Nonlinear System Fault Detection Method and Device for Machine Learning Guided by Domain Knowledge

Abstract

The present invention provides a method and device for fault detection of a nonlinear system guided by domain knowledge in machine learning, relating to the technical field of fault detection. The method includes: designing an adjoint system of a complex nonlinear system in the sense of Hamilton as an encoder to output latent variables; using the image representation of system stability as a decoder to obtain historical reconstruction process data; thereby obtaining a trained autoencoder; and constructing a detection statistic according to the reconstruction gap for fault detection. The present invention proposes a nominal dynamic description method and a fault detection scheme for complex nonlinear systems, integrating relevant domain knowledge of the image representation of system stability, autoencoder technology, control theory, and information theory, and establishing an autoencoder that can better represent and reconstruct system dynamics. On this basis, using the reconstruction error to construct a detection statistic, the fault detection method for complex nonlinear systems has high accuracy, strong interpretability, and a wide range of applications.

Description

Technical Field

[0001] The present invention relates to the technical field of fault detection, and in particular to a fault detection method and device for a non-linear system guided by domain knowledge to machine learning. Background Art

[0002] Emerging technologies such as artificial intelligence have empowered the traditional industrial production and manufacturing processes, greatly promoting the improvement of production efficiency and system performance. However, this has also led to the increasing scale and complexity of today's complex industrial processes, and their safe and reliable operation has become even more important. Once a certain subsystem (link) fails and is not detected in time, it may lead to the continuous propagation of the fault and eventually cause the system to malfunction, or even trigger catastrophic accidents. Therefore, it is very necessary to detect the faults in the production operation of complex industrial processes in time and take corresponding maintenance measures to ensure the safe and reliable operation of the system.

[0003] In the past few decades, driven by both technological progress and market demand, rich research results have been achieved in the study of fault detection technology, and a large number of fault detection systems that can be used in actual industrial processes have been developed. Nowadays, there are mainly three common fault detection technologies: knowledge-based methods, analytical model-based methods, and data-driven methods. Knowledge-based methods and analytical model-based methods rely to a large extent on domain knowledge and analytical models, and the diagnostic accuracy of the models depends on the richness of expert experience and the generalization of the analytical models. However, today's industrial processes often have complex structures and exhibit difficult-to-handle characteristics such as high order, nonlinearity, and strong coupling during actual operation, posing great challenges to the establishment of system analytical models and the integration of expert experience knowledge. This severely restricts the application of knowledge-based methods and analytical model-based methods in complex industrial production processes. With the advent of the big data era, data-driven fault detection technology has received more and more attention from scholars and experts. As one of the typical data-driven technologies, machine learning technology has received extensive attention and application in the field of fault detection due to its powerful feature extraction ability and nonlinear fitting ability. For example, AE (Autoencoder, self-encoder technology) 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, while the data reconstruction error is large when abnormal situations (faults) occur. Therefore, a residual generator can be constructed by means of the reconstruction error to achieve fault detection for complex industrial processes. However, existing fault detection technologies based on autoencoders often directly use the reconstruction error of data for fault detection evaluation, lacking an evaluation of the information quality (interpretability) contained in the latent variables. In addition, since the neural network is essentially a "black box" model, existing machine learning-based fault detection technologies (including Autoencoder) lack a certain degree of interpretability, which hinders their application in industrial production and manufacturing processes.

[0004] Inspired by PINN (Physical Informed Neural Network), integrating specific domain knowledge into the training and learning process of neural networks helps improve the accuracy and interpretability of neural network learning. For complex industrial processes, it is necessary to develop an autoencoder design that integrates relevant domain knowledge of control theory and information theory and apply it to the fault detection process of complex industrial processes. In the context of control theory, the Hamilton System, which has received extensive attention and research, can be interpreted as an autoencoder. That is, by means of coprime factorization technology, the SIR (Stable Image Representation) of the original system is interpreted as the decoder, and the Hamiltonian adjoint system of the SIR of the original system is interpreted as the encoder. Through the connection of these two parts, the original system process data is dimensionally reduced and compressed into latent variables, and then the process data is decoded and reconstructed. It should be noted that an ideal latent variable should be generated through the maximum compression mapping of the process input data to retain as much information of the output variables as possible. In the framework of information theory, in order to be able to completely reconstruct the process data, the latent variable should be a minimum sufficient statistic. It is worth noting that the Hamiltonian extension of complex industrial processes can have the characteristics of lossless compression through certain designs, and at this time the latent variable can be equivalent to a minimum sufficient statistic. Therefore, combining autoencoder technology, control theory, and specific domain knowledge of information theory to achieve fault detection of complex industrial processes is an urgent research topic with strong practical value.

[0005] At present, the fault detection method based on autoencoder technology has not been integrated with specific domain knowledge and still belongs to the "black box" category, making it difficult to be practically applied. Generally speaking, the existing autoencoder-based fault detection methods first extract the features or information contained in the system process data (output data) through a specific neural network and dimensionally reduce and compress it into latent variables, and then decode the latent variables through a specific neural network to achieve the reconstruction of the process data. Further, the fault detection of complex industrial processes is achieved by evaluating the gap between the original process data and the reconstructed process data. It should be noted that this method does not evaluate the amount of information contained in the latent variables. In addition, the neural network learning and training processes involved in the encoder and decoder are completely "black box" and lack interpretability, making it difficult to reasonably and effectively constrain the network output results. Therefore, the traditional autoencoder-based fault detection method is difficult to analyze and interpret faults and is difficult to play practical value in industrial processes. Summary of the Invention

[0006] For the nonlinear systems in general complex industrial processes, aiming at the problems that model-based and knowledge-based fault detection methods rely heavily on analytical models and expert experience knowledge, and data-driven (machine learning) fault detection methods have low accuracy and are difficult to interpret faults, as well as the poor interpretability of traditional fault detection methods based on autoencoder technology, the embodiments of the present invention provide a method and device for fault detection of nonlinear systems guided by domain knowledge for machine learning. The technical solutions are as follows:

[0007] On the one hand, a method for fault detection of nonlinear systems guided by domain knowledge for machine learning is provided. This method is implemented by a nonlinear system fault detection device, and the method includes:

[0008] S1. Based on control theory, design the adjoint system of the complex nonlinear system in the sense of Hamilton, use the adjoint system of the complex nonlinear system in the sense of Hamilton as the encoder, and encode the historical process data through the encoder to output latent variables.

