A Multi - operating - condition Fault Detection Method Based on Least Error Least Maximum Probability Machine

Abstract

The present invention discloses a multi - condition fault detection method based on the minimum error minimum - maximum probability machine, belonging to the field of detection technology, which includes the following steps: obtaining normal historical multi - condition data as a training set, extracting features from the training set and performing min - max normalization processing; performing condition division by using the density - based spatial clustering of applications with noise algorithm; establishing an L1 - minimum error minimum - maximum probability machine fault detection subsystem for the corresponding condition by using different normal condition data and offline fault data; extracting the same features from the data to be measured and performing min - max normalization processing; judging the condition to which the current data belongs based on the distance between the normalized data and the center point of the normal condition; calling the fault detection subsystem of the belonging condition, removing redundant features and judging whether the system has a fault. The present invention establishes a minimum error minimum - maximum probability machine fault detection subsystem for the corresponding condition for different conditions, and solves the problem of fault detection for a single condition.

Description

Technical Field

[0001] The present invention belongs to the technical field of detection, and particularly relates to a multi-condition fault detection method based on a minimum error minimum maximum probability machine. Background Technique

[0002] With the rapid development of science and technology such as computers, the Internet, and electronic information, the degree of automation of modern industrial systems is increasing day by day, and the system scale is getting larger and larger. Once a system fails, if it cannot be detected and effectively processed in time, it may cause serious economic losses at best, and even threaten people's lives and safety in severe cases. As an important means to improve the safety and reliability of the system, data-driven fault detection technology has been increasingly applied to various industrial systems, such as satellite systems, chemical systems, wind energy conversion systems, etc. after decades of development. Generally speaking, data-driven fault detection methods can be roughly divided into methods based on multivariate statistics, signal processing methods, machine learning methods, information fusion methods, and rough set methods.

[0003] The minimum error minimax probability machine is a data-driven method based on a probability framework. It does not need to assume the distribution form of process variables. Given the mean and variance of process variables, it can give an upper bound on misclassified data. In recent years, the minimum error minimax probability machine and its extended forms have been successfully applied to the field of fault detection. In the 2019 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY journal, the paper "Dynamic Minimax Probability Machine-Based Approach for Fault Diagnosis Using Pairwise Discriminate Analysis" by Jiang et al. proposed a fault diagnosis method based on the dynamic minimax probability machine. Compared with traditional diagnosis methods, the dynamic minimax probability machine does not need to make any assumptions about the distribution form of process variables and has the superior ability to obtain dynamic information from process data. In the 2019 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS: SYSTEMS journal, the paper "Parity Space Vector Machine Approach to Robust Fault Detection for Linear Discrete-Time Systems" by Zhong et al. combined the parity space method with the minimum error minimax probability machine method and proposed a fault detection method for the parity vector machine, achieving an optimal trade-off between the false alarm rate and the fault detection rate. However, the traditional minimum error minimax probability machine method is usually used for fault detection under a single operating condition. In actual industrial processes, changes in factors such as product load and raw material components will cause changes in the production operating conditions, resulting in multi-operating condition processes. Therefore, how to apply the minimum error minimax probability machine method to multi-operating condition industrial processes remains an open question.

[0004] With the increasing automation of modern systems, the requirements for the safety and reliability of systems are also getting higher and higher. As an important means to improve system safety and reliability, data-driven fault detection technology is widely used in various industrial systems. The minimum error minimax probability machine is a data-driven classification method that does not need to assume the probability distribution of variables. In recent years, it has been successfully applied to the field of fault detection. However, the existing minimum error minimax probability machine method is usually used for fault detection under a single operating condition. In actual industrial processes, changes in factors such as product load and raw material components will cause changes in the production operating conditions, resulting in multi-operating condition processes. Summary of the Invention

