A reversible left manifold-based closed-loop system fault diagnosis method and system

Abstract

The application relates to a reversible left manifold-based closed-loop system fault diagnosis method and system, which comprises the following steps: step 1, constructing a reversible left manifold according to a reversible neural network, and parameterizing a nonlinear closed-loop system; step 2, constructing a reversible residual generator of a nonlinear closed-loop control system according to the reversible neural network; and step 3, obtaining online data of the nonlinear closed-loop system, and performing online fault diagnosis based on a test statistic of the residual generator and a set diagnosis threshold. Compared with the prior art, the application has the advantages of low memory cost requirement and high fault diagnosis precision.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of closed-loop system fault diagnosis, and in particular to a closed-loop system fault diagnosis method and system based on reversible left invariant manifold. BACKGROUND

[0002] Fault diagnosis technology plays an important role in the fields of railway, steel, chemical industry, etc. The existing fault diagnosis methods can be basically divided into three categories: model-based fault diagnosis method, data-driven fault diagnosis method and their combination. Due to the increasing complexity of modern engineering systems, various noises, unstable working environment and aging components cause strong uncertainty, and the model-based fault diagnosis method relying on accurate system model encounters bottlenecks, on the contrary, the data-driven method is gradually widely used.

[0003] Data-driven fault diagnosis: using machine learning, statistical analysis, signal analysis and other methods to analyze and process a large amount of offline data and online data, find out fault features, determine fault causes, locations and times. The common fault diagnosis technology currently uses linear models to perform fault diagnosis using statistical information between input and output data. However, due to its linear structure, its performance is limited.

[0004] The non-linear activation unit feature makes the fault diagnosis technology based on deep neural network widely used to consider the non-linearity in the behavior fault system. However, the existing fault diagnosis technology based on deep neural network uses back propagation for training, and the storage of network activation of back propagation will cause the memory requirement to increase with the number of units, which has considerable demand for memory and high training cost.

[0005] Therefore, a closed-loop system fault diagnosis method with low memory cost and high precision is continuously designed. SUMMARY

[0006] The purpose of the present application is to overcome the defects of the prior art and provide a closed-loop system fault diagnosis method and system based on reversible left invariant manifold with low memory cost and high fault diagnosis precision.

[0007] The purpose of the present application can be achieved by the following technical solutions:

[0008] According to a first aspect of the present application, a closed-loop system fault diagnosis method based on reversible left invariant manifold is provided, which comprises the following steps:

[0009] Step 1: constructing a reversible left invariant manifold according to a reversible neural network, and parameterizing a non-linear closed-loop system;

[0010] Step 2, constructing a reversible residual generator of the nonlinear closed-loop control system according to the reversible neural network;

[0011] Step 3, obtaining online data of the nonlinear closed-loop system, and performing online fault diagnosis based on a test statistic of the residual generator and a set diagnostic threshold.

[0012] Preferably, the step 1 comprises the following sub-steps:

[0013] Step 1.1, defining a nonlinear closed-loop control system {G d,f ,K} whose state space equation and control equation are respectively:

[0014]

[0015] u(k+1)=Ky(k) (2)

[0016] wherein: x(k) is the system state; y d,f (k) is the output signal; and represents a nonlinear mapping containing structural faults; u(k) is the input signal; d(k) is the noise signal; f(k) is the sensor brake fault signal; k represents the time; K is the controller;

[0017] Step 1.2, constructing a reversible left invariant based fault diagnosis framework according to the reversible neural network; wherein the reversible neural network is a reversible neural network with master-slave objective functions, and the signals satisfy a strict reversible relationship in the original space and the left invariant;

[0018] Step 1.3, after parameterizing the nonlinear closed-loop control system, obtaining:

[0019] G d,f :U→Y·D·F,f∈F (3)

[0020] wherein U and Y correspond to the signal spaces of the input u and the output y respectively, and D and F correspond to the signal spaces of the noise signal d and the sensor brake fault signal f respectively.

[0021] Preferably, the step 1.2 is specifically:

[0022] Constructing a reversible neural network H(θ,·) to generate a projection P t , obtaining a reversible left invariant based fault diagnosis framework:

[0023]

[0024] wherein the projection P t is a reversible function, including an observer P mo for generating a residual signal r and a calibration operator Pso , the expression is:

[0025]

[0026] where P t is a bijective function, P mo , P so are invertible functions, P1 is a continuous mapping, and P2 is a linear invertible operator constructed by a neural network.