[0009] S2. Construct the image representation of system stability, use the image representation of system stability as the decoder, and use the latent variables as the feed-forward input in the image representation of system stability to obtain historical reconstructed process data.

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

[0011] S4. Obtain the process data to be detected, obtain the 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 the fault detection of the nonlinear system in the complex industrial process according to the detection statistic and the preset detection threshold.

[0012] Optionally, the design of the adjoint system of the complex nonlinear system in the sense of Hamilton in S1 includes:

[0013] S11. Construct the nonlinear system in the complex industrial process .

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

[0015] S13. Based on control theory, according to the state-space form of the image representation of system stability , obtain the Hamiltonian extension of the state-space form of the image representation of system stability of ; wherein, is the state - space form of the stable image representation of the system of the adjoint system.

[0016] S14. Connect the state - space form of the stable image representation of the system with the adjoint system of the state - space form of the stable image representation of the system Based on the Hamiltonian system theory, obtain the Hamilton - Jacobi equation.

[0017] S15. According to the Hamilton - Jacobi equation, design the adjoint system of the complex nonlinear system in the sense of Hamilton .

[0018] Optionally, in S1, encoding the historical process data through an encoder to output a latent variable, including:

[0019] Encoding and compressing the historical process data through the adjoint system of the complex nonlinear system in the sense of Hamilton, and outputting a low - dimensional variable; wherein, the historical process data includes historical input data and historical output data.

[0020] Estimate the feed - forward input in the stable image representation of the system according to the historical input data and the feedback control system to obtain an estimated value of the feed - forward input.

[0021] Generate the system state and , , , , , , , the partial derivatives of the system state with respect to; wherein,

[0022] Based on the adjoint system of the complex nonlinear system in the sense of Hamilton being an anti - stable system, according to the system state, , , , the partial derivatives of the system state with respect to, the termination value of the preset co - state variable, and the preset number of iterations to obtain the latent variable.

[0023] Optionally, in S2, construct the stable image representation of the system, use the stable image representation of the system as a decoder, and use the latent variable as the feed - forward input in the stable image representation of the system to obtain the historical reconstruction process data, including:

[0024] S21. Construct a neural network and use the neural network to approximate , , , , according to the said , , , Construct a system-stable image representation.

[0025] S22. Use the latent variable as the feed-forward input in the system-stable image representation, and decode the latent variable according to the system-stable image representation to obtain the historical reconstruction process data.

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

[0027] S31. Obtain the reconstruction error according to the historical process data and the historical reconstruction process data.

[0028] S32. Construct the constraints for the autoencoder training process according to the domain knowledge of control theory and information theory.

[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] In the formula, represents the loss function, , , represent the weight coefficients, represents the reconstruction error loss term, represents the idempotency loss term of the projection operator, represents the limiting term for the losslessness of the Hamiltonian system, represents the number of batch data points, represents the batch process input-output data, represents the reconstructed batch process input-output data, represents the projection value of the reconstructed batch process input-output data, represents the estimated value of the latent variable, represents the projection of the estimated value of the latent variable, represents the th moment process input-output data point, represents the reconstructed th moment process input-output data point, represents the reconstructed The projection of the input and output data points of each moment process, denotes the estimated value of the latent variable at the denotes the projection of the estimated value of the latent variable at the denotes the decoder, denotes the encoder.

[0033] Optionally, the detection statistic is as shown in Equation (2) below:

[0034] (2)

[0035] In the formula, denotes the detection statistic, denotes the system input vector, denotes the system output vector, denotes the reconstructed system input vector, denotes the reconstructed system output vector, denotes the number of batch data points, denotes the decoder, denotes the decoder parameters, denotes the encoder, denotes the encoder parameters.

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

[0037] An encoder design module, which is used to design the adjoint system of a complex non - linear system in the sense of Hamilton based on control theory, use the adjoint system of the complex non - linear system in the sense of Hamilton as the encoder, and encode the historical process data through the encoder to output the latent variable.

[0038] A decoder design module, which is used to construct the image representation of the stable system, use the image representation of the stable system as the decoder, and use the latent variable as the feed - forward input in the image representation of the stable system to obtain the historical reconstructed process data.

[0039] A training module, which is used to construct an auto - encoder according to the encoder and the decoder; based on the domain knowledge of control theory and information theory, train the auto - encoder according to the historical process data and the historical reconstructed process data to obtain the trained auto - encoder.

[0040] 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 implement fault detection of a nonlinear system in a complex industrial process according to the detection statistic and a preset detection threshold.

[0041] Based on control theory, design an adjoint system of a complex nonlinear system in the sense of Hamilton, including:

[0042] S11. Construct a nonlinear system in a complex industrial process .

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

[0044] S13. Based on control theory, according to the state - space form of the image representation for system stability , obtain the Hamiltonian extension of the state - space form of the image representation for system stability ; where is the adjoint system of the state - space form of the image representation for system stability .

[0045] S14. Connect the state - space form of the image representation for system stability with the adjoint system of the state - space form of the image representation for system stability , and based on Hamiltonian system theory, obtain the Hamilton - Jacobi equation.

[0046] S15. According to the Hamilton - Jacobi equation, design an adjoint system of a complex nonlinear system in the sense of Hamilton .