[0005] In view of the above technical problems existing in the prior art, the present invention proposes a multi-condition fault detection method based on the minimum error min-max probability machine, which is reasonably designed, overcomes the deficiencies of the prior art, and has good effects.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A multi-condition fault detection method based on the minimum error min-max probability machine, comprising the following steps:

[0008] Step 1: Obtain normal historical multi-condition data as a training set, extract features from the training set, and perform min-max normalization processing;

[0009] Step 2: Perform condition division based on the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm;

[0010] Step 3: Use different normal condition data and offline fault data to establish an L1-minimum error min-max probability machine fault detection subsystem for the corresponding conditions;

[0011] Step 4: Extract the same features from the data to be measured, and perform min-max normalization processing;

[0012] Step 5: Judge the condition to which the current data belongs based on the distance between the normalized data and the center point of the normal condition;

[0013] Step 6: Call the fault detection subsystem of the belonging condition, remove redundant features, and judge whether the system has a fault.

[0014] Preferably, in Step 1, it specifically includes the following steps:

[0015] Step 1.1: Obtain normal historical multi-condition data as a training set, extract time-domain features from the training set data; define the feature data set after extracting the time-domain features as where x(i), i = 1, 2 ···, n represents the i-th normal data sample, n represents the number of normal data samples, and m represents the number of feature variables;

[0016] Step 1.2: Perform min-max normalization processing on the feature data set X:

[0017]

[0018] where, represents the normalized data, x maxis the maximum value of each variable of the feature data x(k), where k = 1, 2, ···, n, and x min is the minimum value of each variable of the feature data x(k), where k = 1, 2, ···, n.

[0019] Preferably, in step 2, it specifically includes the following steps:

[0020] Step 2.1: Detect the unexamined samples z(k) in the dataset, where k = 1, 2, ···, n. If z(k) has not been processed, check its eps neighborhood. If the number of samples it contains is not less than minpts, establish a new working condition C i , and add all other samples in its eps neighborhood to C i , where the eps neighborhood represents a region with a radius of eps, and minpts represents the number of minimum points for determining whether a sample belongs to the current working condition;

[0021] Step 2.2: For all unprocessed samples in C i , check their eps neighborhoods. If at least minpts object samples are included, add the samples in their neighborhoods that have not been assigned to any working condition to C i ;

[0022] Step 2.3: Repeat step 2.2 until no new objects are added to the current working condition;

[0023] Step 2.4: Repeat steps 2.1 - 2.3 until all samples have been processed.

[0024] Preferably, in step 3, it specifically includes the following steps:

[0025] Step 3.1: Define to represent the sampling of the feature data containing m variables at the k-th moment when the system is operating in the i-th normal working condition or a fault f j occurs, where j = 1, 2, ···, p, and p represents the number of relevant faults; J th = b ij 2 respectively represent the threshold and the evaluation function, where is a parameter related to the design of the threshold and the evaluation function; Based on the following logic, determine whether the system has a fault:

[0026]

[0027] Without loss of generality, define the false alarm rate and the fault detection rate as follows:

[0028]

[0029] where fj (k) represents the fault vector to be detected, and Pr{·} represents the probability of {·};

[0030] Therefore, the false alarm rate and the fault detection rate of the system are:

[0031]

[0032] Step 3.2: Assume that the probability distribution of the feature data z(k) is difficult to estimate, but the mean of its normal data is 0 and the covariance matrix is known; to make the above assumption hold, perform the following z-score normalization processing on the data after extracting the time-domain features under different working conditions:

[0033]

[0034] where z(k) represents the real-time data to be measured after feature extraction, represents the mean of the feature data z(k), k = 1, 2 ···, n under normal working conditions, and E[·] represents the expectation of [·];

[0035] Define represent the normal data and the fault data sets respectively; characterize these two sets by the mean and covariance matrix of the normalized data, that is:

[0036]

[0037]

[0038] where, and represent the mean and covariance matrix of the normalized data under normal and fault conditions respectively;

