Nonlinear system fault detection method and device for domain knowledge guided machine learning

Abstract

The invention provides a nonlinear system fault detection method and device for domain knowledge guided machine learning, and relates to the technical field of fault detection. The method comprises the following steps: designing an adjoint system of a complex nonlinear system under Hamilton meaning as an encoder, and outputting potential variables; using the stable image representation of the system as a decoder to obtain historical reconstruction process data; further obtaining a trained auto-encoder; and performing fault detection according to the reconstruction gap structure detection statistics. The invention provides a nominal dynamic description mode and a fault detection scheme for a complex nonlinear system, integrates related field knowledge of image representation of system stability, an auto-encoder technology, a control theory and an information theory, and establishes an auto-encoder capable of better representing and reconstructing system dynamics. On the basis, the reconstruction error is utilized to construct the detection statistics, so that the fault detection method for the complex nonlinear system is high in accuracy, high in interpretability and wide in application range.

Description

Technical Field

[0001] The present invention relates to the field of fault detection technology, and in particular to a nonlinear system fault detection method and device based on domain knowledge-guided machine learning. Background Art

[0002] Emerging technologies such as artificial intelligence have greatly enhanced traditional industrial manufacturing processes, significantly improving production efficiency and system performance. However, this has also led to the increasing scale and complexity of today's complex industrial processes, making their safe and reliable operation increasingly important. Once a subsystem (link) fails and is not detected in a timely manner, the failure may propagate continuously, ultimately causing the system to fail to operate normally, or even leading to catastrophic accidents. Therefore, timely detection of failures in complex industrial process production operations and the implementation of appropriate maintenance measures are essential to ensure the safe and reliable operation of the system.

[0003] Over the past few decades, driven by both technological advancements and market demand, research in fault detection technology has yielded significant results, resulting in the development of numerous fault detection systems applicable to practical industrial processes. Currently, three main types of fault detection techniques are commonly used: knowledge-based, analytical model-based, and data-driven. These approaches rely heavily on domain knowledge and analytical models, and their diagnostic accuracy depends on the richness of expert experience and the generalizability of the analytical models. However, today's industrial processes are often complex and exhibit challenging characteristics such as high-order, nonlinear, and strongly coupled systems. This poses significant challenges to the development of analytical models and the integration of expert knowledge, severely restricting their application in complex industrial production processes. With the advent of the big data era, data-driven fault detection techniques have gained increasing favor among scholars and experts. As a typical data-driven technique, machine learning, with its powerful feature extraction and nonlinear fitting capabilities, has garnered widespread attention and application in the field of fault detection. For example, AE (Autoencoder) can extract the information contained in process data and represent it in the form of low-dimensional latent variables, and further reconstruct the process data through the latent variables. Generally speaking, the data reconstruction error is small when the industrial process is operating normally, but the data reconstruction error is large when an abnormal situation (fault) occurs. Therefore, the reconstruction error can be used to construct a residual generator to realize fault detection of complex industrial processes. However, existing fault detection technologies based on autoencoders often directly use the reconstruction error of the data to evaluate fault detection, and lack the evaluation of the quality of the information contained in the latent variables (interpretability). In addition, because neural networks are essentially a "black box" model, existing fault detection technologies based on machine learning (including Autoencoders) lack a certain degree of interpretability, which hinders their application in industrial production and manufacturing processes.

[0004] Inspired by the Physically Informed Neural Network (PINN), incorporating specific domain knowledge into the training and learning process of neural networks can help improve the accuracy and interpretability of neural network learning. For complex industrial processes, it is necessary to develop autoencoder designs that integrate relevant knowledge from control theory and information theory and apply them to fault detection in complex industrial processes. Within the control theory context, the widely studied Hamiltonian system can be interpreted as an autoencoder. Specifically, using coprime factorization techniques, the original system's SIR (Stable Image Representation) is interpreted as a decoder, and the Hamiltonian adjoint system of the original system's SIR is interpreted as an encoder. By connecting these two components, the original system process data is reduced in dimension and compressed into latent variables, which are then decoded to reconstruct the process data. It should be noted that an ideal latent variable should be generated through a maximally compressed mapping of the process input data, thereby preserving as much information about the output variable as possible. Within the framework of information theory, to fully reconstruct the process data, the latent variable should be a minimum sufficient statistic. It's worth noting that the Hamiltonian expansion of complex industrial processes can, through certain designs, achieve lossless compression, where the latent variable is equivalent to a minimum sufficient statistic. Therefore, combining autoencoder technology with specific domain knowledge from control theory and information theory to enable fault detection in complex industrial processes is urgently needed and has significant practical value.

[0005] Currently, fault detection methods based on autoencoder technology have yet to be integrated with specific domain knowledge and remain a "black box" approach, hindering practical application. Briefly, existing autoencoder-based fault detection methods first extract features or information from system process data (output data) using a specific neural network, reduce its dimensionality and compress it into latent variables. These latent variables are then decoded using a specific neural network to reconstruct the process data. Furthermore, fault detection in complex industrial processes is achieved by assessing the gap between the original and reconstructed process data. It is important to note that this method does not assess the amount of information contained in the latent variables. Furthermore, the neural network learning and training processes involved in the encoder and decoder are completely "black box" and lack interpretability, making it difficult to impose reasonable and effective constraints on the network output. Therefore, traditional autoencoder-based fault detection methods are difficult to analyze and interpret faults, making them difficult to apply to industrial processes. Summary of the Invention

[0006] Aiming at the nonlinear systems in general complex industrial processes, the present invention addresses the problems of model-based and knowledge-based fault detection methods, which rely heavily on analytical models and expert experience, the low accuracy and difficulty in fault interpretation of data-driven (machine learning) fault detection methods, and the poor interpretability of traditional autoencoder-based fault detection methods. This invention provides a method and device for nonlinear system fault detection using domain knowledge-guided machine learning. The technical solution is as follows:

[0007] In one aspect, a nonlinear system fault detection method based on domain knowledge-guided machine learning is provided. The method is implemented by a nonlinear system fault detection device and includes:

[0008] S1. Based on control theory, the adjoint system of the complex nonlinear system in the Hamiltonian sense is designed. The adjoint system of the complex nonlinear system in the Hamiltonian sense is used as an encoder. The encoder is used to encode the historical process data and output the latent variables.

