Power supply system key equipment fault diagnosis method based on digital twinning

Abstract

The application provides a power supply system key equipment fault diagnosis method based on digital twinning, first, according to expert knowledge and a design scheme, modeling of power supply system key equipment is carried out, fault mode analysis is carried out, and a fault behavior twinning model is established, and experimental results prove that the twinning modeling method is effective, and the expected result is better adapted. Then, by adding random noise, the actual operation is better simulated, and the twinning modeling of the fault behavior dimension is successfully realized. The application also takes the data set generated by the fault behavior twinning model as the basis, analyzes the transient stability of the system key equipment, obtains a differential algebraic equation capable of describing physical information, combines the differential algebraic equation with a neural network loss function, and the construction of PINN is completed with a relatively ideal effect, and after 400 times of training, the training error reaches the order of magnitude of 10 ‑3 .

Description

Technical Field

[0001] This invention relates to the field of fault diagnosis technology, and specifically to a fault diagnosis method for key equipment in a power supply system based on digital twins. Background Technology

[0002] The aircraft power supply system is a crucial component of the aircraft's functional systems. It generates, converts, transmits, and distributes electrical energy, providing power to all aircraft electrical equipment to meet specified requirements. With the rapid development of more electric and all-electric aircraft, aircraft power systems have become more complex due to electrification, placing higher demands on their safety, maintainability, reliability, and testability.

[0003] To improve equipment safety and mission success rates while reducing safety costs, fault prediction and health management are considered key technologies for next-generation equipment. Under specific operating conditions, it combines multi-source information such as historical system status, fault information, and operating condition information, along with historical parameter data, to use intelligent algorithms to identify whether the system's operating status is normal or has deteriorated. Then, based on data characteristics, it achieves fault isolation and location. Fault diagnosis is a crucial component of fault prediction and health management technology. Existing fault diagnosis methods for power systems mainly include model-based and data-driven approaches. Model-based methods use system composition principles and fault mode analysis to construct mathematical models of the object for power supply system fault diagnosis. However, the modeling process often struggles to consider the coupling between components and their interaction with the environment, resulting in limited ability to represent faults in real-world situations and high model complexity. Data-driven fault diagnosis requires a large amount of historical data to support model construction and training. However, power supply system fault data suffers from imbalanced samples and small sample sizes, leading to weak interpretability and poor fault diagnosis results for existing data-driven algorithms. Summary of the Invention

[0004] This invention aims to improve the fault diagnosis effect of key equipment in power systems and provides a fault diagnosis method for key equipment in power supply systems based on digital twins.

[0005] To achieve this objective, the present invention adopts the following technical solution:

[0006] A method for fault diagnosis of key equipment in a power supply system based on digital twin is provided, the steps of which include:

[0007] S1, Construct fault behavior twin models for key equipment in the power supply system to generate fault datasets for each key equipment;

[0008] S2, Based on the fault dataset and a physical information neural network, construct and update a fault state perception twin model that represents the fault pattern;

[0009] S3, use the updated fault state-aware twin model to diagnose the fault in the sample under test.

[0010] Preferably, step S1, which constructs the fault behavior twin model, specifically includes the following steps:

[0011] S11, Analyze the failure modes of each key device and identify the failure behavior twin modeling part in the key device model;

[0012] S12, Simulate the fault behavior of the corresponding fault mode at the fault behavior twin modeling part, and collect the three-phase output voltage and current of the key equipment under normal and fault conditions.

[0013] S13. By comparing the three-phase output voltage and current of the key equipment under normal and fault conditions, and verifying the correctness of the identified fault behavior twin modeling location, the fault behavior twin model of the key equipment is obtained.

[0014] Preferably, each failure mode of the key equipment has a corresponding failure dataset, and each failure dataset includes several sets of samples, with Gaussian noise signals of a specified signal-to-noise ratio added to each set of samples.

[0015] Preferably, the specified signal-to-noise ratio is 15;

[0016] The method for generating the fault dataset corresponding to the key equipment under the fault mode is as follows: the fault behavior of the fault mode is simulated in the fault behavior twin modeling part of the model of the key equipment, and then data samples are collected in the fault behavior twin modeling part according to the preset sampling time and sampling rate, and several data points within the preset sampling time period are extracted as samples.

[0017] As a preferred embodiment, in step S11, the fault modes obtained from the analysis and the corresponding fault behavior twin modeling parts are shown in Table 1 below:

[0018] Table 1

[0019]

[0020] Preferably, the key equipment in the power supply system includes the aircraft's power system, which includes a main power supply and / or a secondary power supply. The main power supply includes any one or more of a main generator, an exciter, and a rotating rectifier. The secondary power supply includes any one or more of a static converter, a DC-DC boost converter, and a transformer rectifier. Any one or more components of the main power supply and / or the secondary power supply serve as fault behavior twins.

[0021] Preferably, the main power supply includes a single-channel power supply system and / or a multi-channel power supply system, with at least two generators connected in parallel to form the multi-channel power supply system.

[0022] Preferably, the multi-channel power supply system is a four-channel power supply system. Each channel of the four-channel power supply system includes the generator, a transformer rectifier electrically connected to the generator, and a load. The transformer rectifier includes a 270V transformer rectifier and a 28V transformer rectifier. The load includes an AC load and a DC load. The AC load is a three-phase resistor, and the DC load includes a high-voltage DC load and a low-voltage DC load. The high-voltage DC load is a hydraulic pump, and the low-voltage DC load is a resistor. The transformer rectifier is connected to the electrical output terminal of the generator to convert the AC power output by the generator into DC power and output it to the DC load. The AC load is connected to the electrical output terminal of the generator.

[0023] Preferably, the main power supply is a constant speed and constant frequency power supply system, and the generator is a three-phase AC generator.

[0024] Preferably, step S2, the method for constructing and updating the fault state-aware twin model, includes the following steps:

[0025] S21, based on Hilbert-Huang transform and RMS values ​​to extract fault data features;

[0026] S22, The physical information of the key equipment in the power supply system is expressed as a built-in parameter of DAE-PINN based on differential algebraic equations;

[0027] S23, build and update the fault state awareness twin model based on DAE-PINN.

[0028] Preferably, in step S21, the extracted fault data features include the instantaneous frequency ω(t) and instantaneous phase of the original signal x(t). Instantaneous amplitude a(t) and effective value X rms Any one or more of the above can be decomposed into ω(t) by Hilbert-Huang transform. a(t),

[0029] The effective value Xrms The calculation method is expressed by the following formula (1):

[0030]

[0031] In formula (1), X i This represents the current value at the i-th sampling point;

[0032] N represents the number of sampling points;

[0033] i represents sampling point i.

[0034] Preferably, the input of the rotating rectifier is connected to the output of the main exciter, the input of the main motor is connected to the output of the rotating rectifier, and the output of the main motor is connected to the key equipment in the topology relationship of AC load, 270V transformer rectifier and 28V transformer rectifier respectively. Step S22 specifically includes the following steps:

[0035] S221, Construct the differential algebraic equations for expressing the physical information of each key device in the power supply system under the topological relationship;

[0036] S222, Obtain the equipment parameters of each key device under the topological relationship;

[0037] S223, substitute each of the device parameters into the differential algebraic equation constructed in step S221, and set the physical information as a built-in parameter of DAE-PINN.

[0038] Preferably, the differential-algebraic equations constructed in step S221 are expressed as follows: (2)-(9)

[0039]

[0040] -(1 / V A (g) = 0 Formula (3)

[0041] f1 = B 12 V1V2 sin(δ1-δ2)-P1 formula (4)

[0042] f2 = B 21 V2V1 sin(δ2-δ1)+B 23 V2V3 sin(δ2-δ3)-P2 formula (5)

[0043]

[0044]

[0045]

[0046]

[0047] In formulas (2)-(9), m k Let d be the inertial constant. k The damping coefficient is... Angular frequency, f is the angular velocity. k V represents the zeroth-order differential term in (2). A Let g represent the voltage of the AC load, g represent the zeroth-order differential term in the algebraic equation, and k = 1, 2, 3, H, L, A represent the main exciter, the rotating rectifier, the main motor, the 270V transformer rectifier, the 28V transformer rectifier, and the AC load, respectively. 21 B represents the magnetization matrix between the rotating rectifier and the main exciter. 23 B represents the magnetization matrix between the rotating rectifier and the main motor. 31 B represents the magnetization matrix between the main motor and the main exciter. 3A B represents the magnetization matrix between the main motor and the AC load. 3H B represents the magnetization matrix between the main motor and the 270V transformer rectifier. 2L B represents the magnetization matrix between the rotating rectifier and the 28V transformer rectifier. H3 B represents the magnetization matrix between the 270V transformer rectifier and the main motor. HA B represents the magnetization matrix between the 270V transformer rectifier and the AC load. HL B represents the magnetization matrix between the 270V transformer rectifier and the 28V transformer rectifier. L3 B represents the magnetization matrix between the 28V transformer rectifier and the main motor. LA B represents the magnetization matrix between the 28V transformer rectifier and the AC load. LH B represents the magnetization matrix between the 28V transformer rectifier and the 270V transformer rectifier. A3 B represents the magnetization matrix between the AC load and the main motor. AH B represents the magnetization matrix between the AC load and the 270V transformer rectifier. AL This represents the magnetization matrix between the AC load and the 28V transformer rectifier; where the dynamic unknowns characterizing the system state are y = (δ1, δ2, δ3, δ...). H ,δ L ,δ A ) T The algebraic unknown is z = V A ;

[0048] In step S222, the equipment parameters include the voltage V1 of the main exciter, the voltage V2 of the rotating rectifier, the voltage V3 of the main motor, and the voltage V of the AC load. A The voltage V of the 270V transformer rectifier H The voltage V of the 28V transformer rectifier L ;

[0049] In step S223, the built-in parameters of DAE-PINN include m1, m2, m3, m H ,m L ,d1,d2,d3,d H ,d L and voltages V1, V2, V3, V H V L V A Power P1, P2, P3, P H ,P L ,P A Q A .

[0050] Preferably, step S23 specifically includes the following steps:

[0051] S231, The implicit Runge-Kutta method is used to solve the differential-algebraic equation;

[0052] S232, Construct a neural network based on physical information;

[0053] S233, a fault state perception twin model of the key equipment is trained using a neural network based on physical information.

[0054] Preferably, the method for solving the differential-algebraic equation in step S231 is as follows:

[0055] When the step size is h = t n+1 -t n >0, the integral starts from (t) n ,y n ,z n ) proceed to (t) n+1 ,y n+1 ,z n+1 When applying the implicit Runge-Kutta method of order v to the differential-algebraic equations expressed by equations (5)-(9), we obtain...

[0056]

[0057] 0=g(ξ i ,ζ i ), j=1,2,...,v Formula (11)

[0058]

[0059] 0 = g(y n+1 ,z n+1 ) Formula (13)

[0060] Where ξ j =y(t) n +c j h), ζ j =z(t) n +c j h), {a j,i ,b j ,c i} represents the unknown parameters of the implicit Runge-Kutta method, and the parameters are specified.

[0061] ξ j This represents the y-value corresponding to the j-th discrete point at a certain time step;

[0062] c j Represents the node coefficients;

[0063] y(t n +c j h) represents the value of the dynamic variable at the j-th discrete point at the n-th time step;

[0064] z(t n +c j h) represents the value of the algebraic variable at the j-th discrete point at the n-th time step;

[0065] a j,i Indicates coefficient;

[0066] b j Indicates coefficient;

[0067] y n This represents the value of the dynamic variables in the differential algebraic equation at the nth time step;

[0068] z n This represents the value of the algebraic variable in the differential-algebraic equation at the nth time step;

[0069] t n This represents the nth time step;

[0070] n represents the time step number;

[0071] v represents the order of the implicit Runge-Kutta method;

[0072] ζ i This represents the z-value corresponding to the j-th discrete point at a certain time step;

[0073] f(ξ i ,ζi () represents the value of the zeroth-order term of the dynamic equation corresponding to the j-th discrete point at a certain time step;

[0074] g(ξ i ,ζ i () represents the value of the non-zero term in the algebraic equation corresponding to the j-th discrete point at a certain time step;

[0075] g(y n+1 ,z n+1 ) represents the value of the non-zero term in the algebraic equation at the (n+1)th time step.

[0076] Preferably, in step S232, the method for constructing a neural network based on physical information is as follows:

[0077] Define a neural network with physical information:

[0078]

[0079] In formula (14), f(t,x) is an algebraic term containing physical information;

[0080] N[u;λ] is a nonlinear operator connecting the state variable u and the system parameter λ;

[0081] t represents time;

[0082] x represents system input;

[0083] The shared parameters of a neural network are optimized by minimizing the loss function, MSE, which is expressed as follows:

[0084]

[0085] In equation (15), MSE u N represents the mean squared error loss corresponding to the initial data. u Let be the total number of training data, and i represent the i-th training data. This represents the time of the i-th training data. This represents the input of the i-th training data. This represents the dynamic value corresponding to the i-th training data;

[0086] MSE f Let N be the mean square error over a finite set of points. f The total number of configuration points. This represents the time of the i-th configuration point. This represents the input of the i-th configuration point. It represents the algebraic value corresponding to the i-th configuration point. The finite configuration point set is the point set of the physical information algebraic terms during discrete processing.