[0039] To ensure the optimal trade-off between the false alarm rate and the fault detection rate and remove the redundant information between features at the same time, the above problem is formulated as the following optimization problem:

[0040]

[0041]

[0042] where n l represents the penalty parameter used to impose sparsity on the weight w ij , α ij , β ij ∈(0, 1) represent the upper bound of the false alarm rate and the lower bound of the fault detection rate respectively, and θ ij represents the preset parameter used to achieve the optimal trade-off between the false alarm rate and the fault detection rate;

[0043] It should be noted that:

[0044]

[0045] ensures that Therefore, the false alarm rate in the worst case satisfies the following inequality:

[0046] FAR ≤ α ij (11);

[0047] For β ij ∈(0, 1], the following inequality holds:

[0048]

[0049] In addition, the following inequality also holds:

[0050]

[0051] Let The optimization problems (8)-(9) are transformed into the following single-sided min-max problem:

[0052]

[0053]

[0054] Given w ij ≠ 0, b ij , such that w ij T z ≤ b ij , the condition holds if and only if where

[0055] Similarly, the condition holds if and only if where

[0056] Therefore, equations (14)-(15) are transformed into the following optimization problem:

[0057]

[0058]

[0059] According to the definitions of κ(η ij ) and κ(β ij ), the following equation holds:

[0060]

[0061] The optimization problems (16)-(17) are further transformed into the following minimization problem:

[0062]

[0063]

[0064] According to the Lagrange multiplier method, (19)-(20) are further transformed as follows:

[0065]

[0066]

[0067] where λ is the Lagrange factor used to impose sparsity on w ij .

[0068] Two vectors u ij and v ij are introduced to solve the non-linear objective function, where the two vectors satisfy the following conditions:

[0069] w ij = u ij - v ij , ||w ij ||1 = (u ij + v ij ) T e, u ij ≥ 0, v ij ≥ 0

[0070] The optimization problem (21)-(22) is further transformed as follows:

[0071]

[0072]

[0073] where the parameter λ determines the sparsity of the solution.

[0074] To solve the optimization problem (23)-(24), the above problem is solved by an iterative search method;

[0075] First, η ij , β ij are fixed as the preset constant values η0 and β0, and the optimization problem is transformed into finding the sparse solution w ij at η0 + (1 - θ ij )β0; is fixed as an arbitrary constant value, and the optimization problem is transformed into a second-order cone problem, which is solved by a second-order cone solver or an iterative least squares method; subsequently, η ij and β ij are further updated according to the quadratic interpolation method until the optimal solutions η ij and β ij * and βij * , b ij * , while obtaining the optimal solution w according to the optimal solutions u ij * and v ij * . ij * .

[0076] Preferably, in step 5, the specific content is as follows:

[0077] C i = min i∈M |z(k) - c i | (25);

[0078] where z(k) represents the k-th normalized real-time data, c i represents the i-th normal operating condition center point, and C i represents belonging to the i-th normal operating condition, and M represents the number of normal operating conditions.

[0079] Preferably, in step 6, it specifically includes the following steps:

[0080] Step 6.1: Determine that the current data is operating in the i-th operating condition according to step 5. To detect the j-th fault, call the fault detection subsystem parameters w ij * , b ij * , i = 1, 2 ···, M, j = 1, 2 ···, p;

[0081] Step 6.2: For the data z ij (k) to be measured, the evaluation function and the threshold are respectively expressed as:

[0082] J(z) = (w ij *T z ij (k)) 2 , J th = b ij *2 (26);

[0083] Step 6.3: Based on the following logic, determine whether the system has a fault:

[0084]

[0085] The beneficial technical effects brought by the present invention:

[0086] The multi - condition fault detection method based on the minimum error minimum - maximum probability machine provided by the present invention uses the DBSCAN algorithm to divide working conditions, establishes a minimum error minimum - maximum probability machine fault detection subsystem corresponding to each working condition for different working conditions, determines the belonging working condition for real - time data and detects whether a fault occurs, solving the problem that the traditional minimum error minimum - maximum probability machine method is only applicable to fault detection in a single working condition.