[0009] S2. Construct a stable image representation of the system, use the stable image representation of the system as a decoder, use the latent variables as feedforward inputs in the stable image representation of the system, and obtain historical reconstruction process data.

[0010] S3. Construct an autoencoder based on the encoder and decoder; based on the domain knowledge of control theory and information theory, train the autoencoder according to the historical process data and the historical reconstruction process data to obtain a trained autoencoder.

[0011] S4. Obtain the process data to be detected, obtain reconstructed process data based on the process data to be detected and the trained autoencoder, construct a detection statistic based on the gap between the process data and the reconstructed process data, and implement fault detection of nonlinear systems in complex industrial processes based on the detection statistic and a preset detection threshold.

[0012] Optionally, based on control theory, the adjoint system of the complex nonlinear system in the Hamiltonian sense is designed in S1, including:

[0013] S11. Constructing nonlinear systems in complex industrial processes .

[0014] S12, according to the nonlinear system , define the state space form of the system stability image representation .

[0015] S13. Based on control theory, the state space form of the system stability image representation , we get the state space form of the system stability image representation Hamiltonian expansion ;in, It is the state space form of the system stability image representation accompanying system.

[0016] S14. State space representation of the stability of the connected system The state space form of the image representation of the system stability The adjoint system of is obtained based on Hamiltonian system theory, and the Hamilton-Jacobi equation is obtained.

[0017] S15. Design the adjoint system of a complex nonlinear system in the Hamiltonian sense based on the Hamilton-Jacobi equation .

[0018] Optionally, the encoder in S1 encodes the historical process data and outputs latent variables, including:

[0019] Through the adjoint system of the complex nonlinear system in the Hamiltonian sense, the historical process data is encoded and compressed to output low-dimensional variables; wherein the historical process data includes historical input data and historical output data.

[0020] According to historical input data and the feedback control system, the feedforward input in the image representation of system stability is estimated to obtain an estimated value of the feedforward input.

[0021] Generate system state and 、 、 、 The partial derivative of the system state; where 、 、 、 Represents a manifold-like description of an affine nonlinear system.

[0022] The adjoint system of the complex nonlinear system in the Hamiltonian sense is an anti-stable system. 、 、 、 The latent variables are obtained by taking partial derivatives of the system state, the terminal values ​​of the preset co-state variables, and the preset number of iterations.

[0023] Optionally, the process of constructing a stable image representation of the system in S2 uses the stable image representation of the system as a decoder, uses the latent variables as feedforward inputs in the stable image representation of the system, and obtains historical reconstruction process data, including:

[0024] S21. Construct a neural network and use neural network approximation 、 、 、 , according to the 、 、 、 Construct a stable image representation of the system.

[0025] S22, using the latent variables as feedforward inputs in the image representation of system stability, decoding the latent variables according to the image representation of system stability, and obtaining historical reconstruction process data.

[0026] Optionally, the autoencoder is trained according to the historical process data and the historical reconstruction process data in S3 to obtain a trained autoencoder, including:

[0027] S31. Obtain a reconstruction error based on historical process data and historical reconstruction process data.

[0028] S32. Based on the domain knowledge of control theory and information theory, construct constraints for the autoencoder training process.

[0029] S33. Train the autoencoder according to the reconstruction error and the constraints to obtain a trained autoencoder.

[0030] Optionally, the loss function of the autoencoder training process is as shown in the following formula (1):

[0031] (1)

[0032] Where, represents the loss function, 、 、 represents the weight coefficient, represents the reconstruction error loss term, represents the idempotent loss term of the projection operator, represents the restriction term for the losslessness of the Hamiltonian system, Indicates the number of batch data points, Represents batch process input and output data, Represents the reconstructed batch process input and output data, represents the projection value of the reconstructed batch process input and output data, represents the estimated value of the latent variable, represents the projection of the latent variable estimate, Indicates the The input and output data points of the process at each moment, Reconstructed The input and output data points of the process at each moment, Reconstructed The projection of the input and output data points of the process at each moment, Indicates the The estimated value of the latent variable at time t, Indicates the The projection of the estimated value of the latent variable at time t, Describes the decoder, Indicates an encoder.

[0033] Optionally, the detection statistic is as follows (2):

[0034] (2)

[0035] Where, represents the test statistic, represents the system input vector, represents the system output vector, represents the reconstructed system input vector, represents the reconstructed system output vector, Indicates the number of batch data points, Describes the decoder, Describes the decoder parameters, represents the encoder, Represents encoder parameters.

[0036] On the other hand, a nonlinear system fault detection device based on domain knowledge-guided machine learning is provided. The device is applied to a nonlinear system fault detection method based on domain knowledge-guided machine learning. The device includes:

[0037] The encoder design module is used to design the adjoint system of the complex nonlinear system in the Hamiltonian sense based on control theory. The adjoint system of the complex nonlinear system in the Hamiltonian sense is used as an encoder to encode the historical process data and output the latent variables.

[0038] The decoder design module is used to construct a stable image representation of the system, use the stable image representation of the system as a decoder, and use the latent variables as feedforward inputs in the stable image representation of the system to obtain historical reconstruction process data.

[0039] The training module is used to construct an autoencoder based on the encoder and decoder; based on the domain knowledge of control theory and information theory, the autoencoder is trained according to the historical process data and the historical reconstruction process data to obtain the trained autoencoder.

[0040] The fault detection module is used to obtain the process data to be detected, obtain reconstructed process data based on the process data to be detected and the trained autoencoder, construct a detection statistic based on the gap between the process data and the reconstructed process data, and realize fault detection of nonlinear systems in complex industrial processes based on the detection statistic and a preset detection threshold.

[0041] Based on control theory, design the adjoint system of complex nonlinear systems in the Hamiltonian sense, including:

[0042] S11. Constructing nonlinear systems in complex industrial processes .

[0043] S12, according to the nonlinear system , define the state space form of the system stability image representation .