[0027] Preferably, the constructed invertible neural network H(θ,·) generates a projection P t , and the residual generator of G d contained therein is

[0028]

[0029]

[0030] where m l (k) is the input-output matrix of a nonlinear closed-loop system, q(k) is a reference signal; θ * is the optimal parameter of the invertible neural network, and θ * = argmin L t = λL1+L2, L1 and L2 are the primary and secondary objective functions of the invertible neural network, corresponding to the observer P mo and the calibration operator P so , respectively.

[0031] Preferably, the primary and secondary objective functions L1 and L2 of the invertible neural network satisfy:

[0032]

[0033] where n is the number of training samples; q is regarded as a normalized residual signal r, which is subject to a Gaussian distribution and satisfies q ~ N(0, I).

[0034] Preferably, the input-output matrix of the nonlinear closed-loop system uses a delay operator to expand the input-output range of the nonlinear closed-loop system.

[0035] Preferably, the linear invertible operator P2 constructed by the neural network has the specific expression:

[0036] P2(r):=W T r-b ~ N(0, I), P2:=(W T , b) (9)

[0037] where W and b are the weights and biases of the neural network, respectively, and r is the residual signal.

[0038] Preferably, the test statistic of the residual generator in step 3 is T 2 statistic, including T 2 of r(k) 2 , the diagnostic threshold set The expression is:

[0039]

[0040] In the formula, χ 2 is a chi-square distribution, represents the defined significance level, which is mathematically equivalent to the acceptable false positive rate.

[0041] Preferably, online fault diagnosis is performed in step 3, specifically:

[0042]

[0043] Or

[0044]

[0045] According to the second aspect of the present application, a closed-loop system fault diagnosis system based on reversible left manifold is provided, which adopts the above method to perform closed-loop system fault diagnosis, and the system comprises:

[0046] A nonlinear closed-loop system parameterization module is configured to construct a reversible left manifold according to a reversible neural network, and parameterize a nonlinear closed-loop system.

[0047] A reversible residual generator construction module is configured to construct a reversible residual generator of a nonlinear closed-loop control system according to a reversible neural network.

[0048] A fault diagnosis module is configured to acquire online data of the nonlinear closed-loop system, and perform online fault diagnosis based on a test statistic of the residual generator and a diagnostic threshold set.

[0049] Compared with the prior art, the present application has the following advantages:

[0050] 1) The present application parameterizes a nonlinear closed-loop system according to a reversible left manifold, realizes lossless identification of the closed-loop system, and can ensure the explainability of the entire design and learning process according to control theory guidance.

[0051] 2) The reversible neural network adopted in the present application takes into account the low memory cost and high precision fault diagnosis requirements, and the master-slave objective function setting effectively avoids the overfitting problem in fault diagnosis training and learning, thereby improving the accuracy of fault diagnosis.

[0052] 3) The delay operator adopted in the present application expands the input-output range of the nonlinear closed-loop system, thereby improving the accuracy of fault diagnosis.

[0053] 4) Using system characteristic signals to define the corresponding statistical quantities and set reasonable thresholds, the accuracy of fault diagnosis is improved. BRIEF DESCRIPTION OF DRAWINGS

[0054] Figure 1 is a flow chart of the method of the present application;

[0055] Figure 2 is a schematic diagram of the framework for parameter identification and fault diagnosis using reversible left-invariant manifold;

[0056] Figure 3 is a schematic diagram of two reversible manifold structures;

[0057] Figure 4 is an observer static model based on delay operator;

[0058] Figure 5 is a DC motor in two control loops;

[0059] Figure 6 is the training result using the neural network-based nonlinear least squares method;

[0060] Figure 7 is the training result obtained using the proposed reversible left-invariant manifold-based method;

[0061] Figure 8 is the dynamic data of the online system;

[0062] Figure 9 is the training result using the neural network-based nonlinear least squares method;

[0063] Figure 10 is the training result obtained using the reversible left-invariant manifold-based method of the present application. DETAILED DESCRIPTION

[0064] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor should fall within the scope of protection of the present application.

