A quality-related early fault detection method based on MW-OCCA

Abstract

The present invention discloses a quality-related early fault detection method based on MW-OCCA. Aiming at the problem that the amplitude of early fault is small, the moving time window method is used to accumulate the error between fault data and normal data, increase the gap between fault data and normal data, and achieve the effect of amplifying early faults. On this basis, a quality-related fault detection model is established. Compared with traditional methods, the method of the present invention can not only detect early faults more timely, but also determine whether early faults will affect quality. It is a better quality-related early fault detection method.

Description

Technical Field

[0001] The present invention relates to data-driven fault detection, and in particular to a quality-related early fault detection method based on MW-OCCA. Background Art

[0002] Fault detection plays an important role in maintaining high-quality product production and ensuring industrial production safety. Model-based and data-driven methods are two common types of fault detection methods. Model-based methods simulate actual industrial processes by establishing process mechanism models, but the nonlinear, high-coupling, non-stationary, and multimodal characteristics of industrial processes make it difficult and inaccurate to establish mechanism models. With the development of sensor technology and computers, data collection and storage have become simple, and a large amount of industrial data can be used for fault detection. Data-driven fault detection methods have developed rapidly. Multivariate statistical analysis methods, as a typical data-driven method, are widely used in fault detection. Typical multivariate statistical analysis methods include principal component analysis (PCA), partial least squares (PLS), canonical correlation analysis (CCA), etc. PCA is a linear dimensionality reduction method that reduces the dimensionality of raw data through linear changes, extracts the main features of the data, and then uses squared prediction error (SPE) and Hotelling's T2 to monitor the sample state in the low-dimensional space. However, the PCA-based fault detection method cannot determine whether the fault will affect product quality. The PLS-based method and the CCA-based method use process variables to predict quality variables. In the offline stage, the historical quality variable data are used to guide the decomposition of process data to obtain quality-related parts and quality-irrelevant parts. In the online monitoring stage, measurable process data are used for quality-related and quality-irrelevant fault detection, but the PLS-based and CCA-based fault detection methods cannot determine the occurrence of early faults.

[0003] Early faults refer to faults with small amplitude and insignificant impact. For many serious faults, their early stages can be regarded as early faults. If serious faults exist in the early stages, it is possible to take measures to avoid their destructive impact. Timely detection of early faults, reduction of detection delay, and improvement of fault detection rate are crucial to prevent serious deterioration of system performance and ensure optimal operation of the process. However, due to the small fault amplitude and the insignificant change in process data, traditional fault detection methods are not effective in detecting changes in the early stages of faults. Moreover, the existing early fault detection methods do not consider whether early faults will affect product quality. Therefore, in order to detect early faults and determine whether early faults will affect quality, a quality-related early fault detection method based on moving window-orthogonal canonical correlation analysis (MW-OCCA) is proposed. This method uses the moving time window method to enhance the representation of faults in the detection model; at the same time, OCCA is used to construct quality-related and quality-orthogonal subspaces. When the fault occurs in the quality-related subspace, it can be determined that the early fault will affect the quality. Summary of the invention

[0004] The main technical problem to be solved by the present invention is: how to detect early faults and determine whether early faults will affect product quality. The main method is to use the moving time window method to enhance the representation of faults in the detection model, overcome the problem that early faults have small amplitudes and are difficult to detect; at the same time, in order to be able to determine whether early faults will affect product quality, an orthogonal CCA is used to establish a monitoring model, and the relationship between process variables and quality variables is constructed through CCA. The quality variables are used to guide the decomposition of the process space, and the process space is decomposed into quality-related and quality-orthogonal subspaces. When a fault occurs in a quality-related subspace, it can be determined that a quality-related fault has occurred.

[0005] The technical solution adopted by the present invention to solve the above problems is: a quality-related early fault detection method based on MW-OCCA, comprising the following steps:

[0006] (1): Collect sample data of industrial production objects under normal operation to form a training data set, where the process variable set is The quality variable set is Each column of the training data set is a measurement point, and each row is a sample data. The mean μ x and standard deviation σ x , and according to formula (1) Standardize and obtain the standardized process variable set In the same way Standardize and obtain the standardized quality variable set

[0007]

[0008] in After standardization, the dataset A row of data, μ x =[μ1,μ2,…,μ m ],σ x =diag(σ1,σ2,…,σ m )

[0009] (2): Select the time window length as k, and For the sample at time t (t=k, k+1,…,k+n-1) Add it to the standardized samples at the previous k moments and average them to get the processed data x t ∈R 1×m , as shown in formula (2). Do the same processing as shown in formula (3). Get the processed training data set X∈R n×m ,Y∈R n×l .

