A complex process refinement fault detection method based on local subspace-neighborhood preserving embedding

Abstract

The application discloses a complex process fine fault detection method based on local subspace-neighborhood preserving embedding, aiming at dividing the original space into different local subspaces by considering the problem that the data collected by different types of sensors have different characteristics and are subject to different distributions, and constructing a complex process fine monitoring model on the basis. The method firstly divides the original space into four local subspaces according to whether the data collected by different types of sensors are subject to Gaussian distribution; secondly, the features of the local subspaces are extracted by NPE for fault detection, and the moving window strategy and mutual information method are adopted to measure the correlation between the local subspaces; finally, the local outlier probability method is adopted to construct a comprehensive monitoring index to implement fine fault detection. In addition, the method further considers the extraction of neighborhood information in the local subspaces on the basis of considering the local subspace division. In a word, the method is a brand-new fault detection method.

Description

Technical Field

[0001] This invention relates to a data-driven fault detection method, and more particularly to a refined fault detection method for complex processes based on local subspace-neighborhood preservation embedding. Background Technology

[0002] With the rapid development of sensor technology and information science, the integration level of industrial production is increasing, and a wealth of process data is being collected and stored. This data reflects the operational status of the production process, and data-driven fault detection plays a crucial role in ensuring production safety and product quality. Therefore, accurately and fully extracting characteristic information reflecting the process's operational status from massive amounts of process data is key to fault detection. Since process data is acquired through various sensors, which can be divided into two main categories: component sensors (e.g., concentration, composition) and process sensors (e.g., temperature, pressure), the data collected by component and process sensors differ significantly in their characteristics. Therefore, it is not advisable to place component and process sensor data in the same space to build a fault detection model. To address this issue, the original space is divided into a component subspace and a process subspace based on whether the data originates from a component sensor or a process sensor. Furthermore, considering that data collected in actual industrial processes does not always follow a Gaussian distribution, the Jarque-Bera test method is used to verify the normal distribution characteristics of the data, further dividing the two local subspaces into four local subspaces. This allows for better focus on local information and improves fault detection performance.

[0003] Local features describe the spatial distribution of neighboring data points and are an important source of information. The loss of local information inevitably weakens the feature extraction capability of algorithms, leading to a decrease in fault detection performance. To address this, a neighborhood-preserving embedding (NPE) algorithm is used to learn low-dimensional spatial features to maintain the neighborhood structure relationships of the original space, preserving the local structure of the data while reducing dimensionality. Currently, no sophisticated fault detection method considers the complex process of dividing the original data space into Gaussian-component subspaces, Gaussian-process subspaces, non-Gaussian-component subspaces, and non-Gaussian-process subspaces. Summary of the Invention

[0004] The main technical problem this invention aims to solve is how to extract local features of data within a local subspace while considering the different characteristics and distributions of data collected by sensors, and then implement refined fault detection based on this. Specifically, this invention first divides the original space into a component subspace and a process subspace based on the different characteristics of data collected by different types of sensors. Then, it uses the Jarque-Bera test method to verify the normal distribution characteristics of the data, further dividing the two local subspaces into four local subspaces. Next, it uses the NPE algorithm to extract features in different local subspaces to establish fault detection models within each subspace, constructing fault detection statistics for each local subspace. Furthermore, to consider not only information within the local subspace but also changes in information between different local subspaces, it uses a moving window strategy and mutual information methods to construct fault detection statistics between different local subspaces. Finally, by combining the fault detection statistics within and between local subspaces, it uses the Local Outlier Probability (LOOP) method to construct a comprehensive fault detection statistic to accurately determine whether a process fault has occurred.

