Nonlinear closed-loop system fault diagnosis method and system based on reversible right invariant manifold

Abstract

The application relates to a nonlinear closed-loop system fault diagnosis method and system based on a reversible right manifold. First, by constructing a homeomorphism mapping in a topological space, system input and output are mapped to a latent variable space, and then the latent variable is reconstructed into input and output data through inverse mapping, so that information losslessness in the learning process is ensured. The homeomorphism mapping is a forward and reverse mapping network constructed by using a condition reversible neural network, joint training is carried out by introducing a master and slave two optimization objective functions, the master objective function realizes parameter identification through reconstruction residual, the slave objective function relieves the overfitting problem by mapping the residual into a Gaussian distribution, so that high-precision modeling of the nonlinear system and residual generation are realized. Finally, a detection mechanism is designed by using the generated Gaussian residual signal, and fault alarm is realized by monitoring the residual offset in real time. The application fully combines the advantages of control theory and deep learning, and effectively solves the problem that traditional data-driven methods lack interpretability.

Description

Technical Field

[0001] This invention relates to the field of closed-loop system fault diagnosis technology, and in particular to a method and system for fault diagnosis of nonlinear closed-loop systems based on a reversible right manifold. Background Technology

[0002] In modern industrial systems, fault diagnosis technology serves as a key means to improve system reliability and safety. It enables timely identification of fault type, location, and severity when system anomalies occur, providing a basis for subsequent fault-tolerant control and maintenance decisions. Existing fault diagnosis methods are mainly divided into two categories: model-based methods and data-driven methods. Real-world engineering systems, especially nonlinear systems, often possess highly complex dynamic characteristics, and their physical mechanisms are difficult to accurately characterize with simple mathematical models. Model uncertainty, unmodeled dynamics, and external disturbances severely limit the application effectiveness of model-based methods in practical systems. Data-driven fault diagnosis methods directly utilize process data collected during system operation, extracting fault features through machine learning and statistical analysis, thus avoiding the difficulties of accurate modeling. In particular, with the development of deep learning technology, neural network-based fault diagnosis methods have achieved significant results in multiple industrial fields.

[0003] However, existing neural network-based fault diagnosis methods still face several key challenges: First, information compression leads to the loss of fault information. Traditional data-driven methods inevitably lose some information when projecting high-dimensional observation data into a low-dimensional latent space. Second, overfitting is a serious problem. Existing methods often use minimizing the residual signal as the sole optimization objective, causing the model to overfit the noise components in the training data during training. Third, the methods lack interpretability. Existing deep learning-based fault diagnosis methods are mostly black-box models, and their internal working mechanisms are difficult to understand and trust.

[0004] To address the aforementioned issues, some researchers have begun exploring technical approaches that combine control theory with machine learning. The theories of stable kernel representation and stable image representation provide a systematic theoretical framework for constructing interpretable observers.

[0005] Chinese patent application publication number CN116700208A discloses a fault diagnosis method and system for closed-loop systems based on invertible left-manifolds. This method utilizes invertible neural networks and delay operators to expand the input-output range, solving the problems of high memory requirements and high training costs in existing technologies. However, the invertible left-manifold is an equivalent manifold space constructed based on the theory of stable kernel representation of nonlinear systems, which has the following limitations: (1) The breakdown and reconstruction disaster of physical causality. The left manifold scheme is essentially a null space projection based on a stable kernel representation. The standard invertible network it constructs requires joint splicing of the system's control input and observed output. This symmetrical processing destroys the causal property of "input-driven output" in the control system. When tracing the source of fault states, the left manifold cannot achieve generative reconstruction of the output state under a given control command, resulting in a lack of its root cause analysis capability.

[0006] (2) Curse of Dimensionality and Waste of Computational Resources. The left manifold concatenates the input and output and inputs them into the invertible network, resulting in bijective mapping in a high-dimensional space. The network not only needs to learn the changes in the system output, but is also forced to consume a large number of parameters to maintain the bijective relationship of the known input variables, resulting in a huge waste of computational resources. Moreover, it is very prone to overfitting when facing large dynamic time-varying conditions.

