Dynamic system data-driven fault detection method based on distributed canonical correlation analysis

Abstract

The application discloses a dynamic system data-driven fault detection method based on distributed typical correlation analysis, and comprises the following steps: in an offline process, historical data collected by sensors in each subsystem under normal working conditions is used to construct a centralized CCA residual generator; according to the network topology structure among the subsystems in the dynamic system, the weight coefficients of information transmission among the subsystems are determined based on an average consistency algorithm, an iteration matrix for solving CCA parameters of each subsystem is constructed, and the centralized CCA residual generator is converted into a distributed CCA residual generator; the CCA parameters of each subsystem are solved; in an online process, each subsystem uses the solved CCA parameters to construct a CCA-based residual generator, and the residual signals of each subsystem are distributedly fused based on the average consistency algorithm; finally, a control statistic is designed, a threshold is determined, and distributed optimal fault detection based on data driving in the dynamic system is carried out.

Description

Technical Field

[0001] This invention relates to the field of control, monitoring and diagnosis technology for complex industrial processes, and in particular to a dynamic system data-driven fault detection method based on distributed canonical correlation analysis. Background Technology

[0002] In recent decades, fault detection in industrial processes has been a hot research topic in the field of control engineering, attracting increasing attention. With the continuous expansion of factory scale, the complexity of system mechanisms leading to modeling difficulties, the surge in measurement data due to intricate processes, and the challenges of handling dynamic characteristics make fault detection paramount. If such a large system experiences a fault and fails to address it promptly in its early stages, the consequences could be disastrous, ranging from equipment damage to system collapse and even safety accidents. Therefore, designing a suitable fault detection method is urgently needed. This method should be able to detect faults in their early stages through real-time monitoring of the dynamic system, thereby ensuring the system's reliability and safety.

[0003] In traditional fault detection methods, centralized fault diagnosis is widely used. The centralized approach involves transmitting measured data to a central node, where fault detection is performed. This process incurs significant computational overhead at the central node, is cumbersome in data transmission, and carries a high risk factor. While CCA (Computational Capability Analysis) is a commonly used method in centralized fault diagnosis, its computational demands for solving key parameters are too high, placing an excessive burden on the central node and limiting its application in large-scale interconnected systems.

[0004] In recent years, advancements in sensor technology and computing power have driven the development of distributed fault diagnosis strategies. The average consensus algorithm has been successfully applied to distributed systems. However, research on developing data-driven distributed fault diagnosis (CCA) based on CCA in dynamic systems, and on solving CCA-related parameters in a distributed manner, is very limited. Most approaches to applying CCA to dynamic systems perform CCA locally, without considering global fault detection, or only address specific topologies for fault diagnosis based on CCA. Summary of the Invention

[0005] This invention addresses the aforementioned problems in fault detection of large-scale dynamic systems by providing a data-driven fault detection method for dynamic systems based on distributed canonical correlation analysis. In the offline part, the relevant CCA parameters of each subsystem are solved in a distributed manner. In the online part, a distributed residual generator is constructed, and the average consensus algorithm is used to fuse the residual signals to achieve optimal fault detection.

[0006] To address the aforementioned technical problems, embodiments of the present invention provide the following solutions:

[0007] A dynamic system data-driven fault detection method based on distributed canonical correlation analysis includes the following steps:

[0008] S1, During the offline process, historical data under normal operating conditions is collected by sensors in each subsystem to construct a centralized CCA residual generator;

[0009] S2, based on the network topology between subsystems in the dynamic system, determines the weight coefficients of information transmission between subsystems based on the average consensus algorithm, constructs an iterative matrix for solving the CCA parameters of each subsystem, and transforms the centralized CCA residual generator into a distributed CCA residual generator for application in distributed systems.

[0010] S3, solve for the CCA parameters of each subsystem. During the online process, each subsystem uses the solved CCA parameters to construct a CCA-based residual generator, and performs distributed fusion of the residual signals of each subsystem based on the average consensus algorithm, and finally performs data-driven distributed optimal fault detection in the dynamic system.