[0044] S13. Based on control theory, the state space form of the system stability image representation , we get the state space form of the system stability image representation Hamiltonian expansion ;in, It is the state space form of the system stability image representation accompanying system.

[0045] S14. State space representation of the stability of the connected system The state space form of the image representation of the system stability The adjoint system of is obtained based on Hamiltonian system theory, and the Hamilton-Jacobi equation is obtained.

[0046] S15. Design the adjoint system of a complex nonlinear system in the Hamiltonian sense based on the Hamilton-Jacobi equation .

[0047] On the other hand, a complex nonlinear system fault detection device is provided, which includes: a processor; a memory, wherein computer-readable instructions are stored in the memory, and when the computer-readable instructions are executed by the processor, any one of the nonlinear system fault detection methods guided by domain knowledge and machine learning is implemented.

[0048] On the other hand, a computer-readable storage medium is provided, wherein the storage medium stores at least one instruction, and the at least one instruction is loaded and executed by a processor to implement any one of the above-mentioned domain knowledge-guided machine learning methods for nonlinear system fault detection.

[0049] The beneficial effects brought about by the technical solution provided by the embodiment of the present invention include at least:

[0050] In the present invention, a fault detection method for general nonlinear systems in complex industrial processes is proposed. This method requires a large amount of historical data on process operation. It integrates the relevant field knowledge of stable image representation of the system, autoencoder technology, control theory and information theory to establish an autoencoder that can better describe the process dynamics in the sense of Hamiltonian system. Furthermore, the error of the autoencoder reconstructed process data is used to construct a fault detection statistic, and a threshold that meets the false alarm rate is set as the detection threshold, thereby realizing fault detection of complex nonlinear systems. This method is completely based on historical data, has excellent detection effect, and is easy to use. At the same time, this method integrates the field knowledge of Hamiltonian system and stable image representation in control theory and minimum sufficient statistics in information theory, and the learned latent variables have strong interpretability. In theory, the fault detection method based on autoencoder that integrates field knowledge proposed in the present invention is applicable to general complex nonlinear systems, can better characterize the dynamics of the nominal system, has excellent detection effect, and has practical application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0052] Figure 1 This is a flow chart of a complex nonlinear system fault detection method using domain knowledge-guided machine learning provided by an embodiment of the present invention;

[0053] Figure 2 This is a flowchart of offline training and online detection provided by an embodiment of the present invention;

[0054] Figure 3 : This is a Hamiltonian system theory explanation (equivalent) diagram of the autoencoder structure provided by an embodiment of the present invention;

[0055] Figure 4 This is a connection diagram of the SIR of a complex nonlinear system and its accompanying system provided by an embodiment of the present invention;

[0056] Figure 5 1 is a neural network implementation diagram of the complex nonlinear system SIR provided by an embodiment of the present invention;

[0057] Figure 6 Schematic diagram of a three-tank system provided by an embodiment of the present invention;

[0058] Figure 7is a liquid level trajectory diagram of water tank No. 1 of a certain training data provided by an embodiment of the present invention;

[0059] Figure 8 This is a comparison chart of the loss function changes during the Vanilla AE and I-AE training processes provided by an embodiment of the present invention;

[0060] Figure 9 1 is a diagram showing the detection results of the actuator failure of water tank No. 1 using the Vanilla AE (a) and I-AE (b) methods provided in an embodiment of the present invention;

[0061] Figure 10 1 is a graph showing the detection results of the leakage fault of water tank No. 2 using the Vanilla AE (a) and I-AE (b) methods provided in an embodiment of the present invention;

[0062] Figure 11 This is a graph showing changes in various loss functions during the I-AE training process with the additional regularization loss term introduced, as provided in an embodiment of the present invention;

[0063] Figure 12 This is a block diagram of a complex nonlinear system fault detection device using domain knowledge-guided machine learning, provided by an embodiment of the present invention;

[0064] Figure 13 It is a structural diagram of a complex nonlinear system fault detection device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0065] The technical solution of the present invention is described below in conjunction with the accompanying drawings.

[0066] In the embodiments of the present invention, words such as "exemplarily" and "for example" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as an "exemplary" in the present invention should not be interpreted as being preferred or advantageous over other embodiments or designs. Rather, the use of the word "exemplary" is intended to present concepts in a concrete manner. Furthermore, in the embodiments of the present invention, "and / or" can mean both or either of the two.

[0067] In the embodiments of the present invention, the terms "image" and "picture" may sometimes be used interchangeably. It should be noted that, when the distinction is not emphasized, the meanings they convey are the same. The terms "of," "corresponding," and "corresponding" may sometimes be used interchangeably. It should be noted that, when the distinction is not emphasized, the meanings they convey are the same.

[0068] In the embodiments of the present invention, sometimes a subscript such as W1 may be written as a non-subscript such as W1. When the difference is not emphasized, the meanings to be expressed are the same.

[0069] In order to make the technical problems, technical solutions and advantages to be solved by the present invention clearer, a detailed description will be given below with reference to the accompanying drawings and specific embodiments.

[0070] The embodiment of the present invention provides a nonlinear system fault detection method guided by domain knowledge and machine learning. The method can be implemented by a complex nonlinear system fault detection device, which can be a terminal or a server. Figure 1 The flowchart of the nonlinear system fault detection method using domain knowledge-guided machine learning is shown. The processing flow of the method may include the following steps:

[0071] S1. Based on control theory, the adjoint system of the complex nonlinear system in the Hamiltonian sense is designed. The adjoint system of the complex nonlinear system in the Hamiltonian sense is used as an encoder. The encoder is used to encode the historical process data and output the latent variables.

[0072] In a feasible implementation, Figure 2 、 Figure 3 As shown in the figure, in the context of control theory, the process input / output data is used as the model input in the sense of the Hamiltonian adjoint system of the complex nonlinear system, and the model output is interpreted as a latent variable, that is, the adjoint system of the complex nonlinear system in the sense of Hamilton is designed as an encoder. Since the encoder system is anti-stable, the training and learning process requires the cooperation of the decoder.

[0073] Specifically, designing the adjoint system of the complex nonlinear system in the Hamiltonian sense based on control theory in S1 may include the following steps S111-S115:

[0074] S111, Constructing nonlinear systems in complex industrial processes .

