Quality-related minor fault detection method based on dynamic orthogonal subspace

Abstract

The present invention discloses a quality-related minor fault detection method based on dynamic orthogonal subspace, which belongs to the field of complex industrial process modeling and fault diagnosis. The method dynamically augments the data by inputting a time lag value, so that the variables with a greater impact on minor faults in the current moment sample can appear multiple times, amplifying the impact of minor faults on the current moment sample, decomposing process data and quality-related data by OSA, effectively separating quality-related components from quality-irrelevant components, so that the method can further determine whether the minor fault will affect the product quality of the process output after detecting the minor fault; at the same time, the method calculates the KL divergence based on two groups of different normal process data to extract the common features of normal data, distinguish minor faults, and constructs a fault detection statistic that is more sensitive to minor faults based on the calculated KL divergence between the score vectors for the low amplitude characteristics of minor faults, thereby improving the alarm rate for minor faults.

Description

Technical Field

[0001] The invention relates to a quality-related minor fault detection method based on dynamic orthogonal subspace, and belongs to the field of complex industrial process modeling and fault diagnosis. Background Art

[0002] Fault detection technology plays an important role in ensuring the safe and stable operation of large-scale complex chemical processes and obtaining continuous and stable product quality. Fault detection methods are mainly divided into two categories: model-based and data-based methods. Among them, data-driven multivariate statistical process monitoring methods have received widespread attention and application because they do not require accurate system models, only rely on system measurement data, and have the ability to effectively process multivariate process data. Common multivariate statistical process monitoring methods include principal component analysis (PCA), partial least squares (PLS), and canonical correlation analysis (CCA). Among them, PLS and CCA can effectively process the correlation between process variables and quality variables and are the most commonly used quality-related fault detection methods. However, both PLS and CCA cannot completely separate the quality-related components of process data (also known as key variables, such as the quality of raw materials, temperature, pressure, time in the production process, etc.) from the quality-irrelevant components (also known as non-key variables, such as the noise level and lighting conditions in the production environment, etc.), thereby reducing the quality-related fault detection capability.

[0003] In order to enhance the ability of PLS ​​to extract quality-related components, Zhou et al. proposed a full latent structure projection algorithm (see ZHOUD H, LI G, QIN S J. Total projection to latent structures for process monitoring [J]. AIChE Journal, 2010, 56 (1): 168-178.). After PLS decomposition, the process variable space is further divided into 4 subspaces to further separate the quality-related components and quality-independent components of the process data, thereby improving the quality-related fault detection capability. Based on the traditional orthogonalization method and kernel method, Ma et al. proposed a kernel direct orthogonal PLS method (see MA H, WANGY, JI ZC, et al. A novel three-stage quality oriented data-driven nonlinear industrial process monitoring strategy [J]. IEEE Transactions on Instrumentation and Measurement, 2022, 71: 1-11.), which effectively enhanced the ability of kernel PLS to extract quality-related components and improved the ability of kernel PLS to detect quality-related faults in nonlinear processes. In order to deal with the quality-related component problem of kernel CCA, Chen et al. proposed two methods to improve kernel CCA through two singular value decompositions to improve the kernel CCA's ability to detect quality-related faults in nonlinear processes (see CHEN Q, WANG Y Q. Key-performance-indicator-related state monitoring based on kernel canonical correlation analysis [J]. Control Engineering Practice, 2021, 107: 104692.).