[0011] Preferably, step S1 specifically includes the following steps:

[0012] S11, Collect historical data of each subsystem in the dynamic system under normal operating conditions, and construct the data matrix as follows using enhancement techniques:

[0013]

[0014] in,

[0015]

[0016]

[0017] and U represents the input and output data values ​​of the k-th sample in the i-th subsystem. i，p and y i，p Let u represent the past input and output data values ​​of the i-th subsystem. i，f and y i，f Let s and s be the future input and output data values ​​of the i-th subsystem, respectively. f The integer is M, where M is the number of subsystems;

[0018] By collecting N samples, we can obtain:

[0019]

[0020] Among them, Z and Y f These are matrices composed of N samples of the data described in the formula;

[0021] S12, Assume the model of the subsystem is as follows:

[0022] x(k+1)=Ax(k)+Bu(k)+w(k) (3)

[0023] y(k)=Cx(k)+Du(k)+v(k) (4)

[0024] Where A, B, C, and D are unknown constant parameter matrices of appropriate dimensions, x(k) is the state variable, w(k) and v(k) are the process noise and measurement noise, respectively, and u(k) and y(k) represent the system's input and output data values, respectively, and their correlation forms are as follows:

[0025]

[0026] For ease of derivation, the predictor form of the system model is used here:

[0027] x(k+1)=A K x(k)+B K u(k)+Ky(k) (6)

[0028] y(k)=Cx(k)+Du(k)+e(k) (7)

[0029] Among them, A K =A-KC,B K =B-KD, where K is the Kalman gain;

[0030] S13, Verify the rationality of using CCA in dynamic systems;

[0031] Based on the above formula, we can conclude that:

[0032]

[0033] Because of A K It is stable when s is large enough. As it approaches 0, the above expression becomes:

[0034]

[0035] in,

[0036]

[0037] z p (k)=[y(k-1) T u(k-1) T …y(ks)T u(ks) T ] T (11)

[0038] get:

[0039]

[0040] in,

[0041]

[0042] Observation shows that,

[0043]

[0044]

[0045] Where T and T′ are both products of elementary matrices;

[0046] Transform into:

[0047]

[0048] make:

[0049]

[0050]

[0051] It can be converted into the same form as CCA:

[0052]

[0053] That is, the use of CCA in dynamic systems is reasonable;

[0054] S14, y is known from above f z(k) and z(k) are related, therefore the residual generator can be constructed using CCA as follows:

[0055] r(k)=L T y f (k)-ΛJ T z(k) (20)

[0056] Where r(k) is the residual signal of the system at time k, and L, J and Λ are the key parameters of CCA, which will be solved later.

[0057] Preferably, step S2 specifically includes the following steps:

[0058] S21, In order to convert the centralized CCA residual generator into a distributed CCA residual generator, let:

[0059]

[0060] Here, parameters J and L are divided according to subsystems, J i and L i The CCA parameter represents subsystem i;

[0061] Substituting, we get:

[0062]

[0063] in, The residual r(k) is the residual r of each subsystem i The sum of (k) means that each subsystem only needs to calculate its own residual, and then use the average consensus algorithm to fuse the residual signals;

[0064] S22, Calculate the weighting coefficients for information transmission between subsystems based on the average consensus algorithm:

[0065]

[0066] Where N = {1, ..., M}, N i ={j|node j is connected to the i-th subsystem, j∈N}, K i This represents the number of neighboring nodes of node i;

[0067] The weighting coefficients between subsystems here mean that when subsystem j wants to pass information to subsystem i, the information to be passed should be multiplied by w. ij This weighting coefficient matrix is ​​also the most critical parameter in the average consensus algorithm iteration process;

[0068] S23, Based on the network topology diagram of the dynamic system, calculate the weight coefficients of information transmission at each node, thereby obtaining the iteration matrix W in the average consensus algorithm: = (w ij ) M×M ;

[0069] S24, each subsystem calculates the average state of all subsystems based on the average consensus algorithm, and each subsystem iterates using the following iterative formula:

[0070]