[0005] The technical solution adopted by this invention to solve the above-mentioned technical problems is as follows: a refined fault detection method for complex processes based on local subspace-neighborhood preservation embedding, comprising the following steps:

[0006] Step (1): Collect data from m sensor variables at n sampling times under normal operating conditions to form a training dataset matrix X = [x1, x2, ..., xm]. m ]∈R n×m , where n is the number of samples in the training set, m is the number of sensor measurement variables, and R is the set of real numbers;

[0007] Step (2): Classify the training data according to the physical quantity category of the sensors. Component-type sensors are used to measure variables related to material composition, including concentration and chemical components, while process-type sensors are used to measure variables related to process state, including temperature and pressure. The training dataset X∈R is then classified according to whether the data originates from component-type sensors or process-type sensors. n×m Divided into subspaces and process subspace

[0008] Step (3): The Jarque-Bera test method is used to test the normal distribution characteristics of the data in the component subspace and the process subspace respectively, thereby further dividing the two local subspaces into four local subspaces: Gaussian-component subspace, Gaussian-process subspace, non-Gaussian-component subspace and non-Gaussian-process subspace. The specific implementation process is as follows:

[0009] Step (3.1): For the variable x in the component subspace ci Its skewness and kurtosis are calculated as follows:

[0010] s(x ci )=mean[(x ci -mean(x ci )) 3 ] / {mean[(x ci -mean(x ci )) 2 ]} 3 / 2 (1)

[0011] k(x ci )=mean[(x ci -mean(x ci )) 4 ] / {mean[(x ci -mean(x ci )) 2 ]} 2 (2)

[0012] Where mean() means taking the mean, s() means skewness, and k() means kurtosis;

[0013] Step (3.2): The Jarque-Bera statistic is constructed as follows:

[0014] Jarque-Bera(x ci )=(nf){[s(x ci )] 2 +[k(x ci )-3] 2 / 4} / 6 (3)

[0015] Where f is the degree of freedom;

[0016] Step (3.3): Calculate the value Jarque-Bera(x) ci ) and the preset probability level JB level For comparison, if Jarque-Bera(x) ci (Greater than JB) level Then it is assumed to follow a Gaussian distribution, and x is... ci Its partitioning is in Gaussian-component subspace Otherwise, partition it into a non-Gaussian-component subspace N. c : middle;

[0017] Step (3.4): Similarly, for the variable x in the process subspace piThe Gaussian-process subspace G is obtained through the above three steps. p : Non-Gaussian-process subspace

[0018] Step (4): The datasets of the four subspaces are preprocessed and normalized using the z-score method, so that the mean of each variable in each subspace is zero and the standard deviation is 1, thus obtaining the new subspaces as follows:

[0019]

[0020] Step (5): In the four standardized subspaces, the projection transformation matrix is ​​obtained using the Local Neighborhood Embedding (NPE) algorithm, and fault detection is performed within the local subspaces. The specific implementation process is as follows:

[0021] Step (5.1): First, in the standardized Gaussian-component subspace, construct a neighborhood graph with n nodes, where the i-th node corresponds to a sample point. calculate Calculate the Euclidean distances to other sample points, sort them in ascending order of distance, and select the first k sample points to form a sample. nearest neighbor set

[0022] Step (5.2): Reconstruct the weight matrix W by minimizing the error according to the following formula. Gc :

[0023]

[0024] The constraint condition is that the sum of the elements in each row (column) of W is 1;

[0025] Step (5.3): Calculate the mapping transformation matrix A according to the formula shown below. Gc :

[0026]

[0027] The constraints are as follows: By introducing the Langron function and combining it with simple algebraic operations, the optimization problem is transformed into a generalized eigenvalue solving problem as shown below:

[0028]

[0029] Among them, M Gc =(IW Gc ) T (IW Gc The smallest d eigenvalues ​​form the mapping transformation matrix A. Gc ;

[0030] Step (5.4): Similarly, in the remaining three subspaces, follow steps (5.1) to (5.3) above to calculate the corresponding mapping transformation matrix A. Gp A Nc and A Np Thus, the corresponding low-dimensional matrix is ​​obtained;

[0031] Step (5.5): In four different feature subspaces, according to the following formula:

[0032]

[0033] Construct T respectively Gp 2 ,T Np 2 ,T Gc 2 and T Nc 2 Statistical measurements are used for spatial monitoring, among which

[0034]

[0035] Y Gp ,Y Np ,Y Gc ,Y Nc covariance matrix .

