A fault diagnosis method based on negative diagonal dominant neural observer

Abstract

The application relates to a fault diagnosis method based on a negative diagonal dominant neural observer, which comprises the following steps: constructing a real-time comprehensive feature vector of to-be-diagnosed data of a current moment of a nonlinear system including a continuous stirred tank reactor, inputting the real-time comprehensive feature vector into a trained negative diagonal dominant neural observer, and outputting a system state estimation value of a next moment; calculating a residual error vector based on the system state estimation value of the next moment and a real measurement output, and calculating T 2 statistical quantity; determining a fault diagnosis result based on the T 2 statistical quantity and a threshold value, effectively solving the problems that the existing method cannot consider the data-driven adaptability and theoretical stability, the fault diagnosis accuracy is not high when facing complex dynamics, and the safety is questionable, and the method can realize effective detection of faults of the continuous stirred tank reactor.

Description

Technical Field

[0001] This application relates to the field of nonlinear system fault diagnosis technology, and in particular to a fault diagnosis method based on a negative diagonally dominant neural observer. Background Technology

[0002] In modern industrial production, fault diagnosis of nonlinear systems is a core element in ensuring production continuity, equipment reliability, and personnel safety. As critical equipment for industrial production and safety assurance, the accuracy and reliability of fault diagnosis for nonlinear systems directly impact production efficiency, equipment lifespan, and maintenance costs, playing a significant role in promoting intelligent industrial transformation. Particularly in fields such as chemical engineering and electrical engineering, latent faults in core equipment (such as bearing wear, winding short circuits, and fluid leaks) are difficult to detect promptly using traditional monitoring methods, necessitating the reliance on efficient fault diagnosis technologies for early detection and isolation.

[0003] Fault diagnosis technology, as a core support for intelligent industrial operation and maintenance, identifies and locates abnormal equipment states by mining fault characteristics from system operation data. Among these technologies, observer technology, capable of estimating unmeasurable internal states of the system in real time and generating residual signals reflecting fault deviations, has become the mainstream method for fault diagnosis of nonlinear systems. In recent years, neural observers incorporating deep learning capabilities have significantly improved the representation of complex nonlinear features, providing a new path for handling unmodeled dynamics and uncertainties. However, nonlinear system data typically possesses complex characteristics such as strong coupling, time-varying nature, nonlinearity, and uncertainty, containing rich dynamic evolution information. Existing neural observer designs often focus on data fitting, failing to effectively integrate the advantages of physical constraints and data-driven approaches. This results in a lack of rigorous theoretical stability guarantees in the observation process and insufficient physical interpretability of diagnostic results, making it difficult to meet the stringent reliability requirements of safety-critical industrial scenarios. Summary of the Invention

[0004] Therefore, it is necessary to provide a fault diagnosis method based on a negative diagonally dominant neural observer, including: S1: Obtain diagnostic data for the current moment of the nonlinear system including the continuous stirred tank reactor, wherein the diagnostic data includes the inlet reactant concentration, inlet material temperature, and inlet coolant temperature of the continuous stirred tank reactor; S2: Construct a real-time comprehensive feature vector of the data to be diagnosed, and input the real-time comprehensive feature vector into the trained negative diagonal dominant neural observer to output the system state estimate for the next time step; the negative diagonal dominant neural observer is an equation that includes a negative diagonal dominance constraint based on the Gershgorin disk theorem to compensate for the gain of the output of the fully connected neural network; the system state estimate for the next time step includes the estimated inlet reactant concentration, inlet material temperature, reactant concentration in the reactor, reactor temperature, coolant flow rate, inlet coolant temperature, and cooling jacket temperature of the continuous stirred tank reactor at the next time step; S3: Calculate the residual vector based on the estimated system state at the next time moment and the actual measurement output, and calculate T based on the residual vector. 2 Statistic; S4: Based on the T 2 Statistics and thresholds determine the fault diagnosis results.

[0005] Preferably, the construction of the real-time comprehensive feature vector of the data to be diagnosed includes: Get the current timestamp; Obtain the current real system state value and the current real measurement output, and transpose the current real system state value and the current real measurement output respectively; Obtain the system state estimate of the current time predicted in the previous time step, and transpose the system state estimate of the current time step; Transpose the data to be diagnosed at the current moment; The current time stamp, the transposed real system state value, the real measurement output, the system state estimate, and the data to be diagnosed are combined to form the feature vector of the current time. The feature vector at the current moment is transposed to obtain the real-time integrated feature vector.