[0004] Although the above methods can separate quality-related components from quality-independent components to a certain extent, there is still the problem of incomplete separation. Different from directly improving PLS and CCA, Lou et al. proposed a new quality-related fault detection method (see LOU ZJ, WANG YQ, SI YB, et al. A novel multivariate statistical process monitoring algorithm: Orthonormal subspace analysis [J]. Automatica, 2022, 138: 110148.), called orthonormal subspace analysis (OSA). This method divides process data and quality-related data into three orthogonal subspaces, and then monitors these three orthogonal subspaces separately through PCA and selects the principal component using the cumulative percent variance (CPV) method, thereby effectively solving the problem of incomplete separation of quality-related and quality-independent components in PLS and CCA, thereby improving the quality-related fault detection capability of PLS ​​and CCA. Hao et al. further extended OSA into a dynamic version based on the input hysteresis value (see HAOW C, LU S, LOU ZJ, et al. A novel dynamic process monitoring algorithm: dynamic orthonormal subspace analysis [J]. Processes, 2023, 11 (7): 1935.). However, OSA cannot distinguish the characteristics of minor faults from noise, and therefore cannot effectively detect minor faults in the process. Minor faults refer to slight anomalies, which are easily masked by noise, interference and normal conditions, making them difficult to detect. However, some minor faults will gradually evolve and accumulate, leading to major accidents. In order to detect minor faults, Liu et al. proposed a PCA-based ensemble detector (see LIU DC, SHANG J, CHEN M Y. Principal component analysis-based ensemble detector for incipient faults in dynamic processes [J]. IEEE Transactions on Industrial Informatics, 2020, 17 (8): 5391-5401.), which effectively detected faults 3, 9 and 15 in the TE process.Deng et al. proposed an enhanced CVDA method to improve the detection capability of canonical variate dissimilarity analysis (CVDA) for minor faults by integrating probability information and fault-sensitive feature information (see DENG XG, LIU XY, CAO YP, et al. Incipient fault detection for dynamic chemical processes based on enhanced CVDA integrated with probability information and fault-sensitive features [J]. Journal of Process Control, 2022, 114: 29-41.). Considering that linear and nonlinear relationships coexist in most industrial processes, Wu et al. used a serial model structure to tightly integrate CVDA and mixed kernel principal component analysis to improve the detection capability of minor faults (see WU P, FERRARI RMG, LIU YC, et al. Data-driven incipient fault detection via canonical variate dissimilarity and mixed kernel principal component analysis [J]. IEEE Transactions on Industrial Informatics, 2020, 17 (8): 5380-5390.).

[0005] Although the above methods have improved the detection capability of minor faults, there is still room for further improvement in the detection capability of quality-related faults. In order to detect minor faults while detecting quality-related faults, Dong et al. combined canonical variate analysis with KL divergence and proposed a new method for minor fault detection (see DONG J, JIANG LZ, ZHANG C, et al. A novel quality-related incipient fault detection method based on canonical variate analysis and Kullback–Leibler divergence for large-scale industrial processes [J]. IEEE Transactions on Instrumentation and Measurement, 2022, 71: 1-10.). However, this method cannot completely separate the quality-related components from the quality-irrelevant components, so its quality-related fault detection rate needs to be further improved, and the false alarm rate of quality-irrelevant faults may be further reduced. Summary of the invention

[0006] In order to achieve complete separation of quality-related components from quality-irrelevant components to further improve the quality-related fault detection rate and reduce the false alarm rate of quality-irrelevant faults, the present invention provides a quality-related minor fault detection method based on dynamic orthogonal subspace. On the one hand, an augmented matrix reflecting the dynamic characteristics of process data and quality-related data is constructed based on the input time lag value, and the OSA is expanded into a dynamic version, thereby enhancing the ability of the OSA method to monitor dynamic processes and effectively extracting the dynamic characteristics of process data. On the other hand, the probability distribution difference of the score vector before and after the fault occurs is measured by the KL divergence of two groups of normal process data, and the probability-related information implicit in the score vector is integrated to realize the detection of quality-related minor faults. The method includes two parts: offline modeling and online detection.

[0007] Optionally, the offline modeling part in the method includes:

[0008] Step (1) Collect process data under normal conditions and quality related data right and Perform augmentation and preprocessing to obtain the corresponding augmented matrix containing the static and dynamic features of the process and

[0009] Step (2) and Perform orthogonal subspace decomposition to obtain each subspace E OSA 、F OSA ;

[0010] Step (3) For each subspace E OSA 、F OSA Perform PCA decomposition, where the subspace Decompose to get the principal component score matrix T com and the residual score matrix T r ;

[0011] Step (4) Collect another set of process data under normal conditions and quality related data Will and Augmented to get X v and Y v , and then preprocessed and decomposed into E v,OSA 、F v,OSA ; Then E v,OSA 、F v,OSA PCA decomposition is performed separately, where After decomposition, we get the principal component score matrix T v,com and the residual score matrix T v,r ;