[0071] Where, Φ i，0 Φ represents the initial value of subsystem i; i，k Let be the value of the k-th iteration of subsystem i; after the average consensus algorithm converges, the final value of each node iteration is:

[0072]

[0073] To balance the relationship between iteration delay and iteration accuracy, a bound γ is added, when ||Φ i，k+1 -Φ i，k When ||≤γ, it is assumed that each subsystem converges to the final value;

[0074] S25, using the average consensus algorithm to obtain the average of the initial values ​​of each subsystem, only requires each node to obtain its own r. i (k), then the average consensus algorithm can be used; subsequently, a distributed algorithm for solving CCA parameters is used to solve r. i L in (k) i and J i parameter.

[0075] Preferably, step S3 specifically includes the following steps:

[0076] S31, Set the iteration count i = 0, and initialize each subsystem separately. and k = 1, ..., M, where the superscript indicates the iteration number;

[0077] Among them, the kth subsystem only needs to be initialized. and That is, the relevant parameters represented in the formula, and the initial parameter values ​​can be random values. The initial parameter values ​​will not affect the final convergence result.

[0078] S32, each subsystem calculates simultaneously:

[0079]

[0080]

[0081] in, and The superscript represents the iteration number, and the subscript represents the k-th subsystem, and Y i，f，L =[y i，f [iΘ]y i，f [iΘ+1]…y i，f [iΘ+Θ-1]] (28)

[0082] Z i，L =[z i [iΘ]z i [iΘ+1]…z i [iΘ+Θ-1]] (29)

[0083] Θ is a constant;

[0084] S33, using the average consensus algorithm to iterate over equations and , eventually each subsystem can converge and be obtained:

[0085]

[0086] in, and This represents the average value of each subsystem after the i-th iteration.

[0087] S34, each subsystem simultaneously constructs an iterative matrix for distributed solving of key CCA parameters. Here, we use subsystem k to illustrate the form of the constructed iterative matrix:

[0088]

[0089] S35, at this point each subsystem has obtained the matrix shown, and each subsystem simultaneously processes the constructed matrix. and Use CCA and obtain the parameters as follows: and update Λ i+1 ;

[0090]

[0091]

[0092]

[0093]

[0094] Where, ∑ x ,∑ y ,∑ x，y and ∑ y，x For the corresponding covariance, the formula is the core step of CCA, and the parameters Γ, Λ and Δ can be obtained by using singular value decomposition;

[0095] Update parameters according to formula and

[0096]

[0097] S36, let the iteration count i = i + 1, jump to step S32 and loop continuously until the parameter... and convergence;

[0098] S37, based on the above steps, each subsystem can obtain the relevant parameters of CCA, and each subsystem obtains r. i After (k), the detection statistic and threshold can be obtained by using average consistency analysis:

[0099]

[0100]

[0101] When the detection statistic Greater than the detection threshold If the condition is met, it is considered a fault; otherwise, it is considered a fault-free condition.

[0102] The beneficial effects of the technical solutions provided in the embodiments of the present invention include at least the following:

[0103] The dynamic system data-driven fault detection method based on distributed canonical correlation analysis provided by this invention is mainly divided into two parts: an offline process and an online process. In the offline process, historical data under normal operating conditions of each subsystem is collected by sensors, and a corresponding data matrix is ​​constructed using boosting techniques. Then, according to the network topology between the subsystems in the dynamic system, an average consensus algorithm iteration matrix is ​​constructed. Based on the average consensus algorithm, the corresponding CCA key parameters of each subsystem are solved. In the online process, each subsystem constructs a residual generator based on CCA. Each subsystem converts the real-time collected data into residual signals, and the average consensus algorithm is used again to perform distributed fusion of the residual signals. Finally, control statistics are designed, thresholds are determined, and the dynamic system is judged according to the fault detection logic.