[0075] In one feasible implementation, a nonlinear system in a complex industrial process is considered, assuming that its true model is:

[0076] (1)

[0077] Where, 、 、 are the system state vector, input vector, and output vector respectively, , , , is a continuously differentiable nonlinear function, is the initial state of the system, represents the derivative of the state vector.

[0078] In the context of feedback control systems, there are:

[0079] (2)

[0080] in, is the feedback control signal, is a feedforward controller, is the reference signal.

[0081] S112, according to the nonlinear system , define the state space form of the system stability image representation :

[0082] (3)

[0083]

[0084] Where, 、 、 、 Represents a manifold-like description of an affine nonlinear system.

[0085] S113. In the context of control theory, The Hamiltonian expansion of is:

[0086] (4)

[0087] in, is the state vector, is the input vector, is the output vector, yes The accompanying system, represents the co-state variable, Represents the input to the adjoint system.

[0088] S114. State space representation of the stability of connected systems The state space form of the image representation of the system stability The adjoint system of is obtained based on Hamiltonian system theory, and the Hamilton-Jacobi equation is obtained.

[0089] In one possible implementation, by connecting the SIR of the system and its accompanying system, , then the above Hamiltonian system can be expressed as:

[0090] (5)

[0091] Where, represents the output of the adjoint system, Image representation of the original system.

[0092] In Hamiltonian system theory, if , and there exists an energy function satisfy:

[0093] (6)

[0094] The system is called is internal (inner), denoted as After equivalent transformation, the following Hamilton-Jacobi equation (HJE) can be derived:

[0095] (7)

[0096] Where, express The partial derivative of Represents the unit matrix.

[0097] S115. Design the adjoint system of a complex nonlinear system in the Hamiltonian sense based on the Hamilton-Jacobi equation .

[0098] In a feasible implementation, in practical applications, for the purpose of fault detection, the accompanying system of the SIR is usually connected to the SIR, that is, , and define , then the connection relationship of the system is as follows Figure 4 As shown, we have: (8)

[0099] Where, represents the input data of the reconstruction process, Represents the output data of the reconstruction process.

[0100] Optionally, encoding the historical process data by an encoder and outputting potential variables in S1 may include the following steps S121-S124:

[0101] S121. Through the adjoint system of the complex nonlinear system in the Hamiltonian sense, the historical process data is encoded and compressed to output low-dimensional variables; wherein the historical process data includes historical input data and historical output data.

[0102] In one possible implementation, consider the accompanying system The input is high-dimensional process input and output data , whose output is a low-dimensional variable , in order to realize the coding compression of process data, namely:

[0103] (9)

[0104] S122 . Estimate the feedforward input in the image representation of system stability based on historical input data and the feedback control system to obtain an estimated value of the feedforward input.

[0105] In a feasible implementation, by means of a feedback control system: , input data through a batch process Estimating feedforward input .

[0106] S123, generating the system state and 、 、 、 Partial derivatives with respect to the state of the system.

[0107] In one possible implementation, based on the estimated value of the feedforward input and the system's SIR and batch process input and output data , generating the system state as well as 、 、 、 Partial derivatives with respect to the state.

[0108] S124、The adjoint system of the complex nonlinear system in Hamiltonian sense is an anti-stable system. 、 、 、 The latent variables are obtained by taking partial derivatives of the system state, the terminal values ​​of the preset co-state variables, and the preset number of iterations.

[0109] In a feasible implementation, since the adjoint system is an anti-stable system, the result generated by S123 is used to calculate the state variable The ending value Continuously iterate forward to output potential variables .

[0110] S2. Construct a stable image representation of the system, use the stable image representation of the system as a decoder, use the latent variables as feedforward inputs in the stable image representation of the system, and obtain historical reconstruction process data.

[0111] In a feasible implementation, based on the coprime factor decomposition technology, the process data of a complex nonlinear system can be represented with the help of the feedforward input in the stable image representation of the system. At this time, by treating the latent variables output by the encoder as the feedforward input, the process data can be reconstructed with the help of the stable image representation of the system, that is, the stable image representation of the system is designed as a decoder.

[0112] Optionally, the above step S2 may include the following steps S21-S22:

[0113] S21. In order to avoid solving the Hamilton-Jacobi equation HJE, a neural network with a certain hidden layer and consistent with the dimension of the process data is constructed to approximate, 、 、 、 , so as to realize the SIR of the system under unknown model, such as Figure 5 At the same time, we use neural networks to approximate , which is used to estimate the feedforward signal during encoder training.

[0114] S22, SIR based on neural network, for latent variables Decoding is performed to reconstruct the process data, namely:

[0115] (10)

[0116] S3. Construct an autoencoder based on the encoder and decoder; based on the domain knowledge of control theory and information theory, train the autoencoder according to the historical process data and the historical reconstruction process data to obtain a trained autoencoder.

[0117] In one feasible implementation, first, because the fundamental purpose of an autoencoder is to reconstruct process data by learning from it, the error between the original and reconstructed process data must be considered during training. Furthermore, drawing on knowledge from control theory and information theory, the Hamiltonian expansion of complex nonlinear systems should exhibit idempotence and lossless compression. Therefore, the learning and training process of the autoencoder should be constrained by these three aspects.

[0118] Optionally, the step of training the autoencoder according to the historical process data and the historical reconstruction process data to obtain a trained autoencoder in S3 may include the following steps S31-S33:

[0119] S31. Obtain a reconstruction error based on historical process data and historical reconstruction process data.

[0120] In a feasible implementation, through steps S1-S2, the error is reconstructed according to batch process data, and the neural network is continuously trained and optimized.

[0121] S32. Based on the domain knowledge of control theory and information theory, construct constraints for the autoencoder training process.