[0012] Step (5), first calculate T com The mean vector μ 1 and variance vector Then in T com and T v,com Slide the window step by step and calculate the mean vector μ of the sliding window data 2 and variance vector Continuously update μ 2 and And calculate and update T com The principal component score vector s at time t t ; while calculating T r The mean vector μ 3 and variance vector Then in T r and T v,r Slide the window step by step and calculate the mean vector μ of the sliding window data 4 and variance vector Continuously update μ 4 and And calculate and update T r The residual score vector g at time t t ;

[0013] Step (6), according to the principal component score vector s t and the residual score vector g t Calculate the KL divergence of the two sets of data to obtain the probability-related principal component score vector The residual score vector associated with the probability And by and Construct probability-dependent fault detection statistics D KL,1 , D KL,2 , the control limits are calculated by the kernel density estimation method;

[0014] Step (7), construct E OSA 、F OSA The probability correlation T 2 and SPE statistic Monitor each subspace independently;

[0015] Step (8), first calculate from arrive The transfer matrix and arrive The transfer matrix Recalculate to T com The transfer matrix Θ X→T and to T com The transfer matrix Θ Y→T ,Will and Transfer to T com and calculate and determine its control limits.

[0016] Optionally, the online detection part in the method includes:

[0017] Step 1: Collect online process data samples and quality-related data samples, augment and preprocess them, and obtain the corresponding augmented matrix X containing process static and dynamic features. w and Y w ;

[0018] Step 2, calculate X w and Y w Each subspace of

[0019] Step 3: The principal component score matrix Instead of the principal component score matrix T corresponding to another set of process data collected in step (4) under normal conditions in the offline modeling processv,com , calculate and update μ 2 and by The residual score matrix Instead of T v,r , calculate and update μ 4 and Calculate the probability correlation T of online samples 2 and SPE statistics;

[0020] Step 4, calculate X w and Y w Common information and And calculate the online sample Statistics;

[0021] Step 5, compare the size of each statistic with the corresponding control limit. If any statistic exceeds the control limit, it is considered that a fault has occurred.

[0022] Optionally, the method may be used to process the process data and quality related data When augmenting, include:

[0023] The original process data and quality-related data are and where x(i)∈R s (i=1,2,…n),y(j)∈R r (j=1,2,…n), according to the following formula and To expand:

[0024]

[0025] in, d is the time lag parameter.

[0026] Optionally, the step (2) is and Before the orthogonal subspace decomposition, and To standardize:

[0027]

[0028] in, and They are The mean vector and standard deviation diagonal matrix of and They are The mean vector and standard deviation diagonal matrix of and is a column vector whose elements are all 1, and T represents the transpose operation.

[0029] Optional, yes Performing PCA decomposition includes:

[0030]

[0031] Where T com ∈R n×k is the principal component score matrix, P com ∈R s×k is the principal component loading matrix, T r ∈R n×(s-k) is the residual score matrix, P r ∈R s×(s-k) is the residual loading matrix, and k is the number of principal components.

[0032] Optionally, the transfer matrix in step 1 is:

[0033] The present application also provides a method for detecting quality-related minor faults in a TE process, which uses the above-mentioned quality-related minor fault detection method based on dynamic orthogonal subspace for detection.

[0034] The TE process consists of five main units, namely, reactor, separator, stripper, condenser and compressor. The process contains 53 variables, including 22 continuous process variables, 19 sampled process variables and 12 manipulated variables; the process data matrix is ​​constructed with 22 of the continuous process variables and sampled process variables and 11 of the manipulated variables. The measured variables XMES(35) and XMES(36) of products G and H are used to construct the quality-related data matrix

[0035] The beneficial effects of the present invention are:

[0036] 1. In order to solve the problem that the low amplitude of minor faults makes them difficult to detect, step (1) in the offline modeling of this scheme dynamically augments the data by inputting the time lag value, so that the variables with greater impact on the minor faults in the current moment sample can appear multiple times, thereby amplifying the impact of the minor faults on the current moment sample. Combined with the subsequent steps, this scheme makes it easier to measure the impact of minor faults on the current moment sample and improve the fault alarm rate of the detection method.

[0037] 2. In order to solve the problem that it is difficult to separate quality-related components from quality-irrelevant components, step (2) in the offline modeling of this solution decomposes the process data and quality-related data through OSA, thereby effectively separating the quality-related components from the quality-irrelevant components, so that the proposed detection method can further determine whether the minor fault will affect the product quality of the process output after detecting the minor fault.