[0007] In summary, there is currently a lack of a fault diagnosis method and system for nonlinear closed-loop systems based on reversible right manifolds to solve or partially solve the aforementioned problems. Summary of the Invention

[0008] The purpose of this invention is to overcome the defects of the prior art by providing a fault diagnosis method and system for nonlinear closed-loop systems based on reversible right manifolds, so as to solve or partially solve the problem of lost fault features when projecting to the null space during the reversible mapping process of methods based on reversible left manifolds.

[0009] The objective of this invention can be achieved through the following technical solutions: One aspect of the present invention provides a fault diagnosis method for a nonlinear closed-loop system based on a reversible right-hand manifold, comprising the following steps: A model is constructed for the controlled object in the target nonlinear closed-loop system. The controller of the controlled object is parameterized in image space, and an invertible right-flow architecture is constructed. The invertible right-flow architecture includes: a first invertible block that maps input data to the latent variable space, a second invertible block that maps the latent variable space to the output space to obtain the estimated value, and a third invertible block that stores the residual between the estimated value and the actual value. Each invertible block includes a multi-layer conditional invertible neural network. Obtain the system input and process output of the target nonlinear closed-loop system under normal conditions, and construct a training dataset; Based on the training dataset, the conditional invertible neural network in the invertible right-flow architecture is trained with the goal of reducing residuals; Based on the trained reversible right-flow architecture, a residual generator is constructed and test statistics and thresholds are obtained from the training dataset. The online system input and process output of the target nonlinear closed-loop system are obtained. The residual signal and test statistic of the target nonlinear closed-loop system are obtained using the trained reversible right-flow architecture. Online fault diagnosis is performed based on the threshold.

[0010] As a preferred technical solution, in the reversible right-flow architecture, the process output is sliced ​​and input into the first reversible block, the system input is used as the conditional input to obtain latent variables, and the latent variables are used as the input of the second reversible block to obtain the estimated value.

[0011] As a preferred technical solution, the controlled object in the target nonlinear closed-loop system is modeled as follows: in, and They represent Time-state variables, system inputs, and process outputs , , These are the dimensions of state variables, system inputs, and process outputs, respectively. and These are two nonlinear mappings.

[0012] As a preferred technical solution, the image space parameterization result of the controller for the controlled object is as follows: in, For parameterized controllers Image space parameterization results, For the image space operator of the controller, For the image space operator of the system, For operator connection symbols, These are the controller's free parameters.

[0013] As a preferred technical solution, any reversible block in the reversible right-flow architecture includes several reversible layers, wherein each reversible layer includes a single hidden layer neural network. and The forward and reverse calculations of a reversible block are implemented using the following formula: in, , These represent the reversible blocks of the first and second order. Each reversible layer is calculated in both forward and reverse directions. Indicates conditional input. and Corresponding to the first The front and back segments of the intermediate variables generated by the reversible layer Indicates the first The output of a reversible layer.

[0014] As a preferred technical solution, the training dataset is: in, The length of the stack, This represents the input data to the reversible block. , For system input and process output Dimensions T This indicates transpose.

[0015] As a preferred technical solution, during the training process of the conditionally invertible neural network in the reversible right-flow architecture, the training objective is: in, For the comprehensive objective function, The main objective function is... To obtain from the objective function, The tuning coefficients, , , These represent the system input, the actual process output, and the predicted process output, respectively. Let be the probability density function of the residual vector. The dimension of the stacked input and output vectors. For the residual vector, T This indicates transpose.

[0016] As a preferred technical solution, the residual generator is modeled as follows: in, , For the residual vector, , These are system inputs and process outputs, respectively. This represents a conditionally invertible neural network in the first and second residual blocks. This represents a conditionally invertible neural network in the third residual block. This represents the input data to the reversible block.

[0017] As a preferred technical solution, the test statistic and threshold are obtained by the following formula: in, For the residual vector The test statistic, T Indicates transpose. Represents the chi-square distribution. Let represent the defined significance level, and represent the Gaussian distribution. I Represents the identity matrix. For the threshold, Let q be the dimension of q.