[0036] Step (6): Measure the changes in the relationship between the four local subspaces using a moving window strategy and mutual information methods. The specific implementation process is as follows:

[0037] Step (6.1): Use a sliding window and mutual information to measure the changes in the relationships between the four local subspaces, assuming... The t-th sample in the data is represented as follows: If the length of the sliding window is set to 2L, then the moving window in each subspace can be constructed as follows: The data in the moving window is represented as

[0038] Step (6.2): ​​Calculate the mutual information between the four local subspaces according to the following formula:

[0039]

[0040] Step (6.3): Then, based on the constructed moving window, construct statistics according to the following formula to calculate the changes in the relationship between the four subspaces:

[0041]

[0042]

[0043] Step (7): Combining the fault detection statistics within the local subspace and the fault detection statistics between local subspaces, the comprehensive fault detection statistics are constructed using the Local Outlier Probability (LOOP) method. The specific implementation process is as follows:

[0044] Step (7.1): Let Y = [T Gc 2 ,T Gp 2 ,T Nc 2 ,T Np 2 M GcGp M GcNc M GcNp M GpNc M GpNp M NcNp Let y be a sample in Y, and its local neighborhood N(y) is constructed using the k-nearest neighbor method determined by Euclidean distance. f It is the f-th neighbor, D(y,(y)). f ) is y and (y) f The Euclidean distance between them;

[0045] Step (7.2): Define the distance between probability sets as follows:

[0046]

[0047] Where 'a' is the weighting coefficient;

[0048] Step (7.3): Define the probability local outlier factor as follows:

[0049] PLOF(y) = pdist(y) / [E N(y) (pdist(y))]-1 (24)

[0050] Where E() is the expected value;

[0051] Step (7.4): To achieve probability factor standardization, a standard deviation parameter is defined as follows:

[0052]

[0053] Step (7.5): Based on the Gaussian error function, the local outlier probability is calculated as follows:

[0054]

[0055] Then, the kernel density estimation (KDE) method was used to determine the control limit (LOOP) of the integrated monitoring statistic. lim .

[0056] Steps (1) to (7) above constitute the offline modeling stage of the method of the present invention, and steps (8) to (14) below constitute the online fault detection implementation process of the method of the present invention.

[0057] Step (8): Collect sample data x at the new sampling time. t The subscript t indicates the latest sampling time;

[0058] Step (9): Based on the four local subspace partitioning criteria obtained during offline modeling, analyze the test sample x. t The data is divided into four local subspaces: x′ Gc ,x′ Gp ,x′ Nc ,x′ Np ;

[0059] Step (10): The test samples of the four subspaces are processed using the mean and standard deviation obtained in step (4) to obtain the standardized test sample data:

[0060] Step (11): For Using the NPE model obtained in offline modeling step (5), local feature extraction is performed to construct T′ respectively. Gc 2 ,T′ Gp 2 ,T′ Nc 2 and T′ Np 2 Statistic;

[0061] Step (12): For By implementing the sliding window and mutual information in step (6), we can further calculate: M′ GcNp ,M′ GcNc ,M′ GcNp ,M′ GpNc ,M′ GpNp ,M′ NcNp ;

[0062] Step (13): Combining the fault detection statistics within the local subspace and the fault detection statistics between local subspaces, construct the comprehensive monitoring statistics LOOP(y) using the local outlier probability method in step (7). t );

[0063] Step (14): Determine whether the monitoring statistic satisfies LOOP(y) t) <LOOP lim If the condition is met, the current sample is determined to be in normal working condition and the process returns to step (8) to continue detecting the next sampling point; otherwise, the current sampled data is determined to be in fault condition.

