CN118643320B - Quality-related minor fault detection method based on dynamic orthogonal subspace - Google Patents

Abstract

The invention discloses a quality-related micro fault detection method based on a dynamic orthogonal subspace, and belongs to the field of complex industrial process modeling and fault diagnosis. According to the method, dynamic amplification is carried out on data through input time lag values, variables with larger influence on micro faults in a sample at the current moment can appear for multiple times, the influence on the sample at the current moment by the micro faults is amplified, process data and quality related data are decomposed through OSA, quality related components and quality unrelated components are effectively separated, whether the micro faults can influence the quality of products output by the process or not can be further judged after the micro faults are detected, meanwhile, KL divergence is calculated according to two groups of different normal process data, common characteristics of normal data are extracted, the micro faults are distinguished, fault detection statistics which are more sensitive to the micro faults are built according to KL divergence among calculated score vectors aiming at the low-amplitude characteristics of the micro faults, and the alarm rate on the micro faults is improved.

Description

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

Technical Field

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

Background

The fault detection technology plays an important role in guaranteeing safe and stable operation of large-scale complex chemical processes and obtaining continuous and stable product quality. The fault detection methods are mainly divided into two types of methods based on models and data, wherein the data-driven multivariate statistical process monitoring method is widely focused and applied because an accurate system model is not needed, only the measurement data of a system is relied on, and the method has the capability of effectively processing the multivariate process data. Common multivariate statistical process monitoring methods are principal component analysis (PRINCIPAL COMPONENT ANALYSIS, PCA), partial least squares (PARTIAL LEAST squares, PLS), and typical correlation analysis (canonical correlation analysis, CCA), among others. Among them PLS and CCA are the most commonly used quality-related fault detection methods that can efficiently handle process variable and quality variable correlations. But neither PLS nor CCA can completely separate quality related components of process data (also known as critical variables such as quality of raw materials, temperature, pressure, time in the production process, etc.) from quality independent components (also known as non-critical variables such as noise level of the production environment, lighting conditions, etc.), thereby reducing quality related fault detection capabilities.

To enhance the ability of PLS to extract quality related components, zhou et al propose full-latent structure projection algorithms (refer to ZHOU D 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, the quality related components of the process data are further separated from the quality independent components, and the quality related fault detection ability is improved. Ma et al propose a core direct orthogonal PLS method (refer to MA H,WANG Y,JI Z C,etal.A novel three-stage quality oriented data-driven nonlinear industrial process monitoring strategy[J].IEEE Transactions on Instrumentation and Measurement,2022,71:1-11.),. Effectively enhance the ability of core PLS to extract quality related components, and improve the quality related fault detection ability of core PLS to nonlinear processes; to deal with the quality related components of core CCA, chen et al propose two methods to improve the core CCA to improve the quality related fault detection ability of core CCA to nonlinear processes by two singular value decomposition (refer to CHEN Q,WANG Y Q.Key-performance-indicator-related state monitoring based on kernel canonical correlation analysis[J].Control Engineering Practice,2021,107:104692.).

Although the above method can separate quality related components from quality independent components to a certain extent, there is still a problem of incomplete separation, unlike directly improving PLS and CCA, lou, etc., a new quality related fault detection method (refer to LOU Z J,WANG Y Q,SI Y B,et al.A novel multivariate statistical process monitoring algorithm:Orthonormal subspace analysis[J].Automatica,2022,138:110148.), as orthogonal subspace analysis (orthonormal subspace analysis, OSA)) is proposed, which divides process data and quality related data into three orthogonal subspaces, then monitors the three orthogonal subspaces individually by PCA and selects principal components by means of cumulative percent variance (cumulative PERCENT VARIANCE, CPV), thereby effectively solving the problem of incomplete separation of quality related and quality independent components existing in PLS and CCA, thereby improving quality related fault detection capability of PLS and CCA, hao, etc., further expanding OSA into dynamic version (refer to HAO W C,LU S,LOU Z J,et al.A novel dynamic process monitoring algorithm:dynamic orthonormal subspace analysis[J].Processes,2023,11(7):1935.)., but unable to distinguish the characteristics of micro faults from noise, so that micro faults in the effective detection process are slightly abnormal, are easily covered by noise, interference and normal conditions, it is difficult to detect evolution, and the result in a linear fault detection is improved by a linear fault detection method (refer to figure of 62, 32, 62, 32, etc., linear fault detection capability is improved, and so on the basis of a linear fault detection method is proposed, and error detection capability is improved to a linear fault detection method (refer to 52, 62, 32, and so on) based on input time lag value, and so on the characteristics of faults are improved, wu et al use serial model structure tightly integrated CVDA and mixed kernel principal component analysis to improve the micro-fault detection capability (cf WU P,FERRARI R M G,LIU Y C,etal.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.).