[0065] Embodiment 1

[0066] This embodiment gives a closed-loop system fault diagnosis method based on reversible left-invariant manifold, which comprises the following steps:

[0067] Step S1: processing of system model architecture

[0068] Step S1.1: Description of the feedback system and explanation of the kernel representation

[0069] Define the feedback system and the kernel representation;

[0070] Define the nonlinear closed-loop system G with input and output k denotes the time instant, its state-space equation is given by:

[0071]

[0072] where is the unknown system state, and a and b are two nonlinear maps;

[0073] The nonlinear closed-loop system G is equipped with a controller K satisfying:

[0074] u(k+1) = Ky(k) (2)

[0075] For the nonlinear closed-loop system G in faulty condition, determine a fault diagnosis framework based on the invertible left invariant manifold.

[0076] Given the initial condition x(0) = X, equations (1) and (2) are expressed as:

[0077] G: U → Y, K: Y → U (3)

[0078] where U and Y correspond to the signal spaces of u and y, respectively, and the complex map is introduced using the cross-product space:

[0079]

[0080] Define the signal space subset S:

[0081]

[0082] where the superscripts s and us denote the stable and unstable parts, respectively.

[0083] Stable kernel representation: stable part S with superscript s s , which is usually formed by defining a norm on the signal vector, typically representing signals in finite norm. In this invention, the stable kernel representation is used to calculate the residual.

[0084] Kernel representation for the feedback system and Parameterize the nonlinear observer:

[0085]

[0086]

[0087] where the internal signal zG ∈Z G and z K ∈Z K not necessarily equal to 0, Z G and Z K denotes the kernel space defined by the input-output pair.

[0088] and When the following conditions are met, the stable kernel representation is established:

[0089]

[0090] Thus, the projection relationship is:

[0091]

[0092] The coprimality of satisfies:

[0093]

[0094] where the right inverse mapping relationship is:

[0095] Since the coprimality of stable kernel representation is a necessary condition for the well-posedness of feedback systems, it is assumed that all stable kernel representations are coprime.

[0096] In the feedback system, it is not necessary to specifically divide u and y through the input and output of the system, so two manifolds can be developed for system modeling and fault diagnosis.

[0097] If there exists a stable operator then for all x0∈X and u∈U s , the stable kernel representation can be well defined:

[0098]

[0099] The well-defined representation means the existence of the inverse function , that is:

[0100]

[0101] It can be said that and are homeomorphic, and the reversible left manifold in the study is obtained through homeomorphic projection.

[0102] Step S1.2: Expression of system problem;

[0103] Since the feedback system will be affected by two random noise correlation terms independent of the input and output under actual working conditions, the nonlinear closed-loop system G will change:

[0104] G d :U→Y·D,G d (u)=y+d=y d (12)

[0105] It is known that the signal-to-noise ratio of the feedback system {G, K} is high, that is, the power of the input u and the output y is higher than the noise d, and although d is unknown, it can be assumed that d ~ N(μ,∑), where the variables are unknown.

[0106] In order to diagnose the target system, the stable kernel representation needs to be reliably identified, which is set to and on this basis, the residual r is generated, that is:

[0107]

[0108] Under ideal conditions is equivalent to that is, when there is no fault, the feedback system exists r = z G , but the limitations of learning samples in the actual process lead to approximation errors and estimation errors in modeling, resulting in r→z G . In addition, because z G and d in the time domain only represent random effects, z G ~ N(μ,∑) does not lose generality.

[0109] Based on the above, the master optimization target and the slave optimization target can be defined as:

[0110]

[0111] r→N(μ,∑) (14b)

[0112] The difficulty of the problem lies in how to optimize the dependent target when the unknown μ and∑ exist. Due to overfitting, the extreme pursuit of optimizing the master target will bring error guidance to parameter identification and fault diagnosis.

[0113] Step S2: Design process of the diagnosis method

[0114] Step S2.1: Determine the state space model and the loss function;

[0115] Process the target system, and the state space equation of the target system with fault influence is:

[0116]

[0117] where, and represents the structural failure, f(k) represents the sensor brake failure, and the feedback system is represented as {G d ,K}. Its parametric representation can be obtained as:

[0118] G d,f :U→Y·D·F,f∈F (16)

[0119] The parameter identification framework for estimating the stable kernel representation is described by the following content, and an interpretable fault diagnosis framework for the target system is proposed, and the overall framework is endowed with interpretability.

[0120] An interpretable fault detection framework is proposed based on the target system, and the framework structure is shown in Figure 2 , and the interpretable principle with theoretical support is associated with the framework.