[0087] Preferably, step S233, the method for training the fault state perception twin model of key equipment, specifically includes the following steps:

[0088] Incorporating the implicit Runge-Kutta method into the loss function MSE expressed by formula (15), the loss function is transformed into:

[0089]

[0090] The parameters of the neural network are trained by minimizing the loss function using the Adam optimizer, as expressed in the following formula (17):

[0091]

[0092] In formulas (16)-(17), Let w represent the total loss function. f The weights represent the weights corresponding to the dynamic loss function. w represents the loss function of the dynamic equation. g The weights represent the weights corresponding to the loss function in the algebraic equation. Represents the loss function of an algebraic equation;

[0093] N τ Let v represent the size of the training dataset, k represent the order of the implicit Runge-Kutta method, j represent the j-th training data point, and y represent the number of implicit Runge-Kutta steps. n,k Let represent the value of the dynamic variable in the differential-algebraic equation at the nth time step and the kth training data point. Let represent the dynamic variables in the differential-algebraic equations at the nth time step and the kth training data at the jth order implicit Runge-Kutta step;

[0094] Represents the loss function of an algebraic equation. Let represent the y-value corresponding to the j-th discrete point and the k-th training data at a certain time step. Let z represent the z-value corresponding to the j-th discrete point and the k-th training data at a certain time step. Let represent the value of the non-zero term in the algebraic equation corresponding to the j-th discrete point and the k-th training data at a certain time step. Let represent the value of the dynamic variable in the differential-algebraic equation at the (n+1)th time step and the kth training data point. Let represent the value of the algebraic variable in the differential-algebraic equation at the (n+1)th time step and the kth training data point. This represents the value of the non-zero term in the algebraic equation for the (n+1)th time step and the kth training data point;

[0095] This represents the dynamic variable in the differential-algebraic equation at the nth time step and the kth training data point at the jth order implicit Runge-Kutta step. Let represent the condition that the dynamic variables in the differential-algebraic equation should satisfy at the nth time step and for the kth training data at the jth order implicit Runge-Kutta step, where h represents the step size, i represents the ith order implicit Runge-Kutta step, and a j,i Indicates a constant coefficient. This represents the value of the zeroth-order term of the differential equation corresponding to the j-th discrete point and the k-th training data at a certain time step;

[0096] This represents the dynamic variable in the differential-algebraic equation at the nth time step and the kth training data point at the (v+1)th order implicit Runge-Kutta step. This represents the condition that the dynamic variables in the differential-algebraic equation should satisfy at the nth time step and for the kth training data at the (v+1)th order implicit Runge-Kutta step. Let b represent the dynamic variable in the differential-algebraic equation of the (n+1)th time step and the kth training data. j Indicates a constant coefficient;

[0097] θ * This represents the optimal parameters obtained by the Adam optimizer.

[0098] As a preferred approach, the following unconstrained optimization problem is solved in the k-th iteration.

[0099]

[0100] in, and It is the penalty coefficient for the k-th iteration;

[0101] At the beginning of each iteration, the penalty coefficient is increased by a constant factor β > 1, expressed as:

[0102]

[0103] This represents the initial value of the penalty coefficient corresponding to the dynamic equation. Let (β) be the initial value of the penalty coefficient corresponding to the algebraic equation. k Represents the k-th power of a constant factor;

[0104] The neural network fitting the differential algebraic equation uses a fully connected structure and a forward propagation structure. The structure of the neural network is expressed as follows:

[0105]

[0106] X is the input tensor of the neural network, d is the number of hidden layers, ⊙ is the Hadamard product or element-wise product, and φ is the pointwise sinusoidal activation function.

[0107] U represents the activated tensor corresponding to the initial weight of 1, H (1) Z represents the input tensor of the first layer. (k) H represents the tensor after activation at the k-th layer. (k) H represents the input tensor of the k-th layer. (k+1) W represents the output tensor of the k-th layer. z,k Let b represent the weight matrix corresponding to the k-th layer after activation. z,k This represents the bias corresponding to the k-th layer after activation;

[0108] Each hidden layer has a width of w, and the network architecture uses the normal Glorot initialization algorithm. The training parameters are as follows:

[0109]

[0110] Preferably, the fault state-aware twin model is trained using a neural network with either a stacked or non-stacked structure, wherein in the non-stacked structure, represents the dynamic state variable in the differential-algebraic equation. and algebraic variables Each corresponding neural network is assigned separately;

[0111] In a stacked structure, all dynamic states are fitted using a single neural network. and state variables

[0112] Preferably, in the stacked structure, the neural network has a width w = 200 and a depth d = 6; in the non-stacked structure, the neural network allocated to the dynamic state variables has a width w = 200 and a depth d = 6, and the neural network allocated to the algebraic variables has a width w = 40 and a depth d = 4, with the sample size ratio of the training set, test set, and validation set being 1:1:2.

[0113] Preferably, in step S3, the method for fault diagnosis includes the following steps:

[0114] S31, Construct the intrinsic feature set S of the fault modes of the sample under test. fault , i m i d i v i p The values ​​for are 1, 2, 3, H, L, A, representing the main exciter, rotating rectifier, main motor, 280V transformer rectifier, 28V transformer rectifier, and AC load, respectively. The magnetization matrix parameters between the key devices represented by 1, 2, 3, H, L, A are uniformly set to b. Q represents the inertia constant, damping coefficient, input voltage, and mechanical power, respectively. A Indicates the virtual power of the AC load;

[0115] S32, the fault state-aware twin model uses the intrinsic feature set S fault The system takes the input as input and outputs the fault diagnosis results for the sample under test.

[0116] The present invention has the following beneficial effects:

[0117] First, based on expert knowledge and design schemes, key equipment of the power supply system was modeled, fault mode analysis was conducted, and a fault behavior twin model was established. Experimental results demonstrated the effectiveness of the twin modeling method, showing good adaptation to expected results. Next, by adding random noise, the actual operating conditions were simulated effectively, successfully achieving twin modeling of the fault behavior dimension. Furthermore, based on the dataset generated by the fault behavior twin model, this invention derived differential-algebraic equations describing physical information by analyzing the transient stability of key system equipment. Combining these equations with a neural network loss function resulted in the successful construction of PINN, achieving a score of 10 after 400 training iterations. -3 Training error on the order of magnitude. Attached Figure Description

[0118] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments of the present invention will be briefly described below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0119] Figure 1 This is an overall technical architecture diagram of the fault diagnosis method for key equipment in a power supply system based on digital twins provided in this embodiment of the invention;

[0120] Figure 2 This is a structural diagram of a power supply system using four three-phase AC generators;

[0121] Figure 3 This is a schematic diagram of the distribution of measuring points of key equipment in the power supply system in an embodiment of the present invention;

[0122] Figure 4 This is a schematic diagram of the main power supply model of the power supply system in an embodiment of the present invention;

[0123] Figure 5 This is a schematic diagram of the single-phase output current and voltage signals of the main power supply model of the power supply system in an embodiment of the present invention;

[0124] Figure 6This is a schematic diagram of a 270V transformer rectifier model in the power supply system of an embodiment of the present invention;

[0125] Figure 7 This is a schematic diagram of the output current and voltage signals of a 270V transformer rectifier model;

[0126] Figure 8 This is a schematic diagram of a 28V transformer rectifier model;

[0127] Figure 9 This is a schematic diagram of the output current and voltage signals of a 28V transformer rectifier model;

[0128] Figure 10 This is a schematic diagram of a three-phase AC resistance model;

[0129] Figure 11 This is a schematic diagram of a fuel pump model;

[0130] Figure 12 This is a schematic diagram of a DC heater model;

[0131] Figure 13 This is a schematic diagram of the rotational speed of a hydraulic pump model;

[0132] Figure 14 This is a schematic diagram of the armature current of a fuel pump model;

[0133] Figure 15 This is a schematic diagram of the torque of a fuel pump model;

[0134] Figure 16 This is a schematic diagram of twin modeling the phase-to-phase short-circuit behavior of the main generator armature winding;

[0135] Figure 17 This is a schematic diagram of the three-phase current and voltage output signals of the main motor under normal conditions during the twin modeling process of the phase-to-phase short-circuit behavior of the main generator armature winding;

[0136] Figure 18 This is a schematic diagram of the three-phase current and voltage output signals of the main motor under phase-to-phase short circuit during the twin modeling process of the phase-to-phase short circuit behavior of the main generator armature winding;

[0137] Figure 19 This is a schematic diagram of twin modeling the single-phase open-circuit behavior of the main generator armature winding;

[0138] Figure 20 This is a schematic diagram of the three-phase current and voltage output signals of the main motor under normal conditions during the twin modeling process of single-phase open-circuit behavior of the main generator armature winding;

[0139] Figure 21This is a schematic diagram of the three-phase current and voltage output signals of the main motor under single-phase open circuit during the twin modeling process of the single-phase open circuit behavior of the main generator armature winding;

[0140] Figure 22 This is a schematic diagram of twin modeling the single-phase open-circuit behavior of the exciter armature winding;

[0141] Figure 23 This is a schematic diagram of the single-phase voltage output signal of the exciter under normal conditions during the twin modeling process of single-phase open-circuit behavior of the exciter armature winding;

[0142] Figure 24 This is a schematic diagram of the single-phase voltage output signal of the exciter under single-phase open circuit during the twin modeling process of the single-phase open circuit behavior of the exciter armature winding;

[0143] Figure 25 This is a schematic diagram of twin modeling the phase-to-phase short-circuit behavior of the exciter armature winding;

[0144] Figure 26 This is a schematic diagram of the C-phase output voltage and current signal of the exciter under normal conditions during the twin modeling process of the phase-to-phase short-circuit behavior of the exciter armature winding;

[0145] Figure 27 This is a schematic diagram of the exciter's C-phase output voltage and current signals under phase-to-phase short-circuit conditions during the twin modeling process of the exciter armature winding phase-to-phase short-circuit behavior;

[0146] Figure 28 This is a schematic diagram of twin modeling the short-circuit behavior of a single diode in a rotating rectifier;

[0147] Figure 29 This is a schematic diagram of the output voltage and current signals of a rotating rectifier under normal conditions during the twin modeling process of the short-circuit behavior of a single diode in a rotating rectifier.

[0148] Figure 30 This is a schematic diagram of the output voltage and current signals of the rotating rectifier under the short-circuit state of a single diode during the twin modeling process of the short-circuit behavior of a single diode in a rotating rectifier;

[0149] Figure 31 This is a schematic diagram of twin modeling the impedance rise behavior of a 28V transformer rectifier;

[0150] Figure 32 This is a schematic diagram of the output voltage and current signals of a 28V transformer rectifier under normal conditions during the twin modeling process of impedance rise behavior of transformer rectifier;

[0151] Figure 33This is a schematic diagram of the output voltage and current signals of a 28V transformer rectifier under the impedance rise state during the twin modeling process of the transformer rectifier impedance rise behavior.

[0152] Figure 34 This is a schematic diagram of twin modeling the open-circuit behavior of the filter inductor in a 270V transformer rectifier;

[0153] Figure 35 This is a schematic diagram of the output voltage and current signals of a 270V transformer rectifier under normal conditions during the twin modeling process of the open-circuit behavior of the filter inductor of a 270V transformer rectifier.

[0154] Figure 36 This is a schematic diagram of the output voltage and current signals of the 270V transformer rectifier under the open-circuit state of the filter inductor during the twin modeling process of the open-circuit behavior of the filter inductor of the 270V transformer rectifier.

[0155] Figure 37 This is a flowchart of the fault data feature extraction method;

[0156] Figure 38 This is a schematic diagram of the output signal of a key device for a phase-to-phase short circuit in the armature winding of a main generator.

[0157] Figure 39 These are the feature extraction results for normal state and three-channel seven types of fault modes;

[0158] Figure 40 This is an example diagram of the topology of key equipment;

[0159] Figure 41 This is a schematic diagram of the multi-output fully connected layer neural network architecture used in this embodiment;

[0160] Figure 42 This is a comparison chart of the training and validation errors of the constructed DAE-PINN neural network;

[0161] Figure 43 This is a comparison chart showing the impact of using stacked and non-stacked neural networks on training error;

[0162] Figure 44 This is a schematic diagram illustrating the impact of neural network depth on training error;

[0163] Figure 45 This is a schematic diagram illustrating the impact of neural network width on training error;

[0164] Figure 46 This is a schematic diagram illustrating the impact of a training method provided in an embodiment of the present invention on training error;

[0165] Figure 47 This is a schematic diagram of the TPE tree structure;

[0166] Figure 48 This is a schematic diagram illustrating the change in the loss function during the training of the fault state-aware twin model;

[0167] Figure 49 This is a schematic diagram of the fault diagnosis results for the test set. Detailed Implementation

[0168] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0169] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0170] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "inner," and "outer" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the accompanying drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0171] In the description of this invention, unless otherwise explicitly specified and limited, the term "connection" or similar designation indicating a connection between components should be interpreted broadly. For example, it can refer to a fixed connection, a detachable connection, or an integral part; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium; it can refer to the internal communication between two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0172] This invention takes aviation power supply systems as the object of fault diagnosis. Addressing the problem of imbalanced fault data in traditional fault diagnosis methods, it establishes a fault behavior twin model based on the typical structure and working mechanism of aviation power supply systems. This generates a typical fault dataset for key equipment in the power supply system, providing a necessary fault data foundation for state-aware twin modeling. To address the weakness of fault representation capabilities of single data-driven or mechanism models, it achieves deep fusion of models and data based on physical information neural networks, constructing a fault state-aware twin network architecture and parameter information foundation. Furthermore, to address the poor dynamic adaptive update capability of traditional fault mechanism models, it utilizes the model and data fusion information contained in the physical information network and the complete fault dataset generated by the fault behavior twin model to achieve dynamic updates of hyperparameters. This updated dataset is then applied to the fault diagnosis of key equipment in the power supply system, improving fault state-aware twin modeling.