[0122] In one feasible implementation, based on the background of control theory and information theory, the autoencoder should be a projection operator and the information transmission should be lossless. This imposes additional constraints on the training and learning process of the autoencoder, making the trained autoencoder more consistent with the actual system operation process. That is, the loss function of the autoencoder training process is:

[0123] (11)

[0124] Where, represents the loss function, 、 、 represents the weight coefficient, represents the reconstruction error loss term, represents the idempotent loss term of the projection operator, represents the restriction term for the losslessness of the Hamiltonian system, Indicates the number of batch data points, Represents batch process input and output data, Represents the reconstructed batch process input and output data, represents the projection value of the reconstructed batch process input and output data, represents the estimated value of the latent variable, represents the projection of the latent variable estimate, Indicates the The input and output data points of the process at each moment, Reconstructed The input and output data points of the process at each moment, Reconstructed The projection of the input and output data points of the process at each moment, Indicates the The estimated value of the latent variable at time t, Indicates the The projection of the estimated value of the latent variable at time t, Describes the decoder, Indicates an encoder.

[0125] S33. Train the autoencoder according to the reconstruction error and the constraints to obtain a trained autoencoder.

[0126] S4. Obtain the process data to be detected, obtain reconstructed process data based on the process data to be detected and the trained autoencoder, construct a detection statistic based on the gap between the process data and the reconstructed process data, and implement fault detection of nonlinear systems in complex industrial processes based on the detection statistic and a preset detection threshold.

[0127] In one feasible implementation, a detection statistic is constructed based on the gap between process data and reconstructed data with the help of a trained autoencoder, and the threshold obtained by running fault-free data under a specific false alarm rate is set as the detection threshold, thereby realizing fault detection of nonlinear systems in complex industrial processes.

[0128] Specifically, based on the trained autoencoder, the detection statistic is constructed according to the process data reconstruction error ,Right now:

[0129] (12)

[0130] Where, represents the test statistic, represents the system input vector, represents the system output vector, represents the reconstructed system input vector, represents the reconstructed system output vector, Indicates the number of batch data points, Describes the decoder, Describes the decoder parameters, represents the encoder, Represents encoder parameters.

[0131] Furthermore, a batch of fault-free process data is run to calculate the fault detection threshold while meeting the set false alarm rate. ,Right now:

[0132] (13)

[0133] Where, Indicates the The process input data at each moment, Indicates the The process output data at each moment, Indicates the set fault detection false alarm rate, Indicates the The process input data reconstructed at each moment, Indicates the The process input data is reconstructed at each moment.

[0134] Furthermore, online detection is performed. The autoencoder model is applied to online data and the detection statistics are observed. Whether the change of exceeds the threshold is used to determine whether a failure has occurred in the process, that is:

[0135] (14)

[0136] It is worth mentioning that the detection statistic used in the present invention is directly generated by the reconstruction error of the autoencoder, which is applicable to general complex industrial processes and avoids Statistics and Statistics require that process data obey a certain distribution assumption, which is more valuable for application.

[0137] This invention targets nonlinear systems in general complex industrial processes and proposes a novel fault detection method that integrates system image representation, autoencoder technology, control theory, and information theory. To address the poor interpretability of traditional fault detection methods based on autoencoder technology, this invention combines Hamiltonian system theory and stable image representation, widely used in control theory, with autoencoder technology. By interpreting the Hamiltonian adjoint of the system's SIR as an encoder and the system's SIR as a decoder, the two components are connected to achieve neural network training and learning under the guidance of control theory. Furthermore, the invention evaluates the information contained in latent variables within the context of information theory to guide and optimize the learning of the autoencoder, further improving the accuracy and interpretability of the proposed autoencoder-based fault detection method. Theoretically, the proposed autoencoder technology can effectively characterize the dynamics of the nonlinear system in the original complex industrial process and maximize the reconstruction of the original process data. Based on this, a detection statistic is constructed using the reconstruction error of the data to achieve highly accurate fault detection in complex industrial processes.

[0138] The effectiveness of the complex nonlinear system fault detection method based on domain knowledge guided machine learning proposed in this invention is verified by using the real process data of the three-tank system. Figure 6 As shown in the figure, the three-tank system consists of three interconnected tanks, where tanks 1 and 2 are connected through tank 3. Pumps 1 and 2 transport water from the reservoir to tanks 1 and 2 respectively through conduits to adjust the tank levels. In this experiment, the pump flow rate is taken as the system input, and the tank level is taken as the system output. The sampling time is 1s, as shown in the following example. Figure 7 As shown in Figure 1, a total of 18 stable working point process operation data were collected, and the specific experimental results are as follows:

[0139] I. Training Autoencoders. To demonstrate the advantages of the domain knowledge-guided autoencoder learning fault detection method proposed in this invention over the traditional autoencoder learning-based fault detection method, a conventional autoencoder with a recurrent neural network as the encoder and decoder is used for experimental comparison, denoted as Vanilla AE, while the autoencoder with domain knowledge fused proposed in this invention is denoted as I-AE. The loss function changes during training are compared. Figure 8 As shown in the experimental results, the conventional autoencoder learning process converges faster and has a smaller reconstruction error. Based on the reconstruction error and the fault detection method proposed in this paper, the false alarm rate is set to 5%, and the fault detection thresholds for Vanilla AE and I-AE are 19.7 and 35.1, respectively.

[0140] II. Fault Detection. In order to compare the fault detection effects of the above two methods, the following quantitative indicators are introduced:

[0141] (15)

[0142] in, is the total number of collected data, and is the total number of fault data and non-fault data, and is the number of false alarms and missed detections. In the experiment, the fault-free process and the fault process were run for 300s respectively. Different types of faults were introduced at 301s. The detection results are as follows: Figure 9 、 Figure 10 The quantitative comparison of the fault detection effects of the two methods is shown in Table 1. From the comprehensive experimental results, it can be seen that the fault detection method of I-AE has a lower false alarm rate and missed detection rate, and the fault detection effect is significantly improved.

[0143] Table 1 Comparison of quantitative indicators of fault detection results of Vanilla AE and I-AE methods

[0144]

[0145] III. Evaluation of the role of latent variables. In order to illustrate the role and value of latent variables in the I-AE proposed in this invention, an additional regularization loss term is added during the training of the above autoencoder. ,Right now:

[0146] (16)

[0147] The loss function changes during I-AE training with additional regularization loss term as follows Figure 11As shown in Table 2, the fault detection results of the three methods are compared. From the above results, it can be seen that the loss function of the I-AE training process with the additional loss term cannot fully converge, indicating that there is a contradiction between the introduced regularization loss term and other loss terms. Further, by comparing the fault detection results, it can be seen that the regularization loss term The introduction of tends to make the latent variable retain all the information in the process data, including uncertainty and redundancy, which will cause the trained autoencoder to learn features that do not belong to the complex nonlinear nominal process. At this time, the latent variable is no longer a minimum sufficient statistic, which will obviously affect the results of fault detection.