[0121] The total loss function in the proposed framework can be defined as:

[0122] L t =λL1+L2 (17)

[0123] where L1, L2 have

[0124]

[0125] Step S2.2: Description of the interpretable module and reversible implementation;

[0126] The projection P represents the projection generated in the machine learning method, and according to Figure 2 , it can be seen that P t is a bijective function, which ensures that the residual signal r passes through the reversible left manifold, and solves the master-slave target at the same time; P mo is reversible, and the loss function is defined by L1, which mainly corresponds to the master target; P so is also reversible, and the loss function is defined by L2, which mainly corresponds to the slave target; the reference signal of q is subject to a Gaussian distribution, where q~N(0, I).

[0127] From the system level, the structure of P t is the same as the feedback system, and the internal P mo is used to design the residual generator, and P so is used to evaluate the available information inside U s ×Y s ·D, and verify the rationality of the residual generator.

[0128] According to the collected stable training data, P mo and its inverse can be obtained:

[0129] P mo :U s ×Y s ·D→U s ×R s (19a)

[0130]

[0131] where D represents the relevant noise.

[0132] P mo contains the kernel representation that needs to be learned has:

[0133]

[0134] Since P t is a left multiplication operation, there exists:

[0135]

[0136]

[0137] Therefore, U s ×Y s ·D and U s ×Q must be reversible topological spaces or manifolds, and P t is a homeomorphism between the two topological spaces, that is, a continuous inverse function. For this purpose, the loss function and functional modules are explained.

[0138] Figure 2 The basic configuration of the fault diagnosis architecture using P t is described. It consists of two functional modules, the observer P mo that can generate the original residual signal r, and the calibration operator P so to try to remove the noise-related quantities, so that r = z G . Here, we will emphasize that the above two functional modules are basic components. Since G d is a nonlinear dynamic system, other functional modules need to be integrated into P t , especially for purely data-driven fault diagnosis algorithms.

[0139] P mo , P so and P t are analyzed respectively. P mo is the basis for the explainability of the proposed fault diagnosis architecture based on left manifold, and P mo generates the mapping relationship for determining its reversible structure:

[0140]

[0141] From the previous derivation, it can be verified that

[0142] Since P mo is an observer-based implementation of the residual generator in the nonlinear form, its observer and residual generator can be expressed as

[0143]

[0144] Therefore, in combination with equation (13), the stable kernel representation identifies the result which explicitly corresponds to

[0145] Next, the confirmation of P so is performed. Since minimizing the loss function L1 will lead to

[0146]

[0147] If P1 has a higher nonlinear complexity than G, the overfitting problem will occur because P1 obtains an excessively small empirical error, i.e., has learned the noise information. It is obvious that r→0 is not a reliable learning goal. This challenge is largely due to the unknown mean and variance, which motivates the introduction of P so and the loss function L2 in Figure 2 .

[0148] As shown in Figure 2 , P so is represented by P2. Since the linear transformation of a Gaussian variable is also a property of the Gaussian distribution, P2 constructed by a neural network can normalize r by choosing a linear activation function such that

[0149] P2(r):=W T r-b ~ N(0, I), P2:=(W T , b) (25)

[0150] However, if P mo is not well trained, the difference between P2(r) and N(0, 1) will lead to an increase in the L2 loss. Since P2 is chosen as a linear operator in this study, its derivative with respect to W and b is always present. Therefore, P so is also invertible. In addition, it is worth emphasizing that the introduction of the invertible P so can make a big difference. Of course, there are many ways to optimize P so , which are not listed here.

[0151] Consider the internal stable feedback system {G dK}. Given the system input u, if P1 is a continuous mapping, P2 is a reversible operator, P t is a homeomorphism between U s x Y s · D and U s x Q.

[0152] It is known that P t is a bijection, and P t and P t -1 are continuous, and

[0153]

[0154] Since P2 is invertible, P mo is a homeomorphism, so it is known that P t is a homeomorphism.