[0006] The preferred construction process of the negative diagonally dominant neural observer includes: A fully connected neural network is constructed, which is used to map the current data to be diagnosed and the actual system state value to the preliminary estimate of the system state at the next moment. The Jacobian matrix of the mapping process is calculated in real time using automatic differentiation; Substituting the Jacobian matrix into the Lyapunov matrix yields the stability matrix; Based on Gershgorin's disk theorem, a negative diagonal dominance constraint is constructed for the stability matrix. The negative diagonal dominance constraint includes the following: all system eigenvalues ​​on the main diagonal of the stability matrix are negative, and the absolute value of any system eigenvalue on the main diagonal is greater than the sum of the absolute values ​​of all system eigenvalues ​​off the main diagonal. The observer gain matrix is ​​obtained by solving the gain matrix in the negative diagonal dominance constraint and the Schur complement Lyapunov matrix. The system state at the next time step is initially estimated based on the observer gain matrix to compensate for the loss of the negative diagonal dominant neural observer.

[0007] Preferably, the formula for calculating the stability matrix is: ; ; in, Represents the stability matrix. Describes a positive definite matrix. Represents the Jacobian matrix. Represents the gain matrix. Represents the system output matrix. Indicates transpose. This represents a fully connected neural network. This represents the actual system state value at time k. This represents the data to be diagnosed at time k. This represents the gradient operator.

[0008] Preferably, the step of solving for the gain matrix in the Lyapunov matrix based on the negative diagonal dominance constraint and the Schur complement includes: The stability matrix is ​​structured into system intrinsic terms and gain influence terms based on the system output matrix and positive definite matrix; the system intrinsic terms are denoted as... The gain effect term is denoted as ; The gain matrix and positive definite matrix are divided into observable and unobservable parts; For the observable part, a diagonal matrix satisfying the negative diagonal dominance constraint is constructed based on each element in the system's intrinsic terms; For the unobservable part, the inverse relation is established through Schur complement. and Decoupling the unobservable components yields the observer gain matrix; where Schur complement The inverse matrix, Represents a diagonal matrix. Represents the observer gain matrix The block matrix corresponding to the observable part. Represents the system output matrix reversible blocks The inverse matrix, Represents the observer gain matrix The block matrix corresponding to the unobservable part. Represents a positive definite matrix The bottom right sub-block after partitioning The inverse matrix, Represents a positive definite matrix The bottom left sub-block after partitioning.

[0009] Preferably, constructing a diagonal matrix satisfying the negative diagonal dominance constraint based on the elements in the system's inherent terms includes: Based on the negative diagonal dominance constraint and the main diagonal and off-diagonal elements in the system's intrinsic terms, a criterion for the values ​​of each element on the main diagonal of the diagonal matrix is ​​constructed, which is expressed as: ; in, This represents the value of the element in the i-th row / column on the main diagonal of a diagonal matrix. This represents the value of the element in the i-th row and i-th column of the system's intrinsic item. For positive integers, This represents the value of the element in the i-th row and j-th column of the system's intrinsic item. This represents the max function. Represents absolute value; Based on the value selection criteria, values ​​are selected for each element on the main diagonal of the diagonal matrix to construct the diagonal matrix.

[0010] The preferred expression for the negative diagonally dominant neural observer is: ; in, This represents the system state estimate output at time k+1. This represents a fully connected neural network. This represents the actual system state value at time k. This represents the system state estimate output at time k. This represents the data to be diagnosed at time k. This represents the observer gain matrix at time k. This represents the actual measurement output at time k. This represents the system output matrix.

[0011] Preferably, the step of calculating the residual vector based on the estimated system state value at the next time moment and the actual measurement output includes: ; in, This represents the residual vector at time k+1. This represents the actual measurement output at time k+1. Represents the system output matrix. This represents the system state estimate output at time k+1.

[0012] Preferably, the step of calculating T based on the residual vector 2 Statistics, including: ; in, T represents the time at time k+1. 2 Statistic, This represents the residual vector at time k+1. Indicates transpose. This represents the inverse of the covariance matrix.