[0148] Table 2 Comparison of quantitative indicators of fault detection results of three methods

[0149]

[0150] In an embodiment of the present invention, a fault detection method for general nonlinear systems in complex industrial processes is proposed. This method requires a large amount of historical process operation data and integrates relevant domain knowledge such as stable image representation of the system, autoencoder technology, control theory, and information theory to establish an autoencoder that can effectively describe process dynamics in the context of a Hamiltonian system. Furthermore, the error in the autoencoder-reconstructed process data is used to construct a fault detection statistic, and a threshold value that satisfies the false alarm rate is set as the detection threshold, thus achieving fault detection for complex nonlinear systems. This method, based entirely on historical data, offers excellent detection results and is easy to use. Furthermore, this method integrates domain knowledge of Hamiltonian systems and stable image representations from control theory, as well as minimal sufficient statistics from information theory, resulting in highly interpretable latent variables. Theoretically, the autoencoder-based fault detection method proposed in this invention, which integrates domain knowledge, is applicable to general complex nonlinear systems, effectively characterizes the dynamics of nominal systems, and has excellent detection results and practical application value.

[0151] Figure 12 This is a block diagram of a nonlinear system fault detection device based on domain knowledge-guided machine learning according to an exemplary embodiment. The device is used in a nonlinear system fault detection method based on domain knowledge-guided machine learning. Figure 12 The device includes an encoder design module 310, a decoder design module 320, a training module 330, and a fault detection module 340.

[0152] The encoder design module 310 is used to design an adjoint system of a complex nonlinear system in the Hamiltonian sense based on control theory, and use the adjoint system of the complex nonlinear system in the Hamiltonian sense as an encoder to encode historical process data and output potential variables.

[0153] The decoder design module 320 is used to construct a stable image representation of the system, use the stable image representation of the system as a decoder, use the latent variables as feedforward inputs in the stable image representation of the system, and obtain historical reconstruction process data.

[0154] The training module 330 is used to construct an autoencoder based on the encoder and the decoder; based on the domain knowledge of control theory and information theory, the autoencoder is trained according to the historical process data and the historical reconstruction process data to obtain a trained autoencoder.

[0155] The fault detection module 340 is used to obtain the process data to be detected, obtain reconstructed process data based on the process data to be detected and the trained autoencoder, construct a detection statistic based on the gap between the process data and the reconstructed process data, and realize fault detection of nonlinear systems in complex industrial processes based on the detection statistic and a preset detection threshold.

[0156] Based on control theory, design the adjoint system of complex nonlinear systems in the Hamiltonian sense, including:

[0157] S11. Constructing nonlinear systems in complex industrial processes .

[0158] S12, according to the nonlinear system , define the state space form of the system stability image representation .

[0159] S13. Based on control theory, the state space form of the system stability image representation , we get the state space form of the system stability image representation Hamiltonian expansion ;in, It is the state space form of the system stability image representation accompanying system.

[0160] S14. State space representation of the stability of the connected system The state space form of the image representation of the system stability The adjoint system of is obtained based on Hamiltonian system theory, and the Hamilton-Jacobi equation is obtained.

[0161] S15. Design the adjoint system of a complex nonlinear system in the Hamiltonian sense based on the Hamilton-Jacobi equation .

[0162] In an embodiment of the present invention, a fault detection method for general nonlinear systems in complex industrial processes is proposed. This method requires a large amount of historical process operation data and integrates relevant domain knowledge such as stable image representation of the system, autoencoder technology, control theory, and information theory to establish an autoencoder that can effectively describe process dynamics in the context of a Hamiltonian system. Furthermore, the error in the autoencoder-reconstructed process data is used to construct a fault detection statistic, and a threshold value that satisfies the false alarm rate is set as the detection threshold, thus achieving fault detection for complex nonlinear systems. This method, based entirely on historical data, offers excellent detection results and is easy to use. Furthermore, this method integrates domain knowledge of Hamiltonian systems and stable image representations from control theory, as well as minimal sufficient statistics from information theory, resulting in highly interpretable latent variables. Theoretically, the autoencoder-based fault detection method proposed in this invention, which integrates domain knowledge, is applicable to general complex nonlinear systems, effectively characterizes the dynamics of nominal systems, and has excellent detection results and practical application value.

[0163] Figure 13 FIG. 1 is a structural diagram of a complex nonlinear system fault detection device provided by an embodiment of the present invention. Figure 13 As shown, the complex nonlinear system fault detection device may include the above Figure 12 The nonlinear system fault detection device guided by domain knowledge and machine learning is shown. Optionally, the complex nonlinear system fault detection device 410 may include a first processor 2001.

[0164] Optionally, the complex nonlinear system fault detection device 410 may further include a memory 2002 and a transceiver 2003 .

[0165] The first processor 2001, the memory 2002 and the transceiver 2003 may be connected via a communication bus.

[0166] The following combination Figure 13 The components of the complex nonlinear system fault detection device 410 are described in detail:

[0167] The first processor 2001 is the control center of the complex nonlinear system fault detection device 410 and can be a single processor or a collective term for multiple processing elements. For example, the first processor 2001 can be one or more central processing units (CPUs), an application-specific integrated circuit (ASIC), or one or more integrated circuits configured to implement embodiments of the present invention, such as one or more microprocessors (digital signal processors, DSPs) or one or more field programmable gate arrays (FPGAs).

[0168] Optionally, the first processor 2001 may execute various functions of the complex nonlinear system fault detection device 410 by running or executing a software program stored in the memory 2002 and calling data stored in the memory 2002 .

[0169] In a specific implementation, as an embodiment, the first processor 2001 may include one or more CPUs, such as Figure 13 CPU0 and CPU1 are shown in FIG.