[0064] Compared with traditional methods, the advantages of the method of the present invention are as follows:

[0065] First, the method of this invention takes into account the different characteristics and distributions of data collected by different types of sensors, as well as the local features of the data. Second, the method of this invention can not only perform fault detection within each local subspace, but also between different local subspaces, which is rarely studied in current literature and patents, and represents a novel fault detection method for complex industrial processes. In short, the method of this invention is a more preferred fault detection method. Attached Figure Description

[0066] Figure 1 This is a flowchart illustrating the implementation of the method of the present invention.

[0067] Figure 2 A comparison chart showing the details of TE process fault detection. Detailed Implementation

[0068] The method of the present invention will be described in detail below with reference to the accompanying drawings and specific implementation examples.

[0069] like Figure 1 As shown, this invention discloses a refined fault detection method for complex processes based on local subspace-neighborhood preservation embedding. The specific implementation process of this method, and its advantages over existing methods, are illustrated below with a concrete example of an industrial process.

[0070] The application is based on the Eastman (TE) process experiment in Tennessee, USA, and the prototype is an actual process flow in the Eastman Chemical Plant. Currently, due to its complexity, the TE process is widely used as a standard experimental platform for fault detection research. The entire TE process includes 22 measurement variables, 12 operational variables, and 19 component measurement variables. This TE process object can simulate various fault types, such as step changes in material inlet temperature, cooling water malfunctions, etc. To perform fault detection on this process, the 22 measurement variables and 19 component measurement variables shown in Tables 1 and 2 are selected. The specific implementation steps of this invention will then be described in detail using this TE process as an example.

[0071] Table 1: TE process monitoring variables.

[0072] Serial Number Variable description Serial Number Variable description 1 Material A flow rate 12 Separator liquid level 2 Material D flow rate 13 Separator pressure 3 Material E flow rate 14 separator bottom flow 4 Total feed flow rate 15 stripping tower liquid level 5 Circulating flow 16 stripping tower pressure 6 Reactor feed 17 bottom flow rate of stripping tower 7 reactor pressure 18 stripping tower temperature 8 Reactor liquid level 19 Steam flow rate at the top of the stripping tower 9 Reactor temperature 20 Compressor power 10 Emptying rate 21 Reactor cooling water outlet temperature 11 Separator temperature 22 Separator cooling water outlet temperature

[0073] Table 2: Component variables of the TE process.

[0074]

[0075]

[0076] First, the implementation process of the method of the present invention is as follows: Figure 1 As shown, a fault detection model is established using n=960 sample data points collected under normal operating conditions of the TE process, including the following steps:

[0077] Step (1): Collect samples from the normal operation of the production process and form a training dataset X∈R according to the sampling time. 960×41 ;

[0078] Step (2): Divide the training dataset into subspaces X according to the different characteristics of the data. C and process subspace X P ;

[0079] Step (3): Apply the KS test to space X C and X P In this way, we can test whether the data follows a Gaussian distribution, and thus divide the above two spaces into four local subspaces, as shown in Table 3 (process variables are variables 1-22, and component variables are variables 19-41):

[0080] Gaussian-component subspace G c :X Gc ∈R 960×3 ,

[0081] Gaussian-process subspace G p :X Gp ∈R 960×9 ,

[0082] Non-Gaussian - component subspace N c :X Nc ∈R 960×16 ,

[0083] Non-Gaussian process subspace N p :X Np ∈R 960×13 ;

[0084] Table 3. TE process variables contained in the four subspaces

[0085] Subspace name Variable number Gaussian-component subspace 23,29,35 Gaussian-process subspace 1,4,5,6,8,14,15,17,22 Non-Gaussian-component subspace 24,25,26,27,28,30,31,32,33,34,36,37,38,39,30,41 Non-Gaussian-process subspace 2,3,7,9,10,11,12,13,16,18,19,20,21