[0104] The fault detection method described in this invention can perform distributed fault detection on dynamic systems in real time, with low loss, and effectively, providing a new technical solution for fault detection in dynamic systems. This method reduces the computational overhead of centralized fault detection, enhances the security of data transmission, and, in solving the CCA parameters, applies the average consensus algorithm to the distributed CCA parameter solving process, greatly reducing the complexity of the solution. It has advantages such as low loss, less data transmission, and high security. Attached Figure Description

[0105] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0106] Figure 1 This is a flowchart of a dynamic system data-driven fault detection method based on distributed canonical correlation analysis provided in an embodiment of the present invention;

[0107] Figure 2 This is a network topology diagram of a dynamic system provided in an embodiment of the present invention;

[0108] Figure 3 This is a schematic diagram of a model for data simulation of a TE chemical process provided in an embodiment of the present invention;

[0109] Figures 4a-4f This is a schematic diagram of the detection results of subsystems 1 to 6 provided in the embodiments of the present invention;

[0110] Figure 5 This is a schematic diagram illustrating the consistency of the effects of the fault detection method provided in this embodiment of the invention with that of the centralized fault detection method.

[0111] As shown in the figure, specific structures and devices are marked in the figure to clearly illustrate the structure of the embodiments of the present invention. However, this is only for illustrative purposes and is not intended to limit the present invention to the specific structure, device and environment. According to specific needs, those skilled in the art can adjust or modify these devices and environments, and such adjustments or modifications are still included in the protection scope of the present invention. Detailed Implementation

[0112] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0113] Embodiments of the present invention provide a dynamic system data-driven fault detection method based on distributed canonical correlation analysis, such as... Figure 1 As shown, the method includes the following steps:

[0114] S1, During the offline process, historical data under normal operating conditions is collected by sensors in each subsystem to construct a centralized CCA residual generator;

[0115] S2, based on the network topology between subsystems in the dynamic system, determines the weight coefficients of information transmission between subsystems based on the average consensus algorithm, constructs an iterative matrix for solving the CCA parameters of each subsystem, and transforms the centralized CCA residual generator into a distributed CCA residual generator for application in distributed systems.

[0116] S3, solve for the CCA parameters of each subsystem. During the online process, each subsystem uses the solved CCA parameters to construct a CCA-based residual generator, and performs distributed fusion of the residual signals of each subsystem based on the average consensus algorithm, and finally performs data-driven distributed optimal fault detection in the dynamic system.

[0117] Furthermore, step S1 specifically includes the following steps:

[0118] S11, Collect historical data of each subsystem in the dynamic system under normal operating conditions, and construct the data matrix as follows using enhancement techniques:

[0119]

[0120] in,

[0121]

[0122]

[0123] and U represents the input and output data values ​​of the k-th sample in the i-th subsystem. i，p and y i，p Let u represent the past input and output data values ​​of the i-th subsystem. i，f and y i，f Let s and s be the future input and output data values ​​of the i-th subsystem, respectively. f The integer is M, where M is the number of subsystems;

[0124] By collecting N samples, we can obtain:

[0125]

[0126] Among them, Z and Y f These are matrices composed of N samples of the data described in the formula;

[0127] S12, Assume the model of the subsystem is as follows:

[0128] x(k+1)=Ax(k)+Bu(k)+w(k) (3)

[0129] y(k)=Cx(k)+Du(k)+v(k) (4)

[0130] Where A, B, C, and D are unknown constant parameter matrices of appropriate dimensions, x(k) is the state variable, w(k) and v(k) are the process noise and measurement noise, respectively, and u(k) and y(k) represent the system's input and output data values, respectively, and their correlation forms are as follows:

[0131]

[0132] For ease of derivation, the predictor form of the system model is used here:

[0133] x(k+1)=A K x(k)+B Ku(k)+Ky(k) (6)

[0134] y(k)=Cx(k)+Du(k)+e(k) (7)

[0135] Among them, A K =A-KC,B K =B-KD, where K is the Kalman gain;

[0136] S13, Verify the rationality of using CCA in dynamic systems;

[0137] Based on the above formula, we can conclude that:

[0138]

[0139] Because of A K It is stable when s is large enough. As it approaches 0, the above expression becomes:

[0140]

[0141] in,

[0142]

[0143] z p (k)=[y(k-1) T u(k-1) T …y(ks) T u(ks) T ] T (11)