Although the above method improves the capability of detecting the micro-faults, there is still room for further improvement in the capability of detecting the quality-related faults, and in order to detect the micro-faults while detecting the quality-related faults, dong et al combine the canonical variable analysis with the KL divergence, a new micro-fault detection method is proposed (refer to 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.). but this method cannot completely separate the quality-related components from the quality-unrelated components, so that the quality-related fault detection rate needs to be further improved, and the quality-unrelated fault false alarm rate may be further reduced.

Disclosure of Invention

In order to realize the complete separation of the quality-related components and the quality-unrelated components so as to further improve the quality-related fault detection rate and reduce the quality-unrelated fault false alarm rate at the same time, the invention provides a quality-related micro fault detection method based on a dynamic orthogonal subspace, on one hand, an augmentation matrix reflecting the dynamic characteristics of process data and quality-related data is constructed based on an input time lag value, OSA is expanded into a dynamic version, the capability of the OSA method for monitoring the dynamic process is enhanced, and the dynamic characteristics of the process data are effectively extracted; on the other hand, the detection of quality-related micro faults is realized by fusing probability-related information implicit in score vectors through the difference of probability distribution of the score vectors before and after faults of KL divergence measurement of two groups of normal process data, and the method comprises two parts of offline modeling and online detection.

Optionally, the offline modeling part in the method includes:

step (1) collecting process data under normal conditions And quality related dataFor a pair ofAndPerforming augmentation and pretreatment to obtain corresponding augmentation matrix containing process static characteristics and dynamic characteristicsAnd

Step (2) pairAndPerforming orthogonal subspace decomposition to obtain each subspaceE_OSA、F_OSA;

Step (3) for each subspaceE _OSA、F_OSA PCA decomposition in which subspaces are takenDecomposing to obtain a principal component score matrix T _com and a residual score matrix T _r;

step (4) collecting another set of normal process data And quality related dataWill beAndAugmentation to X _v and Y _v, further pretreatment and decomposition intoE _v,OSA、F_v,OSA, next toE _v,OSA、F_v,OSA PCA decomposition is performed separately, whereinObtaining a principal component score matrix T _v,com and a residual score matrix T _v,r after decomposition;

Step (5), calculating the mean value vector mu ₁ and the variance vector of T _com Gradually sliding window on T _com and T _v,com, and calculating the mean value vector mu ₂ and variance vector of the sliding window dataContinuously updating mu ₂ andAnd calculates and updates the principal component score vector s _t at the moment T in T _com, and calculates the mean vector mu ₃ and the variance vector of T _r at the same timeGradually sliding window on T _r and T _v,r, and calculating the mean value vector mu ₄ and variance vector of the sliding window dataContinuously updating mu ₄ andAnd calculating and updating a T-moment residual score vector g _t in T _r;

Step (6), calculating KL divergence of the two groups of data according to the principal component score vector s _t and the residual score vector g _t to obtain a principal component score vector with probability correlation Probability-dependent residual score vectorAnd is composed ofAndConstructing probability-related fault detection statistics D _KL,1、D_KL,2, and calculating a control limit by a kernel density estimation method;

step (7) respectively constructing Probability-dependent T ² and SPE statistics of E _OSA、F_OSA Each subspace is independently monitored;

Step (8), calculating the slave first To the point ofIs transferred matrix of (a)AndTo the point ofIs transferred matrix of (a)RecalculatingTransfer matrices Θ _X→T and T _com Transfer matrix Θ _Y→T to T _com willAndTransfer to T _com andCalculation ofAnd determines its control limits.