[0173] like Figure 1 As shown, this invention addresses the problems of fault behavior twins in power supply systems, fault state perception modeling through deep fusion of models and data, and twin network updates and fault diagnosis applications. Based on a typical aircraft power supply system, it utilizes fault mechanism analysis, physical information neural networks, and other technologies to establish digital mappings and achieve dynamic parameter updates for key equipment. This improves the fault representation capabilities of twin networks and enables multi-faceted fault diagnosis, including multi-dimensional, multi-factor, and integrated diagnostics.

[0174] To address the data imbalance shortcomings in traditional fault diagnosis methods, this paper analyzes and studies the fault mechanisms and typical fault modes of aircraft power supply systems, establishing a digital twin fault behavior model (referred to as the "fault behavior twin model"). This model provides knowledge support for the composition and operational mechanisms of aircraft power supply systems and also provides data support for the subsequent training and validation of fault state perception twin networks. Specifically, a power supply system model is constructed based on the design scheme of a specific aircraft model. By combining expert knowledge and fault analysis, typical fault modes of this aircraft model are determined. The model then implements fault behavior twin modeling under these typical fault modes, conducting data analysis and validation to generate a sufficient and complete fault test dataset. This provides the mechanistic knowledge and data foundation for subsequent updates to the fault state perception twin model and fault diagnosis.

[0175] To address the incomplete state representation of existing digital twin models, this paper constructs a fault state-aware digital twin model based on physical information neural networks (PINNs) to represent fault patterns. This achieves model-data fusion, improves the model's fault representation capability and interpretability, and provides parameter information input and reliability assurance for subsequent fault diagnosis. Mechanism-based twin models have low fidelity in simulations of complex systems, making it difficult to achieve a mirror image of the real system. Data-driven twin models require extensive training support and lack the ability to represent underlying mechanisms. Physical information neural networks (PINNs) encode fundamental physical laws into the loss function of a neural network. They are a type of neural network used to solve supervised learning tasks while respecting the given physical laws described by general nonlinear partial differential equations. Therefore, using PINNs can increase the dimensions and means of perception modeling, more completely represent fault states, and establish a highly interpretable state-aware twin network.

[0176] Traditional fault diagnosis models are static and difficult to adapt to changes in the operating environment, affecting diagnostic efficiency and accuracy. Therefore, it is necessary to dynamically update model parameters based on a state-aware twin network and system operation data to achieve adaptive updates of the digital twin model. In this invention, a complete set of samples is generated using a fault behavior twin model, and these samples are used to train and select parameters for the fault state-aware twin network, which fuses the model and data, thereby achieving dynamic updates to the fault state-aware twin model. Fault diagnosis is then performed on the test samples based on the updated fault state-aware twin model.

[0177] The following sections elaborate on the present invention in three main parts: constructing a fault behavior twin model, a fault state perception twin model, and using the fault state perception twin model to diagnose faults in key equipment in a power supply system.

[0178] I. Fault Mechanism Analysis and Fault Behavior Twin Modeling of Key Equipment in Power Supply System

[0179] 1. Modeling of key equipment in a typical aircraft power supply system

[0180] An aircraft's power supply system is generally divided into two main parts: the aircraft power system and the power distribution system. This embodiment of the invention mainly focuses on the power system.

[0181] The aircraft power system consists of a main power supply, secondary power supply, emergency power supply, and auxiliary power supply. The main power supply is the primary power source for the aircraft's electrical system, converting the mechanical energy transmitted from the aircraft engines into electrical energy. Currently, a constant-speed, constant-frequency power supply system is commonly used as the main power supply, with a frequency of 400Hz and an output voltage of 115 / 200V. In current aircraft power supply systems, constant-frequency, constant-speed AC power generation systems have become a widely used type of power supply system. The main power source of this system consists of a constant-speed transmission device, an AC generator, excitation regulation, and control and protection devices. The secondary power supply is used to meet the power demands of various types of aircraft loads by converting the electrical energy generated by the main power supply. Commonly used secondary power supplies include static converters, DC boost converters, and transformer rectifiers. A transformer rectifier is a combination of a transformer and a rectifier, designed to convert the high-voltage AC power generated by the main power supply into corresponding DC power for use by electrical equipment. The secondary power supply used in this invention is primarily a transformer rectifier. Since auxiliary power supplies and emergency power supplies are not connected to the power supply system during normal operation, they are not considered for modeling and analysis in this invention.

[0182] To meet the electrical power demands and reliability requirements of aircraft, modern large aircraft typically employ multiple generators connected in parallel to form a main power system. Common systems include two-channel and four-channel power supply systems. Generally, each channel's AC generator provides its own power, with power integrated and distributed via busbars. If one channel fails, the aircraft can still operate normally. If all main power supplies fail, an emergency power supply will be connected to provide emergency power.

[0183] This embodiment uses an aviation AC main power supply model provided by a partner organization, combined with research data and experimental verification, to construct a typical aircraft four-channel power supply system model using the Simulink tool in MATLAB. The model is then corrected and improved based on real power supply system parameter data provided by the partner organization. In this invention, as... Figure 2 As shown, four three-phase AC generators are used as an independent power supply system, with each AC circuit not connected in parallel. The secondary power supply uses transformer rectifiers, including 270V and 28V transformer rectifiers, with each circuit connected to one 270V and one 28V transformer rectifier (high voltage and low voltage). Simultaneously, the DC power supplies of the first and second circuits are integrated via busbars, while the DC power supplies of the third and fourth circuits are combined. The DC power supplies are connected to two hydraulic pump loads (high voltage loads, operating in parallel) and two resistors (low voltage loads, operating in parallel). The system also has four AC loads, represented by two three-phase resistors, each connected to one of the four generators. Please refer to the structural diagram of the power supply system using four three-phase AC generators. Figure 2 .

[0184] To achieve fault characterization and parameter variation analysis under different fault modes in the power supply system, it is necessary to... Figure 2 The parameters of each level and component in the system shown are collected and analyzed, respectively targeting... Figure 2 The power supply system shown has 4 levels and 24 devices for status monitoring. Therefore, the distribution of parameter acquisition points for this power supply system is shown in the attached figure. Figure 3 As shown (in) Figure 2 (Taking the first and second channels as examples).

[0185] 1) Main power supply modeling

[0186] The power supply system model uses four generators to provide independent power. Figure 3 The system consists of an auxiliary exciter, main exciter, main motor, rotating rectifier, and rectifier bridge. A three-stage brushless AC synchronous generator is primarily used to construct a constant-frequency, constant-speed AC power supply system. The auxiliary exciter powers important equipment such as the main exciter, protection circuit, and excitation controller. The main function of the main exciter is to output AC power. The output three-phase AC power is converted to DC power by the rotating rectifier and supplied to the main motor. The main motor then converts the DC power back to three-phase AC power for output to subsequent circuits. A model of the main power supply system is shown below. Figure 4 As shown.

[0187] The single-phase output current and voltage signals of the main power supply model constructed in this invention are as follows: Figure 5 As shown, the model outputs data points with a sampling frequency of 20,000. 5,000 data points are selected for analysis. Figure 5 As can be seen, the number of voltage cycles within 500 data points (0.025s) is 10. Therefore, it can be deduced that the number of voltage cycles within 1s is 400, that is, the signal frequency is 400Hz, the voltage amplitude is approximately 161V, and the effective value of the sinusoidal signal voltage is... The effective value of the output voltage of this model is 115V, proving that the model meets the power requirements of 400Hz and 115V in constant frequency and constant speed AC voltage. At the same time, the three-phase voltages output by the main motor maintain a certain phase difference, and have a certain stability and consistency in terms of the amplitude and frequency of the output voltage and current, which can achieve the constant frequency and constant speed power supply requirements of the power supply system.

[0188] 2) Modeling of 270V transformer rectifier

[0189] In this embodiment of the invention, the power supply system uses four 270V transformer rectifiers to rectify the AC power output from the generator into 270V DC power for use by high-voltage DC loads. The 270V transformer rectifier mainly consists of a transformer, two rectifiers, and a filter. The transformer's main function is to convert the input 115V / 400Hz AC power into 270V AC power. The rectifiers' function is to eliminate certain high-frequency harmonics and improve power supply stability. The filter's function is to remove high-frequency harmonic components from the rectified voltage, thereby generating stable 270V DC power. The model for the 270V transformer rectifier is as follows: Figure 6 As shown.

[0190] The output current and voltage signals of the 270V transformer-rectifier model constructed in this embodiment of the invention are as follows: Figure 7 As shown, the model outputs data points with a sampling frequency of 20,000. 36,000 data points are selected for analysis. Figure 7 As can be seen, the output voltage of the model remains at around 270V. Therefore, the 270V transformer rectifier model constructed in this embodiment can achieve the function of transformer rectification and power distribution of 115V / 400Hz high-frequency AC power supply, and has a certain degree of stability.

[0191] 3) Modeling of 28V transformer rectifier

[0192] In this embodiment of the invention, the power supply system uses four 28V transformer rectifiers to rectify the AC power output from the generator into 28V DC power for use by low-voltage DC loads. The 28V transformer rectifier mainly consists of three parts: a transformer, a rectifier section, and a filter. This converts the 115V / 400Hz AC power input from the main power supply into 28V DC power. The transformer's main function is to reduce the voltage, and combined with the rectifier section, it can eliminate some high-order harmonics. The rectifier section consists of two rectifiers connected in parallel, primarily using diodes to rectify the AC signal. The filter's function is to remove high-frequency harmonic components from the rectified voltage output from the rectifier section and to block electromagnetic interference. Generally, an LC filter is used; the larger the filter capacitor, the smaller the output impedance, and the better the filtering effect. The model of the 28V transformer rectifier is shown below. Figure 8 As shown.

[0193] The output current and voltage signals of the 28V transformer rectifier model constructed in this embodiment are as follows: Figure 9 As shown, the model outputs data points with a sampling frequency of 20,000. 40,000 data points are selected for analysis. Figure 9As can be seen, the output voltage of the model remains around 28V. Therefore, the 28V transformer rectifier model constructed in this embodiment can achieve the function of transformering and rectifying 115V / 400Hz high-frequency AC power and distributing electrical energy, and has a certain degree of stability.

[0194] 4) Power supply system load modeling

[0195] In this embodiment, to simulate the load conditions in the power supply system, a typical three-phase AC resistor, a DC heater, and a fuel pump are used as loads connected to the circuit to simulate the load conditions in the power supply system. The three-phase AC resistor model, fuel pump model, and DC heater model are respectively referred to [reference needed]. Figure 10-12 .

[0196] In this embodiment, the power supply system model load mainly consists of a three-phase AC resistor, a fuel pump, and a DC heater. The three-phase AC resistor is set to have an impedance of 1 ohm, and the DC heater is set to have an impedance of 1 ohm. The fuel pump's speed, armature current, and torque signals under normal operating conditions are as follows: Figure 13 , Figure 14 , Figure 15 As shown, the fuel pump speed is maintained at around 240 r / s, and the torque is maintained at 0-3 N, which is consistent with the actual operating conditions.

[0197] Based on the power supply system model analysis and structural analysis, the power supply system in this embodiment is divided into four levels: power supply system, subsystem, equipment, and components. The composition of each level is shown in Table 1 below:

[0198] Table 1

[0199]

[0200] 2. Fault behavior twin modeling of key equipment in the power supply system

[0201] 1) Failure Mode Analysis of Key Equipment in Power Supply System

[0202] The main power source in the power supply system is the main power supply. The main power supply is responsible for converting the mechanical energy from the engine into the electrical energy required by the power supply system, as well as rectifying this electrical energy. It significantly impacts the overall power supply and distribution quality of the system and is therefore a critical component. The main motor, exciter, and rotating rectifier within the main power supply are key components, responsible for energy conversion and rectification. Therefore, the main motor, exciter, and rotating rectifier are selected as the twin objects for main power supply fault behavior in the power supply system.

[0203] This embodiment clarifies common and important fault modes of the main power supply, such as phase-to-phase short circuit of the main generator armature winding, single-phase open circuit of the main generator armature winding, single-phase open circuit of the exciter armature winding, phase-to-phase open circuit of the exciter armature winding, and single diode open circuit of the rotating rectifier, and performs fault behavior twin modeling.

