step S5.1, the corresponding OCSVM model is trained. i Calculate α based on KKT conditions i ρ is calculated using formula (10), and then the symbolic function f(x) is obtained using formula (15).

[0159] S6: Calculate the training score S at each sampling time i using formula (19). i The dynamic threshold can be calculated using formula (21). i ;

[0160] S7: Collect data from the industrial production process, process the data using the same method as in step S1, and obtain test data X. test In this example, n is 500, m is 7;

[0161] S8: Extract test data X using the same sliding window method as S5.tsi According to formula (23), the corresponding model is used i Calculate the anomaly score S for the corresponding test data. ti ;

[0162] S9: Use formula (24) to obtain the anomaly score S ti With dynamic threshold i By comparing the results, it can be determined whether a fault has occurred at this sampling point, thus completing the online detection process.

[0163] Following the steps above, a dynamic covariance Mahalanobis kernel-based single-class support vector machine model is trained. Test data is then fed into the trained model to obtain the score matrix. Fault detection is then performed by comparing this matrix with a dynamic threshold. The fault detection performance of Principal Component Analysis (PCA), Mahalanobis distance (MD), and single-class support vector machine (OCSVM) methods is compared with that of the present invention. Experimental results show that the fault detection method of the present invention is more sensitive to and more accurate in detecting minute faults in complex industrial systems, achieving the highest fault detection rate. Specific values ​​for the fault detection rate are detailed in Table 3.

[0164] Sensor accuracy degradation faults refer to sensor accuracy degradation faults that occur during the CSTH process. Because sensor accuracy degradation faults have a minimal impact on the CSTH process, with almost no change in the mean and variance of the fault data, traditional data-driven methods cannot detect sensor accuracy degradation faults.

[0165] Following the same steps as for deviation faults, a dynamic covariance Mahalanobis kernel-based single-class support vector machine model is trained. Test data is then fed into the trained model to obtain a score matrix, which is compared with a dynamic threshold to complete fault detection. The fault detection performance of principal component analysis (PCA), Mahalanobis distance (MD), and single-class support vector machine (OCSVM) methods is compared with that of the present invention. Experimental data show that, compared to other methods, the fault detection technology proposed in this invention is more sensitive to minor faults in complex industrial systems, yields more accurate detection results, and achieves the highest fault detection rate. Specific values ​​for the fault detection rate are detailed in Table 3.

[0166] Sensor drift fault:

[0167] This addresses sensor drift faults that occur during the CSTH process. Because sensor drift faults have a minimal impact on the CSTH process, with almost no change in the mean and variance of the fault data, traditional data-driven methods cannot detect sensor drift faults.

[0168] Following the same steps as for deviation faults, a dynamic covariance Mahalanobis kernel-based single-class support vector machine model is trained. Test data is then fed into the trained model to obtain a score matrix, which is compared with a dynamic threshold to complete fault detection. The fault detection performance of principal component analysis (PCA), Mahalanobis distance (MD), and single-class support vector machine (OCSVM) methods is compared with that of the present invention. Experimental results show that the fault detection method of the present invention has significantly stronger perception capabilities and higher detection accuracy for subtle faults in complex industrial systems. Specific values ​​for the fault detection rate are detailed in Table 3.

[0169] Table 3 Comparison of fault detection rates among different CSTH methods

[0170]

[0171] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for detecting minute faults based on Dynamic Covariance Markov Kernel OCSVM, characterized in that, Includes the following steps: Step S1: Obtain normal operating condition data from the historical database Using its mean and standard deviation Historical data Standardization, to obtain standardized training data ; Step S2: Calculate the training data after adding a regularization term. global covariance ; Step S3: Using a sliding window Calculate local covariance By dynamically fusing local and global covariances through sliding window size and attenuation coefficient, a hybrid covariance matrix is ​​constructed. ; Step S4: Based on the mixture covariance matrix Construct a dynamic Markov kernel function; In step S4, based on the mixed covariance matrix The dynamic Markov kernel function is constructed as follows: For the sample , Its dynamic Mahalanobis distance is: ； Dynamic Markov kernel function based on mixed covariance matrix Mahalanobis distance is used to measure the similarity between samples, and its mathematical form is: ； In the formula, A value greater than 0 indicates the scaling parameter of the kernel function. For the first The mixture covariance matrix at each sampling time; Step S5: Using a sliding window Extract training data For each window, a single-class support vector machine (OCSVM) model is trained. ; Step S6: Based on each training data The abnormal score is used to calculate the corresponding dynamic threshold; Step S7: Collect data from the industrial production process and process the data using the same method as in Step S1 to obtain the test dataset. ; Step S8: For Use the same sliding window method as in step S5 to capture test data. Using the OCSVM model trained in S5 Calculate the anomaly score for the corresponding test data; Step S9: Compare the abnormal score of the obtained test data with the corresponding dynamic threshold. If the abnormal score is greater than the dynamic threshold, a fault has occurred; otherwise, no fault has occurred.