[0155] In summary, by Figure 3 two manifolds with the same topological structure are depicted, where the bottom one (i.e., the reversible left manifold) can be directly used for fault diagnosis. According to any given u0, define Then, using two coordinate maps, the Figure 3 , i.e.,

[0156] P t : Y0|u0→ Q0|u0, P t -1 : Q0|u0→ Y0|u0 (27)

[0157] The results show that the proposed scheme can eliminate the dynamics caused by u, so that the changes in y d caused by d can be estimated and evaluated. Mathematically, the conditional entropy can be used to quantify the information level of the two manifolds in Figure 3

[0158] It is known that det(P mo ) = 1, and according to other optimization methods of P2, it is known that

[0159]

[0160] In addition, for the trained P t , (28) can be divided into the following two parts:

[0161] H(y d |u) = H(d) = H(r|u) = H(r) (28a)

[0162] H(q|u) = H(q) = H(r) + log |det P so |. (28b) ​

[0163] where log |det P so | is the final entropy.

[0164] In the proposed solution based on reversible left-invariant, both r and q can be applied to the fault diagnosis task, where r has the same uncertainty as d, and based on r the best fault diagnosis performance can be achieved. Because the reversible P so plays a role of normalization, the final entropy | can be calculated as a constant. Therefore, q is considered as a normalized r, which also provides the fault diagnosis power.

[0165] Step S2.3: Data processing and residual operation;

[0166] Although the system state x(k) is unknown, it can be estimated from past and current data, i.e.,

[0167]

[0168] where P est is m l the projection on the space x, the mixed data matrix m l is defined as:

[0169]

[0170] In the equation, about u l (k) and y l-1 (k-1) equation can be extended by using multiple delay operators.

[0171] It is known that a dynamic system can be simplified as a static model, which can be mathematically explained as:

[0172]

[0173] The composite operation β is:

[0174]

[0175] Using external delay operators allows the residual generator of {G, K} to be constructed by a static model, i.e.

[0176]

[0177] The specific structure is shown in Figure 4 With the help of delay operators, the difference dynamics between the reference signal λ(k) and u(k) and y(k) can be eliminated, and the observer based on the static model can be realized.

[0178] Step S3, fault diagnosis

[0179] Step S3.1: determination of threshold and calculation of objective function;

[0180] The projection P is generated by the constructed invertible neural network H(θ,·) t , and its residual generator G d is:

[0181]

[0182]

[0183] where θ * is the optimal parameter, and θ * = argminL t = λL1+L2, the loss function is defined as:

[0184]

[0185] where n is the number of training samples.

[0186] For offline training, there are

[0187]

[0188] For well-trained H(θ * ,·), the residual generator G is independent of r.

[0189] According to the two test statistics, the unified threshold can be set as:

[0190]

[0191] where represents the user-defined significance level, which is mathematically equal to the acceptable false positive rate.

[0192] According to the online data in the actual process, the online input and output are extracted, and online q and r are obtained. Since P so is invertible, the two T 2 statistics about the residual generator are equivalent:

[0193] 1) T 2 of r(k):

[0194]

[0195] where χ 2 is the chi-square distribution, and

[0196] 2) T 2 of q(k):

[0197] T 2 (k)=q T (k)q(k)~χ 2 (k y ) (40)

[0198] where q ~ N(0, I).

[0199] Step S3.2: Processing of online data and implementation of fault diagnosis;

[0200] Online fault detection is obtained for the previous offline threshold calculation:

[0201]

[0202] or

[0203]

[0204] Faults can also be directly identified by online q and r if necessary.

[0205] Since faults will cause bias f rel i.e.

[0206]

[0207] where f is also independent of d, thus

[0208] ||r f ||=||r||+||f rel || (44)

[0209] The above relationship can be used to find the optimal fault diagnosis performance of the proposed solution based on reversible left-invariant manifold.

[0210] Specifically, since P so causes the following impact:

[0211]

[0212] Combining (26) and (33) gives:

[0213]

[0214] where subscript i represents the i-th element, and the last equation applies to mutually independent noise.

[0215] In summary, it can be shown that the proposed solution based on reversible left-invariant manifold has the optimal fault diagnosis power, because for a given f of the feedback system, there exists:

[0216]

[0217] Considering a DC motor located in two closed loops, its feedback structure is as shown in the left side of Figure 5 The left side shows that U is a subunit. Figure 6 The training results of the neural network-based nonlinear least squares method are obviously over-fitted. Figure 7 The method can effectively alleviate over-fitting. Considering the dynamic data of the online system Figure 8 , the effects of the two methods can be compared by Figure 9 , Figure 10 .