Optionally, the online detection part in the method includes:

Step 1, acquiring an online process data sample and a quality related data sample, and performing amplification and pretreatment to obtain corresponding amplification matrixes X _w and Y _w containing process static characteristics and dynamic characteristics;

Step 2, calculating the respective subspaces of X _w and Y _w

Step 3, byPrincipal component score matrix of (a)Calculating and updating mu ₂ and replacing principal component score matrix T _v,com corresponding to another set of normally process data acquired in step (4) of the offline modeling processTo be used forResidual score matrix of (2)Instead of T _v,r, mu ₄ andCalculating probability correlation T ² and SPE statistics of the online sample;

step 4, calculating the common information of X _w and Y _w AndAnd calculate the on-line sampleStatistics;

and 5, comparing the statistics with the corresponding control limits, and if any statistics exceed the control limits, considering that faults occur.

Optionally, the method includes comparing the process data with the process dataAnd quality related dataThe process of amplifying comprises the following steps:

recording the original process data and the quality-related data as respectively AndWhere x (i) ∈r ^s(i＝1,2,…n),y(j)∈R^r (j=1, 2,..n), for a given formulaAndAnd (5) performing augmentation:

Wherein, D is a time lag parameter.

Optionally, the step (2) is performed onAndThe method also comprises the following steps of, before orthogonal subspace decompositionAndAnd (3) performing standardization:

Wherein, AndRespectively isIs a mean vector and standard deviation diagonal matrix of (c),AndRespectively isIs a mean vector and standard deviation diagonal matrix of (c),AndFor a column vector of all elements 1, T represents the transpose operation.

Alternatively, toPerforming PCA decomposition includes:

Wherein T _com∈R^n×k is a principal element scoring matrix, P _com∈R^s×k is a principal element loading matrix, T _r∈R^n×(s-k) is a residual scoring matrix, P _r∈R^s×(s-k) is a residual loading matrix, and k is the number of principal elements.

Optionally, the transfer matrix in step1 is:

The application also provides a TE process quality-related micro-fault detection method, which adopts the quality-related micro-fault detection method based on the dynamic orthogonal subspace to detect.

The TE process comprises five main units, namely a reactor, a separator, a stripper, a condenser and a compressor. The process comprises 53 variables, 22 of the continuous process variables, 19 of the sampled process variables, 12 of the manipulated variables, constructing a process data matrix with 22 of the continuous process variables and the sampled process variables and 11 of the manipulated variablesThe measured variables XMES (35) and XMES (36) of products G and H to construct a quality-related data matrix

The invention has the beneficial effects that:

1. Aiming at the problem that the detection is difficult due to the low amplitude of the micro fault, the step (1) in the offline modeling of the scheme dynamically amplifies the data through the input time lag value, so that the variable with larger influence on the micro fault in the sample at the current moment can appear for multiple times, the influence of the micro fault on the sample at the current moment is amplified, and the later steps are combined, so that the influence of the micro fault on the sample at the current moment is more easily measured, and the fault alarm rate of the detection method is improved.

2. Aiming at the problem that the quality-related components and the quality-unrelated components are difficult to separate, in the offline modeling of the scheme, the step (2) decomposes the process data and the quality-related data through OSA, so that the quality-related components and the quality-unrelated components are effectively separated, and the detection method can further judge whether the micro-faults can influence the quality of products output by the process after the micro-faults are detected.

3. Aiming at process noise, interference and measurement errors, the KL divergence of accurate process data is difficult to directly calculate, and the method is different from the existing method in offline modeling, which calculates the KL divergence according to only one group of normal process data, but calculates the KL divergence according to two groups of different normal process data. This allows normal data common characteristics to be extracted to distinguish between minor faults.

4. Aiming at the problem that the detection is difficult due to the low amplitude of the micro faults, fault detection statistics which are more sensitive to the micro faults are constructed according to KL divergence among the calculated score vectors in the line modeling of the scheme, and the alarm rate of the detection method on the micro faults is improved.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.

FIG. 1 is a partial flow chart of a fault detection method based on dynamic orthogonal subspace analysis and KL divergence provided by the application.