[0087] The present invention considers that in the multi - condition process, redundant information is inevitably present in the artificial feature extraction. By integrating feature selection and fault detection performance design, not only redundant information is removed, but also an optimal trade - off between the false alarm rate and the fault detection rate is achieved in the multi - condition process where the probability distribution of process variables is difficult to estimate. Description of the Drawings

[0088] Figure 1 It is a flow chart of the multi - condition fault detection method based on the minimum error minimum - maximum probability machine of the present invention;

[0089] Figure 2 It is a schematic diagram of the density - based spatial clustering of noise application for working condition division in an embodiment of the present invention;

[0090] Figure 3 It is a schematic diagram of the multi - condition fault detection result based on the minimum error minimum - maximum probability machine in an embodiment of the present invention. Detailed Embodiment

[0091] The present invention will be further described in detail below in conjunction with the drawings and specific embodiments:

[0092] As Figure 1 shown, a multi - condition fault detection method based on the minimum error minimum - maximum probability machine includes the following steps:

[0093] Step 1: Obtain normal historical multi - condition data as a training set, extract features from the training set and perform min - max normalization processing; specifically including the following steps:

[0094] Step 1.1: Obtain normal historical multi - condition data as a training set, and extract time - domain features from the training set data; define the feature data set after extracting time - domain features as where x(i), i = 1, 2 ···, n represents the i - th normal data sample, n represents the number of normal data samples, and m represents the number of feature variables;

[0095] Step 1.2: Perform min - max normalization processing on the feature data set X:

[0096]

[0097] where, Represents the normalized data, x max Is the maximum value of each variable of the feature data x(k), k = 1, 2 ···, n, x min Is the minimum value of each variable of the feature data x(k), k = 1, 2 ···, n.

[0098] Step 2: Use the density-based spatial clustering of applications with noise algorithm for working condition division; as Figure 2 Shown, specifically including the following steps:

[0099] Step 2.1: Detect the samples z(k) in the dataset that have not been checked yet, k = 1, 2, ···, n. If z(k) has not been processed, check its eps neighborhood. If the number of samples it contains is not less than minpts, establish a new working condition C i , and add all other samples in its eps neighborhood to C i , where the eps neighborhood represents a region with a radius of eps, and minpts represents the number of minimum points for determining whether a sample belongs to the current working condition;

[0100] Step 2.2 For all the samples in C i that have not been processed yet, check their eps neighborhoods. If at least minpts object samples are included, add the samples in their neighborhoods that have not been assigned to any working condition to C i ;

[0101] Step 2.3 Repeat Step 2.2 until no new objects are added to the current working condition;

[0102] Step 2.4 Repeat Steps 2.1 - 2.3 until all samples are processed.

[0103] Step 3: Use different normal working condition data and offline fault data to establish an L1-minimum error minimum maximum probability machine fault detection subsystem for the corresponding working conditions; specifically including the following steps:

[0104] Step 3.1: Define to represent the sampling of the feature data containing m variables at the kth moment when the system is operating in the ith normal working condition or when the fault f j occurs, where j = 1, 2 ···, p, and p represents the number of relevant faults; define J th = b ij 2 respectively represent the threshold and the evaluation function, where is a parameter related to the design of the threshold and the evaluation function; Based on the following logic, determine whether the system has a fault:

[0105]

[0106] Without loss of generality, the false alarm rate and the fault detection rate are defined as follows:

[0107]

[0108] where f j (k) represents the fault vector to be detected, and Pr{·} denotes the probability of {·};

[0109] Therefore, the false alarm rate and the fault detection rate of the system are:

[0110]

[0111] Step 3.2: Assume that the probability distribution of the feature data z(k) is difficult to estimate, but the mean of its normal data is 0 and the covariance matrix is known; to make the above assumption hold, the following z-score normalization processing is performed on the data after extracting the time-domain features under different working conditions:

[0112]

[0113] where z(k) represents the real-time data to be measured after feature extraction, represents the mean of the feature data z(k), k = 1, 2 ···, n under normal working conditions, and E[·] denotes the expectation of [·];

[0114] Define represent the normal data and the fault data sets respectively; the two sets are characterized by the mean and covariance matrix of the normalized data, that is:

[0115]

[0116]

[0117] where, and represent the mean and covariance matrix of the normalized data under normal and fault conditions respectively;

[0118] To ensure the optimal trade-off between the false alarm rate and the fault detection rate and at the same time remove the redundant information between features, the above problem is formulated as the following optimization problem:

[0119]

[0120]

[0121] where n l represents the penalty parameter used to impose sparsity on the weight w ij , α ij , β ij∈(0,1) represent the upper bound of the false alarm rate and the lower bound of the fault detection rate, respectively, and θ ij represents a preset parameter used to achieve the optimal trade-off between the false alarm rate and the fault detection rate;

[0122] It should be noted that:

[0123]

[0124] guarantees that Therefore, the false alarm rate in the worst case satisfies the following inequality:

[0125] FAR ≤ α ij (11);

[0126] For β ij ∈(0,1], the following inequality holds:

[0127]

[0128] In addition, the following inequality also holds:

[0129]

[0130] Let The optimization problems (8)-(9) are transformed into the following one-sided min-max problem:

[0131]

[0132]

[0133] Given w ij ≠0, b ij , such that w ij T z ≤ b ij , the condition holds if and only if where

[0134] Similarly, the condition holds if and only if where

[0135] Therefore, equations (14)-(15) are transformed into the following optimization problem:

[0136]

[0137]

[0138] According to κ(η ij ) and κ(β ij)'s definition, the following equation holds:

[0139]

[0140] The optimization problems (16)-(17) are further transformed into the following minimization problem:

[0141]

[0142]

[0143] According to the Lagrange multiplier method, (19)-(20) are further transformed as follows:

[0144]

[0145]

[0146] where λ is the Lagrange factor used to impose sparsity on w ij imposed sparsity.

[0147] Introduce two vectors u ij and v ij to solve the non-linear objective function, where the two vectors satisfy the following conditions:

[0148] w ij = u ij - v ij , ||w ij ||1 = (u ij + v ij ) T e, u ij ≥0, v ij ≥0

[0149] The optimization problems (21)-(22) are further transformed as follows:

[0150]

[0151]

[0152] where the parameter λ determines the sparsity of the solution.

[0153] To solve the optimization problems (23)-(24), the above problems are solved by an iterative search method;

[0154] First, fix η ij , β ij as the preset constant values η0 and β0, and the optimization problem is transformed into finding the sparse solution w ij η0 + (1 - θ ij )β0 for the given θ ij; will be fixed as any constant value, and the optimization problem is transformed into a second-order cone problem, which is solved by means of a second-order cone solver or iterative least squares method; subsequently, η is further updated according to the quadratic interpolation method ij and β ij , until the optimal solutions η ij * and β ij * , b ij * , and at the same time, according to the optimal solutions u ij * and v ij * the optimal solution w is obtained ij * .

[0155] Step 4: Extract the same features from the data to be measured and perform min-max normalization processing;

[0156] Step 5: Determine the working condition to which the current data belongs based on the distance between the normalized data and the center point of the normal working condition; the specific content is as follows:

[0157] C i = min i∈M |z(k)-c i | (25);

[0158] where z(k) represents the kth normalized real-time data, c i represents the center point of the ith normal working condition, C i represents belonging to the ith normal working condition, and M represents the number of normal working conditions.

[0159] Step 6: Call the L1-minimum error minimum-maximum probability machine fault detection subsystem of the working condition to which it belongs, remove redundant features and determine whether the system has a fault; the fault detection result is as Figure 3 shown.