[0170] In a specific implementation, as an embodiment, the complex nonlinear system fault detection device 410 may also include multiple processors, such as Figure 13 1 and 2. The first processor 2001 and the second processor 2004 are shown in FIG. Each of these processors can be a single-core processor (single-CPU) or a multi-core processor (multi-CPU). A processor herein can refer to one or more devices, circuits, and / or processing cores for processing data (e.g., computer program instructions).

[0171] The memory 2002 is used to store the software program for executing the solution of the present invention, and is controlled by the first processor 2001 for execution. The specific implementation method can refer to the above method embodiment and will not be repeated here.

[0172] Alternatively, the memory 2002 may be a read-only memory (ROM) or other type of static storage device capable of storing static information and instructions, a random access memory (RAM) or other type of dynamic storage device capable of storing information and instructions, an electrically erasable programmable read-only memory (EEPROM), a compact disc read-only memory (CD-ROM) or other optical disc storage, an optical disc storage (including a compact disc, laser disc, optical disc, digital versatile disc, Blu-ray disc, etc.), a magnetic disk storage medium or other magnetic storage device, or any other medium capable of carrying or storing desired program code in the form of instructions or data structures and capable of being accessed by a computer, but not limited thereto. The memory 2002 may be integrated with the first processor 2001 or exist independently and accessed through the interface circuit ( Figure 13 (not shown) is coupled to the first processor 2001, which is not specifically limited in this embodiment of the present invention.

[0173] The transceiver 2003 is used to communicate with a network device or a terminal device.

[0174] Optionally, the transceiver 2003 may include a receiver and a transmitter ( Figure 13 The receiver is used to implement a receiving function, and the transmitter is used to implement a sending function.

[0175] Optionally, the transceiver 2003 may be integrated with the first processor 2001, or may exist independently and be connected to the first processor 2001 through the interface circuit ( Figure 13 (not shown) is coupled to the first processor 2001, which is not specifically limited in this embodiment of the present invention.

[0176] It should be noted that Figure 13 The structure of the complex nonlinear system fault detection device 410 shown in the figure does not constitute a limitation on the router. The actual knowledge structure recognition device may include more or fewer components than shown in the figure, or combine certain components, or arrange the components differently.

[0177] In addition, the technical effects of the complex nonlinear system fault detection device 410 can refer to the technical effects of the complex nonlinear system fault detection method guided by domain knowledge and machine learning described in the above method embodiment, and will not be repeated here.

[0178] It should be understood that the first processor 2001 in the embodiment of the present invention may be a central processing unit (CPU), or may be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field programmable gate arrays (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor, or the processor may be any conventional processor, etc.

[0179] It should also be understood that the memory in the embodiments of the present invention may be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. The non-volatile memory may be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory may be random access memory (RAM), which is used as an external cache. By way of example and not limitation, many forms of random access memory (RAM) are available, such as static RAM (SRAM), dynamic random access memory (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), and direct rambus RAM (DR RAM).

[0180] It should be understood that the term "and / or" as used herein simply describes a relationship between associated objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A alone, A and B together, or B alone. A and B can be singular or plural. Furthermore, the character " / " as used herein generally indicates an "or" relationship between the associated objects, but it may also indicate an "and / or" relationship. For specific understanding, please refer to the context.

[0181] In this disclosure, "at least one" means one or more, and "plurality" means two or more. "At least one of the following" or similar expressions refers to any combination of these items, including any combination of single or plural items. For example, "at least one of a, b, or c" can mean: a, b, c, ab, ac, bc, or abc, where a, b, and c can be single or plural.

[0182] It should be understood that in various embodiments of the present invention, the size of the serial numbers of the above-mentioned processes does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0183] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professionals and technicians can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present invention.

[0184] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the above-described equipment, devices and units can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0185] In the several embodiments provided by the present invention, it should be understood that the disclosed devices, apparatuses and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of the units is merely a logical function division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another device, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interface, indirect coupling or communication connection of the device or unit, which can be electrical, mechanical or other forms.

[0186] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0187] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0188] If the functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the portion that contributes to the prior art, or the portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage media include various media that can store program code, such as USB flash drives, mobile hard drives, read-only memories (ROM), random access memories (RAM), magnetic disks, or optical disks.

[0189] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A nonlinear system fault detection method guided by domain knowledge and machine learning, characterized in that: The method comprises: S1. Based on control theory, an adjoint system of a complex nonlinear system in the Hamiltonian sense is designed, and the adjoint system of the complex nonlinear system in the Hamiltonian sense is used as an encoder, and the historical process data is encoded by the encoder to output potential variables; S2, constructing a stable image representation of the system, using the stable image representation of the system as a decoder, using the latent variables as feedforward inputs in the stable image representation of the system, and obtaining historical reconstruction process data; S3, constructing an autoencoder according to the encoder and the decoder; based on the domain knowledge of control theory and information theory, training the autoencoder according to the historical process data and the historical reconstruction process data to obtain a trained autoencoder; S4, obtaining process data to be detected, obtaining reconstructed process data according to the process data to be detected and the trained autoencoder, constructing a detection statistic according to the gap between the process data and the reconstructed process data, and realizing fault detection of nonlinear systems in complex industrial processes according to the detection statistic and a preset detection threshold; The adjoint system of the complex nonlinear system in Hamiltonian sense is designed based on control theory in S1, including: S11. Constructing nonlinear systems in complex industrial processes ; S12, according to the nonlinear system , defining the state space form of the system stability representation ; S13. Based on control theory, the state space form of the system is characterized by the stable image , we get the state space form of the system stability representation Hamiltonian expansion ;in, is the state space form of the system stability image representation The accompanying system; S14, connecting the state space form of the image representation of the system stability The state space form of the image representation of the system stability The adjoint system of is obtained based on Hamiltonian system theory, and the Hamilton-Jacobi equation is obtained; S15. Based on the Hamilton-Jacobi equation, design an adjoint system of a complex nonlinear system in the Hamiltonian sense .