FIG. 2A is a schematic illustration of a method of the present applicationA scatter diagram of the reduced principal component score vector s _t;

FIG. 2B is a principal component score vector of probability correlation in the method of the present application Is a scatter plot of (c).

Fig. 3 is a graph of the detection result of the numerical case fault 1 by the method of the present application.

Fig. 4 is a graph of the detection result of TE process fault 9 using the method of the present application.

Fig. 5 is a graph of the detection result of TE process fault 13 using the method of the present application.

FIG. 6A is a graph of TE process product G sampling results;

fig. 6B is a graph of TE process product H sampling results.

FIG. 7A is a diagram of data augmentation subgraph in PR-DOSA provided by the present application;

FIG. 7B is an orthogonal subspace decomposition sub-graph of PR-DOSA provided by the present application;

FIG. 7C is a graph showing the calculation of KL divergence for a single step sliding window in PR-DOSA provided by the application.

Detailed Description

For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the embodiments of the present invention will be described in further detail with reference to the accompanying drawings.

The related concepts related to the present application are first described as follows:

1. Fault detection method based on OSA

Assuming that the preprocessed process data is X e R ^n×s, the quality related data is Y e 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 breaks X and Y into bilinear forms:

Wherein the method comprises the steps of Is a common latent variable of X and Y, satisfies T _com＝XΞ_X＝YΞ_Y,And Is a transfer matrix.

AndThe common component space for X and Y can be expressed as:

Wherein, For variable Y to variableIs used for the transfer matrix of (a),As a variableTransfer matrix to variable Y.

E _OSA and F _OSA are residual matrices of X and Y:

thus, three subspaces can be obtained (1) the joint molecular space of X and Y And(2) A residual subspace E _OSA of X, and a residual subspace F _OSA of Y. The three subspaces are mutually orthogonal,Orthogonal to E _OSA、F_OSA, i.e Orthogonal to E _OSA、F_OSA, i.eE _OSA is orthogonal to F _OSA E _OSA ^TF_OSA =0, so that each space can be separately fault-detected by PCA.

2. KL divergence

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

according to the formula (5), the KL divergence is asymmetric and does not meet the characteristic of distance, and a symmetrical KL divergence measurement index with distance meaning is constructed:

KL(f,g)=I(f,g)+I(g,f). (6)

According to formula (6), KL (f, g) is non-negative, KL (f, g) =0 if and only if f=g. Assuming that the probability density function of two Gaussian distribution signals is AndI (f, g) can be expressed as:

KL (f, g) can be written according to formula (6) and formula (7):

3. micro fault detection method based on probability-dependent dynamic OSA

According to the OSA method, each subspace obtained through PCA decomposition is respectively modeled, T ² and SPE statistics are constructed to serve as fault detection statistics, quality-related faults and quality-independent faults are effectively detected, and the detection capability of the faults is insufficient.

In order to improve the capability of the OSA to detect micro faults, the application improves the OSA from two aspects and provides a fault detection method (probability-RELATED DYNAMIC OSA, PR-DOSA) based on dynamic orthogonal subspace analysis and KL divergence. The proposed method structure is shown in fig. 1, wherein detailed sub-diagrams of the parts are shown in fig. 7A, 7B and 7C.

In one aspect, the OSA is extended to a dynamic version. Considering that chemical processes often show dynamic characteristics, in order to enhance the capability of the OSA method for monitoring the dynamic processes, the dynamic characteristics of process data are effectively extracted, and an augmentation matrix for reflecting the dynamic characteristics of the system is constructed. On the other hand, the probability-related information implicit in the score vector obtained after the PCA decomposition is fused. And constructing probability correlation detection statistics based on KL divergence to detect faults through the probability distribution difference of the score vectors before and after the occurrence of the KL divergence measurement faults.

Embodiment one:

the embodiment provides a fault detection method (probability-RELATED DYNAMIC OSA, PR-DOSA) based on dynamic orthogonal subspace analysis and KL divergence, comprising:

assuming that the original process data and quality-related data are respectively AndWhere x (i) ∈r ^s(i＝1,2,…n),y(j)∈R^r (j=1, 2,..n), will beAndThe amplification is performed as shown in formula (9).