[0047] On the other hand, provide a complex nonlinear system fault detection device, where the complex nonlinear system fault detection device includes: a processor; a memory, and computer - readable instructions are stored on the memory. When the computer - readable instructions are executed by the processor, any one of the methods in the above - mentioned nonlinear system fault detection method guided by domain knowledge for machine learning is implemented.

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

[0049] The beneficial effects brought by the technical solutions provided in the embodiments of the present invention at least include:

[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 of process operations, and integrates relevant field knowledge such as system stability image representation, autoencoder technology, control theory, and information theory to establish an autoencoder that can better describe the process dynamics in the sense of Hamiltonian system. Further, a fault detection statistic is constructed using the error of the autoencoder for reconstructing process data, and a threshold value that meets the false alarm rate is set as the detection threshold, realizing the fault detection of complex nonlinear systems. This method starts entirely from historical data, has excellent detection effects, is easy to use, and at the same time, this method integrates field knowledge such as Hamiltonian system and stable image representation in control theory, and minimum sufficient statistic in information theory, and the learned latent variables, etc. have strong interpretability. Theoretically, the fault detection method based on autoencoder integrating 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 effects, and has practical application value. Description of the Drawings

[0051] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0052] Figure 1 It is a flowchart of a fault detection method for complex nonlinear systems guided by field knowledge in machine learning provided by an embodiment of the present invention;

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

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

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

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

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

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

[0059] Figure 8 It is the comparison diagram of the change of the loss function in the training process of Vanilla AE and I-AE provided by an embodiment of the present invention;

[0060] Figure 9 It is the detection result diagram of the actuator fault of the No. 1 water tank by the Vanilla AE (a) and I-AE (b) methods provided by an embodiment of the present invention;

[0061] Figure 10 It is the detection result diagram of the leakage fault of the No. 2 water tank by the Vanilla AE (a) and I-AE (b) methods provided by an embodiment of the present invention;

[0062] Figure 11 It is the change diagram of each loss function in the training process of I-AE introducing an additional regularization loss term provided by an embodiment of the present invention;

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

[0064] Figure 13 It is the structural schematic diagram of a fault detection device for a complex nonlinear system provided by an embodiment of the present invention. Detailed implementation manners

[0065] Next, the technical solutions in the present invention will be described with reference to the accompanying drawings.

[0066] In the embodiments of the present invention, words such as "exemplarily" and "for example" are used to represent examples, illustrations or explanations. Any embodiment or design solution described as "example" in the present invention should not be construed as being more preferred or having more advantages than other embodiments or design solutions. Exactly speaking, the use of the word "example" is intended to present concepts in a specific way. In addition, in the embodiments of the present invention, the meaning expressed by "and / or" can be both, or either one of the two can be selected.

[0067] In the embodiments of the present invention, "image" and "picture" can sometimes be used interchangeably. It should be noted that when the difference is not emphasized, the meanings they express are the same. "(of)", "corresponding", and "corresponding" can sometimes be used interchangeably. It should be noted that when the difference is not emphasized, the meanings they express are the same.

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

[0069] To make the technical problems, technical solutions, and advantages to be solved by the present invention clearer, the following will be described in detail with reference to the accompanying drawings and specific embodiments.

[0070] The embodiments of the present invention provide a method for detecting faults in a non-linear system guided by domain knowledge in machine learning. This method can be implemented by a complex non-linear system fault detection device, which can be a terminal or a server. As Figure 1 shown in the flowchart of the method for detecting faults in a non-linear system guided by domain knowledge in machine learning, the processing flow of this method can include the following steps:

[0071] S1. Based on control theory, design the adjoint system of the complex non-linear system in the sense of Hamilton. Use the adjoint system of the complex non-linear system in the sense of Hamilton as an encoder, and encode the historical process data through the encoder to output latent variables.

[0072] In a feasible implementation, as Figure 2 、 Figure 3 shown, in the context of control theory, use the process input / output data as the model input in the sense of the Hamilton adjoint system of the complex non-linear system, and interpret the model output as latent variables, that is, design the adjoint system of the complex non-linear system in the sense of Hamilton as an encoder. Since this encoder system is anti-stable, the training and learning process requires the cooperation of a decoder.

[0073] Specifically, the design of the adjoint system of the complex non-linear system in the sense of Hamilton in S1 based on control theory can include the following steps S111 - S115:

[0074] S111. Construct the non-linear system in the complex industrial process .

[0075] In a feasible implementation, consider the non-linear system in the complex industrial process, and assume its true model is:

[0076] (1)

[0077] In the formula, 、 、 are the system state vector, input vector, and output vector respectively, , , , is a continuously differentiable non - linear function, is the initial state of the system, represents the derivative of the state vector.

[0078] In the context of a feedback control system, there is:

[0079] (2)

[0080] where, is the feedback control signal, is the feed - forward controller, is the reference signal.

[0081] S112. According to the non - linear system , define the state - space form characterized by the stable image of the system :

[0082] (3)

[0083]

[0084] In the formula, , , , represent the image - manifold description of the affine non - linear system.

[0085] S113. In the context of control theory, the Hamiltonian of

[0086] (4)

[0087] where, is the state vector, is the input vector, is the output vector, is the adjoint system of represents the co - state variable, represents the input of the adjoint system.

[0088] S114. Connect the state - space form characterized by the stable image of the system with the adjoint system of the state - space form characterized by the stable image of the system . Based on the Hamiltonian system theory, the Hamilton - Jacobi equation is obtained.

[0089] In a feasible implementation, by connecting the SIR of the system and its adjoint system, that is, by setting , at this time the above - mentioned Hamiltonian system can be expressed as:

[0090] (5)

[0091] In the formula, represents the output of the adjoint system, and the image representation of the original system.