[0086] Step (4): The datasets of the four subspaces are preprocessed and normalized using the z-score method, so that the mean of each variable in each subspace is zero and the standard deviation is 1, thus obtaining the new subspaces as follows:

[0087] Step (5): In the four standardized subspaces, the projection transformation matrix A is obtained by using the Local Neighborhood Embedding (NPE) algorithm. Gc A Gp A Nc and A Np This allows the data in the four subspaces to be projected onto relatively low-dimensional feature subspaces. and This yields the corresponding low-dimensional matrix, and then T is constructed in the eigenspace respectively. Gc 2 ,T Gp 2 ,T Nc 2 and T Np 2 Statistical measures are used for fault detection within a local subspace;

[0088] Step (6): Apply the moving window strategy and mutual information method to the sample sets of the four local subspaces respectively, and further calculate the relationship between the four subspaces: M GcGp M GcNc M GcNp M GpNc M GpNp M NcNp ;

[0089] Step (7): Combining the fault detection statistics within the local subspace and the fault detection statistics between local subspaces, the comprehensive fault detection statistic LOOP(y) is constructed using the local outlier probability (LOOP) method. Then, the comprehensive monitoring statistic LOOP(y) is determined using the kernel density estimation (KDE) method. t The control limit is LOOP. lim =0.8717, confidence level α is set to 0.99.

[0090] The offline modeling phase is now complete. The next step is to implement online fault detection. Online fault detection is performed using 960 sampled data points under TE process test conditions, with the first 160 samples representing normal conditions and the remaining 800 samples collected from faulty operating conditions.

[0091] Step (8): Collect sample data x at the new sampling time. t The subscript t indicates the latest sampling time;

[0092] Step (9): Based on the four local subspace partitioning criteria obtained during offline modeling, analyze the test sample x. t The data is divided into four local subspaces: x′Gc ,x′ Gp ,x′ Nc ,x′ Np ;

[0093] Step (10): The test samples of the four subspaces are processed using the mean and standard deviation obtained in step (4) to obtain the standardized test sample data:

[0094] Step (11): For Using the NPE model obtained in offline modeling step (5), local feature extraction is performed to construct T′ respectively. Gc 2 ,T′ Gp 2 ,T′ Nc 2 and T′ Np 2 Statistic;

[0095] Step (12): For By implementing the sliding window and mutual information in step (6), we can further calculate: M′ GcGp ,M′ GcNc ,M′ GcNp ,M′ GpNc ,M′ GpNp ,M′ NcNp ;

[0096] Step (13): Combining the fault detection statistics within the local subspace and the fault detection statistics between local subspaces, construct the comprehensive monitoring statistics LOOP(y) using the local outlier probability method in step (7). t );

[0097] Step (14): Determine whether the monitoring statistic satisfies LOOP(y) t ) <LOOP lim If the condition is met, the current sample is determined to be in normal working condition and the process returns to step (8) to continue detecting the next sampling point; otherwise, the current sampled data is determined to be in fault condition.

[0098] Finally, a comparison chart showing the detection details of the random variation fault at the inlet temperature of material C using the method of this invention, as well as traditional fault detection methods based on PCA and NPE, is shown below. Figure 2The results show that the false negative rate of the method of this invention is 15.125%, while the false negative rates of the PCA method (T2 statistic and SPE statistic) are 76.25% and 52.75%, respectively, and the false negative rate of the NPE method (T2 statistic) is 54.5%. Compared with the PCA and NPE methods, the method of this invention has the best detection effect for this fault, and the false negative rate after the fault occurs is significantly lower than that of the other two traditional methods.

[0099] The above embodiments are only used to illustrate specific implementations of the present invention and are not intended to limit the invention. Any modifications made to the present invention within the spirit and scope of the claims fall within the protection scope of the present invention.