[0204] In the secondary power supply, the 28V and 270V transformer rectifiers directly affect the input power quality of the load in the power supply system, and are therefore important components for ensuring power quality in the power supply system. In this embodiment, the 28V and 270V transformer rectifiers are selected as twin objects for modeling.

[0205] The fault mode types involved in this embodiment are shown in Table 2 below:

[0206] Table 2

[0207]

[0208] 2) Twin modeling of phase-to-phase short-circuit behavior of main generator armature winding

[0209] Due to the complexity of aircraft missions and the complex operating conditions of the power supply system, the insulation medium between the turns of the main generator windings may age during long-term use. This can lead to degradation of the inter-turn insulation performance, resulting in inter-turn short circuits, disrupting the balance between the three phases, causing output voltage deviations, and affecting the normal operation of the power supply system. This is reflected in the parameters as a gradual decrease in inter-turn resistance.

[0210] The following combination Figure 16 This paper provides a detailed explanation of the twin modeling method for this type of fault behavior:

[0211] Since the three-phase windings are symmetrical, only the inter-turn connection relationship of two of them needs to be changed. The parameter characteristics of the other two inter-turn short circuit cases are consistent with the first one. In this embodiment, in Figure 16 The simulation shows the fault behavior between phases B and C. The initial inter-turn resistance is set to 1e6 ohms, and the fault resistance is 0 ohms. Each simulation has a sampling time of 3 seconds and a sampling rate of 20000. 1000 data points are selected for analysis. The three-phase output voltage and current of the main motor under normal and fault conditions are shown below. Figure 17 , Figure 18 As shown.

[0212] Depend on Figure 17 and Figure 18The comparison of the main motor output voltage signals under different states shows that under normal conditions, the main motor output voltage amplitude remains at 161V, the current amplitude remains at 80A, and the frequency remains at 400Hz, meeting normal power supply requirements. Under a phase-to-phase short circuit in the armature winding, the frequency of the main motor output current and voltage remains unchanged, and the output voltage and current of phase A also remain stable. However, in phases B and C, the voltage amplitude drops to 85V, and the current amplitude drops to 46A, with both current and voltage decreasing to about 50% of their previous values. This indicates that phases B and C are connected and operating, with their current and voltage remaining consistent. Meanwhile, the frequencies of the three phases remain stable, proving that the twin model of this fault behavior is reasonable.

[0213] 3) Twin modeling of single-phase open-circuit behavior of main generator armature winding

[0214] Due to the complexity of aircraft missions and the complex operating conditions of the power supply system, during long-term use, the main generator armature winding may experience loose connections or burnout due to shock waves in high-vibration environments, leading to single-phase open circuits and affecting the three-phase current output and normal operation of the power supply system. This manifests as an increase in the resistance of a single-phase conductor in the armature winding. Therefore, in the model, the single-phase open circuit of the main generator armature winding is simulated by changing the resistance of the main generator winding conductors. In the main generator, the twin modeling method for this type of fault behavior is as follows: Figure 19 As shown.

[0215] The following combination Figure 19 This paper provides a detailed explanation of the twin modeling method for this type of fault behavior:

[0216] Since the three-phase windings are symmetrical, only the resistance of one winding needs to be changed. The parameters of the other two windings are the same as in the first scenario. In this embodiment, a single-phase open-circuit fault behavior twin is performed on phase A. The initial state winding resistance is set to 0 ohms, and the fault state resistance is set to 1e6 ohms. The sampling time for each simulation is set to 3 seconds, and the sampling rate is 20000. 500 data points are extracted for data analysis. The three-phase output voltage and current of the main motor under normal and fault states are as follows: Figure 20 , Figure 21 As shown.

[0217] Depend on Figure 20 , Figure 21The comparison of the main motor output voltage signals under different states shows that under normal conditions, the main motor output voltage amplitude remains at 161V, the current amplitude remains at 80A, and the frequency remains at 400Hz, meeting normal power supply requirements. Under the fault of an open circuit in phase A of the armature winding, both the output voltage and current of the main motor change. The voltages of phases A and C increase, while the voltage of phase B decreases. Due to the open circuit in phase A, the output current of phase A is 0. To meet the power demand, the currents of phases B and C both increase to some extent compared to normal conditions. The current of phase C increases more significantly due to its higher output voltage. The frequency of the three-phase output voltage remains stable, proving that the twin model of this fault behavior is reasonable.

[0218] 4) Twin modeling of single-phase open-circuit behavior of exciter armature winding

[0219] During long-duration flight, the armature winding of the main power exciter may experience loosening of joints or burnout due to shock waves in a high-vibration environment, leading to a single-phase open circuit and affecting the three-phase current output and normal operation of the power supply system. This manifests as an increase in the resistance of the single-phase conductor in the armature winding. Therefore, in the model, the single-phase open circuit of the exciter armature winding is simulated by changing the resistance of the armature winding conductor. In the exciter, a twin modeling method for this type of fault behavior is as follows: Figure 22 As shown.

[0220] Since the three-phase windings are symmetrical, only the resistance of one of the conductors needs to be changed. The parameter characteristics of the other two conductors are the same as in the first case. In this embodiment, a single-phase open-circuit fault behavior twin is performed in phase A. The initial conductor resistance is set to 0 ohms, and the fault resistance is set to 1e6 ohms. The sampling time for each simulation is set to 3 seconds, and the sampling rate is 20000. 500 data points are extracted for data analysis. The exciter output voltage under normal and fault conditions is as follows: Figure 23 , Figure 24 As shown, since the current is 0 when a single phase is open, there is no need to make a comparison.

[0221] Depend on Figure 23 and Figure 24 The comparison between the normal state and the single-phase voltage output signal of the exciter under a single-phase open circuit in the armature winding shows that, under normal conditions, the single-phase voltage signal range remains within the 15V-50V range, exhibiting certain fluctuation characteristics. Under a single-phase open circuit fault in the armature winding, the output voltage frequency increases significantly compared to the normal state due to the open circuit of one phase. Regarding the output voltage, the overall resistance of the exciter increases due to the single-phase open circuit, causing the output voltage of the exciter armature winding to rise accordingly, changing the voltage range to 0V-80V. This proves that the twin model of this fault behavior is reasonable.

[0222] 5) Twin modeling of phase-to-phase short-circuit behavior of exciter armature winding

[0223] A phase-to-phase short circuit in the exciter armature winding manifests in the parameters as a gradual decrease in inter-turn resistance, rather than a completely open-circuit state. Therefore, the model simulates the degradation of inter-turn insulation performance by altering the connection relationships within the exciter armature winding. In exciters, a twin modeling method for this type of fault behavior is as follows: Figure 25 As shown.

[0224] Since the three-phase windings are symmetrical, only the inter-turn connection relationship of two of them needs to be changed. The parameter characteristics of the other two inter-turn short circuit cases are consistent with the first one. In this embodiment, phase B and phase C are simulated as a phase-to-phase short circuit fault behavior twin. The initial state resistance of the 28V transformer coil is set to 0 ohms, and the fault state resistance is set to 1 ohm. The sampling time for each simulation is set to 3 seconds, and the sampling rate is 20000. 10000 data points are extracted for data analysis. The exciter phase C output voltage and current under normal and fault states are as follows: Figure 26 , Figure 27 As shown.

[0225] Depend on Figure 26 and Figure 27 The comparative analysis of the exciter C-phase output voltage and current signals under normal and armature winding phase-to-phase short circuit conditions shows that under normal conditions, the maximum output voltage of the exciter C-phase remains at 50V with strong signal stability, and the maximum current remains at 18V. However, under fault conditions, the maximum voltage increases to some extent, and the voltage signal fluctuations also increase to some extent. As for the current signal, due to the phase-to-phase short circuit, the current increases to a maximum of 50V, proving that the twin model of fault behavior is reasonable.

[0226] 6) Twin modeling of short-circuit behavior of a single diode in a rotating rectifier

[0227] A single diode short circuit in a rotating rectifier manifests parametrically as a failure of the diode's filtering function and circuitically as a short circuit. Therefore, in the model, a single diode short circuit fault in the rotating rectifier is simulated by connecting a wire in parallel next to the single diode. In rotating rectifiers, a twin modeling method for this type of fault behavior is as follows: Figure 28 As shown.

[0228] The initial state is set with the diode currently connected to the circuit; in the fault state, the diode is short-circuited. Each simulation is set with a sampling time of 3 seconds and a sampling rate of 20,000. 20,000 data points are selected for analysis. The output voltage and current of the rotating rectifier under normal and fault states are as follows: Figure 29 , Figure 30 As shown.

[0229] Depend on Figure 29 and Figure 30 The comparison of the output voltage and current signals of the rotating rectifier under normal and fault conditions shows that, under normal conditions, the voltage remains in the range of 20V to 50V and the current remains in the range of 15A to 20A. However, a short circuit in a single diode affects the rectification effect of the rotating rectifier, causing the voltage range to expand to 0 to 100V and the current signal to expand to the range of 5A to 25A. This proves that the twin modeling of this fault behavior is reasonable.

[0230] 7) Twin modeling of impedance rise behavior of 28V transformer rectifier

[0231] The function of a transformer rectifier is to convert alternating current (AC) to direct current (DC) and transform the voltage to supply the DC load on the machine. In the model, the resistance value of a single-phase winding of the transformer is changed to simulate the fault mode where the winding impedance increases and copper losses increase with transformer use. In a 28V transformer rectifier, the twin modeling method for this type of fault behavior is as follows: Figure 31 As shown.

[0232] Since the three-phase transformer windings are symmetrical, only one impedance relationship needs to be changed. The impedance increase of the other two phases is characterized in the same way as in the first scenario. The initial impedance is set to 0 ohms, and the fault impedance to 1 ohm. The sampling time for each simulation is set to 3 seconds, and the sampling rate to 20000. The output voltage and current of the 28V transformer rectifier under normal and fault conditions are as follows: Figure 32 , Figure 33 As shown.

[0233] Depend on Figure 32 and Figure 33 The comparison of the 28V transformer output voltage and current signals under normal and fault conditions shows that the voltage regulation capability of the transformer component is reduced due to the increased transformer impedance. Under normal conditions, the voltage remains within the range of 27.6–28V, while under fault conditions, the voltage drops to 27.5–27.9V, indicating a significant decrease. Simultaneously, the increased transformer impedance causes a substantial reduction in the 28V transformer output current. This comparative analysis verifies the rationality of the fault behavior twin model.

[0234] 8) Twin modeling of open-circuit behavior of 270V transformer rectifier filter inductor

[0235] The function of a 270V transformer rectifier is to convert AC power to 270V DC power and then transform the voltage to supply the DC load on the machine. In the model, the transformer inductance value is changed to simulate the fault mode of filter inductor open circuit as the transformer is used. In the 270V transformer rectifier, the twin modeling method for this type of fault behavior is as follows: Figure 34 As shown.

[0236] The initial state filter is connected to the circuit, and the fault state filter is disconnected and not connected to the circuit. Each simulation is set to a sampling time of 3 seconds and a sampling rate of 20000. The output voltage and current of the 270V transformer rectifier under normal and fault states are as follows: Figure 35 , Figure 36 As shown.

[0237] Depend on Figure 35 and Figure 36 A comparison of the 270V transformer output voltage and current signals under normal and fault conditions reveals that the open circuit in the 270V transformer rectifier filter inductor reduces the filtering capability of the high-frequency signals. Therefore, while maintaining the normal voltage range, the fluctuation of the 270V transformer output voltage signal when the filter inductor is open is significantly higher than in the normal state. Simultaneously, due to the open circuit in one filter, an internal open circuit occurs within the 270V transformer rectifier, preventing a certain current component from passing through. Consequently, a portion of the output current is zero, changing the current range from the normal 3A–5V to 0–5A. This comparative analysis verifies the rationality of the fault behavior twin model.

[0238] Since the power supply system channels have certain similarities and symmetries, fault behavior twin models of the four channels are performed according to the above-mentioned method, and the experimental data are organized.

[0239] 3. Construction of a fault dataset containing random noise

[0240] Based on the fault behavior twin model, a fault dataset is constructed using Simulink, with the following main parameters:

[0241] 1) Fault Type

[0242] The dataset includes twin modes of seven typical fault behaviors: phase-to-phase short circuit in the main generator armature winding, single-phase open circuit in the main generator armature winding, single-phase open circuit in the exciter armature winding, phase-to-phase short circuit in the exciter armature winding, single diode short circuit in the rotating rectifier, impedance rise in the 28V transformer rectifier, and open circuit in the filter inductor of the 270V transformer rectifier.

[0243] 2) Data length

[0244] In the experiment, the sampling time was set to 3 seconds for each simulation and the sampling rate was 20,000. To ensure the stability of the data, 20,000 data points within the 2-3 second time period were selected as samples.

[0245] 3) Sample generation

[0246] Since the power supply system is a typical circuit model, its signals are often relatively stable. However, due to factors such as the accuracy of signal acquisition equipment and the electromagnetic environment, noise often exists in signal measurement, affecting signal collection and analysis. Therefore, to better simulate the power supply system monitoring environment, random noise is added to the original signal to generate samples with the same characteristics as the real data. Based on expert experience, Gaussian noise with a signal-to-noise ratio of 15 is added to the data. Twenty sets of samples are generated for each fault mode. Table 4 shows the composition of the fault data. For the seven fault modes, fault behavior twin modeling is performed on each of the four channels, with details shown in Table 4 below.