[0144] get:

[0145]

[0146] in,

[0147]

[0148] Observation shows that,

[0149]

[0150]

[0151] Where T and T′ are both products of elementary matrices;

[0152] Transform into:

[0153]

[0154] make:

[0155]

[0156]

[0157] It can be converted into the same form as CCA:

[0158]

[0159] That is, the use of CCA in dynamic systems is reasonable;

[0160] S14, y is known from above f z(k) and z(k) are related, therefore the residual generator can be constructed using CCA as follows:

[0161] r(k)=L T y f (k)-ΛJ T z(k) (20)

[0162] Where r(k) is the residual signal of the system at time k, and L, J and Λ are the key parameters of CCA, which will be solved later.

[0163] Furthermore, step S2 specifically includes the following steps:

[0164] S21, In order to convert the centralized CCA residual generator into a distributed CCA residual generator, let:

[0165]

[0166] Here, parameters J and L are divided according to subsystems, J i and L i The CCA parameter represents subsystem i;

[0167] Substituting, we get:

[0168]

[0169] in, The residual r(k) is the residual r of each subsystem i The sum of (k) means that each subsystem only needs to calculate its own residual, and then use the average consensus algorithm to fuse the residual signals;

[0170] S22, Calculate the weighting coefficients for information transmission between subsystems based on the average consensus algorithm:

[0171]

[0172] Where N = {1, ..., M}, N i={j|node j is connected to the i-th subsystem, j∈N}, K i This represents the number of neighboring nodes of node i;

[0173] The weighting coefficients between subsystems here mean that when subsystem j wants to pass information to subsystem i, the information to be passed should be multiplied by w. ij This weighting coefficient matrix is ​​also the most critical parameter in the average consensus algorithm iteration process;

[0174] S23, Based on the network topology diagram of the dynamic system, calculate the weight coefficients of information transmission at each node, thereby obtaining the iteration matrix W: = (w... ij ) M×M ;

[0175] S24, each subsystem calculates the average state of all subsystems based on the average consensus algorithm, and each subsystem iterates using the following iterative formula:

[0176]

[0177] Where, Φ i，0 Φ represents the initial value of subsystem i; i，k Let be the value of the k-th iteration of subsystem i; after the average consensus algorithm converges, the final value of each node iteration is:

[0178]

[0179] To balance the relationship between iteration delay and iteration accuracy, a bound γ is added, when ||Φ i，k+1 -Φ i，k When ||≤γ, it is assumed that each subsystem converges to the final value;

[0180] S25, using the average consensus algorithm to obtain the average of the initial values ​​of each subsystem, only requires each node to obtain its own r. i (k), then the average consensus algorithm can be used; subsequently, a distributed algorithm for solving CCA parameters is used to solve r. i L in (k) i and J i parameter.

[0181] Furthermore, step S3 specifically includes the following steps:

[0182] S31, Set the iteration count i = 0, and initialize each subsystem separately. and k = 1, ..., M, where the superscript indicates the iteration number;

[0183] Among them, the kth subsystem only needs to be initialized. and That is, the relevant parameters represented in the formula, and the initial parameter values ​​can be random values. The initial parameter values ​​will not affect the final convergence result.

[0184] S32, each subsystem calculates simultaneously:

[0185]

[0186]

[0187] in, and The superscript represents the iteration number, and the subscript represents the k-th subsystem, and Y i，f，L =[y i，f [iΘ]y i，f [iΘ+1]…y i，f [iΘ+Θ-1]] (28)

[0188] Z i，L =[z i [iΘ]z i [iΘ+1]…z i [iΘ+Θ-1]] (29)

[0189] Θ is a constant;

[0190] S33, using the average consensus algorithm to iterate over equations and , eventually each subsystem can converge and be obtained:

[0191]

[0192] in, and This represents the average value of each subsystem after the i-th iteration.