Claims

1. A method for fine-grained fault detection in complex processes based on local subspace-neighborhood preserving embedding, characterized in that, The method comprises the following steps: The implementation process of the offline modeling stage is shown as follows: Step (1): Collecting m sensor variables data at n sampling time under normal operation condition to form training data set matrix X=[x1,x2,…,x m ]∈R n×m where n is the number of samples in the training set, m is the number of sensor measurement variables, and R is the real number set; Step (2): Classify the training data according to the physical quantity category of the sensor, where the class of sensors is used to measure material composition related variables, including concentration and chemical components, and the process class of sensors is used to measure process state related variables, including temperature and pressure, and according to whether the data is derived from the class of sensors or the process class of sensors, the training data set X e R n×m Divide into composition subspace and process subspace Step (3): The normal distribution characteristics of the data are tested in the component subspace and the process subspace respectively by using the Jarque-Bera test method, so as to further divide the two local subspaces into four local subspaces: Gaussian-component subspace Gaussian-process subspace Non-Gaussian-component subspace and non-Gaussian-process subspace Wherein, m Gc +m Nc =m c , m Gp +m Np =m p ; Step (4): The data sets of the four subspaces are pre-processed and normalized by z-score method, so that the mean of each variable of each subspace is zero and the standard deviation is 1, thereby obtaining new subspaces as follows: Step (5): In the four normalized subspaces, the projection transformation matrix A Gc ,A Gp ,A Nc and A Np is obtained by using the local neighborhood preserving embedding (NPE) algorithm, respectively, so as to project the data in the four subspaces into the relatively low-dimensional feature subspaces, respectively: and and In the feature subspaces, the T Gc 2 ,T Gp 2 ,T Nc 2 and T Np 2 statistical quantities are constructed according to the formula and for local subspace-based fault detection;​ Step (6): The relationship changes between four local subspaces are measured by using sliding windows and mutual information. It is assumed that The tthsample in is denoted as The length of the sliding window is set to 2L, and the moving window in each subspace can be constructed as The data in the moving window is denoted as The mutual information between the local subspaces is calculated according to the following formula: Then, on the basis of the constructed sliding window, the statistical quantity is constructed according to the following formula, and the relationship change between the four local subspaces is calculated: Step (7): Combining the local subspace within fault detection statistics and the local subspace between fault detection statistics, the local outlier probability (LOOP) method is used to construct the comprehensive fault detection statistics, and set Then for a sample y in Y, the LOOP of y can be calculated as: Then, the control limit LOOP of the comprehensive monitoring statistic is determined by using the kernel density estimation (KDE) method lim ; The implementation process of the online fault detection is shown as follows: Step (8): Collecting the sample data x at the new sampling time t where the subscript number t represents the current latest sampling time; Step (9): According to the four local subspace partition criteria obtained in the offline modeling, the test sample x is partitioned t to obtain sample data in the four local subspaces: x' Gc , x' Gp , x' Nc , x' Np ; Step (10): The test samples of the four subspaces are processed using the mean and standard deviation obtained in step (4) respectively, so as to obtain the standardized test sample data: Step (11): For The local feature extraction using the NPE model obtained from the offline modeling step (5) respectively constructs T' Gc 2 T' Gp 2 T' Nc 2 T' Np 2 statistical quantities; Step (12): Compute M' = M - M Step (6) and mutual information, further compute: GcGp M' GcNc M' GcNp M' GpNc M' GpNp M' NcNp ; Step (13): Combining the local subspace-based fault detection statistics and the inter-local subspace-based fault detection statistics, a comprehensive monitoring statistic LOOP(y t ) is constructed using the local outlier probability method in step (7). Step (14): judging whether the monitoring statistics satisfies LOOP(y t )<LOOP lim , if yes, it is determined that the current sample is normal working condition and returns to step (8) to continue detecting the next sampling point, otherwise, it is determined that the current sampling data is fault working condition.