[0013] Preferably, the one based on the T 2 Statistics and thresholds determine the fault diagnosis results, including: Using kernel density estimation to fit T 2 The historical distribution of the statistics is used to select the fault diagnosis threshold from the historical distribution based on the preset quantiles; When the T 2 When the statistic is less than or equal to the fault diagnosis threshold, the nonlinear system is determined to be fault-free. When the T 2 If the statistical value is greater than the fault diagnosis threshold, the nonlinear system is determined to be faulty and an alarm is issued.

[0014] Beneficial effects: This method constructs a real-time comprehensive feature vector of the current-moment data of the nonlinear system including a continuous stirred tank reactor, and inputs the real-time comprehensive feature vector into a trained negative diagonally dominant neural observer to output the system state estimate for the next moment; based on the system state estimate for the next moment and the actual measurement output, a residual vector is calculated, and T is calculated based on the residual vector. 2 Statistics; based on the T 2 The use of statistics and thresholds to determine fault diagnosis results effectively solves the problems of low accuracy and questionable safety in fault diagnosis when facing complex dynamics, which are caused by the inability of existing methods to balance the adaptability of data-driven approaches with theoretical stability. This enables effective detection of faults in continuous stirred tank reactors. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a flowchart of a fault diagnosis method based on a negative diagonally dominant neural observer in an embodiment of this application.

[0017] Figure 2 This is a framework diagram of the fault diagnosis method based on the negative diagonally dominant neural observer in the embodiments of this application.

[0018] Figure 3 This is a process diagram of hydrocracking based on a continuous stirred tank reactor in the embodiments of this application.

[0019] Figure 4 This is a schematic diagram of the fault diagnosis results in the embodiments of this application. Detailed Implementation

[0020] To make the above-mentioned objectives, features, and advantages of this application more apparent and understandable, the specific embodiments of this application are described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of this application. However, this application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0021] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0022] Fault diagnosis of nonlinear systems is indispensable in safety-critical fields such as chemical engineering, power, and autonomous driving. However, the strong nonlinearity, time-varying parameters, and multiple operating conditions of modern industrial systems make traditional diagnostic methods difficult to adapt. Existing model-based methods rely on accurate system models, which are prone to performance degradation in complex scenarios due to unmodeled dynamics and uncertainties. Pure data-driven methods, while not requiring physical models, lack theoretical guarantees of stability and interpretability, failing to meet reliability certification requirements. Hybrid methods also fail to address core issues such as stability guarantees under uncertain conditions and adaptive mechanisms for time-varying systems, and traditional observers struggle to balance stability and fault sensitivity.

[0023] To address the aforementioned technical challenges, this application proposes a diagonal dominance gain observer framework that integrates deep learning and matrix diagonal dominance theory. This framework overcomes the technical bottleneck through a hybrid design combining "model basis constraints + data-driven optimization." First, the nonlinear system is linearized, and a state-space model incorporating faults and disturbances is established, deriving the error dynamics equations. Then, based on Gershgorin's theorem, the observer gain design is transformed into a constraint optimization problem, ensuring the exponential stability of the error system through strict diagonal dominance conditions. Subsequently, a deep neural network with residual connections is used to learn the optimal gain that satisfies the constraints, trained as a recurrent neural network with multi-dimensional system operational information as input. Finally, a closed-loop observer structure is constructed to adaptively adjust the gain in real time and monitor stability. Combined with residual signals and statistical tests, accurate fault detection and isolation are achieved. The core advantage of this scheme lies in retaining the powerful representational ability of deep learning for complex nonlinear relationships, enabling adaptive handling of unmodeled dynamics and uncertainties, while providing rigorous theoretical guarantees through matrix diagonal dominance constraints and Lyapunov stability analysis, thus achieving a dynamic balance between stability and fault sensitivity. Its core objective is to address the problems of existing methods such as "lack of guaranteed stability, poor adaptability to complex scenarios, and insufficient diagnostic accuracy," and to provide a fault diagnosis solution that combines reliability, adaptability, and accuracy for safety-critical fields, possessing clear practical value and broad prospects for promotion.

[0024] like Figure 1 , Figure 2 As shown, this embodiment provides a fault diagnosis method based on a negative diagonally dominant neural observer, including: S1: Obtain diagnostic data for the current moment of the nonlinear system including the continuous stirred tank reactor, wherein the diagnostic data includes the inlet reactant concentration, inlet material temperature, and inlet coolant temperature of the continuous stirred tank reactor.