[0018] Another aspect of the present invention provides a fault diagnosis system for a nonlinear closed-loop system based on a reversible right-hand manifold, for implementing the aforementioned fault diagnosis method for nonlinear closed-loop systems, the system comprising: A reversible right-flow architecture is used to model the controlled object in a target nonlinear closed-loop system. The controller of the controlled object is parameterized in image space, and a reversible right-flow architecture including multiple reversible blocks is constructed. Each reversible block includes a multi-layer conditional reversible neural network. The dataset construction module is used to obtain the system input and process output of the target nonlinear closed-loop system under normal conditions and construct the training dataset; The training module is used to train the conditional invertible neural network in the invertible right-flow architecture based on the training dataset with the goal of reducing the residual. The statistics construction module is used to construct a residual generator based on the trained reversible right-flow architecture and obtain test statistics and thresholds based on the training dataset. The online diagnostic module is used to acquire the online system input and process output of the target nonlinear closed-loop system, obtain the residual signal and test statistics of the target nonlinear closed-loop system using the trained reversible right-flow architecture, and perform online fault diagnosis based on the threshold.

[0019] Compared with the prior art, the present invention has at least one of the following beneficial effects: (1) Overcoming the problem of information loss in high-dimensional data projection: In view of the problem that fault features are lost when projecting to the null space during the reversible mapping process based on the reversible left manifold method, this method uses a conditional reversible neural network to construct a reversible right manifold architecture. Through the unique homeomorphism mapping property, a bijective relationship between the system output and the reconstructed output is established under the given system input and output, which ensures the information losslessness in the learning process, thereby preserving the fault-sensitive features in the original signal to the greatest extent and significantly improving the detection sensitivity for small faults or complex evolutionary faults.

[0020] (2) Reducing colored noise interference in closed-loop systems: In feedback control systems, noise is often colored due to the closed-loop effect, i.e., the energy of each frequency is uneven, which interferes with the residual generator projected onto the zero space by the reversible left-flow manifold. The reversible right-flow manifold scheme of this invention takes into account the characteristics of the closed-loop system in its design. Through the reconstruction of the right manifold, the resulting reversible right-flow manifold architecture includes a first reversible block that maps the input data to the latent variable space, a second reversible block that maps the latent variable space to the output space to obtain the estimated value, and a third reversible block that stores the residual between the estimated value and the actual value. This can more effectively separate the true dynamics of the system from the colored noise generated by the closed loop. The reversible right-flow manifold can utilize the manifold structure learned by the conditionally reversible neural network to extract the fault component more purely from the residual, reducing false alarms caused by noise.

[0021] (3) Provides a basis for fault analysis: The residual generated by the reversible left flow is a projection of the null space. If the residual is too large, it only means that it does not belong to the normal space, and its physical meaning is not intuitive enough. The reversible right flow of the present invention, through reconstruction, the residual is the difference between the reconstruction input and output and the real value, which can reflect the change of the real value of the fault impact, and provides a solid theoretical basis for subsequent fault location and root cause analysis. Attached Figure Description

[0022] Figure 1 This is a flowchart of a nonlinear closed-loop system fault diagnosis method based on an invertible right manifold, as illustrated in the embodiments. Figure 2 This is a schematic diagram of an offline fault diagnosis algorithm based on reversible right-flow propagation in the embodiment. Figure 3 A schematic diagram illustrating the parameterized description of a closed-loop system; Figure 4 for Diagram of a reversible block network architecture; Figure 5 for Diagram of a reversible block network architecture; Figure 6 A schematic diagram of the overall data-driven fault diagnosis model; Figure 7 This is a schematic diagram of the closed-loop control structure of the flight attitude control system. Figure 8 A comparison of the probability density of the residuals output by the right manifold architecture with that of the Gaussian signal; Figure 9 This is a schematic diagram of the monitoring results of the test statistics corresponding to the residual signal. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0024] Example 1 To address the problems of the aforementioned existing technologies, this embodiment provides a fault diagnosis method for nonlinear closed-loop systems based on invertible right-hand manifolds. Within the fault diagnosis framework, left-hand manifolds directly map input and output data to the null space, while right-hand manifolds construct homeomorphic mappings between system inputs, outputs, and latent space variables. The residual generator is defined as the deviation between the actual observed data and the estimated values ​​reconstructed based on the latent space. Based on this theory, an invertible fault diagnosis structure can be constructed by learning the left or right coprime decomposition of the system.