2. The method according to claim 1, wherein, The normal distribution characteristics of the data are tested by using the Jarque-Bera test method in the step (3), so that the two local subspaces are further divided into four local subspaces: a Gaussian-component subspace, a Gaussian-process subspace, a non-Gaussian-component subspace and a non-Gaussian-process subspace, and the specific implementation process is shown as follows: Step (3.1): For the variables x in the ingredient subspace ci , the skewness and kurtosis are calculated as follows: s(x ci )=mean[(x ci -mean(x ci )) 3 ] / {mean[(x ci -mean(x ci )) 2 ]} 3 / 2 (9) k(x ci ) = mean[(x ci -mean(x ci )) 4 ] / {mean[(x ci -mean(x ci )) 2} 2 (10) Wherein, mean() represents taking the mean, s() represents skewness, and k() represents kurtosis; Step (3.2): the Jarque-Bera statistic is constructed as follows: Jarque-Bera(x ci ) = (n - f){[s(x ci ) 2 + [k(x ci )-3] 2 / 4} / 6 (11) Wherein, f is the degree of freedom; Step (3.3): compare the calculated value Jarque-Bera(x ci ) with the preset probability level JB level , if Jarque-Bera(x ci ) is greater than JB level , it is considered to be subject to Gaussian distribution, x ci is divided in Gaussian-component subspace , otherwise, it is divided in non-Gaussian-component subspace ; Step (3.4): Similarly, for the variables x in the process subspace pi Also by the above three steps, the Gaussian-process subspace and the non-Gaussian-process subspace 3. The method according to claim 1, wherein, The specific implementation process of establishing the corresponding NPE model in the step (5) is shown as follows: Step (5.1): First, construct a neighborhood graph with n nodes in the normalized Gaussian-component subspace, where the i-th node corresponds to the sample point Compute the Euclidean distance between the i-th node and other nodes, and sort the distances from small to large, and select the first k sample points to form the neighborhood set of the i-th node Step (5.2): The weight matrix W is reconstructed from the error minimization according to the following equation Gc : Wherein, the constraint condition is that the sum of each row (column) element of W is 1; Step (5.3): Calculate the mapping transformation matrix A according to the following formula Gc : where the constraints are Introducing the Lagrange function, and combining simple algebraic operations, the optimization problem is converted into the generalized eigenvalue problem as shown below: wherein M Gc = (I-W Gc ) T (I-W Gc ), the smallest d eigenvalues form the mapping transformation matrix A Gc ; Step (5.4): Similarly, in the remaining three subspaces, the mapping transformation matrix A is calculated according to the above steps (5.1) to (5.3), respectively Gp Nc Np , and A Np , so as to obtain the corresponding low-dimensional matrix.

4. The method according to claim 1, wherein, The specific implementation process of constructing the comprehensive fault detection statistic LOOP(y) by using the local outlier probability method in the step (7) is shown as follows: Step (7.1): Let Y = [T Gc 2 ,T Gp 2 ,T Nc 2 ,T Np 2 ,M GcGp ,M GcNc ,M GcNp ,M GpNc ,M GpNp ,M NcNp ], y is a sample in Y, its local neighborhood N(y) is established by knn nearest neighbors determined by Euclidean distance, let (y) f be the fth neighbor, then D(y, (y) f ) is the Euclidean distance between y and (y) f . Step (7.2): the probability set distance is defined as follows: Wherein, a is a weight coefficient; Step (7.3): the probability local outlier factor is defined as follows: PLOF(y) = pdist(y) / [E N(y) (pdist(y)) -1 (16) Wherein, E() is the expectation calculation; Step (7.4): in order to realize the standardization of the probability factor, a standard deviation parameter is defined as follows: Step (7.5): based on the Gaussian error function, the local outlier probability is calculated as follows:

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