[0247] Table 4

[0248]

[0249] To simulate monitoring parameter data under real-world operating conditions as closely as possible, this invention generates samples by adding noise. This allows the newly generated samples to mimic the data noise caused by electromagnetic interference, signal fluctuations, and instrument distortion during actual operation, making the generated fault sample data more consistent with real-world monitoring conditions. Although the noise-added data still retains some fault characteristic information, it is easily overwhelmed by the noise signal, thus affecting the accuracy of the fault diagnosis model. Furthermore, high-frequency signals contain a large amount of information; directly using them for fault diagnosis would significantly increase the model's complexity. Therefore, signal feature extraction and analysis of the fault sample data are necessary to extract the fault characteristic information from the data and reduce the model's complexity.

[0250] Thus far, behavioral twin modeling of fault behavior of key equipment in the power supply system has been completed through behavioral twinning and data generation, providing a data foundation for fault state perception twin network modeling.

[0251] II. Twin Modeling of Fault State Awareness for Key Equipment in Power Supply Systems Based on Physical Information Networks

[0252] 1. Fault data feature extraction based on Hilbert-Huang transform and RMS values

[0253] The current generated in a power supply system is mostly an alternating current signal, characterized by high frequency and high fluctuation. Time-domain signal processing methods often cannot directly analyze this signal, easily leading to information loss. Preprocessing is necessary to extract the required fault state characteristics from the complex signal. Common signal analysis methods include time-domain analysis, frequency-domain analysis, and time-frequency-domain analysis. Time-domain analysis uses statistical methods such as mean, variance, root mean square, and kurtosis to analyze and extract features from time-series data, including stability and distribution characteristics. Frequency-domain analysis transforms time-domain signals into frequency-domain signals using methods like Fourier transform, analyzing signal characteristics through the distribution of signals at different frequencies. Time-frequency-domain analysis can extract features from both the time and frequency domains, analyzing frequency information that changes over time, providing a more comprehensive analysis and feature extraction. A common method is the Hilbert-Huang Transform.

[0254] First, Empirical Mode Decomposition (EMD) is performed on the original signal x(t), and the original signal is decomposed into...

[0255]

[0256] Among them, c i (t) represents the i-th Intrinsic Mode Function (IMF), r n (t) represents the residual value sequence, and the basic modal components are c. i (i = 0, 1, 2, ...) represent signals in different frequency bands.

[0257] Let the IMF component be c(t), then its complex analytic signal h(t) is:

[0258]

[0259] in, The result of performing a Hilbert transform on c(t)

[0260]

[0261] a(t) is the amplitude function, and also the envelope signal of the IMF component c(t), expressed as:

[0262]

[0263] in phase function

[0264]

[0265] Taking its derivative yields the instantaneous frequency.

[0266]

[0267] Therefore, the original signal x(t) can be represented by a time-frequency function that includes the instantaneous amplitude and instantaneous frequency.

[0268]

[0269] The instantaneous amplitude of the IMF component is its envelope signal. The envelope signal is similar to a periodic signal, which is helpful for fault identification, and has a great advantage even for fault detection of weak signals. In this study, the envelope of the first analytical signal h(t), i.e., the principal component, is taken to obtain a(t), which is the envelope curve of the IMF component, and then further decomposed.

[0270] Meanwhile, since both DC and AC power signals exist in the power supply system, and due to the high frequency of the power supply system signals and the large instantaneous voltage changes, there are peak value variations. In order to analyze and measure the overall trend of AC signal changes, the alternating current is evaluated from the perspective of the electrical energy generated by the AC power, i.e., the effective value is used. The effective value is calculated as shown in formula (3.8).

[0271]

[0272] X i This represents the current value at the i-th sampling point;

[0273] N represents the number of sampling points;

[0274] i represents sampling point i.

[0275] Effective values ​​can clearly capture the changing trends and information characteristics of signals, and are of great significance in the study of power supply system fault diagnosis.

[0276] As the above analysis shows, the HHT transform can decompose high-frequency signals and obtain their instantaneous frequency and phase. The RMS characteristic, a commonly used parameter in circuit analysis, reflects the energy change trend of a circuit over a period of time. Therefore, the feature extraction method presented in this paper can obtain the characteristic information of the data in four aspects: frequency, phase, amplitude, and trend, enabling the preservation and even enhancement of fault characteristics. Figure 37 This is a flowchart for feature extraction from fault data.

[0277] The following is an example of a phase-to-phase short circuit in the armature winding of the main generator. Figure 2 Taking the first channel fault shown in the diagram as an example, the time-domain signals of three key devices in the main power supply, the high-voltage and low-voltage transformers and rectifiers, and the AC load are as follows: Figure 38As shown.

[0278] The HHT transform can capture the instantaneous phase, frequency, and amplitude characteristics of data. To reduce computational complexity, the instantaneous phase and frequency of the first component after the HHT transform are used as feature parameters. Furthermore, the effective value of the signal clearly reflects its changing trend and information content characteristics; therefore, these three-dimensional features are selected as the signal feature extraction results. The results for all seven fault modes and normal conditions are as follows: Figure 39 (For three-channel applications)

[0279] Depend on Figure 39 It can be seen that different fault modes have a certain degree of response to the trend of the effective value, and the changes in instantaneous phase and instantaneous frequency are more reflected in the numerical changes. Thus, the Hilbert-Huang transform and effective value proposed in this paper can play a role in identifying and classifying the characteristics of different fault modes, effectively reducing noise interference, and extracting effective features from high-frequency signal data.

[0280] 2. Physical Information Representation Based on Differential Algebraic Equations

[0281] 1) Transient stability analysis and differential-algebraic equations of power supply system

[0282] The transient stability of a power system refers to whether, when a power system suffers a major disturbance (such as a fault, generator disconnection, load shedding, or reclosing), the generator components can return to their previous synchronous and stable operating state after the transient process, and maintain acceptable voltage and frequency levels.

[40] Currently, there are two main methods for transient stability analysis of power systems: time-domain simulation, also known as step-by-step integration, and the direct method, also known as the transient energy function method.

[0283] The time-domain simulation method first constructs a holistic system model of the power system by modeling the various components according to their topological relationships. This model consists of a system of differential equations and algebraic equations. Then, starting with the steady-state condition or power flow solution, it progressively solves for numerical solutions under disturbances, obtaining the curves showing the changes in system state variables and algebraic variables over time. The analysis of the generator rotor oscillation curve can be used to determine whether the system can maintain transient stability under significant disturbances.

[0284] The aforementioned system of simultaneous differential and algebraic equations, also known as differential-algebraic equations (DAEs), can be viewed as an extension of the explicit ordinary differential equation y' = f(t,y). It belongs to a constrained type of ordinary differential equation, such as...

[0285] x'=f(t,x,z) (3.9a)

[0286] In the case of 0 = g(t,x,z) (3.9b), the ordinary differential equation (3.9a) describing the dynamic evolution of the differential variable depends on another algebraic variable, and its solution must also satisfy the constraints of the algebraic equation (3.9b). Compared with the classical ordinary differential equation form of power systems, it contains more topological information about each node and network, which helps to achieve deep integration of model and data in this study.

[0287] Solving DAEs involves complex mixed differentiation and integration processes. Therefore, it is desirable to obtain an explicit ordinary differential equation system with all variables by analytically differentiating (and repeating analytical differentiation if necessary) and eliminating variables from a given system (the problem to be solved must be nonsingular). The degree of differentiation required for this transformation is called the index of the DAE. Trivially, the index of the ODE is 0. The DAE system equations of the Hessenberg index-1 are in the form of (3.9). When solving, z = G(y,t) can be obtained from (3.9b) and then substituted into (3.9a), which means that its Jacobian matrix... It is invertible and bounded in the neighborhood of the exact solution.

[0288] 2) Physical information representation of key equipment in the power supply system

[0289] Ignoring transmission losses and bus voltage deviations, and combining time-domain simulation and dynamics, for generator k,

[0290]

[0291] Where the parameter m k Let d be the inertial constant. k B is the damping coefficient. kj P is the magnetization matrix between nodes {k,j}. k It is the mechanical power of the generator, V k V j For voltage, δ k δ j This represents the transient voltage phase angle behind the reactance. It is the angular frequency, usually denoted as ω. k Generally, m is ignored for load. k And Pk <0.

[0292] In this embodiment, based on the aforementioned fault behavior twin modeling, a physical information representation based on differential algebraic equations is established for key equipment. Taking a certain channel as an example, the topological relationship of the key equipment is abstracted as follows: Figure 40 At that time, the dynamic equations are obtained.

[0293]

[0294] and algebraic equations

[0295] -(1 / V A (g)=0 (3.11b)

[0296] In (3.11a), k represents the symbols 1, 2, 3, H, and L, respectively, which represent the main exciter, rotating rectifier, main motor, 270V transformer, and 28V transformer, and have...

[0297] f1 = B 12 V1V2 sin(δ1-δ2)-P1 (3.12a)

[0298] f2 = B 21 V2V1 sin(δ2-δ1)+B 23 V2V3 sin(δ2-δ3)-P2 (3.12b)

[0299]

[0300]

[0301]

[0302]

[0303] Where, m k Let d be the inertial constant. k The damping coefficient is... Angular frequency, f is the angular velocity. k V represents the zeroth-order differential term in (2). A Let g represent the voltage of the AC load, g represent the zeroth-order differential term in the algebraic equation, and k = 1, 2, 3, H, L, A represent the main exciter, rotating rectifier, main motor, 270V transformer rectifier, 28V transformer rectifier, and AC load, respectively. 21 B represents the magnetization matrix between the rotating rectifier and the main exciter. 23 B represents the magnetization matrix between the rotating rectifier and the main motor. 31 B represents the magnetization matrix between the main motor and the main exciter. 3AB represents the magnetization matrix between the main motor and the AC load. 3H B represents the magnetization matrix between the main motor and the 270V transformer rectifier. 2L B represents the magnetization matrix between the rotating rectifier and the 28V transformer rectifier. H3 B represents the magnetization matrix between the 270V transformer rectifier and the main motor. HA B represents the magnetization matrix between the 270V transformer rectifier and the AC load. HL B represents the magnetization matrix between the 270V and 28V transformer rectifiers. L3 B represents the magnetization matrix between the 28V transformer rectifier and the main motor. LA B represents the magnetization matrix between the 28V transformer rectifier and the AC load. LH B represents the magnetization matrix between the 28V and 270V transformer rectifiers. A3 B represents the magnetization matrix between the AC load and the main motor. AH B represents the magnetization matrix between the AC load and the 270V transformer rectifier. AL This represents the magnetization matrix between the AC load and the 28V transformer rectifier; where the dynamic unknowns characterizing the system state are y = (δ1, δ2, δ3, δ...). H ,δ L ,δ A ) T The algebraic unknown is z = V A .

[0304] Next, based on the equipment parameters and model, set m1, m2, m3, m H ,m L ,d1,d2,d3,d H ,d L and voltages V1, V2, V3, V H V L V A (V1 voltage of the main exciter, V2 voltage of the rotating rectifier, V3 voltage of the main motor, V...) A The voltage V of the 270V transformer rectifier H The voltage V of the 28V transformer rectifier L ;), power P1, P2, P3, P H ,P L ,P A Q A These are built-in parameters of DAE-PINN. These parameters will be adjusted during subsequent training using samples from different failure modes.

[0305] 3) Fault state perception twin modeling based on DAE-PINN

[0306] (1) Implicit Runge-Kutta Method

[0307] After listing the DAE (Digital Equation for Power Systems), various numerical integration methods can be applied to solve it, such as the explicit Euler method, the modified Euler method, the explicit Runge-Kutta method, and the implicit trapezoidal integration method. When the generator adopts a non-classical model, the system differential equations cannot be numerically integrated using simple explicit methods (such as the explicit Runge-Kutta method). If the differential equations in the DAE system not only include electromechanical equations (swing equations) but also model rotor flux linkage (fast dynamic process), AVR (Automatic Voltage Regulator), governor, and turbine, it becomes a rigid equation system, requiring robust integration methods to simulate its dynamic behavior. Given the stability requirements for rigid problems in power systems, this invention employs the implicit Runge-Kutta (IRK) method for numerical solution.

[0308] Specifically, when the step size is h = t n+1 -t n >0, the integral starts from (t) n ,y n ,z n ) proceed to (t) n+1 ,y n+1 ,z n+1 When applying the implicit Runge-Kutta method of order v to the DAE of (3.12), we obtain...

[0309]

[0310] 0=g(ξ i ,ζ i ), j = 1, 2, ..., v (3.13b)

[0311]

[0312] 0 = g(y n+1 ,z n+1 (3.13d)

[0313] Where ξ j =y(t) n +c j h), ζ j =z(t) n +c j h), {a j,i ,b j ,c i} represents the unknown parameters of the implicit Runge-Kutta method, and the parameters are specified.