[0193] S34, each subsystem simultaneously constructs an iterative matrix for distributed solving of key CCA parameters. Here, we use subsystem k to illustrate the form of the constructed iterative matrix:

[0194]

[0195] S35, at this point each subsystem has obtained the matrix shown, and each subsystem simultaneously processes the constructed matrix. and Use CCA and obtain the parameters as follows: and update Λ i+1 ;

[0196]

[0197]

[0198]

[0199]

[0200] Where, ∑ x ,∑ y ,∑ x，y and ∑ y，x For the corresponding covariance, the formula is the core step of CCA, and the parameters Γ, Λ and Δ can be obtained by using singular value decomposition;

[0201] Update parameters according to formula and

[0202]

[0203] S36, let the iteration count i = i + 1, jump to step S32 and loop continuously until the parameter... and convergence;

[0204] S37, based on the above steps, each subsystem can obtain the relevant parameters of CCA, and each subsystem obtains r. i After (k), the detection statistic and threshold can be obtained by using average consistency analysis:

[0205]

[0206]

[0207] When the detection statistic Greater than the detection threshold If the condition is met, it is considered a fault; otherwise, it is considered a fault-free condition.

[0208] To verify the effectiveness and practicality of the dynamic system data-driven fault detection method based on distributed canonical correlation analysis proposed in this invention, a simulation of a dynamic system will be used to illustrate this in detail below.

[0209] This embodiment uses data simulation from the TE Chemical Process in Tennessee, USA. The TE Process, based on data from actual chemical reactions, can be widely used to test fault diagnosis models for complex industrial processes (such as...). Figure 3(As shown in the figure). The model is mainly divided into five operating units: product stripping tower, circulating compressor, gas-liquid separator condenser, product condenser, and reactor. The TE process has 41 measurement data points and 12 operating variables. To verify the feasibility of the proposed method, six measurement variables and six output variables (as shown in Table 1) are selected to represent the inputs and outputs of the six subsystem nodes, respectively. The topology diagram between the subsystems is shown in the figure. Figure 2 As shown. The TE process includes one fault-free sample dataset and 21 batches of datasets with different faults, each dataset containing 960 samples. The fault is introduced at the 160th sample. In the simulation, the parameters are set to s = 5, N = 960, s f =5, the acceptable false alarm rate is a = 0.01.

[0210] Table 1 Relationship between subsystems and variables

[0211]

[0212] Note: XMEAS represents the measured quantity, and XMV represents the control quantity.

[0213] Fault 1 was used for online verification of the distributed method, and the detection results of each subsystem are as follows: Figures 4a-4f As shown, each subsystem solves for its own relevant CCA parameters in a distributed manner, and uses these parameters in conjunction with the average consensus algorithm for fault detection. Ultimately, each subsystem achieves consistent detection performance, comparable to centralized fault detection (such as...). Figure 5 The effect is the same as shown.

[0214] In summary, the embodiments of the present invention provide a data-driven fault detection method for dynamic systems based on distributed canonical correlation analysis (CCA). This method mainly consists of two parts: an offline process and an online process. In the offline process, historical data under normal operating conditions in each subsystem is collected using sensors, and a corresponding data matrix is ​​constructed using boosting techniques. Then, based on the network topology between the subsystems in the dynamic system, an average consensus algorithm iteration matrix is ​​constructed. Based on the average consensus algorithm, the corresponding CCA key parameters are solved for each subsystem. In the online process, each subsystem constructs a CCA-based residual generator. Each subsystem converts the real-time collected data into residual signals, and the average consensus algorithm is used again to perform distributed fusion of the residual signals. Finally, control statistics are designed, thresholds are determined, and the dynamic system is judged according to the fault detection logic.

[0215] The fault detection method described in this invention can perform distributed fault detection on dynamic systems in real time, with low loss, and effectively, providing a new technical solution for fault detection in dynamic systems. This method reduces the computational overhead of centralized fault detection, enhances the security of data transmission, and, in solving the CCA parameters, applies the average consensus algorithm to the distributed CCA parameter solving process, greatly reducing the complexity of the solution. It has advantages such as low loss, less data transmission, and high security.