[0038] 3. In view of the fact that process noise, interference and measurement errors make it difficult to directly calculate the KL divergence of accurate process data, this offline modeling solution is different from the existing method of calculating the KL divergence based on only one set of normal process data, but calculates the KL divergence based on two different sets of normal process data. In this way, the common features of normal data can be extracted to distinguish minor faults.

[0039] 4. In view of the problem that the low amplitude of minor faults makes them difficult to detect, this scheme constructs a fault detection statistic that is more sensitive to minor faults based on the calculated KL divergence between the score vectors in line modeling, thereby improving the alarm rate of the detection method for minor faults. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0041] Figure 1 This is a partial flow chart of the fault detection method based on dynamic orthogonal subspace analysis and KL divergence provided in this application.

[0042] Figure 2A This application method The principal component score vector s after dimensionality reduction t Scatter plot of ;

[0043] Figure 2B is the probability-related principal component score vector in this application method A scatter plot of .

[0044] Figure 3 This is a diagram showing the detection results of the numerical case fault 1 using the method of the present application.

[0045] Figure 4 This is a diagram showing the detection results of TE process fault 9 using the method of the present application.

[0046] Figure 5 This is a diagram showing the detection results of TE process fault 13 using the method of the present application.

[0047] Fig. 6AThis is the sampling result diagram of TE process product G;

[0048] Figure 6B This is the sampling result diagram of TE process product H.

[0049] Fig. 7A is the data augmentation subgraph in PR-DOSA provided by this application;

[0050] Figure 7B is the orthogonal subspace decomposition subgraph in PR-DOSA provided by this application;

[0051] Figure 7C It is the KL divergence subgraph calculated by single-step sliding window in PR-DOSA provided by this application. DETAILED DESCRIPTION

[0052] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0053] First, the relevant concepts involved in this application are introduced as follows:

[0054] 1. OSA-based fault detection method

[0055] Assume that the preprocessed process data is X∈R n×s , quality-related data is Y∈R n×r , where n is the number of samples, s is the number of process variables, and r is the number of quality variables. OSA decomposes X and Y into a bilinear form:

[0056]

[0057] in is a common latent variable of X and Y, satisfying T com =XΞ X =YΞ Y , and is the transfer matrix.

[0058] and is the common component space of X and Y, which can be expressed as:

[0059]

[0060] in, For variable Y to variable The transfer matrix, For variables Transfer matrix to variable Y.

[0061]

[0062] E OSA and F OSA is the residual matrix of X and Y:

[0063]

[0064] From this, we can get three subspaces: (1) The common component subspace of X and Y and (2) The residual subspace E of X OSA ; (3) The residual subspace F of Y OSA These three subspaces are mutually orthogonal. With E OSA 、F OSA Orthogonal, that is With E OSA 、F OSA Orthogonal, that is E OSA With F OSA Orthogonal E OSA T F OSA =0, so PCA can be used to perform fault detection on each space separately.

[0065] 2. KL divergence

[0066] KL divergence, also known as relative entropy, is an important statistical measurement method, usually used to measure the difference between two probability density functions. [21-22] For two probability density functions, the larger the KL divergence, the greater the difference between the functions. The KL divergence between two probability density functions f(x) and g(x) is defined as:

[0067]

[0068] According to formula (5), KL divergence is asymmetric and does not satisfy the distance characteristics. A symmetric KL divergence metric with distance significance is constructed:

[0069] KL(f,g)=I(f,g)+I(g,f). (6)

[0070] According to equation (6), KL(f,g) is non-negative, KL(f,g) = 0 if and only if f = g. Assume that the probability density function of two Gaussian distribution signals is and Then I(f,g) can be expressed as:

[0071]

[0072] According to equations (6) and (7), KL(f,g) can be written as:

[0073]

[0074] 3. Minor fault detection method based on probability-dependent dynamic OSA

[0075] The OSA method uses PCA to model each subspace obtained by decomposition and constructs T 2 As fault detection statistics, the SPE statistic can effectively detect quality-related and quality-irrelevant faults, but the detection capability of minor faults is insufficient.