[0314] ξj This represents the y-value corresponding to the j-th discrete point at a certain time step;

[0315] c j Represents the node coefficients;

[0316] y(t n +c j h) represents the value of the dynamic variable at the j-th discrete point at the n-th time step;

[0317] z(t n +c j h) represents the value of the algebraic variable at the j-th discrete point at the n-th time step;

[0318] a j,i Indicates coefficient;

[0319] b j Indicates coefficient;

[0320] y n This represents the value of the dynamic variables in the differential algebraic equation at the nth time step;

[0321] z n This represents the value of the algebraic variable in the differential-algebraic equation at the nth time step;

[0322] t n This represents the nth time step;

[0323] n represents the time step number;

[0324] v represents the order of the implicit Runge-Kutta method;

[0325] ζ i This represents the z-value corresponding to the j-th discrete point at a certain time step;

[0326] f(ξ i ,ζ i () represents the value of the zeroth-order term of the dynamic equation corresponding to the j-th discrete point at a certain time step;

[0327] g(ξ i ,ζ i () represents the value of the non-zero term in the algebraic equation corresponding to the j-th discrete point at a certain time step;

[0328] g(y n+1 ,z n+1 ) represents the value of the non-zero term in the algebraic equation at the (n+1)th time step.

[0329] (2) Neural Networks Based on Physical Information

[0330] The principle behind training neural networks lies in adjusting the input weight matrix and hidden layer biases to minimize the difference between the neural network's predictions and the training data. Neural networks can be used as general function approximators to learn the nonlinear mapping between the input and output of differential equations. However, if the underlying physical model is not considered during training, a large amount of training data and neurons are required. Physics-informed neural networks (PINNs) consider physical constraints during training, thus requiring less training data and a smaller neural network size, which helps to learn models with greater generalization ability.

[41] The general form of the function approximating PINNs is:

[0331]

[0332] Where u(t,x) is the solution, N[u;λ] is the nonlinear operator connecting the state variable u and the system parameter λ, t represents time, x represents the system input, the domain Ω can be based on prior knowledge of the dynamic system and is bounded, and [0,T] is the time interval of system evolution. The model parameter λ can be constant or unknown. When λ is unknown, the approximation problem of function (2.3) becomes a system identification problem, requiring the search for parameter λ that satisfies the expression in (2.3). To strengthen the description of the physical laws of the dynamic system, a neural network with physical information is defined:

[0333]

[0334] Optimize the shared parameters of the two neural networks by minimizing the loss function.

[0335]

[0336] In the formula, MSE u N represents the mean squared error loss corresponding to the initial data. u Let be the total number of training data, and i represent the i-th training data. This represents the time of the i-th training data. This represents the input of the i-th training data. This represents the dynamic value corresponding to the i-th training data;

[0337] MSE f Let N be the mean square error over a finite set of points. f The total number of configuration points. This represents the time of the i-th configuration point. This represents the input of the i-th configuration point. It represents the algebraic value corresponding to the i-th configuration point. The finite configuration point set is the point set of the physical information algebraic terms during discrete processing.

[0338] Given a training dataset and known system parameters λ, the goal is to find neural network parameters that minimize the weights and biases. When the parameters λ are unknown, the system parameters are considered as additional variables.

[0339] (3) Twin modeling of fault state perception for key equipment in power supply system

[0340] To overcome the limitations of computing power, this invention aims to establish a discrete DAE-PINN framework and, based on expressing the physical laws of key equipment in the power supply system, construct a state-aware twin model that is driven by data and model fusion.

[0341] First, as can be seen from the DAE hierarchical structure, the neural network needs to be trained separately using differential equations and algebraic equations as physical information. Two approaches can be used: stacked and unstacked. The following section will compare the solution performance of these two approaches on this problem. The input is y. n When, the output is and

[0342] Next, the IRK method is integrated into the iterative calculation of the neural network loss function (dividing the dynamical and algebraic equations, calculating two loss functions, thus the loss function consists of two parts; the Runge-Kutta method is a numerical analysis (solving differential equations) method that transforms continuous differentials into discrete iterative steps, therefore the original continuous function is transformed into a discrete form using IRK (implicit Runge-Kutta method)). The loss function form is as follows:

[0343]

[0344] Finally, a gradient-based optimizer is used to minimize the loss function to train the neural network parameters; for example, using the Adam optimizer:

[0345]

[0346] Let w represent the total loss function. f The weights represent the weights corresponding to the dynamic loss function. w represents the loss function of the dynamic equation. g The weights represent the weights corresponding to the loss function in the algebraic equation. Represents the loss function of an algebraic equation;

[0347] N τ Let v represent the size of the training dataset, k represent the order of the implicit Runge-Kutta method, j represent the j-th training data point, and y represent the number of implicit Runge-Kutta steps. n,kLet represent the value of the dynamic variable in the differential-algebraic equation at the nth time step and the kth training data point. Let represent the dynamic variables in the differential-algebraic equations at the nth time step and the kth training data at the jth order implicit Runge-Kutta step;

[0348] Represents the loss function of an algebraic equation. Let represent the y-value corresponding to the j-th discrete point and the k-th training data at a certain time step. Let z represent the z-value corresponding to the j-th discrete point and the k-th training data at a certain time step. Let represent the value of the non-zero term in the algebraic equation corresponding to the j-th discrete point and the k-th training data at a certain time step. Let represent the value of the dynamic variable in the differential-algebraic equation at the (n+1)th time step and the kth training data point. Let represent the value of the algebraic variable in the differential-algebraic equation at the (n+1)th time step and the kth training data point. This represents the value of the non-zero term in the algebraic equation for the (n+1)th time step and the kth training data point;

[0349] This represents the dynamic variable in the differential-algebraic equation at the nth time step and the kth training data point at the jth order implicit Runge-Kutta step. Let represent the condition that the dynamic variables in the differential-algebraic equation should satisfy at the nth time step and for the kth training data at the jth order implicit Runge-Kutta step, where h represents the step size, i represents the ith order implicit Runge-Kutta step, and a j,i Indicates a constant coefficient. This represents the value of the zeroth-order term of the differential equation corresponding to the j-th discrete point and the k-th training data at a certain time step;

[0350] This represents the dynamic variable in the differential-algebraic equation at the nth time step and the kth training data point at the (v+1)th order implicit Runge-Kutta step. This represents the condition that the dynamic variables in the differential-algebraic equation should satisfy at the nth time step and for the kth training data at the (v+1)th order implicit Runge-Kutta step. Let b represent the dynamic variable in the differential-algebraic equation of the (n+1)th time step and the kth training data. j Indicates a constant coefficient;

[0351] θ * This represents the optimal parameters obtained by the Adam optimizer.

[0352] It should be noted that incorporating the IRK method into the neural network loss function yields... The conversion process is as follows:

[0353] The loss function is solved separately based on the mean square error of the two equations, dynamics and algebra, and the mean square error is calculated by summing the implicit Runge-Kutta by order and the training data by number; (3.17) The last two equations are (3.13a) and (3.13c) derived.

[0354] This invention uses a weighting coefficient ω f and ω g To balance differential dynamic variables and algebraic variables The remaining loss term. It is easy to see that ω f and ω g When ω is too large, the convergence of the neural network deteriorates; f and ω g If the value is too small, the optimization result may not satisfy the dynamic equation, or it may satisfy the dynamic equation but not the manifold described by the algebraic equation. To prevent the optimization problem from becoming ill-conditioning, this invention uses a penalty method to update the weight coefficients ω. f and ω g The value of is used to add an approximate hard constraint to this DAE problem. Specifically, in the k-th iteration, the following unconstrained optimization problem is solved.

[0355]

[0356] in, and This is the penalty coefficient for the k-th iteration. Furthermore, at the beginning of each iteration, the penalty coefficient is increased by a constant factor β > 1, therefore we have...

[0357]

[0358] This represents the initial value of the penalty coefficient corresponding to the dynamic equation. Let (β) be the initial value of the penalty coefficient corresponding to the algebraic equation. k Represents the k-th power of a constant factor;

[0359] Assuming the neural network is well trained, the solution to the sequence of unconstrained optimization problems will converge to a solution that approximately satisfies the hard constraints of the DAEs.

[0360] By minimizing the loss function To train the model, use the Adam optimizer with default hyperparameters and an initial learning rate η = 10. -3 When the loss function When the value of the learning rate plateaus or begins to increase, the learning rate should be reduced.

[0361] In this invention, both the neural networks for fitting the dynamic equations and the algebraic equations use fully connected structures and forward propagation structures:

[0362]

[0363] Here, X is the input tensor of the neural network, d is the number of hidden layers (i.e., the network depth), ⊙ is the Hadamard product or element-wise product, and φ is the pointwise sinusoidal activation function. U represents the activated tensor corresponding to the initial weight 1, and H... (1) Z represents the input tensor of the first layer. (k) H represents the tensor after activation at the k-th layer. (k) H represents the input tensor of the k-th layer. (k+1) W represents the output tensor of the k-th layer. z,k Let b represent the weight matrix corresponding to the k-th layer after activation. z,k This represents the bias corresponding to the k-th layer after activation.

[0364] Meanwhile, assuming the width of each hidden layer is w, and using the normal Glorot initialization algorithm, the trainable parameters of the network architecture are as follows:

[0365]

[0366] This new architecture outperforms traditional fully connected architectures. This is because it explicitly explains the multiplicative interactions between different inputs and enhances the hidden state representation with residual connections, as illustrated below. Figure 41 As shown:

[0367] Therefore, a fault state-aware twin network model can be constructed based on the above network structure. By setting the model hyperparameters, fault data generated by the fault behavior twin network can be used for training, validation, and prediction. Clearly, when the model hyperparameters are selected and trained using a dataset of the same fault mode, the resulting twin networks are equivalent after sufficient training iterations. Prediction can be performed based on neural networks and historical data; therefore, the network model obtained from historical data is a twin of the real model, i.e., a state-aware twin network, which can synchronize with real equipment based on data generated by the behavior twin of a specific fault mode.

[0368] Furthermore, by training the model using new fault data, the twin network can dynamically interact with the real entity, automatically updating and easily ensuring their consistency, thus fulfilling the requirement of adaptive updating capability of digital twins. Moreover, due to the model-data fusion characteristics of physical information neural networks, the twin network can more completely represent the system state. Therefore, the fault state perception twin model established in this invention effectively solves the problems existing in current methods. At the same time, the dataset generated by the fault behavior twin model avoids the disadvantages such as imbalanced fault data. Thus, this invention establishes the twin model architecture required for fault diagnosis of key equipment in power supply systems.

[0369] With a network width of 200 and a depth of 6 layers, a Siamese network model was trained using 100 samples under normal conditions and iterated 1500 times. The results are as follows. Figure 42 As shown in the figure, the mean squared error of both training and validation has essentially converged to 10^4 after 400 iterations. -3 The magnitude of the data demonstrates the convergence of the network and the feasibility of the model.

[0370] III. Fault Status Perception Twin Model Update and Fault Diagnosis of Key Equipment in Power Supply System

[0371] 1. Fault State Awareness Twin Network Optimization

[0372] In this embodiment, the convergence of the network architecture, network size, and training dataset applied to the proposed state-aware Siamese network was also investigated. A time step h = 0.1 and the number of iterations epochs = 1500 were uniformly selected to complete the model convergence experiment. w represents the neural network width (number of channels per layer), and d represents the depth of the hidden layers in the neural network.

[0373] Network architecture includes stacked and non-stacked structures. Non-stacked structures are dynamic state variables. Assign a neural network as the algebraic variable. Assign another neural network; in the stacked structure, fit all dynamic variables with a separate neural network. and state variables To determine which Siamese network structure performs better, multiple trials were conducted with fixed, moderate widths, depths, and training schemes. For stacked structures, a suitable dataset with [w=200, d=5] and normal conditions was used to train the network; for non-stacked structures, a neural network with [w=200, d=5] was used to train differential equations, and a neural network with [w=100, d=3] was used to train algebraic equations. The trials were run 10 times, and the mean squared errors (MSE) of training and validation were compared between stacked and non-stacked structures. The results after 10 runs are as follows: Figure 43 As shown, the non-stacked structure exhibits better performance in this problem.

[0374] Furthermore, the impact of depth and width on the performance of non-stacked Siamese networks is discussed. Numerous experiments show that the influence of both width and depth on training loss is not monotonic. Too small a width makes it difficult to learn rich features, limiting model performance; too large a width leads to repetitive feature extraction and excessive computation. Too small a depth results in weak nonlinear representation, while too large a depth leads to gradient instability and network degradation. Therefore, several possible values ​​for width and depth were set, and multiple experiments were conducted under suitable training schemes. On one hand, with a fixed depth d=5, the width was varied, with w=20, 40, 100, 200, 500, and 1000 for comparison. On the other hand, with w=200 fixed, the network depth was varied with d=1, 2, 4, 6, 8, and 10 for comparison. After 10 runs, the optimal combination was found to be w=200 and d=6.