[0216] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0217] The use of terms such as "an embodiment," "an embodiment," "an exemplary embodiment," and "some embodiments" in the specification indicates that the described embodiment may include a specific feature, structure, or characteristic, but not every embodiment necessarily includes that specific feature, structure, or characteristic. Furthermore, when a specific feature, structure, or characteristic is described in connection with an embodiment, implementing such a feature, structure, or characteristic in conjunction with other embodiments (whether explicitly described or not) should be within the knowledge of those skilled in the art.

[0218] Generally, terms can be understood at least partly from their use in context. For example, depending at least partly on the context, the term "one or more" as used herein can be used to describe any feature, structure, or characteristic in a singular sense, or a combination of features, structures, or characteristics in a plural sense. Additionally, the term "based on" can be understood not necessarily to convey an exclusive set of factors, but rather, alternatively, depending at least partly on the context, to allow for the presence of other factors that are not necessarily explicitly described.

[0219] As used herein, the term "nominal / nominally" refers to the expected or target value of a characteristic or parameter for the operation of a component or process, set during the design phase of the production or manufacturing process, and the range of values ​​higher and / or lower than the expected value. The range of values ​​may be due to slight variations in the manufacturing process or tolerances. As used herein, the term "about" indicates a value of a given quantity that can vary based on a specific technology node associated with the subject semiconductor device. Based on a specific technology node, the term "about" can indicate a value of a given quantity that varies, for example, within 5% to 15% of the value (e.g., ±5%, ±10%, or ±15% of the value).

[0220] It is understood that the meanings of “on”, “above” and “above” in this disclosure should be interpreted in the broadest sense, such that “on” means not only “directly on” something, but also includes something with an intermediary feature or layer, and that “above” or “above” means not only “on” something, but also includes something “above” or “above” without an intermediary feature or layer.

[0221] Furthermore, spatially related terms such as “below,” “under,” “lower,” “above,” and “upper” are used herein for convenience to describe the relationship of one element or feature to one or more other elements or features, as illustrated in the accompanying drawings. Spatially related terms are intended to cover different orientations in the use or operation of the device other than those depicted in the accompanying drawings. The device may be oriented in other ways, and the spatially related descriptive terms used herein can be interpreted similarly.

[0222] This invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this invention. To provide the public with a thorough understanding of this invention, specific details are described in detail in the following preferred embodiments; however, those skilled in the art will fully understand the invention even without these details. Furthermore, to avoid unnecessary misunderstanding of the essence of this invention, well-known methods, processes, procedures, components, and circuits are not described in detail.

[0223] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc.