[0076] In order to improve the detection capability of OSA for minor faults, this application improves OSA from two aspects and proposes a fault detection method based on dynamic orthogonal subspace analysis and KL divergence (probability-related dynamic OSA, PR-DOSA). The structure of the proposed method is as follows: Figure 1 As shown, the detailed sub-graphs of each part are as follows Fig. 7A , Figure 7B and Figure 7C shown.

[0077] On the one hand, OSA is extended to a dynamic version. Considering that chemical processes often exhibit dynamic characteristics, in order to enhance the ability of OSA method to monitor dynamic processes, the dynamic characteristics of process data are effectively extracted, and an augmented matrix of the dynamic characteristics of the reaction system is constructed. On the other hand, the probability-related information implicit in the score vector obtained after PCA decomposition is integrated. The KL divergence is used to measure the difference in the probability distribution of the score vector before and after the fault occurs, and a probability-related detection statistic based on KL divergence is constructed for fault detection.

[0078] Embodiment 1:

[0079] This embodiment provides a fault detection method based on dynamic orthogonal subspace analysis and KL divergence (probability-related dynamic OSA, PR-DOSA), including:

[0080] Assume that the original process data and quality-related data are and where x(i)∈R s (i=1,2,…n),y(j)∈R r (j=1,2,…n), and The augmentation is performed as shown in formula (9).

[0081]

[0082]

[0083] d is the time lag parameter, and the number of variables in the augmented data is s = m(d+1). Thus, an augmented matrix containing the static and dynamic characteristics of the process is generated.

[0084] Next, and To standardize:

[0085]

[0086] in and They are The mean vector and standard deviation diagonal matrix of and They are The mean vector and standard deviation diagonal matrix of and is a column vector whose elements are all 1. Then and Perform PCA decomposition:

[0087]

[0088] So we can get from formula (12) and The principal component with a CPV (Cumulative Proportion of Variance) exceeding 99.9% is selected, so that and The column is full rank, so that and Reversible.

[0089]

[0090] Then, through equations (13)-(14) and Perform orthogonal subspace decomposition to obtain E OSA 、F OSA Considering the situation that quality-related data is unavailable during the online testing phase, it is necessary to calculate from arrive arrive The transfer matrix and Thus we get and When the degrees of freedom of the latent variable is no greater than that of the original data,

[0091]

[0092] Then, for each subspace E OSA 、F OSA Perform PCA decomposition. Decomposition as an example:

[0093]

[0094] Where T com ∈R n×k is the principal component score matrix, P com ∈R s×k is the principal component loading matrix, T r ∈R n×(s-k) is the residual score matrix, P r ∈R s×(s-k) is the residual loading matrix, k is the number of principal components, and the principal components with CPV exceeding 85% are selected.

[0095] remember Decomposed T com The principal component score vector at time t is s t =[s t,1 s t,2 …s t,a ] T (a=k), for the i-th component s t,i , assuming s t,i If the data is normally distributed, then the two different groups of data correspond to the i-th component s t,i The KL divergence between can be calculated as:

[0096]

[0097] where μ 1,i and for and Corresponding t,i Mean and variance of the components, μ 2,i and for and Corresponding t,i Ingredients The mean and variance of and Another set of normal samples is used to calculate the process data and quality-related data for the control limit. and is the online test data, and p is the number of samples. At the tth moment, μ 2,i and The sliding window technique yields:

[0098]

[0099] Where l is the sliding window length. Thus, the probability-related principal component score vector is obtained remember Decomposed T r The residual score vector at time t is g t =[g t,1 g t,2 …g t,b ] T (b=sk), then the probability-related residual score vector And by and Construct probability-dependent fault detection statistics D KL,1 , D KL,2 , the control limits are calculated by the kernel density estimation method:

[0100]

[0101] Through equations (16)-(22), we can construct E OSA 、F OSA The probability correlation T 2 and SPE statistic Each subspace is monitored independently.

[0102] is the common component space, and the common component can be calculated as or So ideally where Θ X→T for to T com The transfer matrix, Θ Y→T for to T com The transfer matrix can be calculated as:

[0103]

[0104] T com and The probability-related principal component score matrix is ​​obtained by equations (18)-(20). and The corresponding fault detection statistics are constructed by equations (21)-(22): and To monitor the common component space, another statistic can be constructed:

[0105]

[0106] This statistic can monitor the relationship between online process data samples and quality data samples. Its control limit is obtained by kernel density estimation method.