D is a time lag parameter, and the variable number s=m (d+1) of the amplified data is recorded. Thereby generating an augmentation matrix comprising static and dynamic characteristics of the process.

Next, toAndAnd (3) performing standardization:

Wherein the method comprises the steps of AndRespectively isIs a mean vector and standard deviation diagonal matrix of (c),AndRespectively isIs a mean vector and standard deviation diagonal matrix of (c),AndIs a column vector with all elements of 1. Then toAndPCA decomposition is carried out:

thereby obtaining from the formula (12) AndWherein the principal component of CPV (Cumulative Proportion of Variance, cumulative contribution variance) is selected to exceed 99.9% such thatAndRank is full, thereby makingAndAnd is reversible.

Then by the pairs of formulae (13) - (14)AndPerforming orthogonal subspace decomposition to obtainE _OSA、F_OSA. Considering the case where quality-related data is not available in the online test phase, it is necessary to calculate the slave by equation (15)To the point ofTo the point ofIs transferred matrix of (a)And (3) withThereby obtainingAndWhen the degrees of freedom of the latent variables are not greater than the original data,

Then for each subspaceE _OSA、F_OSA PCA decomposition was performed. To be used forThe decomposition is as follows:

Wherein T _com∈R^n×k is a principal element scoring matrix, P _com∈R^s×k is a principal element loading matrix, T _r∈R^n×(s-k) is a residual scoring matrix, P _r∈R^s×(s-k) is a residual loading matrix, k is the number of principal elements, and principal elements with CPV more than 85% are selected.

Recording deviceThe principal component score vector at time T in T _com obtained by decomposition is s _t＝[s_t,1s_t,2…s_t,a]^T (a=k), and for the ith component s _t,i, assuming that s _t,i is subject to normal distribution, the KL divergence between two different sets of data corresponding to the ith component s _t,i can be calculated as:

Wherein mu _1,i and Is thatAndMean and variance of corresponding s _t,i components, μ _2,i andIs thatAndCorresponding to the s _t,i componentMean and variance of (1), when modeling offlineAndFor calculating control limits, for process data and quality-related data consisting of another set of normal samples, on-lineAndFor on-line test data, p is the number of samples. Mu _2,i and at time tObtained by a sliding window technique:

Where l is the sliding window length. Thereby obtaining a probability-dependent principal component score vector Recording deviceThe residual score vector at the time T in the T _r obtained by decomposition is g _t＝[g_t,1g_t,2…g_t,b]^T (b=s-k), and the residual score vector related to probability is obtainedAnd is composed ofAndConstructing probability-related fault detection statistics D _KL,1、D_KL,2, and calculating a control limit by a kernel density estimation method:

By the formulae (16) - (22), it is possible to construct respectively Probability-dependent T ² and SPE statistics of E _OSA、F_OSA Each subspace is monitored independently.

For the common component space, the common component can be calculated asOr (b)Thus ideally underWherein Θ _X→T isTransfer matrix to T _com, Θ _Y→T isThe transfer matrix to T _com can be calculated as:

t _com Obtaining a probability-dependent principal component score matrix by equations (18) - (20) for the principal component score matrixAndAnd constructing corresponding fault detection statistics from equations (21) - (22)AndTo monitor the common component space, another statistic may be constructed:

the statistic may monitor a relationship between the online process data sample and the quality data sample. The control limit is obtained by a nuclear density estimation method.

When online quality data is available, all detection statistics are available, when online quality data is not available,Can be used. All or a portion of the statistics may be selected for use as desired.

The application expands the orthogonal subspace analysis method to dynamic process monitoring, utilizes KL divergence to construct new probability-related fault detection statistics, and provides a quality-related micro fault detection method based on dynamic orthogonal subspaces and KL divergence. The method mainly comprises two parts of off-line modeling and on-line detection, and comprises the following specific steps:

offline modeling:

(1) Collecting process data under normal conditions And quality related dataBy pairs (9) - (12)AndPerforming amplification and pretreatment to obtainAnd

(2) By pairs (13) - (14)AndDecomposing to obtainE_OSA、F_OSA;

(3) By pairs (16) - (17)PCA decomposition is carried out onE _OSA、F_OSA performs the same PCA decomposition;

(4) Collecting another set of normal process data And quality related dataWill beAndAugmentation to X _v and Y _v, further pretreatment and decomposition intoE _v,OSA、F_v,OSA. Then toE _v,OSA、F_v,OSA PCA decomposition is performed separately, whereinAnd decomposing to obtain a principal component score matrix T _v,com and a residual score matrix T _v,r.