[0010]

[0011]

[0012] (3): Use orthogonal CCA to establish a monitoring model for X and Y. The specific steps are as follows:

[0013] 1): Calculate the covariance matrix ∑ of X X , the covariance matrix of Y∑ Y , the cross-covariance matrix of X and Y ∑ XY .

[0014] 2): for (∑ X ) -1 / 2 ∑ XY (∑ Y ) -1 / 2 Perform SVD decomposition and get (∑ X ) -1 / 2 ∑ XY (∑ Y ) -1 / 2 =ΓΣΨ T J=(∑ X ) -1 / 2 Γ,L=(∑ Y ) -1 / 2 Ψ, kp =rank(Σ),

[0015] 3):Yes Perform SVD decomposition and get

[0016] (4): Construct statistic T 2 =x t V1 T inv(cov(XV1 T ))V1x t T , Where inv() is the inverse function and cov() is the covariance function.

[0017] (5): Determine the confidence level α and calculate the control limit Where n is the number of samples, F is the F distribution, m is the number of features of data set X, and l is the number of features of data set Y.

[0018] The above steps (1) to (5) are the offline modeling stage of the method of the present invention, and the following steps (6) to (9) are the online detection implementation process of the method of the present invention.

[0019] (6): Samples collected online Use formula (1) to standardize it.

[0020] (7): The standardized data and The sample data after standardization at the first k moments is processed according to formula (2) to obtain the new data x new .

[0021] (8): Calculate the online sample x new Statistics

[0022] (9): If the statistics of the sample collected online It is judged that a quality-related early failure has occurred; if and It is judged that an early failure unrelated to quality has occurred; if and The judgment process is normal.

[0023] Compared with the traditional method, the advantages of the method of the present invention are:

[0024] First, based on the traditional CCA algorithm, this method further considers the detection of early faults and the impact of early faults on quality variables. A time window is added to CCA to achieve the accumulation of small errors, making the differentiation between fault sample data and normal sample data more obvious, and realizing the amplification of early faults; and considering that quality is unmeasurable online, the relationship matrix between measurable variables and quality variables is used to construct quality-related projections and quality-independent projections, and to construct quality-related subspaces and quality-independent subspaces. When a fault is detected, it is determined whether the fault is a quality-related fault. Therefore, the method of the present invention is a better quality-related early fault detection method. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 The present invention is a flowchart for implementing the method.

[0026] Figure 2 This is the detection result of fault 1 by the method of the present invention.

[0027] Figure 3 This is the detection result of fault 1 using the CCA method.

[0028] Figure 4 This is the detection result of fault 2 by the method of the present invention.

[0029] Figure 5 This is the detection result of fault 2 using the CCA method. DETAILED DESCRIPTION

[0030] The method of the present invention is compared in detail with specific implementation examples in conjunction with the accompanying drawings.

[0031] like Figure 1 A quality-related early fault detection method based on MW-OCCA is shown. The following is combined with a numerical example to illustrate the specific implementation process of the present invention and its superiority over the traditional fault detection method based on canonical correlation analysis.

[0032] Process variable set Quality variable set and Generated by formula (4). Collect 210 fault-free data to establish the fault detection model of the invented method. Then collect 200 faulty data as test samples.

[0033]

[0034] Among them, e1, e2, e3, e4, e5 are white noise with mean 0, standard deviation 0.01, and t∈[0.01,2].

[0035] Construction of fault data, Fault 1: Variable x1 changes slowly at the 101st sampling point according to x'1=x1+0.01×(k-100), where k is the sampling point number. Fault 2: Variable x4 changes slowly at the 101st sampling point according to x'4=x4+0.01×(k-100), where k is the sampling point number. It can be seen from the formula that the change of x1 will affect the change of y, so Fault 1 is a quality-related fault; the change of x4 will not affect the change of y, so Fault 2 is a quality-independent fault.

[0036] First, the fault detection model is established by offline training using 210 samples collected in the fault-free state of the numerical example, including the following steps:

[0037] (1): Collect samples under normal working conditions to form a training data set And standardize it to get

[0038] (2): Select the time window as 10. and Do the processing to get the processed training data X∈R 200×3 ,y∈R 200 ×1 .

[0039] (3): Use orthogonal CCA to establish a monitoring model for X and y. The specific implementation process is as follows:

[0040] 1): Calculate the covariance ∑ of X X , the covariance of y∑ y , the mutual covariance of X and y∑ Xy .