[0224] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A dynamic system data-driven fault detection method based on distributed canonical correlation analysis, characterized in that, Includes the following steps: S1, During the offline process, historical data under normal operating conditions is collected by sensors in each subsystem to construct a centralized CCA residual generator; Step S1 specifically includes the following steps: S11, Collect historical data of each subsystem in the dynamic system under normal operating conditions, and construct the data matrix as follows using enhancement techniques: (1) in, ； ； ； ； ； It is the first The first subsystem Input and output data values ​​of the next sample. and The first Past input and output data values ​​in each subsystem and The first The future input and output data values ​​of each subsystem and It is an integer. The number of subsystems; collect One sample is enough to obtain: (2) in, and The data described in formula (1) are respectively A matrix composed of samples; S12, Assume the model of the subsystem is as follows: (3) (4) Where A, B, C, and D are unknown constant parameter matrices of appropriate dimensions. It is a state variable. and These are process noise and measurement noise, respectively. and These represent the system's input and output data values, respectively, and their relevant forms are as follows: (5) For ease of derivation, the predictor form of the system model is used here: (6) (7) in, , Kalman gain; S13, Verify the rationality of using CCA in dynamic systems; Based on the above formula, we can conclude that: (8) because It is stable, when When large enough, As it approaches 0, equation (8) above becomes: (9) in, (10) (11) get: (12) in, (13) Observation (12) shows that, (14) (15) in, and All are products of elementary matrices; (12) Transformed into: (16) make: (17) (18) It can be converted into the same form as CCA: (19) That is, the use of CCA in dynamic systems is reasonable; S14, as known above They are related, therefore the residual generator is constructed using CCA as follows: (20) in, for The residual signal of the system at time t. L , J and These are key parameters for CCA, and we will solve for them later. S2, based on the network topology between subsystems in the dynamic system, determines the weight coefficients of information transmission between subsystems based on the average consensus algorithm, constructs an iterative matrix for solving the CCA parameters of each subsystem, and transforms the centralized CCA residual generator into a distributed CCA residual generator for application in distributed systems. Step S2 specifically includes the following steps: S21, In order to convert the centralized CCA residual generator into a distributed CCA residual generator, let: (21) Here the parameters and Divide into subsystems. and Representative subsystem CCA parameters; Substituting, we get: (22) in, residual For the residuals of each subsystem The sum means that each subsystem only needs to calculate its own residual, and then the average consensus algorithm is used to fuse the residual signals; S22, Calculate the weighting coefficients for information transmission between subsystems based on the average consensus algorithm: (23) in, , Represents a node The number of its neighboring nodes; The meaning of the weight coefficient between subsystems here is that when the subsystems... Want to give subsystem When transmitting information, the transmitted information should be multiplied by 1. This weighting coefficient matrix is ​​also the most critical parameter in the average consensus algorithm iteration process; S23. Based on the network topology diagram of the dynamic system, calculate the weight coefficients of information transmission at each node to obtain the iteration matrix in the average consensus algorithm. ; S24, each subsystem calculates the average state of all subsystems based on the average consensus algorithm, and each subsystem iterates using the following iterative formula: (24) in, For subsystem The initial value; For subsystem The The value of the next iteration; after the average consensus algorithm converges, the final value of each node iteration is: (25) To balance the relationship between iteration latency and iteration accuracy, a boundary is added. ,when At that time, it is assumed that each subsystem converges to the final value; S25, using the average consensus algorithm to obtain the average of the initial values ​​of each subsystem, only requires each node to obtain its own... Then, the average consensus algorithm can be used; subsequently, a distributed algorithm for solving CCA parameters will be used to solve the problem. In and parameter; S3, solve the CCA parameters of each subsystem. During the online process, each subsystem uses the solved CCA parameters to construct a CCA-based residual generator, and performs distributed fusion of the residual signals of each subsystem based on the average consensus algorithm. Finally, data-driven distributed optimal fault detection is performed in the dynamic system. Step S3 specifically includes the following steps: S31, Set the number of iterations Each subsystem is initialized separately. The superscript indicates the iteration number; Among them, the Each subsystem only needs initialization That is, the relevant parameters represented in equation (21), and the initialized parameter values ​​can be random values. The initialized parameter values ​​will not affect the final convergence result. S32, each subsystem calculates simultaneously: (26) (27) in, and The superscript indicates the iteration number, and the subscript indicates the iteration number. Each subsystem, and (28) (29) It is a constant; S33, using the average consensus algorithm (24) to iterate over equations (26) and (27) respectively, finally each subsystem can converge and be obtained: (30) in, and For each subsystem The average value after each iteration; S34, each subsystem simultaneously constructs an iterative matrix for distributed solving of key CCA parameters. Here, we take the subsystem as an example. To illustrate the form of the constructed iteration matrix: (31) S35, at this point each subsystem has obtained the matrix shown in (31), and each subsystem simultaneously modifies the constructed matrix. Use CCA and obtain the parameters as follows: and updates ; (32) (33) (34) (35) in, and For the corresponding covariance, equation (35) is the core step of CCA, and the parameters can be obtained by using singular value decomposition. and ; Update parameters according to equations (32)-(35) ; (36) S36, let the number of iterations be... Jump to step S32 and loop continuously until the parameter is obtained. convergence; S37, according to the above steps, each subsystem can obtain the relevant parameters of CCA, and each subsystem obtains... Then, the detection statistic and threshold can be obtained by using average consistency analysis: (37) (38) When the detection statistic Greater than the detection threshold If the condition is met, it is considered a fault; otherwise, it is considered a fault-free condition.

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