[0025] S2: Construct a real-time comprehensive feature vector of the data to be diagnosed, and input the real-time comprehensive feature vector into the trained negative diagonal dominant neural observer to output the system state estimate for the next time step; the negative diagonal dominant neural observer is an equation that includes a negative diagonal dominant constraint based on the Gershgorin disk theorem to compensate for the gain of the output of the fully connected neural network; the system state estimate for the next time step includes the estimated inlet reactant concentration, inlet material temperature, reactant concentration in the reactor, reactor temperature, coolant flow rate, inlet coolant temperature, and cooling jacket temperature of the continuous stirred tank reactor at the next time step.

[0026] In some optional embodiments, constructing the real-time comprehensive feature vector of the data to be diagnosed includes: Get the current timestamp; Obtain the current real system state value and the current real measurement output, and transpose the current real system state value and the current real measurement output respectively; Obtain the system state estimate of the current time predicted in the previous time step, and transpose the system state estimate of the current time step; The diagnostic data at the current moment Transpose; The current timestamp and the actual system state value after transposition at the current moment. Actual measurement output System state estimates With the data set to be diagnosed Synthesize the feature vector at the current moment; The feature vector at the current moment is transposed to obtain the real-time integrated feature vector, denoted as . This is to comprehensively characterize real-time operating conditions.

[0027] It is worth noting that the construction process of the negative diagonally dominant neural observer includes: A fully connected neural network is constructed, which is used to map the current data to be diagnosed and the actual system state value to the preliminary estimate of the system state at the next moment. The Jacobian matrix of the mapping process is calculated in real time using automatic differentiation; Substituting the Jacobian matrix into the Lyapunov matrix, we obtain the stability matrix; the formula for calculating the stability matrix is: ; ; in, Represents the stability matrix. Describes a positive definite matrix. Represents the Jacobian matrix. Represents the gain matrix. Represents the system output matrix. Indicates transpose. This represents a fully connected neural network. This represents the actual system state value at time k. This represents the data to be diagnosed at time k. Represents the gradient operator; Based on Gershgorin's disk theorem, a negative diagonal dominance constraint is constructed for the stability matrix. This constraint includes ensuring that all system eigenvalues ​​located on the main diagonal of the stability matrix are negative. ), and the absolute value of any system eigenvalue on the main diagonal is greater than the sum of the absolute values ​​of all system eigenvalues ​​off the main diagonal. ); The observer gain matrix is ​​obtained by solving the gain matrix in the negative diagonal dominance constraint and the Schur complement Lyapunov matrix. Based on the observer gain matrix, the preliminary estimate of the system state at the next time step is compensated to construct a negative diagonally dominant neural observer. The expression for the negative diagonally dominant neural observer is as follows: ; in, This represents the system state estimate output at time k+1. This represents a fully connected neural network. This represents the actual system state value at time k. This represents the system state estimate output at time k. This represents the data to be diagnosed at time k. This represents the observer gain matrix at time k. This represents the actual measurement output at time k. This represents the system output matrix.

[0028] It is worth noting that, based on the Gershgorin disk theorem analysis of the feasible eigenvalue region conditions for system stability, a stability matrix with all negative diagonal elements and a dominant diagonal norm is designed to ensure the stable convergence of error dynamics. The specific principle is explained below: The state estimation error vector is defined as the difference between the true system state value and the estimated system state value. By subtracting the nonlinear state equation of the physical system from the observer mapping equation, the differential equation of the error as a function of time is derived: ; in, This represents the state estimation error vector after the differential change at time k. Represents a nonlinear state equation. Represents the observer mapping equation, This represents the state estimation error vector at time k. This represents the fault input matrix, used to describe the fault. How does it affect the dynamics of state error? Indicates the first The fault vector at any given time represents the magnitude of the anomaly or fault that occurred in the system. This represents the external disturbance input matrix, used to describe the disturbance. How does it affect the dynamics of state error? Let represent the external disturbance vector at time k.

[0029] Subsequently, the difference of nonlinear terms is expanded at the estimation point using a first-order Taylor expansion, and the Jacobian matrix is ​​introduced. Under the nominal condition of neglecting external higher-order perturbations, the nominal error dynamic equation is derived: ; in, Represents the Jacobian matrix. Represents the gain matrix. This represents the system output matrix; the equation shows that the error system matrix determines whether the observation error can asymptotically converge to zero. To ensure the asymptotic stability of the observation error, all eigenvalues ​​of the error system matrix must be located in the left half of the complex plane, i.e., forming a negative diagonal dominance.