2. The method for nonlinear system fault detection based on domain knowledge-guided machine learning according to claim 1, characterized in that: The encoder in S1 encodes the historical process data and outputs potential variables, including: Through the adjoint system of the complex nonlinear system in the Hamiltonian sense, the historical process data is encoded and compressed to output low-dimensional variables; wherein the historical process data includes historical input data and historical output data; According to the historical input data and the feedback control system, estimating the feedforward input in the image representation of system stability to obtain an estimated value of the feedforward input; Generate the system state and , , , The partial derivative of the system state; where , , , Represents a manifold-like description of an affine nonlinear system; The adjoint system of the complex nonlinear system in the Hamiltonian sense is an anti-stable system. , , , The latent variables are obtained by taking partial derivatives of the system state, the terminal values ​​of the preset co-state variables, and the preset number of iterations.

3. The method for nonlinear system fault detection based on domain knowledge-guided machine learning according to claim 2, characterized in that: The step of constructing a stable image representation of the system in S2, using the stable image representation of the system as a decoder, using the latent variables as feedforward inputs in the stable image representation of the system, and obtaining historical reconstruction process data includes: S21, constructing a neural network, using the neural network to approximate , , , , according to the , , , Construct a stable image representation of the system; S22, using the latent variable as a feedforward input in the image representation of system stability, decoding the latent variable according to the image representation of system stability, and obtaining historical reconstruction process data.

4. The method for nonlinear system fault detection based on domain knowledge-guided machine learning according to claim 1, characterized in that: The step of training the autoencoder according to the historical process data and the historical reconstruction process data to obtain a trained autoencoder in S3 includes: S31, obtaining a reconstruction error according to the historical process data and the historical reconstruction process data; S32. Construct constraints for the autoencoder training process based on domain knowledge of control theory and information theory. S33. Training the autoencoder according to the reconstruction error and the constraint to obtain a trained autoencoder.

5. The method for nonlinear system fault detection based on domain knowledge-guided machine learning according to claim 4, characterized in that: The loss function of the training process of the autoencoder is shown in the following formula (1): （1） In the formula, represents the loss function, , , represents the weight coefficient, represents the reconstruction error loss term, represents the idempotent loss term of the projection operator, represents the restriction term for the losslessness of the Hamiltonian system, Indicates the number of batch data points, Represents batch process input and output data, represents the reconstructed batch process input and output data, represents the projection value of the reconstructed batch process input and output data, represents the estimated value of the latent variable, represents the projection of the latent variable estimate, Indicates The process input and output data points at each moment, Represents the reconstruction The process input and output data points at each moment, Represents the reconstruction The projection of the input and output data points of the process at each moment, Indicates The estimated value of the latent variable at time Indicates The projection of the estimated value of the latent variable at time instant, Represents a decoder, Represents an encoder.

6. The method for nonlinear system fault detection based on domain knowledge-guided machine learning according to claim 1, characterized in that: The detection statistic is shown in the following formula (2): （2） In the formula, represents the test statistic, represents the system input vector, represents the system output vector, represents the reconstructed system input vector, represents the reconstructed system output vector, Indicates the number of batch data points, Represents a decoder, Describes the decoder parameters, represents the encoder, Represents encoder parameters.

7. A nonlinear system fault detection device guided by domain knowledge and machine learning, wherein the nonlinear system fault detection device guided by domain knowledge and machine learning is used to implement the nonlinear system fault detection method guided by domain knowledge and machine learning as claimed in any one of claims 1 to 6, characterized in that: The device comprises: An encoder design module is used to design an adjoint system of a complex nonlinear system in the Hamiltonian sense based on control theory, and use the adjoint system of the complex nonlinear system in the Hamiltonian sense as an encoder to encode historical process data and output potential variables. A decoder design module is used to construct a stable image representation of the system, use the stable image representation of the system as a decoder, use the latent variables as feedforward inputs in the stable image representation of the system, and obtain historical reconstruction process data; A training module is used to construct an autoencoder according to the encoder and the decoder; based on the domain knowledge of control theory and information theory, the autoencoder is trained according to the historical process data and the historical reconstruction process data to obtain a trained autoencoder; A fault detection module is used to obtain process data to be detected, obtain reconstructed process data according to the process data to be detected and the trained autoencoder, construct a detection statistic according to the gap between the process data and the reconstructed process data, and realize fault detection of nonlinear systems in complex industrial processes according to the detection statistic and a preset detection threshold; The control theory-based design of the adjoint system of the complex nonlinear system in the Hamiltonian sense includes: S11. Constructing nonlinear systems in complex industrial processes ; S12, according to the nonlinear system , defining the state space form of the system stability representation ; S13. Based on control theory, the state space form of the system is characterized by the stable image , we get the state space form of the system stability representation Hamiltonian expansion ;in, is the state space form of the system stability image representation The accompanying system; S14, connecting the state space form of the image representation of the system stability The state space form of the image representation of the system stability The adjoint system of is obtained based on Hamiltonian system theory, and the Hamilton-Jacobi equation is obtained; S15. Based on the Hamilton-Jacobi equation, design an adjoint system of a complex nonlinear system in the Hamiltonian sense .

8. The nonlinear system fault detection device guided by domain knowledge and machine learning according to claim 7, characterized in that: The encoding of the historical process data by the encoder to output potential variables includes: Through the adjoint system of the complex nonlinear system in the Hamiltonian sense, the historical process data is encoded and compressed to output low-dimensional variables; wherein the historical process data includes historical input data and historical output data; According to the historical input data and the feedback control system, estimating the feedforward input in the image representation of system stability to obtain an estimated value of the feedforward input; Generate the system state and , , , The partial derivative of the system state; where , , , Represents a manifold-like description of an affine nonlinear system; The adjoint system of the complex nonlinear system in the Hamiltonian sense is an anti-stable system. , , , The latent variables are obtained by taking partial derivatives of the system state, the terminal values ​​of the preset co-state variables, and the preset number of iterations.

9. A complex nonlinear system fault detection device, characterized in that: The complex nonlinear system fault detection device comprises: processor; A memory having computer-readable instructions stored thereon, wherein when the computer-readable instructions are executed by the processor, the method according to any one of claims 1 to 6 is implemented.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores program codes, which can be called by a processor to execute the method according to any one of claims 1 to 6.

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