[0107] When online quality data are available, all test statistics are available; when online quality data are not available, Available. You can choose to use all or some of the statistics as needed.

[0108] This application extends the orthogonal subspace analysis method to dynamic process monitoring, and uses KL divergence to construct a new probability-related fault detection statistic, and proposes a quality-related minor fault detection method based on dynamic orthogonal subspace and KL divergence. The method mainly consists of two parts: offline modeling and online detection. The specific steps are as follows:

[0109] Offline Modeling:

[0110] (1) Collecting process data under normal conditions and quality related data Through equations (9)-(12) and After augmentation and preprocessing, we can obtain and

[0111] (2) Through equations (13)-(14) and Decompose and obtain E OSA 、F OSA ;

[0112] (3) Through equations (16)-(17) Perform PCA decomposition on E OSA 、F OSA Perform the same PCA decomposition;

[0113] (4) Collect another set of process data under normal conditions and quality related data Will and Augmented to get X v and Y v , and then preprocessed and decomposed into E v,OSA 、F v,OSA Then E v,OSA 、F v,OSA PCA decomposition is performed separately, where After decomposition, we get the principal component score matrix T v,com and the residual score matrix T v,r .

[0114] (5) Calculate T first com The mean vector μ 1 and variance vector Then in T com and T v,com The window is gradually sliding upward, and the mean vector μ of the sliding window data is calculated by equations (19)-(20) 2 and variance vector Continuously update μ 2 and And calculate and update s through formula (18) t ; Similarly, T can be calculated r The mean vector μ 3 and variance vector Then in T r and T v,r Slide the window step by step and calculate the mean vector μ of the sliding window data 4 and variance vector Continuously update μ 4 and And calculate and update g t ; Construct the probability correlation T through equations (21)-(22) 2 and SPE monitoring statistics And calculate the control limits, It is also constructed in the same way;

[0115] (6) First calculate through formula (14) and Then calculate Θ using formula (23) X→T and θ Y→T ,Will and Transfer to T com and Calculated by formula (24) and determine its control limits.

[0116] Online detection:

[0117] (1) Collect online process data samples and quality-related data samples, augment and preprocess them, and obtain X w and Y w ;

[0118] (2) Calculate X using equations (13) and (15): w and Y w Each subspace of

[0119] (3) The principal component score matrix Instead of Tv,com , calculate and update μ 2 and by The residual score matrix Instead of T v,r , calculate and update μ 4 and Calculate the probability correlation T of online samples 2 and SPE statistics;

[0120] (4) Calculate X by formula (23) w and Y w Common information and And calculate the online sample through (24) Statistics.

[0121] This application uses fault detection rate (FDR) and false alarm rate (FAR) as method evaluation indicators, which are defined as follows:

[0122]

[0123] Where N 1 and N 2 are the number of fault samples and the number of normal samples, N 1,f and N 2,f are the number of faulty samples detected in faulty samples and normal samples, respectively.

[0124] This scheme improves the OSA algorithm, verifies the effectiveness of the proposed algorithm through numerical simulation and applies it to the TE process, which contains five main units, namely, reactor, separator, stripper, condenser and compressor. The process contains 53 variables, including 22 continuous process variables, 19 sampling process variables, and 12 manipulated variables. In this embodiment, 22 continuous process variables and 11 manipulated variables (the 12 manipulated variables include stirring speed, which is usually kept unchanged, so it is not selected) are selected to construct the process data matrix The measured variables XMES(35) and XMES(36) of products G and H are used to construct the quality-related data matrix For a detailed introduction, please refer to the record in "DOWNS JJ, VOGEL E FA plant-wide industrial process control problem [J]. Computers & Chemical Engineering, 1993, 17 (3): 245-255." The description of 21 types of faults in the process is shown in Table 1 below:

[0125] Table 1 TE process fault description

[0126]

[0127] Both PR-DOSA and OSA have 9 statistics, among which the statistics of PR-DOSA are Statistics with OSA SPE Y , SPE F It can be used directly to determine whether the fault is related to quality.

[0128] The statistics of PR-DOSA and OSA are divided into two categories according to whether they can directly distinguish quality-related and quality-independent faults. The numerical simulation results of various statistics are shown in Tables 2 and 3. Comparative analysis shows that PR-DOSA can effectively detect all the above 9 faults, while OSA can only effectively detect 5 of them, which effectively verifies the detection ability of PR-DOSA for minor faults compared with OSA.