[0092] In the theory of Hamiltonian systems, if is satisfied, and there exists an energy function satisfying:

[0093] (6)

[0094] then the system is called inner at this time, denoted as . Through equivalent transformation, the following Hamilton-Jacobi equation (HJE) can be deduced:

[0095] (7)

[0096] In the formula, represents the partial derivative of, and represents the identity matrix.

[0097] S115. According to the Hamilton-Jacobi equation, design the adjoint system of the complex nonlinear system in the sense of Hamilton .

[0098] In a feasible implementation, in practical applications, for the purpose of fault detection, usually the adjoint system of SIR is connected to SIR, that is, let , and define . At this time, the connection relationship of the system is as shown in Figure 4 , so there is:

[0099] (8)

[0100] In the formula, represents the reconstructed process input data, and represents the reconstructed process output data.

[0101] Optionally, the encoding of the historical process data by the encoder in S1 to output the latent variable may include the following steps S121 - S124:

[0102] S121. Encode and compress the historical process data through the adjoint system of the complex nonlinear system in the sense of Hamilton to output low-dimensional variables; where the historical process data includes historical input data and historical output data.

[0103] In a feasible implementation, consider the adjoint system The input is high-dimensional process input-output data and its output is low-dimensional variables , thus realizing the encoding and compression of process data, that is:

[0104] (9)

[0105] S122. Estimate the feedforward input in the image representation of system stability according to historical input data and the feedback control system, and obtain the estimated value of the feedforward input.

[0106] In a feasible implementation, with the help of the feedback control system: , estimate the feedforward input through batch process input data .

[0107] S123. Generate the system state and , , , the partial derivative of the system state according to historical process data, the estimated value of the feedforward input, and the image representation of system stability.

[0108] In a feasible implementation, according to the estimated value of the feedforward input and the SIR of the system and batch process input-output data , generate the system state and , , , the partial derivative of the state.

[0109] S124. Based on the fact that the adjoint system of the complex nonlinear system in the sense of Hamilton is an anti-stable system, obtain the latent variable according to the system state, , , , the partial derivative of the system state, the termination value of the preset co-state variable, and the preset number of iterations.

[0110] In a feasible implementation, since the adjoint system is an anti-stable system, with the help of the result generated by S123, continuously iterate forward through the termination value of the co-state variable to output the latent variable .

[0111] ​S2. Construct a stable image representation of the system. Use the stable image representation of the system as the decoder, and use the latent variable as the feedforward input in the stable image representation of the system to obtain historical reconstruction process data.

[0112] In a feasible implementation, based on the coprime factorization technique, the process data of a complex nonlinear system can be represented by the feedforward input in the stable image representation of the system. At this time, by regarding the latent variable output by the encoder as the feedforward input, the process data can be reconstructed by means of the stable image representation of the system, that is, the stable image representation of the system is designed as the decoder.

[0113] Optionally, the above step S2 may include the following steps S21 - S22:

[0114] S21. To avoid solving the Hamilton-Jacobi equation (HJE), construct a neural network with a certain number of hidden layers and conforming to the dimension of the process data to approximate... 、 、 、 , so as to construct the SIR of the system under unknown model, as shown in... Figure 5 At the same time, use the neural network to approximate... to be used for estimating the feedforward signal during the training process of the encoder.

[0115] S22. Based on the SIR implemented by the neural network, decode the latent variable... to realize the reconstruction of the process data, that is:

[0116] (10)

[0117] S3. Construct an autoencoder according to the encoder and the 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.

[0118] In a feasible implementation, first, since the fundamental purpose of the autoencoder is to learn the process data and then reconstruct the process data, the error between the original process data and the reconstructed process data needs to be considered during the training process; in addition, with the help of the domain knowledge of control theory and information theory, the Hamiltonian extended system of a complex nonlinear system should have the characteristics of idempotency and lossless compression. Therefore, the learning and training process of the autoencoder should be constrained by these three parts.

[0119] Optionally, training the autoencoder according to the historical process data and the historical reconstruction process data in S3 to obtain a trained autoencoder may include the following steps S31 - S33:

[0120] S31. Obtain the reconstruction error based on the historical process data and the historical reconstruction process data.

[0121] In a feasible implementation, through steps S1 - S2, continuously train and optimize the neural network according to the batch process data reconstruction error.

[0122] S32. Construct the constraints for the training process of the auto - encoder based on the domain knowledge of control theory and information theory.

[0123] In a feasible implementation, in the context of control theory and information theory, due to the requirement that the auto - encoder should be a projection operator and the losslessness of information transmission, impose additional constraints on the training and learning process of the auto - encoder, making the trained auto - encoder more in line with the actual system operation process. That is, the loss function for the auto - encoder training process is:

[0124] (11)

[0125] In the formula, represents the loss function, 、 、 represent the weight coefficients, represents the reconstruction error loss term, represents the idempotency loss term of the projection operator, represents the restriction term for the losslessness of the Hamiltonian system, represents the number of batch data points, represents the batch process input - output data, represents the reconstructed batch process input - output data, represents the projection value of the reconstructed batch process input - output data, represents the estimated value of the latent variable, represents the projection of the estimated value of the latent variable, represents the th - moment process input - output data point, represents the reconstructed th - moment process input - output data point, represents the projection of the reconstructed th - moment process input - output data point, represents the th - moment estimated value of the latent variable, represents the th - moment projection of the estimated value of the latent variable, represents the decoder, represents the encoder.

[0126] S33. Train the auto - encoder according to the reconstruction error and the constraints to obtain the trained auto - encoder.

[0127] S4. Obtain the process data to be detected, obtain the reconstructed process data according to 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 for the nonlinear system in the complex industrial process according to the detection statistic and the preset detection threshold.

[0128] In a feasible implementation manner, with the aid of the trained autoencoder, construct a detection statistic based on the gap between the process data and the reconstructed data, and set the threshold obtained by running the fault-free data under a specific false alarm rate as the detection threshold, so as to implement fault detection for the nonlinear system in the complex industrial process.