[0030] Furthermore, the step of solving for the gain matrix in the Lyapunov matrix based on the negative diagonal dominance constraint and the Schur complement includes: The stability matrix is ​​structured into system intrinsic terms and gain influence terms based on the system output matrix and positive definite matrix; the system intrinsic terms are denoted as... The gain effect term is denoted as ; The gain matrix and positive definite matrix are divided into observable and unobservable parts; For the observable part, a diagonal matrix satisfying the negative diagonal dominance constraint is constructed based on each element in the system's intrinsic terms; For the unobservable part, the inverse relation is established through Schur complement. and Decoupling the unobservable components yields the observer gain matrix; where Schur complement The inverse matrix, Represents a diagonal matrix. Represents the observer gain matrix The block matrix corresponding to the observable part (dimension 1) , (for output dimension) Represents the system output matrix reversible blocks The inverse matrix, Represents the observer gain matrix The block matrix corresponding to the unobservable part (dimension 1) ), Represents a positive definite matrix The bottom right sub-block after partitioning The inverse matrix, Represents a positive definite matrix The lower left sub-block after partitioning, due to the positive definite matrix symmetry, , which represents the cross covariance between the observable and unobservable components.

[0031] It is worth noting that the process of decoupling the unobservable parts through Schur complement and solving for the observer gain matrix includes: Let the system state dimension be... The output dimension is ( The system output matrix has a structure. ,in for An invertible square matrix of dimension 1. The observer gain matrix to be solved is... and positive definite matrix Divide into blocks based on observable and unobservable states: ; in, Represents the observer gain matrix The block matrix corresponding to the observable part has a dimension of . , Represents the observer gain matrix The block matrix corresponding to the unobservable part has a dimension of . ; Represents a positive definite matrix The top-left sub-block after partitioning has a dimension of [dimensional value]. , Represents a positive definite matrix The bottom right sub-block after partitioning has a dimension of [dimensional value]. , Represents a positive definite matrix The top right sub-block after partitioning Represents a positive definite matrix The bottom left sub-block after partitioning, and because Symmetrical, with .

[0032] Gain Influence Term Expand: ; As can be seen, the matrix The second column (corresponding to the unobservable state) is all zero, which means the observer gain matrix... The stability matrix is ​​affected only by the first column block. To simplify the design and eliminate the coupling of unobservable parts to stability conditions, the following is selected:

[0033] At this point, the second line block becomes ,thereby The first column block is simplified to:

[0034] in, for about Schur complement is an invertible matrix.

[0035] At this point, the unobservable part is completely decoupled, and the stability matrix... The negative diagonal dominance condition only needs to be achieved through design. To satisfy. To make ,but It is a dimension The matrix. To ensure that the negative diagonal is dominant, the matrix is... Designed as a diagonal matrix Its main diagonal element Values ​​are determined according to the value selection criteria; Depend on and and Both are reversible and can be solved:

[0036] In combination with the above This yields the complete observer gain matrix.

[0037] Furthermore, the construction of a diagonal matrix satisfying the negative diagonal dominance constraint based on the elements in the system's inherent terms includes: Based on the negative diagonal dominance constraint and the main diagonal and off-diagonal elements in the system's intrinsic terms, a criterion for the values ​​of each element on the main diagonal of the diagonal matrix is ​​constructed, which is expressed as: ; in, This represents the value of the element in the i-th row / column on the main diagonal of a diagonal matrix. This represents the value of the element in the i-th row and i-th column of the system's intrinsic item. For positive integers, This represents the value of the element in the i-th row and j-th column of the system's intrinsic item. This represents the max function. Represents absolute value; Based on the value selection criteria, values ​​are selected for each element on the main diagonal of the diagonal matrix to construct the diagonal matrix.

[0038] S3: Calculate the residual vector based on the estimated system state at the next time moment and the actual measurement output, and calculate T based on the residual vector. 2 Statistics.

[0039] Specifically, the calculation process includes: The residual vector is calculated based on the estimated system state at the next time moment and the actual measurement output, including: ; in, This represents the residual vector at time k+1. This represents the actual measurement output at time k+1. Represents the system output matrix. This represents the system state estimate output at time k+1.