[0160] Specifically, it includes the following steps:

[0161] Step 6.1: Determine that the current data is running in the ith working condition according to Step 5. In order to detect the jth fault, call the parameters w ij * , b ij * , i = 1, 2 ···, M, j = 1, 2 ···, p;

[0162] Step 6.2: For the data z ij (k) to be measured, the evaluation function and the threshold are respectively expressed as:

[0163] J(z)=(w ij*T z ij (k)) 2 ,J th = b ij *2 (26);

[0164] Step 6.3: Determine whether the system fails based on the following logic:

[0165]

[0166] Of course, the above description is not a limitation of the present invention, nor is it limited to the above examples. Changes, modifications, additions, or substitutions made by those skilled in the art within the scope of the essence of the present invention should also fall within the protection scope of the present invention.

Claims

1. A multi-condition fault detection method based on the minimum error minimum maximum probability machine, characterized in that: Including the following steps: Step 1: Obtain normal historical multi-condition data as the training set, extract features from the training set and perform min-max normalization processing; Step 2: Perform condition division using the density-based spatial clustering of applications with noise (DBSCAN) algorithm; Step 3: Use different normal condition data and offline fault data to establish an L1-minimum error minimum maximum probability machine fault detection subsystem for the corresponding condition; specifically including the following steps: Step 3.1: Define representing the sampling of the characteristic data containing m variables at the k-th moment when the system operates in the i-th normal condition or the fault f occurs, where j = 1, 2 ···, p, and p represents the number of relevant faults; j J th = b ij 2 representing the threshold and the evaluation function respectively, where are parameters related to the design of the threshold and the evaluation function respectively; judging whether the system has a fault based on the following logic:​ Without loss of generality, define the false alarm rate and the fault detection rate as follows: where f j (k) represents the fault vector to be detected, and Pr{·} denotes the probability of {·}; Therefore, the false alarm rate and the fault detection rate of the system are: Step 3.2: Assume that the probability distribution of the feature data z(k) is difficult to estimate, but the mean of its normal data is 0 and the covariance matrix is known; in order to make the above assumption hold, perform the following z-score normalization processing on the data after extracting the time-domain features under different conditions: Among them, \(z(k)\) represents the real-time data to be measured after feature extraction. represents the mean value of the feature data \(z(k)\) under normal working conditions, where \(k = 1, 2, \cdots, n\), and \(E[\cdot]\) represents the expectation of \([\cdot]\). Definition respectively represent the normal data and the fault data sets; these two sets are characterized by the mean and covariance matrix of the standardized data, that is: wherein, and respectively represent the mean and covariance matrix of the standardized data under normal and fault conditions; Formulate the problem of how to simultaneously achieve the optimal trade-off between the false alarm rate and the fault detection rate and remove the redundant information between features into the following optimization problem: Among them, n l represents a penalty parameter used to impose sparsity on the weight w ij , α ij , β ij ∈(0, 1) respectively represent the upper bound of the false alarm rate and the lower bound of the fault detection rate, and θ ij represents a preset parameter used to achieve the optimal trade-off between the false alarm rate and the fault detection rate; It should be noted that: Ensured that Therefore, the false positive rate in the worst case satisfies the following inequality: FAR ≤ α ij (11); For β ij ∈ (0, 1], the following inequality holds: In addition, the following inequality also holds: Let the optimization problems (8)-(9) be transformed into the following one-sided min-max problem: Given w ij ≠ 0, b ij such that w ij T z ≤ b ij The condition holds if and only if where Similarly, the condition holds if and only if where Therefore, formulas (14)-(15) are transformed into the following optimization problem: According to the definitions of κ(η ij ) and κ(β ij ), the following equation holds: Optimization problems (16)-(17) are further transformed into the following minimization problem: According to the Lagrange multiplier method, (19)-(20) are further transformed as follows: where λ is the Lagrange factor for imposing sparsity on w ij ; Introduce two vectors u ij and v ij to solve the non-linear objective function, where the two vectors satisfy the following conditions: w ij = u ij - v ij , || w ij ||1 = (u ij + v ij ) T e, u ij ≥ 0, v ij ≥ 0 Optimization problems (21)-(22) are further transformed as follows: Among them, the parameter λ determines the sparsity of the solution; To solve the optimization problems (23)-(24), solve the above problems through an iterative search method; First, η ij , β ij Fixed to preset constant values ​​η0 and β0, the optimization problem is transformed into finding ij η0+(1-θ ij )The sparse solution w under β0 ij ; Fix to an arbitrary constant value, convert the optimization problem into a second-order cone problem, and solve it with the help of a second-order cone solver or iterative least squares method; then, further update η according to the quadratic interpolation method ij and β ij , until the optimal solution η is found ij * and β ij * , b ij * , and according to the optimal solution u ij * and v ij * Get the optimal solution w ij * ; Step 4: Extract the same features from the data to be measured and perform min-max normalization processing; Step 5: Based on the distance between the normalized data and the center point of the normal condition, determine the condition to which the current data belongs; Step 6: Call the fault detection subsystem of the belonging condition, remove the redundant features and judge whether the system has a fault.