[0129] Specifically, based on the trained autoencoder, construct a detection statistic according to the process data reconstruction error , that is:

[0130] (12)

[0131] In the formula, represents the detection statistic, represents the system input vector, represents the system output vector, represents the reconstructed system input vector, represents the reconstructed system output vector, represents the number of batch data points, represents the decoder, represents the decoder parameters, represents the encoder, represents the encoder parameters.

[0132] Furthermore, run the batch fault-free process data, and calculate the fault detection threshold under the condition of meeting the set false alarm rate , that is:

[0133] (13)

[0134] In the formula, represents the process input data at the -th moment, represents the process output data at the -th moment, represents the set fault detection false alarm rate, represents the reconstructed process input data at the -th moment, represents the -th moment reconstructed process input data.

[0135] Further, for online detection, an autoencoder model is used for online data, and it is observed whether the change of the detection statistic exceeds the threshold, so as to judge whether a fault has occurred in the process, that is:

[0136] (14)

[0137] It is worth mentioning that the detection statistic adopted in the present invention is directly generated by the reconstruction error of the autoencoder, which is applicable to general complex industrial processes, avoiding the statistic and the assumption that the process data of the statistic requires a certain distribution, and has more application value.

[0138] The present invention is directed to a non-linear system in a general complex industrial process, and proposes a brand-new fault detection method that integrates knowledge related to system image representation, autoencoder technology, control theory, and information theory. Aiming at the problems such as poor interpretability of traditional fault detection methods based on autoencoder technology, the present invention combines the widely used Hamiltonian system theory in control theory, stable image representation with autoencoder technology. By interpreting the Hamiltonian adjoint system of the SIR of the system as the encoder, interpreting the SIR of the system as the decoder, and connecting the two parts to realize the training and learning of the neural network under the guidance of control theory. At the same time, the present invention also evaluates the amount of information contained in the latent variables in the context of information theory to guide and optimize the learning of the autoencoder, further improving the accuracy and interpretability of the fault detection method based on autoencoder technology proposed by the present invention. Theoretically, the autoencoder technology proposed by the present invention can better characterize the dynamics of the non-linear system in the original complex industrial process, and can reconstruct the original process data to the greatest extent. Based on this, a detection statistic is constructed through the reconstruction error of the data to realize the fault detection of the complex industrial process, which should have a very accurate detection effect.

[0139] Next, the real process data of the three-tank system is used to verify the effectiveness of the complex non-linear system fault detection method guided by domain knowledge for machine learning proposed by the present invention. As Figure 6 shown, the three-tank system consists of three interconnected tanks. Among them, Tank 1 and Tank 2 are connected through Tank 3. Pump 1 and Pump 2 transport the water in the reservoir to Tank 1 and Tank 2 respectively through pipelines to adjust the water levels in the tanks. In this experiment, the water flow rate of the pump is taken as the system input quantity, and the water level in the tank is taken as the system output quantity. The sampling time is 1 s. As Figure 7 shown, a total of 18 sets of process operation data at stable working points are collected. The specific experimental results are as follows:

[0140] I Training the autoencoder. To demonstrate the advantages of the fault detection method based on the domain knowledge-guided autoencoder learning proposed in the present invention compared to the traditional fault detection method based on autoencoder learning, a common autoencoder using a recurrent neural network as the encoder and decoder was adopted for experimental comparison, denoted as Vanilla AE, while the autoencoder integrating domain knowledge proposed in the present invention is denoted as I-AE. The comparison of the changes in the loss function during the training process is as Figure 8 shown. It can be seen from the experimental results that the learning process of the common autoencoder converges faster and has a smaller reconstruction error. Based on the reconstruction error and the fault detection method proposed in the present invention, with a false alarm rate set at 5%, the fault detection thresholds of Vanilla AE and I-AE are 19.7 and 35.1 respectively.

[0141] Ⅱ Fault detection. To compare the fault detection effects of the above two methods, the following quantitative indicators were introduced:

[0142] (15)

[0143] where, is the total number of collected data, and are the total numbers of faulty data and non-faulty data, and are the numbers of false alarms and missed detections. In the experiment, the non-faulty process and the faulty process were each run for 300 s, and different types of faults were introduced at the 301st second. The detection results are as Figure 9 、 Figure 10 shown. The quantitative comparison of the fault detection effects of the two methods is shown in Table 1. Based on 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.

[0144] Table 1 Comparison of quantitative indicators of fault detection results of Vanilla AE and I-AE methods

[0145]

[0146] Ⅲ Evaluation of the role of latent variables. To illustrate the role and value of the latent variables in the I-AE proposed in the present invention, an additional regularization loss term was added during the above autoencoder training process, that is:

[0147] (16)

[0148] The change in the loss function during the training process of I-AE with the additional regularization loss term is as Figure 11As shown in the figure, the fault detection results of the three methods are compared in Table 2. From the above results, it can be seen that the loss function of the I-AE training process with additional extra loss terms cannot converge completely, 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 introduction of the regularization loss term tends to make the latent variables retain all the information in the process data, including uncertainty and redundancy. This will cause the trained autoencoder to learn features that do not belong to the complex nonlinear nominal process. At this time, the latent variables are no longer a minimum sufficient statistic, which will obviously affect the fault detection results.

[0149] Table 2 Comparison table of quantitative indicators of fault detection results of three methods

[0150]

[0151] In the embodiments 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 data of process operation, and integrates relevant field knowledge of system stable image representation, autoencoder technology, control theory, and information theory to establish an autoencoder that can better describe the process dynamics in the sense of Hamiltonian system. Further, a fault detection statistic is constructed using the error of the autoencoder to reconstruct the process data, and a threshold value that satisfies the false alarm rate is set as the detection threshold, realizing the fault detection of complex nonlinear systems. This method starts completely from historical data, has excellent detection effects and is easy to use. At the same time, this method integrates the field knowledge of Hamiltonian systems and stable image representation in control theory, and the minimum sufficient statistic in information theory. The learned latent variables, etc. have strong interpretability. In theory, the fault detection method based on autoencoder integrating field knowledge proposed by the present invention is applicable to general complex nonlinear systems, can better characterize the dynamics of the nominal system, has excellent detection effects, and has practical application value.