[0375] Finally, the size N of the training dataset was investigated. τ The impact of |τ| on the convergence of Siamese network training. Generally, the training data can be appropriately increased, but when the network layers are insufficient, feature training will be inadequate, prediction results will deteriorate, and problems such as overfitting will occur. Several possible values ​​for the training dataset size were set for experimentation. Simultaneously, to eliminate the influence of the stacked structure, width, and depth of the neural network, non-stacked structures were selected: a dynamical network [w=200, d=6] and an algebraic network [w=40, d=4]. The N values ​​were varied. τ =50,100,500,1000,2000, after running 10 times, the result is as follows Figure 46 As shown, when the number of training iterations is 100, better training results can be obtained with less training cost.

[0376] In summary, a non-stacked DAE-PINN with [w=200, d=6] is selected as the basic structure of the twin network; and [N] is adopted. train =100, N test =100, N valid The training scheme of [=200] was tested. At this point, the optimization of the Siamese network structure was completed. However, since several hyperparameters in the differential-algebraic equations are still undetermined, this network is not yet a complete Siamese model of the key equipment in the power supply system. It is necessary to train and update the unknown parameter values ​​of the DAE based on fault datasets under different fault modes, characterize the fault modes of the key equipment, establish a state-aware Siamese model, and apply it to fault diagnosis.

[0377] 2. Fault State Awareness Twin Network Update Based on Bayesian Optimization

[0378] TPE (Tree-structured Parzen Estimator) is a method for adjusting model hyperparameters based on tree-structured Bayesian methods. Let P(θ|y) be the probability that the hyperparameter is θ given a model error of y, which is defined by two density functions:

[0379]

[0380] Where l(θ) is based on the observation space {θ (i)}Establish, θ (i) Let θ represent the hyperparameter of the i-th observation, and let f(θ) be the loss in this observation space. (i) ) is less than y*, y * This represents the model error threshold; g(θ) is established based on the remaining observation space. Typically, methods based on Gaussian processes directly fit P(y|θ), aiming to obtain a larger y*; while the TPE strategy combines Bayesian optimization ideas, indirectly obtaining P(y|θ) by fitting P(θ|y) and P(y), searching for a larger y* based on the current observation f(θ). The process of fitting P(y|θ) is as follows: The Expected Improvement (EI) function is the objective of maximizing the Total Physical Equilibrium (TPE). The expression for the Expected Improvement function is as follows:

[0381] The desired improvement function, after transformation according to Bayes' theorem, takes the following form:

[0382]

[0383] This method uses the Parzen–Rosenblatt Window, which employs a Gaussian function as the window function to estimate the probability density based on the prior distribution and current observations. Simultaneously, it restricts the search for the optimal solution to the objective function to a tree-like structure, such as... Figure 47 As shown.

[0384] Using TPE, all hyperparameters are set based on a tree structure, ensuring their independence from each other, thus allowing some hyperparameters to be fixed while others are optimized. Furthermore, Parzen window sampling is applied from top to bottom of the tree root node to obtain the hyperparameter set and calculate the joint probability, which is then substituted into the desired improvement function for optimization.

[0385] To achieve automatic hyperparameter selection based on TPE (Distributed Hyperparameter Optimization), the Hyperopt optimization tool is used to adjust several hyperparameters of the fault state-aware twin network, specifically the values ​​of m, d, V, P, Q, and B for each device in the DAE equation. Hyperopt is a Python library for serial and parallel optimization based on Bayesian methods in a search space. The search values ​​can include real-valued continuous points, discrete points, etc. Hyperopt uses algorithms including random search, simulated annealing, and TPE; this paper selects the TPE algorithm. The key to the algorithm's application is specifying the objective function, search variables, and search space. After several parameter selection trials, the loss and hyperparameter set for each trial are recorded, and suitable hyperparameter values ​​are given based on minimizing the loss.

[0386] Therefore, the hyperparameters of the fault state-aware twin network under different fault modes are selected based on the above methods.

[0387] 3. Fault diagnosis of key equipment in power supply systems based on convolutional neural networks

[0388] 1) Construction of the intrinsic feature set of failure modes

[0389] The above analysis shows that the specific differences between multiple fault state-aware twin networks are uniquely determined by the values ​​of several variables in the DAE equation, while the network parameters iterate gradually during training. Therefore, the set of values ​​for these hyperparameters differs for different fault modes. Let the hyperparameter value space for a certain fault mode be denoted as...

[0390]

[0391] Where i m i d i V i P The values ​​include 1, 2, 3, H, and L, which represent the main exciter, rotating rectifier, main motor, 280V transformer rectifier, 28V transformer rectifier, and AC load, respectively. The magnetization matrix parameter between the equipment is uniformly set to b.

[0392] It can be seen that S under different fault modes fault The differences can serve as a basis for fault diagnosis. This invention utilizes the hyperparameter feature space S... fault The intrinsic feature set of the fault mode is the key task in the following text, which is to search for the intrinsic feature set of the seven fault modes and the normal operation state, and to carry out fault diagnosis based on this.

[0393] First, estimate the eigenvalue set S under normal conditions. normalWhen modeling the key equipment of the power supply system, some parameter values ​​have been set in MATLAB / Simulink, including the inertia constant m, damping coefficient d, and mechanical power P of the main exciter and main motor, as well as the input voltage V of all key equipment. Therefore, based on these fixed values, the remaining hyperparameters are selected based on Hyperopt.TPE.

[0394] For different hyperparameters, upper and lower bounds were set for the search, and training was performed 1500 times for each. This training task was then repeated 200 times using Hyperopt, constituting one hyperparameter iteration. The specific operations in each iteration were as follows: the minimum training error values ​​from the 200 training tasks were sorted, the top 10% of intrinsic feature values ​​were selected, a box plot was plotted, and the upper and lower quartile values ​​were used as the new upper and lower bounds for the next iteration. A total of 5 iterations were performed. For large search spans, the step size was gradually reduced from 100 to 1; simultaneously, the parameter order of magnitude was standardized, and the units of physical quantities were set as shown in the table below to improve convergence during training.

[0395] Table 5 Intrinsic characteristics and related physical quantities (units)

[0396]

[0397] Combining model information, expert knowledge, and automatic parameter optimization results, the estimated values ​​of the normal state intrinsic feature set after 5 search iterations are as follows:

[0398] Table 6. Values ​​of intrinsic characteristics under normal conditions

[0399]

[0400]

[0401] Furthermore, input data for seven fault modes and obtain the intrinsic feature sets according to the above experimental scheme. It is important to note that after obtaining relatively stable upper and lower bounds for the search through five iterations, conduct ten more experiments without changing these bounds. For each fault mode and normal state, generate a set of intrinsic feature observations under the minimum loss condition, which will be applied to the next step of fault diagnosis.

[0402] 2) Fault diagnosis based on convolutional neural networks

[0403] A convolutional neural network (CNN) is a deep learning technique that utilizes convolutional structures for computation. It is a supervised learning, multi-layered neural network primarily composed of convolutional layers, downsampling layers, and fully connected layers. Each layer contains multiple feature maps, where each feature map extracts a specific feature from the input data through convolutional filters and multiple neurons. These three layered structures constitute the key components of a convolutional neural network, enabling the extraction of data features.

[0404] Convolutional layers: These typically use a trainable filter to progressively convolve the input image (input vector) and add biases to obtain the convolutional layer. This is because convolution operations can enhance certain features of the original signal and reduce noise.

[0405] Downsampling layers, also known as pooling layers, compress the linear features of the input layer by weighted merging of neighboring pixels, adding a bias, and using an activation function to generate a smaller feature map. Downsampling reduces data processing while retaining important information. Furthermore, the sampling operation can obfuscate the positional information of features because it only requires relative positional information, making it useful for handling deformations and distortions of similar objects. Fully connected layers typically use Softmax full connections, and the resulting activation values ​​are the feature results extracted by the convolutional neural network.

[0406] Fully connected layer: Softmax full connection is often used, and the activation values ​​obtained are the feature results extracted by the convolutional neural network.

[0407] This invention uses a CNN model for fault diagnosis of critical equipment in a power supply system. When solving for the intrinsic feature set, the hyperparameters of non-faulty critical equipment are fixed, and the power and input voltage feature values ​​of faulty critical equipment are selected using the Hyperopt library to obtain feature results. After assigning labels 1 to 7 to seven fault modes, a CNN is used to perform supervised multi-class classification diagnosis on the intrinsic feature set.

[0408] The parameters of the fault identification model are as follows:

[0409] First layer (input layer): The layer type is input layer, and the input vector dimension is 10*1*1, which is equal to the dimension of a single sample;

[0410] The second layer (convolutional layer): The layer type is a convolutional layer, with 128 neurons, a 2*1 convolutional kernel, and the activation function is "tanh";

[0411] The third layer (pooling layer): The layer type is a pooling layer, and the pooling size is 2*1;

[0412] The fourth layer (convolutional layer): The layer type is a convolutional layer, with 64 neurons, a 2*1 convolutional kernel, and the activation function is "tanh";

[0413] Fifth layer (pooling layer): The layer type is a pooling layer, and the pooling size is 2*1;

[0414] The sixth layer (fully connected layer): The layer type is a fully connected layer with 40 network nodes and the activation function is "relu". The seventh layer (Dropout1): The layer type is a Dropout layer, which ignores hidden layer nodes at a ratio of 0.1.

[0415] Layer 7 (Fully Connected Layer): This layer is fully connected with 20 network nodes and uses the ReLU activation function. Layer 8 (Dropout2): This layer is a Dropout layer that ignores hidden layer nodes at a ratio of 0.1.

[0416] Layer 9 (Fully Connected Layer): The layer type is fully connected, and the number of network nodes is 40;

[0417] The tenth layer (output layer): The layer type is a fully connected layer, the number of network nodes is equal to the number of fault types, and the activation function of this layer is "softmax".

[0418] The training method is supervised training. The Categorical Cross Entropy function is selected as the loss function, and Adam (Adaptive Momentum) is selected as the optimization algorithm. The first 70% of the data for each fault state is used as training samples, and the rest are used as test samples. The number of training rounds is set to 300, and the batch size is 4.

[0419] The formula for calculating the loss function is as follows:

[0420]

[0421] Where c is the predicted category, and the sign function Y i The value can be 0 or 1. If the true class of the sample is the same as c, the value is 1; otherwise, the value is 0. ic Let ) represent the probability that sample i is predicted as c, and N represent the sample size. In this experiment, N = 20.

[0422] The loss function changes during training as follows Figure 48 As shown. The fault diagnosis results for the test set are as follows. Figure 49 As shown.

[0423] Calculations showed that the intrinsic feature set achieved 100% classification accuracy and 100% fault diagnosis accuracy. The intrinsic parameter set obtained through the hyperparameter selection process of the Siamese network exhibits clear feature differentiation, facilitating fault diagnosis and achieving high accuracy. Therefore, fault diagnosis using the intrinsic feature set demonstrates good accuracy, indicating that the Bayesian optimization-based hyperparameter selection method can effectively identify system features. This further demonstrates that the DAE-PINN-based fault state-aware Siamese network is a high-fidelity twin of the research object, capable of performing system analysis and diagnosis tasks.

[0424] In summary, this invention first modeled the key equipment of the power supply system based on expert knowledge and design schemes, conducted fault mode analysis, and established a twin model of fault behavior. Experimental results demonstrated the effectiveness of the twin modeling method, showing good alignment with expected results. Then, by adding random noise, it effectively simulated real-world operating conditions, successfully achieving twin modeling of the fault behavior dimension.

[0425] This invention also uses a dataset generated by a fault behavior twin model as a basis, and derives differential-algebraic equations that can describe physical information by analyzing the transient stability of key system equipment. Combining these equations with a neural network loss function, the construction of PINN was successfully completed, achieving a score of 10 after 400 training iterations. -3 Training error on the order of magnitude.

[0426] In addition, a reasonable twin network structure was selected based on the structural optimization experiment. The intrinsic feature values ​​under different fault modes were adaptively estimated based on the Bayesian method. The fault diagnosis results showed that the diagnostic accuracy of the method reached 100% for the seven types of faults, proving the effectiveness of the feature recognition method.

[0427] It should be stated that the above-described specific embodiments are merely preferred embodiments of the present invention and the technical principles employed. Those skilled in the art should understand that various modifications, equivalent substitutions, and variations can be made to the present invention. However, such variations, as long as they do not depart from the spirit of the present invention, should be within the scope of protection of the present invention. Furthermore, some terminology used in this specification and claims is not limiting, but merely for ease of description.