[0218] Next, a system embodiment of the present application is given, a closed-loop system fault diagnosis system based on reversible left manifold, which adopts the above method for closed-loop system fault diagnosis, the system comprises:

[0219] A nonlinear closed-loop system parameterization module is used to construct a reversible left manifold according to a reversible neural network, and parameterize a nonlinear closed-loop system.

[0220] A reversible residual generator construction module is used to construct a reversible residual generator of a nonlinear closed-loop control system according to a reversible neural network.

[0221] A fault diagnosis module is used to acquire online data of a nonlinear closed-loop system, and perform online fault diagnosis based on a residual generator test statistic and a set diagnosis threshold.

[0222] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto, any skilled person in the art can easily think of various equivalent modifications or replacements within the technical range disclosed by the present application, and these modifications or replacements should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for diagnosing faults in a closed-loop system based on reversible left- invariant manifold, characterized in that, The method comprises the following steps: Step 1, constructing a reversible left manifold according to a reversible neural network, and parameterizing a nonlinear closed-loop system; Step 2, constructing a reversible residual generator of the nonlinear closed-loop control system according to the reversible neural network; Step 3, obtaining online data of the nonlinear closed-loop system, and performing online fault diagnosis based on a test statistic of the residual generator and a set diagnostic threshold; The step 1 comprises the following sub-steps: Step 1.1, Defining a Nonlinear Closed-Loop Control System whose state-space and control equations are respectively (1) (2) wherein: is the system state; is the output signal; and denotes a nonlinear mapping with structural faults; is the input signal; is the output; is the noise signal; is the sensor-brake fault signal; denotes the time instant; is the controller; Step 1.2, constructing a fault diagnosis framework based on the reversible left manifold according to the reversible neural network; wherein the reversible neural network is a reversible neural network with master-slave objective functions, and signals satisfy a strict reversible relationship on an original space and the left manifold; Step 1.3, after parameterizing the nonlinear closed-loop control system, obtaining: (3) wherein and correspond to the signal spaces of the input and output signals, respectively, correspond to the signal spaces of the noise signal and the sensor brake fault signal , respectively.

2. The method according to claim 1, wherein, The step 1.2 is specifically: Constructing invertible neural networks Generating projections A fault diagnosis framework based on invertible left invariant manifolds is obtained: Let bijective function For the forward mapping, consider it as a left multiplication operation, obtaining its associated definition: (4) wherein the residual signal is considered normalized , obeys a Gaussian distribution, satisfying ; is an invertible function, comprising an observer and a calibration operator for generating the residual signal , expressed as: (5) wherein , are both invertible functions, is a continuous mapping, is a linear invertible operator constructed from a neural network.

3. The method according to claim 2, wherein, The constructed reversible neural network Generating projections , and its inclusion The residual generator is (6) (7) wherein, is an input-output matrix of the nonlinear closed-loop system, is a reference signal; is an optimal parameter of the invertible neural network, and , , is a master and a slave objective function of the invertible neural network, respectively corresponding to the observer and the calibration operator .

4. The method according to claim 3, wherein, The master objective function and the slave objective function of the reversible neural network , , satisfy: (8) wherein, is the number of training samples.

5. The method according to claim 3, wherein, The input and output matrix of the nonlinear closed-loop system is expanded by using a delay operator to expand the input and output range of the nonlinear closed-loop system.

6. The method of claim 2, wherein, Linearly reversible operators constructed from neural networks The specific expression is: (9) wherein, are weights and biases of the neural network, respectively, is a residual signal.

7. The method according to claim 4, wherein, The test statistic of the residual generator in step 3 is the residual generator's statistic, including the , and the diagnostic threshold set is given by the expression: (10) wherein is a chi-square distribution, denotes the defined significance level, which is mathematically equivalent to the acceptable false discovery rate.

8. The method according to claim 7, wherein, In the step 3, the online fault diagnosis is specifically: (11) Or (12)。 9. A closed loop system fault diagnosis system based on reversible left- manifold, characterized in that, The method of claim 1 is used for closed-loop system fault diagnosis, and the system comprises: a nonlinear closed-loop system parameterization module, configured to construct a reversible left manifold according to a reversible neural network, and parameterize a nonlinear closed-loop system; a reversible residual generator construction module, configured to construct a reversible residual generator of the nonlinear closed-loop control system according to the reversible neural network; a fault diagnosis module, configured to obtain online data of the nonlinear closed-loop system, and perform online fault diagnosis based on a test statistic of the residual generator and a set diagnostic threshold.

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