[0152] Figure 12 is a block diagram of a fault detection device for a nonlinear system guided by domain knowledge in machine learning shown according to an exemplary embodiment. This device is used for the fault detection method of a nonlinear system guided by domain knowledge in machine learning. Referring to Figure 12 , this device includes an encoder design module 310, a decoder design module 320, a training module 330, and a fault detection module 340. Among them:

[0153] The encoder design module 310 is used to design the adjoint system of a complex nonlinear system in the sense of Hamiltonian based on control theory, use the adjoint system of the complex nonlinear system in the sense of Hamiltonian as the encoder, and encode the historical process data through the encoder to output latent variables.

[0154] 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 the decoder, take the latent variable as the feedforward input in the stable image representation of the system, and obtain the historical reconstruction process data.

[0155] The training module 330 is used to construct an autoencoder according to the encoder and the 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.

[0156] The fault detection module 340 is used to obtain the process data to be detected, obtain the reconstruction 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 reconstruction process data, and implement fault detection of the nonlinear system in the complex industrial process according to the detection statistic and the preset detection threshold.

[0157] Based on control theory, design the adjoint system of the complex nonlinear system in the sense of Hamilton, including:

[0158] S11. Construct the nonlinear system in the complex industrial process .

[0159] S12. According to the nonlinear system , define the state - space form of the stable image representation of the system .

[0160] S13. Based on control theory, according to the state - space form of the stable image representation of the system , obtain the Hamiltonian extension of the state - space form of the stable image representation of the system ; where ; is the adjoint system of the state - space form of the stable image representation of the system.

[0161] S14. Connect the state - space form of the stable image representation of the system with the adjoint system of the state - space form of the stable image representation of the system, and based on the Hamiltonian system theory, obtain the Hamilton - Jacobi equation.

[0162] S15. According to the Hamilton - Jacobi equation, design the adjoint system of the complex nonlinear system in the sense of Hamilton .

[0163] In an embodiment of the present invention, a fault detection method for a general nonlinear system in a complex industrial process is proposed. This method requires a large amount of historical data of process operation, and integrates the knowledge of relevant fields such as system stability image representation, autoencoder technology, control theory, and information theory to establish an autoencoder that can better describe the process dynamics in the sense of Hamiltonian system. Further, a fault detection statistic is constructed by using the error of the process data reconstructed by the autoencoder, and a threshold value that meets the false alarm rate is set as the detection threshold, realizing the fault detection of the complex nonlinear system. This method starts completely from historical data, has excellent detection effect and is easy to use. At the same time, this method integrates the knowledge of Hamiltonian system and stable image representation in control theory, and the field knowledge of minimum sufficient statistic in information theory, and the learned latent variables, etc. have strong interpretability. In theory, the fault detection method based on autoencoder integrating field knowledge proposed by the present invention is applicable to general complex nonlinear systems, can better depict the dynamics of the nominal system, has excellent detection effect, and has practical application value.

[0164] Figure 13 FIG. is a schematic structural diagram of a fault detection device for a complex nonlinear system provided by an embodiment of the present invention, as Figure 13 shown, the fault detection device for a complex nonlinear system may include the above-mentioned Figure 12 nonlinear system fault detection device guided by field knowledge for machine learning shown. Optionally, the fault detection device 410 for a complex nonlinear system may include a first processor 2001.

[0165] Optionally, the fault detection device 410 for a complex nonlinear system may further include a memory 2002 and a transceiver 2003.

[0166] Among them, the first processor 2001 is connected to the memory 2002 and the transceiver 2003, such as through a communication bus.

[0167] Next, in combination with Figure 13 each component of the fault detection device 410 for a complex nonlinear system will be specifically introduced:

[0168] Among them, the first processor 2001 is the control center of the complex nonlinear system fault detection device 410, which can be a single processor or a collective term for multiple processing elements. For example, the first processor 2001 is one or more central processing units (CPUs), or can be an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of the present invention, such as: one or more digital signal processors (DSPs), or one or more field programmable gate arrays (FPGAs).

[0169] Optionally, the first processor 2001 can execute various functions of the complex nonlinear system fault detection device 410 by running or executing software programs stored in the memory 2002 and invoking data stored in the memory 2002.

[0170] In a specific implementation, as an embodiment, the first processor 2001 can include one or more CPUs, such as Figure 13 the CPU0 and CPU1 shown in

[0171] In a specific implementation, as an embodiment, the complex nonlinear system fault detection device 410 can also include multiple processors, such as Figure 13 the first processor 2001 and the second processor 2004 shown in

[0172] Each of these processors can be a single-core processor (single-CPU) or a multi-core processor (multi-CPU). Here, the processor can refer to one or more devices, circuits, and / or processing cores for processing data (such as computer program instructions).

[0173] Optionally, the memory 2002 may be a read-only memory (ROM) or other type of static storage device that can store static information and instructions, a random access memory (RAM) or other type of dynamic storage device that can store information and instructions, or may also be an electrically erasable programmable read-only memory (EEPROM), a compact disc read-only memory (CD-ROM), or other optical disc storage, optical disc storage (including compact discs, laser discs, optical discs, digital versatile discs, Blu-ray discs, etc.), magnetic disk storage media, or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and can be accessed by a computer, but is not limited thereto. The memory 2002 may be integrated with the first processor 2001 or may exist independently and be coupled to the first processor 2001 through an interface circuit ( Figure 13 not shown) of the complex non-linear system fault detection device 410. The embodiments of the present invention do not make specific limitations in this regard.