[0040] T is calculated based on the residual vector. 2 Statistics, including: ; in, T represents the time at time k+1. 2 Statistic, This represents the residual vector at time k+1. Indicates transpose. This represents the inverse of the covariance matrix.

[0041] S4: Based on the T 2 Statistics and thresholds determine the fault diagnosis results.

[0042] Specifically, the steps include: Using kernel density estimation to fit T 2 The historical distribution of the statistics is used to select the fault diagnosis threshold from the historical distribution based on the preset quantiles; When the T 2 When the statistic is less than or equal to the fault diagnosis threshold, the nonlinear system is determined to be fault-free. When the T 2 If the statistical value is greater than the fault diagnosis threshold, the nonlinear system is determined to be faulty and an alarm is issued.

[0043] As a preferred embodiment, the training process of the negative diagonally dominant neural observer includes: Using a continuous stirred tank reactor (CSTR) fault diagnosis dataset as the data foundation, the observer was trained and the fault diagnosis method was tested. CSTR is a classic nonlinear benchmark for hydrocracking processes, where the reaction involves complex coupled dynamic evolution of concentration and temperature. A schematic diagram of the hydrocracking process based on CSTR is shown below. Figure 3 As shown.

[0044] Historical operating data was collected from the CSTR fault diagnosis dataset. This historical operating data originated from multivariate time-series data collected under normal operating conditions and different fault conditions of the nonlinear system, including 3-dimensional input variables and 7-dimensional state estimation output variables. The 3-dimensional input variables include inlet reactant concentration, inlet material temperature, and inlet coolant temperature. The 7-dimensional observation output variables include inlet reactant concentration, inlet material temperature, reactor reactant concentration, reactor temperature, coolant flow rate, inlet coolant temperature, and cooling jacket temperature. Historical operating data comprehensively reflects the dynamic operating status of the chemical process, providing rich time-series information for constructing a state observer. In this embodiment, normal operating condition data was used as the training set, and a test set containing 10 types of fault scenarios was used to verify the performance of the fault diagnosis method.

[0045] To address the temporal characteristics of historical operational data, a sliding window technique is employed, with the window consisting of 6 (or 5) time steps. Each training sample contains state observations from 6 or 5 consecutive historical moments, forming a feature vector to predict the state at the next moment. Based on this sliding window technique, the CSTR fault diagnosis dataset is proportionally divided into a training set and a test set. The training set includes only operational data under normal conditions for setting the model's convergence region threshold, while the test set contains mixed data from normal and fault conditions.

[0046] During training, the partitioned training set is preprocessed with time-series slices. The comprehensive feature vector of each training sample is extracted according to a preset time step. The comprehensive feature vectors are then input into the negative diagonally dominant neural observer, which outputs the state estimate of the next time step based on the training sample and maps the observer gain matrix corresponding to the training sample. Based on the error between the predicted state estimate and the corresponding real measurement output, and the error between the observer gain matrix and the corresponding real label, a composite loss function containing observation error loss and stability constraint loss is constructed. Based on the composite loss function, algorithms such as backpropagation are used to update the weights and biases of the fully connected neural network in the negative diagonally dominant neural observer, as well as the positive definite matrix in the stability matrix, until convergence. This ensures that while achieving high-precision fitting, the error dynamics system satisfies the exponential stable convergence condition under the Gershgorin disk theorem.

[0047] It is worth noting that the mapping function from the synthetic eigenvectors to the observer gain matrix is ​​constructed in the following way: A nonlinear mapping function is constructed using an L-layer feedforward neural network to achieve an adaptive mapping from the synthesized feature vector to the observer gain matrix. The nonlinear mapping function is expressed as: ; in, Represents a mapping function. This represents the comprehensive feature vector of the training samples. This represents the weights of the Lth layer of the feedforward neural network. This represents the bias of the Lth layer of the feedforward neural network. This represents the weights of the (L-1)th layer of the feedforward neural network. This represents the bias of the (L-1)th layer of the feedforward neural network. This represents the weights of the first layer of the feedforward neural network. This represents the bias of the first layer of the feedforward neural network. This represents the activation function.