[0025] See Figure 1 and Figure 2 This method includes the following steps: Step S1: First, parameterize the nonlinear closed-loop system and construct an invertible right-flow architecture based on the conditional invertible neural network.

[0026] Step S2: Collect normal input and output data under offline conditions and perform stacking processing.

[0027] Step S3: Based on the reversible neural network, define the objective function of the reversible right-flow architecture, and optimize the internal parameters of the reversible neural network through offline training.

[0028] Step S4: Construct the residual generator of the system based on the trained reversible right-flow architecture and determine the test statistic and threshold based on offline data.

[0029] Step S5: Using the trained reversible right-flow architecture, generate the residual signal and test statistic of the closed-loop system through online data, and perform online fault diagnosis through threshold.

[0030] In the actual operation of a closed-loop system, the fault diagnosis method used is divided into two stages, as follows: (1) Offline training stage: Establish the state-space equation of the nonlinear closed-loop control system and perform parameterization description based on the input and output data. The closed-loop system can be parameterized as follows: ,set up and They represent and The signal space. Using operators and To represent nonlinear controlled objects and their controllers: The state-space equation can be defined as: in and These represent state variables, system inputs, and process outputs, respectively. and These are two nonlinear mappings. In a nonlinear system, we introduce... As a unified description of the feedback mechanism that can stabilize the system, It can be described by a stable image representation, and can be parameterized as follows: Among them, parameterized controller By using the nominal controller with by This is achieved by combining parameterized additional dynamic systems. Specifically, To ensure system stability, It can be integrated in a plug-and-play manner without modification. This improves the overall system performance. The parameterized description of its closed-loop system is available in [link to documentation]. Figure 3 ,system and controller The stable kernel representation and stable image representation are given by the following formulas: in It is related to the signal The relevant signal space. The stable kernel of the entire system is represented as: Next, a reversible right-flow architecture is constructed based on the conditionally reversible neural network. The reversible right-flow architecture consists of three reversible blocks, namely: Each reversible block consists of a multi-layer conditional reversible neural network, in which... Map input and output data to the latent variable space. The latent variable space is mapped to the output space to obtain its estimated value. The network architecture is as follows: Figure 4 As shown, The residual signal obtained by subtracting the true value from the estimated value is mapped to a Gaussian signal, and its network architecture is as follows: Figure 5 As shown. In each reversible block Indicates the first A reversible layer, This represents the total number of layers. Each invertible layer is implemented using two single-hidden-layer neural networks, denoted as […]. and , The calculation process is as follows: in Indicates conditional input; and Corresponding to the first The front and back segments of intermediate variables generated by a reversible layer. From arrive The reverse reversible process is as follows: From a systems perspective, the architecture and feedback system of the reversible framework This corresponds to the well-posedness. Within this framework, and As a module for residual generation, and This ensures the consistency of the residual signal. The forward process can be described as follows: in The non-intersection union symbol.

[0031] The reverse process can be described as follows: Includes learning This constitutes a space of latent variables, namely It is a reversible operator, and its effect is: The specific method for stacking offline data during offline training is as follows: in, The length of the stack, This represents the input data to the reversible block.

[0032] Then through neural networks express and , express The objective function for offline training is defined as follows: in, The main objective function is... To obtain from the objective function, For the tuning coefficients, the two objective functions are defined as follows: The primary objective function aims to minimize the residual and improve the fault detection performance of the closed-loop system, while the secondary objective function aims to prevent overfitting of the reversible right-flow architecture.

[0033] Therefore, the optimal invertible neural network architecture obtained by the final solution satisfies: The residual generator is then constructed as shown below, with two options as follows: The system's test statistic and threshold can be obtained using the following formula: in, Represents the chi-square distribution. This represents the defined significance level, mathematically equivalent to the acceptable false alarm rate.