[0129] Fault 9 occurs when the hidden variable s 3 The fault affects all input and output variables and is a quality-related fault. As shown in Tables 2 and 3, all statistics of OSA cannot detect the fault, while the six statistics of PR-DOSA proposed in this application can detect the fault, and the fault detection rate of four of them exceeds 90%.

[0130] In order to verify the effectiveness of the probability correlation score vector constructed by PR-DOSA proposed in this application for fault detection, the The principal component score vector s after dimensionality reduction t and the corresponding probability-related principal component score vector Detection results for fault 9. Figure 2A Given s t A scatter plot of Figure 2B Given A scatter plot of Figure 2A All fault samples are included in Figure 2B It contains the first 400 fault samples, where blue represents the score vector corresponding to normal data and yellow represents the score vector corresponding to fault 9.

[0131] Figure 3 The detection result of PR-DOSA for fault 1 is shown. In the figure, green represents normal samples in the data set, blue represents fault samples, and red represents control limits. Exceeding the control limits indicates that a fault has occurred.

[0132] Table 2 PR-DOSA and OSA fault detection results 1 (%)

[0133]

[0134] Table 3 PR-DOSA and OSA fault detection results 2 (%)

[0135]

[0136] Next, the detection capability of PR-DOSA for all types of faults in the TE process is verified, and a comparative analysis is performed with the OSA method in the quality-related fault detection method proposed by Lou et al. Both methods select the principal component with a CPV of more than 85%. In the PR-DOSA method, the time lag parameter d is set to 4, the sliding window length l is set to 200, and d and l are selected according to the cross-validation method. The confidence level of each statistic is 99%. The TE process detection results of various statistics are shown in Tables 4 and 5.

[0137] Table 4 PR-DOSA and OSA TE process fault detection results 1 (%)

[0138]

[0139] Table 5 PR-DOSA and OSA TE process fault detection results 2 (%)

[0140]

[0141] The fault detection results of the TE process show that PR-DOSA effectively improves the fault detection capability of OSA. By comparing the best detection results of 9 statistics of PR-DOSA and OSA for each fault, it is shown that the detection results of PR-OSA for faults 3, 5, 9, 10, 11, 15, 16, 19, 20, and 21 are significantly better than those of OSA. Especially for minor faults 3, 9, and 15, when the OSA method cannot effectively detect them, the fault detection rates of PR-DOSA reach 96.8%, 98.3%, and 75.3%, respectively. Figure 4 The detection result diagram of PR-DOSA for fault 9 is given. Figure 4 It can be seen that The statistic shows good detection capability for fault 9, while other statistics cannot detect the fault in a timely and effective manner.

[0142] The following is an analysis of the detection capability of PR-DOSA for quality-related faults. From the detection results of the statistics in Table 5, it can be seen that for quality-related faults 1, 2, 5, 6, 7, 8, 10, 12, and 13 among the 21 faults in the TE process, PR-DOSA significantly improves the fault detection rate of faults 1, 2, 5, 7, 8, 10, 12, and 13 compared with OSA, indicating that PR-DOSA effectively improves the detection capability of OSA for quality-related faults. Figure 5 The detection result of PR-DOSA for fault 13 is given. Figure 5 It can be seen that the nine statistics all show good detection capabilities for fault 13. For TE process unknown type faults 16-20, it is also necessary to determine whether they are quality-related faults. As shown in Table 5, most statistics show a high fault detection rate for fault 18, indicating that fault 18 is likely to be a quality-related fault. Fig. 6A and Figure 6B The following are the measured variable diagrams of products G and H, respectively, where green corresponds to normal data and red corresponds to fault 18. Fig. 6A and Figure 6B It can be seen that after fault 18 occurs, both G and H deviate from the set values, indicating that fault 18 is a quality-related fault. Therefore, it is verified that for unknown type faults, both methods can determine whether the fault is related to quality, and both methods have good quality-related fault detection capabilities.

[0143] Some steps in the embodiments of the present invention may be implemented using software, and the corresponding software program may be stored in a readable storage medium, such as a CD or a hard disk.