Claims

1. A method for fault diagnosis of key equipment in a power supply system based on digital twin, characterized in that the steps include... include: S1, Construct fault behavior twin models for key equipment in the power supply system to generate fault datasets for each key equipment; S2, Based on the fault dataset and a physical information neural network, construct and update a fault state perception twin model that represents the fault pattern; S3, use the updated fault state-aware twin model to diagnose the fault in the sample under test; Step S1, which involves constructing the fault behavior twin model, specifically includes the following steps: S11, Analyze the failure modes of each key device and identify the failure behavior twin modeling part in the key device model; S12, Simulate the fault behavior of the corresponding fault mode at the fault behavior twin modeling part, and collect the three-phase output voltage and current of the key equipment under normal and fault conditions. S13. Compare the three-phase output voltage and current of the key equipment under normal and fault conditions. After verifying that the identified fault behavior twin modeling part is correct, the fault behavior twin model of the key equipment is obtained. Each failure mode of the critical equipment has a corresponding failure dataset, and each failure dataset includes several sets of samples, with a Gaussian noise signal with a specified signal-to-noise ratio added to each set of samples. The specified signal-to-noise ratio is 15; The method for generating the fault dataset corresponding to the key equipment under the fault mode is as follows: the fault behavior of the fault mode is simulated in the fault behavior twin modeling part of the model of the key equipment, and then data samples are collected in the fault behavior twin modeling part according to the preset sampling time and sampling rate, and several data points within the preset sampling time period are extracted as samples. In step S11, the fault modes obtained from the analysis and the corresponding fault behavior twin modeling parts are shown in Table 1 below: Table 1 The key equipment in the power supply system includes the aircraft's power system, which includes a main power supply and / or a secondary power supply. The main power supply includes any one or more of a main generator, an exciter, and a rotating rectifier. The secondary power supply includes any one or more of a static converter, a DC-DC boost converter, and a transformer rectifier. Any one or more components of the main power supply and / or the secondary power supply serve as fault behavior twins. The main power supply includes a single-channel power supply system and / or a multi-channel power supply system, wherein at least two generators are connected in parallel to form the multi-channel power supply system; The multi-channel power supply system is a four-channel power supply system. Each channel of the four-channel power supply system includes the generator, a transformer rectifier electrically connected to the generator, and a load. The transformer rectifier includes a 270V transformer rectifier and a 28V transformer rectifier. The load includes AC load and DC load. The AC load is a three-phase resistor, and the DC load includes a high-voltage DC load and a low-voltage DC load. The high-voltage DC load is a hydraulic pump, and the low-voltage DC load is a resistor. The transformer rectifier is connected to the electrical output terminal of the generator to convert the AC power output by the generator into DC power and output it to the DC load. The AC load is connected to the electrical output terminal of the generator. The main power supply is a constant speed and constant frequency power supply system, and the generator is a three-phase AC generator; In step S2, the method for constructing and updating the fault state-aware twin model includes the following steps: S21, based on Hilbert-Huang transform and RMS values ​​to extract fault data features; S22, The physical information of the key equipment in the power supply system is expressed as a built-in parameter of DAE-PINN based on differential algebraic equations; S23, Construct and update the fault state awareness twin model based on DAE-PINN; In step S21, the extracted fault data features include the original signal. instantaneous frequency Instantaneous phase Instantaneous amplitude and effective value Any one or more of them, through the Hilbert-Huang transform Decompose to obtain , , , The effective value The calculation method is expressed by the following formula (1): Official (1) In formula (1), Indicates the first Current values ​​at each sampling point; Indicates the number of sampling points; Indicates sampling point ; The input of the rotating rectifier is connected to the output of the main exciter, and the input of the main motor is connected to the output of the rotating rectifier. The output of the main motor is connected to the key equipment in the topology relationship of AC load, 270V transformer rectifier, and 28V transformer rectifier, respectively. Step S22 specifically includes the following steps: S221, Construct the differential algebraic equations for expressing the physical information of each key device in the power supply system under the topological relationship; S222, Obtain the equipment parameters of each key device under the topological relationship; S223, Substitute each of the device parameters into the differential algebraic equation constructed in step S221, and set the physical information as a built-in parameter of DAE-PINN; The differential algebraic equations constructed in step S221 are expressed as follows: (2)-(9) Official (2) Official (3) Official (4) Official (5) Official (6) Official (7) Official (8) Official (9) In formulas (2)-(9), It is the inertial constant. The damping coefficient is... Angular frequency, Angular velocity, Indicate the zeroth-order differential term in (2), This indicates the voltage of the AC load. This represents the zeroth-order differential term in an algebraic equation. These respectively represent the main exciter, the rotating rectifier, the main motor, the 270V transformer rectifier, the 28V transformer rectifier, and the AC load. This represents the magnetization matrix between the rotating rectifier and the main exciter. This represents the magnetization matrix between the rotating rectifier and the main motor. This represents the magnetization matrix between the main motor and the main exciter. This represents the magnetization matrix between the main motor and the AC load. This represents the magnetization matrix between the main motor and the 270V transformer rectifier. This represents the magnetization matrix between the rotating rectifier and the 28V transformer rectifier. This represents the magnetization matrix between the 270V transformer rectifier and the main motor. This represents the magnetization matrix between the 270V transformer rectifier and the AC load. This represents the magnetization matrix between the 270V transformer rectifier and the 28V transformer rectifier. This represents the magnetization matrix between the 28V transformer rectifier and the main motor. This represents the magnetization matrix between the 28V transformer rectifier and the AC load. This represents the magnetization matrix between the 28V transformer rectifier and the 270V transformer rectifier. This represents the magnetization matrix between the AC load and the main motor. This represents the magnetization matrix between the AC load and the 270V transformer rectifier. This represents the magnetization matrix between the AC load and the 28V transformer rectifier; where the dynamic unknowns characterizing the system state are... The algebraic unknowns are ; In step S222, the equipment parameters include the voltage of the main exciter. The voltage of the rotating rectifier , voltage of the main motor The voltage of the AC load The voltage of the 270V transformer rectifier The voltage of the 28V transformer rectifier ; In step S223, the built-in parameters of DAE-PINN include and voltage ,power .

2. The method for fault diagnosis of key equipment in a power supply system based on digital twin as described in claim 1, characterized in that, Step S23 specifically includes the following steps: S231, The implicit Runge-Kutta method is used to solve the differential-algebraic equation; S232, Construct a neural network based on physical information; S233, a fault state perception twin model of the key equipment is trained using a neural network based on physical information.

3. The method for fault diagnosis of key equipment in a power supply system based on digital twin as described in claim 2, characterized in that, The method for solving the differential algebraic equation in step S231 is as follows: When the step size is The points are from Proceed to At that time, The implicit Runge-Kutta method is applied to the differential-algebraic equations expressed by equations (5)-(9) to obtain... , Official (10) , Official (11) Official (12) Official (13) in , , These are the unknown parameters of the implicit Runge-Kutta method, and the parameters are specified. ; Indicates the time step of a certain time. The discrete points corresponding to value; Represents the node coefficients; Indicates the first The time step The values ​​of the dynamic variables at discrete points; Indicates the first The time step The values ​​of the algebraic variables at discrete points; Indicates coefficient; Indicates coefficient; Indicates the first The values ​​of the dynamic variables in the differential algebraic equation at each time step; Indicates the first The values ​​of algebraic variables in the differential algebraic equation at each time step; Indicates the first One time step; Indicates the time step number; This indicates the order of the implicit Runge-Kutta method; Indicates the time step of a certain time. The discrete points corresponding to value; Indicates the time step of a certain time. Each discrete point corresponds to the value of the zeroth-order term in the dynamic equation; Indicates the time step of a certain time. The values ​​of non-zero terms in the algebraic equation corresponding to each discrete point; Indicates the first The values ​​of the non-zero terms of the algebraic equation at each time step.

4. The method for fault diagnosis of key equipment in a power supply system based on digital twins according to claim 3, characterized in that, In step S232, the method for constructing a neural network based on physical information is as follows: Define a neural network with physical information: Official (14) In formula (14), It is an algebraic term containing physical information; It is a connection state variable and system parameters Nonlinear operators; Indicates time; Indicates system input; The shared parameters of a neural network are optimized by minimizing a loss function. The expression is as follows: In equation (15), The mean squared error loss corresponding to the initial data. The total number of training data. Indicates the first One training data set, Indicates the first The time required for each training data set Indicates the first Input of training data, Indicates the first The dynamic values ​​corresponding to each training data point; For the mean square error on a finite set of points, The total number of configuration points. Indicates the first The time for each configuration point Indicates the first Input of each configuration point, Indicates the first The algebraic value corresponding to each configuration point, and the finite set of configuration points is the point set of the algebraic terms of physical information during discrete processing.

5. The method for fault diagnosis of key equipment in a power supply system based on digital twin as described in claim 4, characterized in that, In step S233, the method for training the fault state awareness twin model of key equipment specifically includes the following steps: The implicit Runge-Kutta method is incorporated into the loss function expressed by formula (15). In this context, the loss function is transformed into: The parameters of the neural network are trained by minimizing the loss function using the Adam optimizer, as expressed in the following formula (17): Official (17) In formulas (16)-(17), Represents the total loss function. The weights represent the weights corresponding to the dynamic loss function. Represents the loss function of the dynamic equation. The weights represent the weights corresponding to the loss function in the algebraic equation. Represents the loss function of an algebraic equation; Indicates the size of the training dataset. Denotes the implicit Runge-Kutta order. Indicates the first One training data set, Indicates the first Steps of the implicit Runge-Kutta method Indicates the first The time step, the first The values ​​of the dynamic variables in the differential-algebraic equations are taken from each training data set. Indicates the first The time step, the first The training data at the th th Dynamic variables in the differential algebraic equations during the implicit Runge-Kutta method; Represents the loss function of an algebraic equation. Indicates the time step of a certain time. The discrete point, the first Each training data corresponds to value, Indicates the time step of a certain time. The discrete point, the first Each training data corresponds to value, Indicates the time step of a certain time. The discrete point, the first The training data correspond to the values ​​of the non-zero terms of the algebraic equation. Indicates the first The time step, the first The values ​​of the dynamic variables in the differential-algebraic equations are taken from each training data set. Indicates the first The time step, the first The values ​​of algebraic variables in the differential-algebraic equations are taken from each training data point. Indicates the first The time step, the first The values ​​of the non-zero terms of the algebraic equation for each training data point; Indicates the first The time step, the first The training data at the th th The dynamic variables in the differential algebraic equations during the steps of the implicit Runge-Kutta method. Indicates the first The time step, the first The training data at the th th The conditions that the dynamic variables in the differential algebraic equations must satisfy during the steps of the implicit Runge-Kutta method. Indicates the step size. Indicates the first Steps of the implicit Runge-Kutta method Indicates a constant coefficient. Indicates the time step of a certain time. The discrete point, the first Each training data point corresponds to the value of the zeroth-order term of the differential equation; Indicates the first The time step, the first The training data at the th th The dynamic variables in the differential algebraic equations during the steps of the implicit Runge-Kutta method. Indicates the first The time step, the first The training data at the th th The conditions that the dynamic variables in the differential algebraic equations must satisfy during the steps of the implicit Runge-Kutta method. Indicates the first The time step, the first Dynamic variables in differential-algebraic equations of training data Indicates a constant coefficient; This represents the optimal parameters obtained by the Adam optimizer.

6. The method for fault diagnosis of key equipment in a power supply system based on digital twins according to claim 5, characterized in that, Solve the following unconstrained optimization problem in the k-th iteration Official (18) in, and It is the first The penalty coefficient for the next iteration; At the beginning of each iteration, the penalty coefficient is increased by a constant factor. , expressed as: Official (19) This represents the initial value of the penalty coefficient corresponding to the dynamic equation. This represents the initial value of the penalty coefficient corresponding to the algebraic equation. Representing constant factors Power of; The neural network fitting the differential algebraic equation uses a fully connected structure and a forward propagation structure. The structure of the neural network is expressed as follows: Official (20) It is the input tensor of the neural network. It is the number of hidden layers. It is either the Hadamard product or the element-wise product. It is a pointwise sinusoidal activation function; This represents the activated tensor corresponding to the initial weight of 1. Indicates the first The input tensor of the layer, Indicates the first Tensors after layer activation Indicates the first The input tensor of the layer, Indicates the first The output tensor of the layer, Indicates the first The layer and the corresponding weight matrix after activation. Indicates the first Layer and corresponding bias after activation; The width of each hidden layer is Using the normal Glorot initialization algorithm, the training parameters of the network architecture are as follows: Official (21).

7. The method for fault diagnosis of key equipment in a power supply system based on digital twin as described in claim 6, characterized in that, The fault state-aware twin model is trained using either a stacked or non-stacked neural network, wherein, in the non-stacked structure, represents the dynamic state variable in the differential-algebraic equation. and algebraic variables Each corresponding neural network is assigned separately; In a stacked structure, all dynamic states are fitted using a single neural network. and state variables ; In the stacked structure, the width of the neural network ,depth In a non-stacked structure, the width of the neural network allocated to the dynamic state variables. ,depth The width of the neural network assigned to the algebraic variables. ,depth The ratio of the sample size of the training set, test set, and validation set is 1:1:

2.

8. The method for fault diagnosis of key equipment in a power supply system based on digital twin as described in claim 1, characterized in that, In step S3, the method for fault diagnosis includes the following steps: S31, Construct the intrinsic feature set of the fault modes of the sample under test. , , The possible values ​​include , representing the main exciter, rotating rectifier, main motor, 280V transformer rectifier, 28V transformer rectifier, and AC load, respectively. The magnetization matrix parameters of the key equipment represented by 1, 2, 3, H, L, and A are uniformly set to b. These represent the inertia constant, damping coefficient, input voltage, and mechanical power, respectively. Indicates the virtual power of the AC load; S32, the fault state-aware twin model uses the intrinsic feature set The system takes the input as input and outputs the fault diagnosis results for the sample under test.

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