[0034] (2) Online detection stage: The input and output data, stacked at each time step, are input into the model to obtain the residuals. The following detection logic is used to determine whether a fault has occurred: The final overall data-driven fault diagnosis model is as follows: Figure 6 As shown.

[0035] Considering the closed-loop control structure of the flight attitude control system, its feedback structure is as follows: Figure 7 As shown.

[0036] Figure 8 This paper demonstrates that a fault diagnosis method based on reversible right-propagation can effectively alleviate overfitting. Considering the dynamic data of online systems, the fault diagnosis effect can be improved through… Figure 9 The results showed that a fault occurred after 1000 samples, indicating that the fault diagnosis accuracy was very high.

[0037] In summary, this method addresses the complex nonlinear dynamics and interpretability challenges in nonlinear feedback control systems by establishing a reversible right-manifold fault detection model based on a conditionally invertible neural network. First, a homeomorphism mapping within the topological space is constructed to map the system's input and output to the latent variable space. Then, an inverse mapping is used to reconstruct the latent variables back into input and output data, ensuring information integrity during the learning process. The homeomorphism mapping utilizes a forward and backward mapping network constructed using a conditionally invertible neural network. Two optimization objective functions, a master and a slave, are introduced for joint training. The master objective function identifies parameters by reconstructing the residuals, while the slave objective function alleviates overfitting by mapping the residuals to a Gaussian distribution, thus achieving high-precision modeling and residual generation for the nonlinear system. Finally, a detection mechanism is designed using the generated Gaussian residual signal to trigger a fault alarm by monitoring residual offsets in real time. This method effectively combines the advantages of control theory and deep learning, addressing the lack of interpretability in traditional data-driven methods and significantly improving the accuracy and robustness of fault diagnosis for nonlinear systems.

[0038] Example 2 Based on Example 1, this example provides a fault diagnosis system for a nonlinear closed-loop system based on an invertible right-hand manifold, used to implement the fault diagnosis method for the nonlinear closed-loop system described in Example 1. The system includes: (1) Reversible right-flow architecture is used to model the controlled object in the target nonlinear closed-loop system, perform image space parameterization on the controller of the controlled object, and construct a reversible right-flow architecture including multiple reversible blocks, each of which includes a multi-layer conditional reversible neural network.

[0039] (2) Dataset construction module, used to obtain the system input and process output of the target nonlinear closed-loop system under normal conditions and construct the training dataset.

[0040] (3) Training module, used to train the conditional invertible neural network in the invertible right-handed architecture based on the training dataset with the goal of reducing residuals.

[0041] (4) Statistics construction module, which is used to build a residual generator based on the trained reversible right-flow architecture and obtain test statistics and thresholds based on the training dataset.

[0042] (5) Online diagnostic module, used to obtain the online system input and process output of the target nonlinear closed-loop system, obtain the residual signal and test statistic of the target nonlinear closed-loop system using the trained reversible right-flow architecture, and perform online fault diagnosis based on the threshold.

[0043] 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 person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A fault diagnosis method for a nonlinear closed-loop system based on a reversible right-hand manifold, characterized in that, Includes the following steps: A model is constructed for the controlled object in the target nonlinear closed-loop system. The controller of the controlled object is parameterized in image space, and an invertible right-flow architecture is constructed. The invertible right-flow architecture includes: a first invertible block that maps input data to the latent variable space, a second invertible block that maps the latent variable space to the output space to obtain the estimated value, and a third invertible block that stores the residual between the estimated value and the actual value. Each invertible block includes a multi-layer conditional invertible neural network. Obtain the system input and process output of the target nonlinear closed-loop system under normal conditions, and construct a training dataset; Based on the training dataset, the conditional invertible neural network in the invertible right-flow architecture is trained with the goal of reducing residuals; Based on the trained reversible right-flow architecture, a residual generator is constructed and test statistics and thresholds are obtained from the training dataset. The online system input and process output of the target nonlinear closed-loop system are obtained. The residual signal and test statistic of the target nonlinear closed-loop system are obtained using the trained reversible right-flow architecture. Online fault diagnosis is performed based on the threshold.