[0041] 2): for (∑ X ) -1 / 2 ∑ Xy (∑ y ) -1 / 2 Perform SVD decomposition and get (∑ X ) -1 / 2 ∑ Xy (∑ y ) -1 / 2 =ΓΣΨ T J=(∑ X ) -1 / 2 Γ,L=(∑ y ) -1 / 2 Ψ, k p =rank(Σ),

[0042] 3):Yes Perform SVD decomposition and get

[0043] (4): Take the confidence level as α = 0.05 and calculate the control line

[0044]

[0045] (5): Samples collected online Standardize it

[0046] (6): Use the moving window strategy to process it and obtain new training data x new .

[0047] (7): Calculate x new T 2 and D 2 Statistics. T 2 =x t V1 T inv(cov(XV1 T ))V1x t T ,

[0048]

[0049] (8): If the statistic T 2 >(T 2 ) lim It is judged that a quality-related early failure has occurred. If T 2 ≤(T 2 ) lim And D 2 >(D 2 ) lim It is judged that an early failure has occurred that is not related to quality. and The judgment process is normal.

[0050] (9): The detection results of the method of the present invention for fault 1 and fault 2 are shown in Figure 2 , 4. The detection results of the CCA method for fault 1 and fault 2 are shown in Figure 3 , 5 in.

[0051] It can be seen from the test results that the method of the present invention can detect early faults related to quality in a timely manner and has a low false alarm rate for early faults unrelated to quality.

[0052] The above-mentioned implementation cases are only used to explain the specific implementation of the present invention, rather than to limit the present invention. Therefore, all changes made according to the shape and principle of the present invention should be included in the scope of the present invention.

Claims

1. A quality-related early fault detection method based on MW-OCCA, characterized by: The method comprises the following steps: The implementation process of the offline modeling phase is as follows: Step (1) collects sample data of industrial production objects under normal operation to form a training data set, where the process variable set is The quality variable set is Each column of the training data set is a measurement point, and each row is a sample data. The mean μ x and standard deviation σ x , and according to formula (1) Standardize and obtain the standardized process variable set In the same way Standardize and obtain the standardized quality variable set in After standardization, the dataset A row of data, μ x =[μ1,μ2,…,μ m ],σ x =diag(σ1,σ2,…,σ m ); Step (2) Use the time window to reconstruct the process variable set and the quality variable set to obtain the reconstructed training data set X∈R n×m ,Y∈R n×l ; Step (3) using orthogonal CCA to establish a monitoring model for X and Y, and obtain a quality-related projection matrix V1 and a quality-independent projection matrix V2; Step (4) Construct statistics Among them, inv() is the inverse function, and cov() is the covariance function; Step (5) Determine the confidence level α and calculate the control limits Where n is the number of samples, F is the F distribution, m is the number of features of the data set X, and l is the number of features of the data set Y; The implementation process of the online monitoring phase is as follows: Step (6) Obtain online samples The training data set is standardized using its mean and standard deviation. Step (7) The standardized data and The sample data after standardization at the first k moments is processed according to formula (2) to obtain the new data x new ; Step (8) Calculate the online sample x new Statistics Step (9) If the statistics of the sample are collected online It is judged that a quality-related early failure has occurred; if and It is judged that an early failure unrelated to quality has occurred; if and The judgment process is normal.

2. A quality-related early fault detection method based on MW-OCCA according to claim 1, characterized in that: In step (2), the process variable set and the quality variable set are reconstructed using the time window to obtain the reconstructed training data set X∈R n×m ,Y∈R n×l The specific method is as follows: Choose the time window length as k, and Processing, for the sample at time t (t = k, k + 1, ..., k + n-1) Add it to the standardized samples at the previous k moments and average them to get the processed data x t ∈R 1×m , as shown in formula (2); right Do the same processing, as shown in formula (3), and get the processed training data set X∈R n×m ,Y∈R n×l .

3. The quality-related early fault detection method based on MW-OCCA according to claim 1, characterized in that: The specific implementation process of step (3) using orthogonal CCA to establish a monitoring model for X and Y to obtain the quality-related projection matrix V1 and the quality-independent projection matrix V2 is as follows: 1) Calculate the covariance matrix ∑ of X X , the covariance matrix of Y∑ Y , the cross-covariance matrix of X and Y ∑ XY ; 2) For (∑ X ) -1 / 2 ∑ XY (∑ Y ) -1 / 2 Perform SVD decomposition and get (∑ X ) -1 / 2 ∑ XY (Σ Y ) -1 / 2 =ΓΣΨ T ,J=(Σ X ) -1 / 2 Γ, L=(Σ Y ) -1 / 2 Ψ, k p =rank(Σ), 3) Yes Perform SVD decomposition and get

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