(5) First, calculate the mean vector μ ₁ and variance vector of T _com Then gradually sliding window on T _com and T _v,com, calculating the mean value vector mu ₂ and variance vector of the sliding window data through (19) - (20)Continuously updating mu ₂ andAnd s _t is calculated and updated by the method (18), and the mean vector mu ₃ and the variance vector of T _r can be calculated by the same methodGradually sliding window on T _r and T _v,r, and calculating the mean value vector mu ₄ and variance vector of the sliding window dataContinuously updating mu ₄ andAnd calculating and updating g _t, and constructing probability correlation T ² and SPE monitoring statistic by using the methods (21) - (22)And a control limit is calculated, Also constructed in the same manner;

(6) First calculate by (14) AndThen computing Θ _X→T and Θ _Y→T by the formula (23)AndTransfer to T _com andCalculation by (24)And determines its control limits.

And (3) online detection:

(1) Acquiring an online process data sample and a quality related data sample, and performing augmentation and pretreatment to obtain X _w and Y _w;

(2) Calculating the respective subspaces of X _w and Y _w by formulas (13) and (15)

(3) To be used forPrincipal component score matrix of (a)Instead of T _v,com, mu ₂ andTo be used forResidual score matrix of (2)Instead of T _v,r, mu ₄ andCalculating probability correlation T ² and SPE statistics of the online sample;

(4) Calculating the common information of X _w and Y _w by the formula (23) AndAnd calculate an online sample by (24)Statistics.

The application adopts fault detection rate (fault detection rate, FDR) and fault false alarm rate (FALSE ALARM RATE, FAR) as method evaluation indexes, and the two are defined as follows:

Where N ₁ and N ₂ are the number of faulty samples and the number of normal samples, respectively, and N _1,f and N _2,f are the number of faulty samples detected in the faulty samples and the number of normal samples, respectively.

The present solution improves on the OSA algorithm by verifying the effectiveness of the proposed algorithm by numerical simulation and applying it to the TE process, which contains five main units, namely the reactor, separator, stripper, condenser and compressor. The process contained 53 variables, 22 of which were continuous, 19 of which were sampled, and 12 of which were manipulated. In this example 22 continuous process variables and 11 manipulated variables (12 of which contain the stirring speed and which are usually kept constant and therefore not selected) were selected to construct a process data matrixThe measured variables XMES (35) and XMES (36) of products G and H to construct a quality-related data matrixA specific description can be found in "DOWNS J J,VOGEL E F.A plant-wide industrial process control problem[J].Computers&Chemical Engineering,1993,17(3):245-255." of the description of 21 faults in this process as shown in table 1 below:

TABLE 1 TE description of Process faults

PR-DOSA and OSA each had 9 statistics, with PR-DOSA statisticsStatistics with OSASPE_Y、SPE _F can be used directly to determine if a fault is quality-related.

The statistics of PR-DOSA and OSA are classified into two categories depending on whether quality related and quality independent faults can be distinguished directly. The numerical simulation results of the various statistics are shown in tables 2 and 3. As can be seen from comparative analysis, PR-DOSA of the above 9 faults can be effectively detected, but OSA can only effectively detect 5 faults, and PR-DOSA is effectively verified to have the capability of detecting micro faults compared with OSA.

Wherein the fault 9 is a fault occurring on the hidden variable s ₃, which affects all input and output variables, and is a quality-related fault. As shown in tables 2 and 3, all the statistics of OSA were unable to detect the failure, while the 6 statistics of PR-DOSA proposed by the present application were able to detect the failure, and the failure detection rate of 4 of them was over 90%.

In order to verify the effectiveness of the probability correlation score vector constructed by PR-DOSA provided by the application on fault detection, the probability correlation score vector is compared with that in PR-DOSADimension-reduced principal component score vector s _t and corresponding probability-dependent principal component score vectorAnd (5) detecting the fault 9. FIG. 2A shows a scatter plot of s _t, and FIG. 2B showsAll fault samples are contained in fig. 2A, and the first 400 fault samples are contained in fig. 2B, wherein blue represents the score vector corresponding to normal data, and yellow represents the score vector corresponding to fault 9.