[0144] 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 principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A quality-related minor fault detection method based on dynamic orthogonal subspace, characterized in that: On the one hand, the method constructs an augmented matrix reflecting the dynamic characteristics of process data and quality-related data based on the input time lag value, expands OSA into a dynamic version, enhances the ability of OSA method to monitor dynamic processes, and effectively extracts the dynamic characteristics of process data; on the other hand, the probability distribution difference of the score vector before and after the fault occurs is measured by the KL divergence of two groups of normal process data, and the probability-related information implicit in the score vector is integrated to realize the detection of quality-related minor faults. The method includes two parts: offline modeling and online detection; the offline modeling part of the method includes: Step (1): Collect process data under normal conditions and quality related data right and Perform augmentation and preprocessing to obtain the corresponding augmented matrix containing the static and dynamic features of the process and Step (2), and Perform orthogonal subspace decomposition to obtain each subspace E OSA 、F OSA ; Step (3), for each subspace E OSA 、F OSA Perform PCA decomposition, where the subspace Decompose to get the principal component score matrix T com and the residual score matrix T r ; Step (4), collect another set of process data under normal conditions and quality related data Will and Augmented to get X v and Y v , and then preprocessed and decomposed into E v,OSA 、F v,OSA ; Then E v,OSA 、F v,OSA PCA decomposition is performed separately, where After decomposition, we get the principal component score matrix T v,com and the residual score matrix T v,r ; Step (5), first calculate T com The mean vector μ1 and variance vector Then in T com and T v,com Slide the window step by step to calculate the mean vector μ2 and variance vector of the sliding window data Continuously update μ2 and And calculate and update T com The principal component score vector s at time t t ; while calculating T r The mean vector μ3 and variance vector Then in T r and T v,r Slide the window step by step to calculate the mean vector μ4 and variance vector of the sliding window data Continuously update μ4 and And calculate and update T r The residual score vector g at time t t ; Step (6), according to the principal component score vector s t and the residual score vector g t Calculate the KL divergence of the two sets of data to obtain the probability-related principal component score vector The residual score vector associated with the probability And by and Construct probability-dependent fault detection statistics D KL,1 , D KL,2 , the control limits are calculated by the kernel density estimation method; Step (7), construct E OSA 、F OSA The probability correlation T 2 and SPE statistic Monitor each subspace independently; Step (8), first calculate from arrive The transfer matrix and arrive The transfer matrix Recalculate to T com The transfer matrix Θ X→T and to T com The transfer matrix Θ Y→T ,Will and Transfer to T com and calculate and determine its control limit; the online detection part in the method includes: Step 1: Collect online process data samples and quality-related data samples, augment and preprocess them, and obtain the corresponding augmented matrix X containing process static and dynamic features. w and Y w ; Step 2, calculate X w and Y w Each subspace of Step 3: The principal component score matrix Instead of the principal component score matrix T corresponding to another set of process data collected in step (4) under normal conditions in the offline modeling process v,com , calculate and update μ2 and by The residual score matrix Instead of T v,r , calculate and update μ4 and Calculate the probability correlation T of online samples 2 and SPE statistics; Step 4, calculate X w and Y w Common information and And calculate the online sample Statistics; Step 5, compare the size of each statistic with the corresponding control limit. If any statistic exceeds the control limit, it is considered that a fault has occurred; The pair Performing PCA decomposition includes: Where T com ∈R n×k is the principal component score matrix, P com ∈R s×k is the principal component loading matrix, T r ∈R n×(s-k) is the residual score matrix, P r ∈R s×(s-k) is the residual loading matrix, k is the number of principal elements; The transfer matrix is:

2. The method according to claim 1, characterized in that In the method, the process data and quality related data When augmenting, include: The original process data and quality-related data are and where x(i)∈R s (i=1,2,…n),y(j)∈R r (j=1,2,…n), according to the following formula and To expand: in, d is the time lag parameter.

3. The method according to claim 2, characterized in that The step (2) is and Before the orthogonal subspace decomposition, and To standardize: in, and They are The mean vector and standard deviation diagonal matrix of and They are The mean vector and standard deviation diagonal matrix of and is a column vector whose elements are all 1, and T represents the transpose operation.

4. A method for detecting minor faults related to TE process quality, characterized in that: The method adopts the method described in any one of claims 1 to 3 for detection.

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