[0174] The transceiver 2003 is used to communicate with a network device or with a terminal device.

[0175] Optionally, the transceiver 2003 may include a receiver and a transmitter ( Figure 13 not shown separately). Among them, the receiver is used to implement the receiving function, and the transmitter is used to implement the transmitting function.

[0176] Optionally, the transceiver 2003 may be integrated with the first processor 2001 or may exist independently and be coupled to the first processor 2001 through an interface circuit ( Figure 13 not shown) of the complex non-linear system fault detection device 410. The embodiments of the present invention do not make specific limitations in this regard.

[0177] It should be noted that Figure 13 the structure of the complex non-linear system fault detection device 410 shown does not constitute a limitation on the router. The actual knowledge structure recognition device may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0178] In addition, the technical effects of the complex non-linear system fault detection device 410 may refer to the technical effects of the complex non-linear system fault detection method guided by domain knowledge in the above method embodiments, and will not be elaborated here.

[0179] It should be understood that the first processor 2001 in the embodiments of the present invention may be a central processing unit (CPU), and the processor may also be other general-purpose processors, digital signal processors (DSPs), application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0180] It should also be understood that the memory in the embodiments of the present invention may be a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories. Among them, the non-volatile memory may be a read-only memory (ROM), a programmable ROM (PROM), an erasable PROM (EPROM), an electrically erasable PROM (EEPROM), or a flash memory. The volatile memory may be a random access memory (RAM), which is used as an external cache. By way of example but not limitation, many forms of random access memory (RAM) are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchlink DRAM (SLDRAM), and direct rambus RAM (DR RAM).

[0181] It should be understood that the term "and / or" in this text is merely a description of the association relationship between associated objects, indicating that three relationships can exist. For example, A and / or B can represent three situations: A exists alone, A and B exist simultaneously, and B exists alone. Here, A and B can be singular or plural. Additionally, the character " / " in this text generally represents an "or" relationship between the preceding and following associated objects, but it may also represent an "and / or" relationship. The specific meaning can be understood by referring to the context before and after.

[0182] In the present invention, "at least one" means one or more, and "a plurality" means two or more. "At least one of the following" or similar expressions refer to any combination of these items, including any combination of single items or plural items. For example, at least one of a, b, or c can represent: a, b, c, a - b, a - c, b - c, or a - b - c, where a, b, and c can be single or multiple.

[0183] It should be understood that in various embodiments of the present invention, the magnitudes of the sequence numbers of the above processes do not imply the order of execution. The order of execution of each process should be determined by its function and internal logic, and should not constitute any limitation to the implementation process of the embodiments of the present invention.

[0184] Those of ordinary skill in the art can realize that the units and algorithm steps of each example described in combination with the embodiments disclosed herein can be implemented by electronic hardware, or by a combination of computer software and electronic hardware. Whether these functions are executed in a hardware or software manner depends on the specific application and design constraints of the technical solution. Professionals can use different methods for each specific application to implement the described functions, but such implementation should not be considered to exceed the scope of the present invention.

[0185] Those skilled in the art can clearly understand that for the convenience and conciseness of description, the specific working processes of the devices, apparatuses, and units described above can refer to the corresponding processes in the foregoing method embodiments, and will not be elaborated herein.

[0186] In 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 only a logical function division, and there can be other division methods in actual implementation. For example, 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 displayed or discussed coupling or direct coupling or communication connection between each other can be through some interfaces, and the indirect coupling or communication connection of the devices or units can be in an electrical, mechanical, or other form.

[0187] The unit described as a separation component may or may not be physically separated. The component displayed as a unit may or may not be a physical unit, that is, it may be located in one place, or it may be distributed to multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0188] In addition, each functional unit in various embodiments of the present invention may be integrated into one processing unit, or each unit may exist physically alone, or two or more units may be integrated into one unit.

[0189] If the above-mentioned function is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of this 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 causing a computer device (which may be a personal computer, a server, or a 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 medium includes: various media such as USB flash drives, mobile hard disks, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical discs that can store program codes.

[0190] As described above, the above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A method for fault detection of a non-linear system in machine learning guided by domain knowledge, characterized in that, The method includes: S1. Based on control theory, design the adjoint system of a complex nonlinear system in the sense of Hamilton. Use the adjoint system of the complex nonlinear system in the sense of Hamilton as an encoder, and encode historical process data through the encoder to output latent variables; S2. Construct an image representation of system stability. Use the image representation of system stability as a decoder, and use the latent variables as the feedforward input in the image representation of system stability to obtain historical reconstructed process data; 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 reconstructed process data to obtain a trained autoencoder; S4. Obtain the process data to be detected. According to the process data to be detected and the trained autoencoder, obtain the reconstructed process data. Construct a detection statistic based on the gap between the process data and the reconstructed process data, and implement fault detection of the nonlinear system in the complex industrial process according to the detection statistic and a preset detection threshold; The design of the adjoint system of a complex nonlinear system in the sense of Hamilton based on control theory in S1 includes: S11. Construct a non-linear system in a complex industrial process , where the non-linear system is a three-tank water system, the water flow rate of the pump is used as the system input, and the water tank level is used as the system output; S12. According to the non-linear system , define the state-space form of the image representation for system stability ; S13. Based on control theory, according to the state-space form of the stable image representation of the system , obtain the Hamiltonian extension of the state-space form of the stable image representation of the system ; wherein is the adjoint system of the state-space form of the stable image representation of the system ; S14. Connect the state - space form of the stable image representation of the system For the state - space form of the stable image representation of the system For its adjoint system, based on the Hamiltonian system theory, obtain the Hamilton - Jacobi equation; S15. Design the adjoint system of the complex nonlinear system in the sense of Hamilton according to the Hamilton-Jacobi equation .