FIG. 3 shows a graph of the detection result of PR-DOSA for failure 1. In the figure, green represents normal samples in the data set, blue represents faulty samples, and red represents control limits. Exceeding the control limit indicates a fault.

TABLE 2PR-DOSA and OSA failure detection result 1 (%)

TABLE 3PR-DOSA and OSA failure detection result 2 (%)

And then verifying the detection capability of PR-DOSA on all types of faults in the TE process, and comparing and analyzing with an OSA method in a quality-related fault detection method proposed by Lou and the like. Both methods select a principal component with CPV exceeding 85%, the time lag parameter d is set to 4 in the PR-DOSA method, the sliding window length l is set to 200, and d and l are selected according to the cross-validation method. The confidence of each statistic was 99%. TE process detection results of various statistics are shown in tables 4 and 5.

TABLE 4PR-DOSA and OSA TE process failure detection result 1 (%)

TABLE 5PR-DOSA and OSA TE process failure detection result 2 (%)

The fault detection result of the TE process shows that PR-DOSA effectively improves the fault detection capability of OSA. By comparing the best detection results of PR-DOSA with the 9 statistics of OSA for each fault, it is shown that PR-OSA has significantly better detection results for faults 3, 5, 9, 10, 11, 15, 16, 19, 20, 21 than OSA. Particularly for the micro faults 3, 9 and 15, the fault detection rates of PR-DOSA respectively reach 96.8%, 98.3% and 75.3% under the condition that the OSA method cannot effectively detect the faults. FIG. 4 shows a graph of the detection result of PR-DOSA on fault 9. As can be seen from the figure 4 of the drawings,The statistics show good detection capability for the fault 9, while none of the other statistics can detect the fault effectively in time.

The ability of PR-DOSA to detect quality-related faults is analyzed as follows. As shown by the detection results of the statistics in the table 5, for quality related faults 1, 2, 5, 6, 7, 8, 10, 12 and 13 in 21 faults of TE process, PR-DOSA obviously improves the fault detection rate of faults 1, 2, 5, 7, 8, 10, 12 and 13 compared with OSA, which indicates that PR-DOSA effectively improves the detection capability of OSA for quality related faults. The result of the PR-DOSA detection of the fault 13 is given in FIG. 5. As can be seen from fig. 5, the 9 statistics all show good detection capability for the fault 13. For TE process unknown type faults 16-20, it is also necessary to determine whether they are quality related faults. As can be seen from table 5, most of the statistics exhibit a higher failure detection rate for the failure 18, indicating that the failure 18 is likely a quality-related failure. Fig. 6A and 6B are graphs of measured variables of products G and H, respectively, where green corresponds to normal data and red corresponds to fault 18. From fig. 6A and 6B, it can be seen that after the occurrence of the fault 18, both G and H deviate from the set values, indicating that the fault 18 is a quality-related fault. Therefore, for unknown types of faults, both methods can judge whether the faults are related to quality, and both methods have good quality-related fault detection capability.

Some steps in the embodiments of the present invention may be implemented by using software, and the corresponding software program may be stored in a readable storage medium, such as an optical disc or a hard disk.

The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.

Claims (4)

1. A quality-related micro fault detection method based on a dynamic orthogonal subspace is characterized in that an augmentation matrix reflecting dynamic characteristics of process data and quality-related data is constructed based on input time lag values, OSA is expanded into a dynamic version, the capability of monitoring a dynamic process of the OSA method is enhanced, the dynamic characteristics of the process data are effectively extracted, on the other hand, probability distribution differences of score vectors before and after faults occur are measured through KL divergence of two groups of normal process data, probability-related information implicit in the score vectors is fused to realize detection of the quality-related micro faults, the method comprises two parts of offline modeling and online detection, and the offline modeling part in the method comprises the following steps:

Step (1), collecting process data under normal conditions And quality related dataFor a pair ofAndPerforming augmentation and pretreatment to obtain corresponding augmentation matrix containing process static characteristics and dynamic characteristicsAnd