[0048] During testing, the real-time integrated feature vector constructed from test samples in the test set is input into the negative diagonally dominant neural observer, which outputs the system state estimate for the next time step. Based on the system state estimate for the next time step and the actual measurement output, the residual vector is calculated, and T is calculated based on the residual vector. 2 Finally, based on T, the statistics... 2 The statistic and threshold determine the fault diagnosis result; and, if the normal samples in the test set correspond to T 2 If the statistical value is greater than the threshold, it is a false alarm; otherwise, it is a false negative. For example... Figure 4 As shown, experimental results demonstrate that, with the re-T2-kde statistic configured, the model achieves a low false alarm rate and good overall detection performance on the test set, with an average false alarm rate (AFAR) of 0.25% and an average false negative rate (AMDR) of 9.03%. These results indicate that the proposed method can effectively detect faults in the CSTR process while maintaining theoretical stability.

[0049] The fault diagnosis method based on the negative diagonally dominant neural observer provided in this embodiment has the following beneficial effects: By transforming the stability eigenvalue constraints of the error system derived from the Gershgorin disk theorem into mechanistic constraints and integrating them into the structural design of a deep network, a nonlinear network mapping from the system's operating state to stable compensation characteristics was established. The observation gain was corrected using designed diagonal negative elements and a diagonal norm-dominated stability matrix, and the observation gain structure was optimized using the Schur complement criterion. This forced the error system matrix to satisfy a strict negative diagonal dominance constraint, thus mathematically guaranteeing that the error system eigenvalues ​​fall within the stable feasible region. This achieved stable convergence of fault diagnosis errors, overcoming the deficiency of purely data-driven fault diagnosis methods that typically lack theoretical stability guarantees. An online learning mechanism alternating between forward prediction and backpropagation was adopted to guide model parameters to converge towards the region satisfying stability requirements through constraints. While ensuring theoretical stability, a hybrid driving strategy was used to update model parameters in real time to adapt to the system's nonlinear dynamics. By integrating physical constraints and data-driven approaches, the problem of existing methods being unable to simultaneously consider the adaptability of data-driven approaches and theoretical stability, leading to low fault diagnosis accuracy and questionable safety when facing complex dynamics, was effectively solved.

[0050] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0051] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A fault diagnosis method based on a negative diagonally dominant neural observer, characterized in that, include: S1: Obtain diagnostic data for the current moment of the nonlinear system including the continuous stirred tank reactor, wherein the diagnostic data includes the inlet reactant concentration, inlet material temperature, and inlet coolant temperature of the continuous stirred tank reactor; S2: Construct a real-time comprehensive feature vector of the data to be diagnosed, and input the real-time comprehensive feature vector into the trained negative diagonal dominant neural observer to output the system state estimate for the next time step; the negative diagonal dominant neural observer is an equation that includes a negative diagonal dominance constraint based on the Gershgorin disk theorem to compensate for the gain of the output of the fully connected neural network; the system state estimate for the next time step includes the estimated inlet reactant concentration, inlet material temperature, reactant concentration in the reactor, reactor temperature, coolant flow rate, inlet coolant temperature, and cooling jacket temperature of the continuous stirred tank reactor at the next time step; S3: Calculate the residual vector based on the estimated system state at the next time moment and the actual measurement output, and calculate T based on the residual vector. 2 Statistic; S4: Based on the T 2 Statistics and thresholds determine the fault diagnosis results.

2. The method according to claim 1, characterized in that, The construction of the real-time comprehensive feature vector of the data to be diagnosed includes: Get the current timestamp; Obtain the current real system state value and the current real measurement output, and transpose the current real system state value and the current real measurement output respectively; Obtain the system state estimate of the current time predicted in the previous time step, and transpose the system state estimate of the current time step; Transpose the data to be diagnosed at the current moment; The current time stamp, the transposed real system state value, the real measurement output, the system state estimate, and the data to be diagnosed are combined to form the feature vector of the current time. The feature vector at the current moment is transposed to obtain the real-time integrated feature vector.