2. The method for detecting minute faults based on dynamic covariance Markov kernel OCSVM according to claim 1, characterized in that, In step S1, normal operating condition data from the historical database is obtained. Using its mean and standard deviation Historical data Standardization, to obtain standardized training data for: ； In the formula, , For the sample size, Number of variables.

3. The method for detecting minute faults based on dynamic covariance Markov kernel OCSVM according to claim 2, characterized in that, In step S2, the training data is calculated after adding a regularization term. global covariance for: ； In the formula, It is a small constant. It is an identity matrix.

4. The method for detecting minute faults based on dynamic covariance Markov kernel OCSVM according to claim 3, characterized in that, In step S3, a sliding window is used. Calculate local covariance By dynamically fusing local and global covariances through sliding window size and attenuation coefficient, a hybrid covariance matrix is ​​constructed. : Sliding window The parameters are set as follows: window width is set to The step size is set to 1, and the data is moved forward once at each sampling time. The number of data samples is... There are a total of The sampling time; for the first sampling time; Each sampling time: ； In the formula, ; Through attenuation coefficient Controlling the fusion ratio of global and local covariance: . ； For sliding windows The width of the sliding window; Constructed covariance matrix The calculation is as follows: 。 5. The method for detecting minute faults based on dynamic covariance Markov kernel OCSVM according to claim 4, characterized in that, In step S5, the sliding window is used. Extract training data For each window, a single-class support vector machine (OCSVM) model is trained. The specific steps are as follows: S5.1: Training process of OCSVM model: Given a training dataset , Given from To a certain high-dimensional feature space nonlinear mapping , making To establish a hyperplane in higher-dimensional space The mapped samples are spaced apart from the origin. Separate, among them Let be the normal vector of the hyperplane. The intercept of the hyperplane; The optimization problem of OCSVM is: ； in, and For hyperplane parameters, It is a predefined percentage parameter estimate. The total number of samples, Similar to the penalty coefficient C in standard support vector machines, representing the upper bound of the boundary support vector rate and the lower bound of the overall support vector rate, we introduce the Lagrange function: ； Minimize each , and have to: ； ； ； Substituting the above three formulas into equation (9), the Mercer kernel function is used to replace the space. The inner product on, i.e. Thus, we arrive at the dual problem: ； And it satisfies the Caro-Kun-Tucker condition (KKT). and ; Parameters in formula (10) , by any satisfying The sample is obtained, that is Then the decision function can be written as: ； S5.2: Sliding Window The parameters are set as follows: window width is set to The step size is set to 1, and the data is moved forward once at each sampling time. The number of data samples is... The total number of windows is One, corresponding to At the sampling time, for the first sampling time... Each sampling time; Training data The extracted data is: ； in, , , ; That is, the first The sliding window data is Mixed covariance within the current window Generated from step S3, i.e., the calculation of the kernel matrix: ； in: ； S5.3: Substitute the kernel matrix above into the OCSVM training process described above, that is, train an OCSVM model for each window, denoted as... Training score for each window ; 。 6. The method for detecting minute faults based on dynamic covariance Markov kernel OCSVM according to claim 5, characterized in that, In step S6, based on the training data The dynamic threshold corresponding to the abnormal score calculation is: As can be seen from step S5, for each time point They all trained a corresponding The model, obtained from formula (19), yields the first... Training score at each sampling time point A window contains At any given moment, that is, within this window there are a total of Training scores: ； calculate mean with standard deviation The dynamic threshold is obtained from the empirical distribution law. : ； in, Set it to 3.

7. The method for detecting minute faults based on Dynamic Covariance Markov Kernel OCSVM according to claim 6, characterized in that, In step S7, data from the industrial production process is collected and processed in the same way as in step S1 to obtain a test dataset. for: ； In the formula, , For the sample size, Number of variables.

8. The method for detecting minute faults based on dynamic covariance Markov kernel OCSVM according to claim 7, characterized in that, In step S8, for Use the same sliding window method as in step S5 to capture test data. Using the OCSVM model trained in S5 The anomaly score for the corresponding test data is calculated as follows: 。 9. The method for detecting minute faults based on dynamic covariance Markov kernel OCSVM according to claim 8, characterized in that, In step S9, the anomaly score of the obtained test data is compared with the corresponding dynamic threshold. If the anomaly score is greater than the dynamic threshold, a fault has occurred; otherwise, no fault has occurred. The specific steps are as follows: In step S8, the Corresponding abnormal scores All have been calculated, and the dynamic threshold has been determined. Comparison : ； The online testing process can then be completed.

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