2. The fault diagnosis method for a nonlinear closed-loop system based on a reversible right-hand manifold according to claim 1, characterized in that, In the reversible right-flow architecture, the process output is sliced ​​and input into the first reversible block. The system input is used as the conditional input to obtain latent variables. The latent variables are used as the input to the second reversible block to obtain the estimated value.

3. The fault diagnosis method for a nonlinear closed-loop system based on a reversible right-hand manifold according to claim 1, characterized in that, The controlled object in the target nonlinear closed-loop system is modeled as follows: in, and They represent Time-state variables, system inputs, and process outputs , , These are the dimensions of state variables, system inputs, and process outputs, respectively. and These are two nonlinear mappings.

4. The fault diagnosis method for a nonlinear closed-loop system based on a reversible right-hand manifold according to claim 1, characterized in that, The image space parameterization result of the controller for the controlled object is as follows: in, For parameterized controllers Image space parameterization results, For the image space operator of the controller, For the image space operator of the system, For operator connection symbols, These are the controller's free parameters.

5. The fault diagnosis method for a nonlinear closed-loop system based on a reversible right-hand manifold according to claim 1, characterized in that, For any reversible block in the reversible right-flow architecture, it includes several reversible layers, wherein each reversible layer includes a single hidden layer neural network. and The forward and reverse calculations of a reversible block are implemented using the following formula: in, , These represent the reversible blocks of the first and second order. Each reversible layer is calculated in both forward and reverse directions. Indicates conditional input. and Corresponding to the first The front and back segments of the intermediate variables generated by the reversible layer Indicates the first The output of a reversible layer.

6. The fault diagnosis method for a nonlinear closed-loop system based on a reversible right-hand manifold according to claim 1, characterized in that, The training dataset is: in, The length of the stack, This represents the input data to the reversible block. , For system input and process output Dimensions T This indicates transpose.

7. The fault diagnosis method for a nonlinear closed-loop system based on a reversible right-hand manifold according to claim 1, characterized in that, During the training of the conditionally invertible neural network in the aforementioned invertible right-flow architecture, the training objective is: in, For the comprehensive objective function, The main objective function is... To obtain from the objective function, The tuning coefficients, , , These represent the system input, the actual process output, and the predicted process output, respectively. Let be the probability density function of the residual vector. The dimension of the stacked input and output vectors. For the residual vector, T This indicates transpose.

8. The fault diagnosis method for a nonlinear closed-loop system based on a reversible right-hand manifold according to claim 1, characterized in that, The residual generator is modeled as follows: in, , For the residual vector, , These are system inputs and process outputs, respectively. This represents a conditionally invertible neural network in the first and second residual blocks. This represents a conditionally invertible neural network in the third residual block. This represents the input data to the reversible block.

9. The fault diagnosis method for a nonlinear closed-loop system based on a reversible right-hand manifold according to claim 1, characterized in that, The test statistic and threshold are obtained by the following formula: in, For the residual vector The test statistic, T Indicates transpose. Represents the chi-square distribution. Let represent the defined significance level, and represent the Gaussian distribution. I Represents the identity matrix. For the threshold, Let q be the dimension of q.

10. A fault diagnosis system for a nonlinear closed-loop system based on a reversible right-hand manifold, characterized in that, For implementing the fault diagnosis method for a nonlinear closed-loop system as described in any one of claims 1-9, the system comprises: A reversible right-flow architecture is used to model the controlled object in a target nonlinear closed-loop system. The controller of the controlled object is parameterized in image space, and a reversible right-flow architecture including multiple reversible blocks is constructed. Each reversible block includes a multi-layer conditional reversible neural network. The dataset construction module is used to obtain the system input and process output of the target nonlinear closed-loop system under normal conditions and construct the training dataset; The training module is used to train the conditional invertible neural network in the invertible right-flow architecture based on the training dataset with the goal of reducing the residual. The statistics construction module is used to construct a residual generator based on the trained reversible right-flow architecture and obtain test statistics and thresholds based on the training dataset. The online diagnostic module is used to acquire the online system input and process output of the target nonlinear closed-loop system, obtain the residual signal and test statistics of the target nonlinear closed-loop system using the trained reversible right-flow architecture, and perform online fault diagnosis based on the threshold.

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