Step (2), pairAndPerforming orthogonal subspace decomposition to obtain each subspaceE_OSA、F_OSA;

Step (3), for each subspaceE _OSA、F_OSA PCA decomposition in which subspaces are takenDecomposing to obtain a principal component score matrix T _com and a residual score matrix T _r;

step (4) collecting another set of normal process data And quality related dataWill beAndAugmentation to X _v and Y _v, further pretreatment and decomposition intoE _v,OSA、F_v,OSA, next toE _v,OSA、F_v,OSA PCA decomposition is performed separately, whereinObtaining a principal component score matrix T _v,com and a residual score matrix T _v,r after decomposition;

Step (5), calculating the mean value vector mu ₁ and the variance vector of T _com Gradually sliding window on T _com and T _v,com, and calculating the mean value vector mu ₂ and variance vector of the sliding window dataContinuously updating mu ₂ andAnd calculates and updates the principal component score vector s _t at the moment T in T _com, and calculates the mean vector mu ₃ and the variance vector of T _r at the same timeGradually sliding window on T _r and T _v,r, and calculating the mean value vector mu ₄ and variance vector of the sliding window dataContinuously updating mu ₄ andAnd calculating and updating a T-moment residual score vector g _t in T _r;

Step (6), calculating KL divergence of the two groups of data according to the principal component score vector s _t and the residual score vector g _t to obtain a principal component score vector with probability correlation Probability-dependent residual score vectorAnd is composed ofAndConstructing probability-related fault detection statistics D _KL,1、D_KL,2, and calculating a control limit by a kernel density estimation method;

step (7) respectively constructing Probability-dependent T ² and SPE statistics of E _OSA、F_OSA Each subspace is independently monitored;

Step (8), calculating the slave first To the point ofIs transferred matrix of (a)AndTo the point ofIs transferred matrix of (a)RecalculatingTransfer matrices Θ _X→T and T _com Transfer matrix Θ _Y→T to T _com willAndTransfer to T _com andCalculation ofAnd determining the control limit thereof, wherein the online detection part in the method comprises the following steps:

Step 1, acquiring an online process data sample and a quality related data sample, and performing amplification and pretreatment to obtain corresponding amplification matrixes X _w and Y _w containing process static characteristics and dynamic characteristics;

Step 2, calculating the respective subspaces of X _w and Y _w

Step 3, byPrincipal component score matrix of (a)Calculating and updating mu ₂ and replacing principal component score matrix T _v,com corresponding to another set of normally process data acquired in step (4) of the offline modeling processTo be used forResidual score matrix of (2)Instead of T _v,r, mu ₄ andCalculating probability correlation T ² and SPE statistics of the online sample;

step 4, calculating the common information of X _w and Y _w AndAnd calculate the on-line sampleStatistics;

Step5, comparing the statistics with the corresponding control limits, and if any statistics exceeds the control limits, considering that faults occur;

The pair of Performing PCA decomposition includes:

Wherein T _com∈R^n×k is a principal element scoring matrix, P _com∈R^s×k is a principal element loading matrix, T _r∈R^n×(s-k) is a residual scoring matrix, P _r∈R^s×(s-k) is a residual loading matrix, and k is the number of principal elements;

the transfer matrix is:

2. the method of claim 1, wherein the method is performed on process data And quality related dataThe process of amplifying comprises the following steps:

recording the original process data and the quality-related data as respectively AndWhere x (i) ∈r ^s(i＝1,2,…n),y(j)∈R^r (j=1, 2,..n), for a given formulaAndAnd (5) performing augmentation:

Wherein, D is a time lag parameter.

3. The method of claim 2, wherein the step (2) is performed onAndThe method also comprises the following steps of, before orthogonal subspace decompositionAndAnd (3) performing standardization:

Wherein, AndRespectively isIs a mean vector and standard deviation diagonal matrix of (c),AndRespectively isIs a mean vector and standard deviation diagonal matrix of (c),AndFor a column vector of all elements 1, T represents the transpose operation.

4. A TE process quality related micro-fault detection method, characterized in that the method is performed by the method according to any one of claims 1-3.