3. The method according to claim 2, characterized in that, The construction process of the negative diagonally dominant neural observer includes: A fully connected neural network is constructed, which is used to map the current data to be diagnosed and the actual system state value to the preliminary estimate of the system state at the next moment. The Jacobian matrix of the mapping process is calculated in real time using automatic differentiation; Substituting the Jacobian matrix into the Lyapunov matrix yields the stability matrix; Based on Gershgorin's disk theorem, a negative diagonal dominance constraint is constructed for the stability matrix. The negative diagonal dominance constraint includes the following: all system eigenvalues ​​on the main diagonal of the stability matrix are negative, and the absolute value of any system eigenvalue on the main diagonal is greater than the sum of the absolute values ​​of all system eigenvalues ​​off the main diagonal. The observer gain matrix is ​​obtained by solving the gain matrix in the negative diagonal dominance constraint and the Schur complement Lyapunov matrix. The system state at the next time step is initially estimated based on the observer gain matrix to compensate for the loss of the negative diagonal dominant neural observer.

4. The method according to claim 3, characterized in that, The formula for calculating the stability matrix is: ； ； in, Represents the stability matrix. Describes a positive definite matrix. Represents the Jacobian matrix. Represents the gain matrix. Represents the system output matrix. Indicates transpose. This represents a fully connected neural network. This represents the actual system state value at time k. This represents the data to be diagnosed at time k. This represents the gradient operator.

5. The method according to claim 4, characterized in that, The process of solving for the gain matrix in the Lyapunov matrix based on the negative diagonal dominance constraint and the Schur complement includes: The stability matrix is ​​structured into system intrinsic terms and gain influence terms based on the system output matrix and positive definite matrix; the system intrinsic terms are denoted as... The gain effect term is denoted as ; The gain matrix and positive definite matrix are divided into observable and unobservable parts; For the observable part, a diagonal matrix satisfying the negative diagonal dominance constraint is constructed based on each element in the system's intrinsic terms; For the unobservable part, the inverse relation is established through Schur complement. and Decoupling the unobservable components yields the observer gain matrix; where Schur complement The inverse matrix, Represents a diagonal matrix. Represents the observer gain matrix The block matrix corresponding to the observable part. Represents the system output matrix reversible blocks The inverse matrix, Represents the observer gain matrix The block matrix corresponding to the unobservable part. Represents a positive definite matrix The bottom right sub-block after partitioning The quasi-matrix, Represents a positive definite matrix The bottom left sub-block after partitioning.

6. The method according to claim 5, characterized in that, The construction of a diagonal matrix satisfying the negative diagonal dominance constraint based on the elements in the system's inherent terms includes: Based on the negative diagonal dominance constraint and the main diagonal and off-diagonal elements in the system's intrinsic terms, a criterion for the values ​​of each element on the main diagonal of the diagonal matrix is ​​constructed, which is expressed as: ； in, This represents the value of the element in the i-th row / column on the main diagonal of a diagonal matrix. This represents the value of the element in the i-th row and i-th column of the system's intrinsic item. For positive integers, This represents the value of the element in the i-th row and j-th column of the system's intrinsic item. This represents the max function. Represents absolute value; Based on the value selection criteria, values ​​are selected for each element on the main diagonal of the diagonal matrix to construct the diagonal matrix.

7. The method according to claim 2, characterized in that, The expression for the negative diagonally dominant neural observer is: ； in, This represents the system state estimate output at time k+1. This represents a fully connected neural network. This represents the actual system state value at time k. This represents the system state estimate output at time k. This represents the data to be diagnosed at time k. This represents the observer gain matrix at time k. This represents the actual measurement output at time k. This represents the system output matrix.

8. The method according to claim 1, characterized in that, The calculation of the residual vector based on the estimated system state at the next time moment and the actual measurement output includes: ； in, This represents the residual vector at time k+1. This represents the actual measurement output at time k+1. Represents the system output matrix. This represents the system state estimate output at time k+1.

9. The method according to claim 1, characterized in that, The calculation of T based on the residual vector 2 Statistics, including: ； in, T represents the time at time k+1. 2 Statistic, This represents the residual vector at time k+1. Indicates transpose. This represents the inverse of the covariance matrix.

10. The method according to claim 1, characterized in that, The based on T 2 Statistics and thresholds determine the fault diagnosis results, including: Using kernel density estimation to fit T 2 The historical distribution of the statistics is used to select the fault diagnosis threshold from the historical distribution based on the preset quantiles; When the T 2 When the statistic is less than or equal to the fault diagnosis threshold, the nonlinear system is determined to be fault-free. When the T 2 If the statistical value is greater than the fault diagnosis threshold, the nonlinear system is determined to be faulty and an alarm is issued.

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