2. The method for detecting faults in a non-linear system of machine learning guided by domain knowledge according to claim 1, characterized in that The encoding of historical process data through the encoder in S1 to output latent variables includes: Encode and compress the historical process data through the adjoint system of the complex nonlinear system in the sense of Hamilton to output low-dimensional variables; where the historical process data includes historical input data and historical output data; Estimate the feedforward input in the image representation of system stability according to the historical input data and the feedback control system to obtain an estimated value of the feedforward input; Generate the system state and the partial derivative of the system state according to the historical process data, the estimated value of the feedforward input, and the image representation of system stability; where represents the image manifold description of the affine nonlinear system; Based on the fact that the adjoint system of the complex nonlinear system in the sense of Hamilton is an anti-stable system, according to the system state, the partial derivative of the system state, the termination value of the preset co-state variable, and the preset number of iterations, a latent variable is obtained.

3. The method for nonlinear system fault detection by guiding machine learning with domain knowledge according to claim 2, characterized in that, The construction of the image representation of system stability in S2, using the image representation of system stability as a decoder, and using the latent variables as the feedforward input in the image representation of system stability to obtain historical reconstructed process data includes: S21. Construct a neural network and use the neural network to approximate and construct a system-stable image representation according to the . S22. Use the latent variables as the feedforward input in the image representation of system stability, and decode the latent variables according to the image representation of system stability to obtain historical reconstructed process data.

4. The method for nonlinear system fault detection by guiding machine learning with domain knowledge according to claim 1, wherein The training of the autoencoder according to the historical process data and the historical reconstructed process data in S3 to obtain a trained autoencoder includes: S31. Obtain a reconstruction error according to the historical process data and the historical reconstructed process data; S32. Based on the domain knowledge of control theory and information theory, construct constraints for the training process of the autoencoder; S33. Train the autoencoder according to the reconstruction error and the constraints to obtain a trained autoencoder.

5. The method for nonlinear system fault detection by guiding machine learning with domain knowledge 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 idempotency loss term of the projection operator, represents the constraint term for the losslessness of the Hamiltonian system, represents the number of batch data points, represents the input and output data of the batch process, represents the reconstructed input and output data of the batch process, represents the projection value of the reconstructed input and output data of the batch process, represents the estimated value of the latent variable, represents the projection of the estimated value of the latent variable, represents the th moment process input and output data point, represents the th moment reconstructed process input and output data point, represents the th moment projection of the reconstructed process input and output data point, represents the th moment estimated value of the latent variable, represents the th moment projection of the estimated value of the latent variable, represents the decoder, represents the encoder.

6. The method for nonlinear system fault detection of 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 detection statistic, represents the system input vector, represents the system output vector, represents the reconstructed system input vector, represents the reconstructed system output vector, represents the number of batch data points, represents the decoder, represents the decoder parameters, represents the encoder, represents the encoder parameters.

7. A non-linear system fault detection device for domain knowledge-guided machine learning, the non-linear system fault detection device for domain knowledge-guided machine learning is used to implement the non-linear system fault detection method for domain knowledge-guided machine learning as described in any one of claims 1-6, characterized in that, The device includes: An encoder design module, configured to design the adjoint system of a complex nonlinear system in the sense of Hamilton based on control theory, use the adjoint system of the complex nonlinear system in the sense of Hamilton as an encoder, and encode historical process data through the encoder to output latent variables; A decoder design module for constructing a stable image representation of the system, using the stable image representation of the system as the decoder, and using the latent variable as the feedforward input in the stable image representation of the system to obtain historical reconstruction process data; A training module for constructing an autoencoder based on the encoder and the decoder; training the autoencoder according to the historical process data and the historical reconstruction process data based on the domain knowledge of control theory and information theory to obtain a trained autoencoder; A fault detection module for obtaining process data to be detected, obtaining reconstruction 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 reconstruction process data, and realizing fault detection of a nonlinear system in a complex industrial process according to the detection statistic and a preset detection threshold; Based on control theory, designing an adjoint system of a complex nonlinear system in the sense of Hamilton, including: S11. Construct a non - linear system in a complex industrial process ; S12. According to the non-linear system , define the state space form of the image representation for system stability ; S13. Based on control theory, according to the state - space form of the stable image representation of the system , obtain the Hamiltonian extension of the state - space form of the stable image representation of the system ; where is the adjoint system of the state - space form of the stable image representation of the system . S14. Connect the state - space form of the stable image representation of the system For the adjoint system of the state - space form of the stable image representation of the system Based on the Hamiltonian system theory, obtain the Hamilton - Jacobi equation; S15. Design an adjoint system of a complex nonlinear system in the sense of Hamilton according to the Hamilton-Jacobi equation .

8. The nonlinear system fault detection device for guiding machine learning by domain knowledge according to claim 7, characterized in that Encoding historical process data through the encoder and outputting a latent variable, including: Encoding and compressing historical process data through the adjoint system of the complex nonlinear system in the sense of Hamilton and outputting a low-dimensional variable; wherein the historical process data includes historical input data and historical output data; Estimating the feedforward input in the stable image representation of the system according to the historical input data and the feedback control system to obtain an estimated value of the feedforward input; Generate the system state and the partial derivative of the system state according to the historical process data, the estimated value of the feedforward input, and the image representation of system stability; wherein, represents the image manifold description of the affine nonlinear system; Based on the fact that the adjoint system of the complex nonlinear system in the sense of Hamilton is an anti-stable system, according to the system state, the partial derivative of the system state, the termination value of the preset co-state variable, and the preset number of iterations, a latent variable is obtained.

9. A fault detection device for a complex non-linear system, characterized in that, The complex nonlinear system fault detection device includes: A processor; A memory storing computer-readable instructions, which when executed by the processor, implement the method according to any one of claims 1 to 6.

10. A computer-readable storage medium, characterized in that, Program code is stored in the computer-readable storage medium, and the program code can be called by the processor to execute the method according to any one of claims 1 to 6.

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