2. The multi-condition fault detection method based on the minimum error minimum maximum probability machine according to claim 1, wherein: In Step 1, it specifically includes the following steps: Step 1.1: Obtain normal historical multi-condition data as the training set, and extract time-domain features from the training set data; define the feature data set after extracting the time-domain features as where x(i), i = 1, 2 ···, n represents the i-th normal data sample, n represents the number of normal data samples, and m represents the number of feature variables; Step 1.2: Perform min-max normalization processing on the feature data set X: Among them, represents the normalized data, and x max is the maximum value of each variable of the feature data x(k), where k = 1, 2, ···, n, and x min is the minimum value of each variable of the feature data x(k), where k = 1, 2, ···, n.

3. The multi-condition fault detection method based on the minimum error minimum maximum probability machine according to claim 1, wherein: In Step 2, it specifically includes the following steps: Step 2.1: Detect the unexamined sample z(k) in the dataset, where k = 1, 2, ···, n. If z(k) has not been processed, check its eps neighborhood. If the number of samples contained therein is not less than minpts, establish a new working condition C i , and add all other samples in its eps neighborhood to C i , where the eps neighborhood represents a region with a radius of eps, and minpts represents the number of minimum points for determining whether a sample belongs to the current working condition; Step 2.2 For all the samples in C that have not been processed yet i check their eps-neighborhoods. If at least minpts object samples are included in a neighborhood, add the samples in this neighborhood that have not been assigned to any working condition to C i ; Step 2.3 Repeat Step 2.2 until no new object is added to the current condition; Step 2.4 Repeat Steps 2.1-2.3 until all samples are processed.

4. The multi - working - condition fault detection method based on the minimum - error minimum - maximum probability machine according to claim 1, wherein: In Step 5, the specific content is: C i = min i∈M |z(k) - c i | (25); Among them, z(k) represents the k-th normalized real-time data, c i represents the center point of the i-th normal operating condition, C i represents belonging to the i-th normal operating condition, and M represents the number of normal operating conditions.

5. The multi-condition fault detection method based on the minimum error minimum maximum probability machine according to claim 1, characterized in that: In Step 6, it specifically includes the following steps: Step 6.1: Determine that the current data runs in the i-th working condition according to Step 5. To detect the j-th fault, call the fault detection subsystem parameters w of the belonging working condition ij * ,b ij * , where i = 1, 2 ···, M and j = 1, 2 ···, p; Step 6.2: For the data to be measured z ij (k), the evaluation function and the threshold are respectively expressed as: J(z) = (w ij *T z ij (k)) 2 , J th = b ij *2 (26); Step 6.3: Based on the following logic, judge whether the system has a fault:

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