Transformer internal fault source positioning method based on vibration signal propagation characteristic analysis

Abstract

The invention discloses a transformer internal fault source positioning method based on vibration signal propagation characteristic analysis, and the method comprises the steps: constructing a finite element model of a transformer, and determining an optimal point distribution scheme of a sensor through employing modal analysis and vibration transmission path simulation; in the finite element model, arranging virtual sensors according to an optimal point arrangement scheme, and applying a plurality of different mechanical fault excitations to all possible fault source positions to obtain a vibration signal of each virtual sensor; for each mechanical fault excitation, a corresponding fault source position and vibration signals of all virtual sensors are adopted to form a sample pair, all the sample pairs are adopted to form a simulation data set, and a deep learning positioning network is trained to obtain a deep learning model for positioning the internal fault source of the transformer; and acquiring vibration signals of sensors arranged according to the optimal point distribution scheme of the transformer to be detected, performing preprocessing and feature extraction, inputting the vibration signals into the deep learning model, and predicting to obtain a fault source position of the transformer.

Description

Technical Field

[0001] This invention belongs to the field of power equipment fault diagnosis technology, specifically relating to a method for locating internal fault sources in transformers based on the analysis of vibration signal propagation characteristics. Background Technology

[0002] As a core device for power transmission and distribution in a power system, the reliability of transformers directly affects the safety and stability of the entire power grid. With the continuous expansion of the power grid and the increasing voltage levels, the working environment of transformers is becoming increasingly complex, and their operating conditions are becoming more demanding. During long-term operation, transformers need to withstand electromagnetic forces, thermal stress, and potential short-circuit current impacts. These factors can easily lead to latent mechanical faults such as winding deformation, loosening of core clamps, and deterioration of the support structure. These faults are often not obvious in their early stages, but as they develop, they can cause serious consequences such as changes in insulation distance and localized overheating and discharge, ultimately leading to sudden insulation breakdown or short-circuit damage to the transformer, causing significant economic losses and social impact.

[0003] Currently, frequency response analysis is the primary method for diagnosing mechanical faults in transformers. While it can determine deformation by scanning changes in the winding transfer function, this method only provides qualitative diagnosis and cannot spatially locate the fault point, and it heavily relies on historical baseline data. Acoustic localization uses microphone arrays to image the sound source of discharge-related faults. This method is sensitive to high-frequency discharge signals but insensitive to low-frequency mechanical vibrations. Oil chromatography, as a traditional fault diagnosis method, can effectively diagnose overheating and discharge-related faults, but it cannot provide any spatial location information for mechanical faults, and its response exhibits significant lag.

[0004] Traditional vibration analysis methods involve deploying a small number of sensors on the tank casing and roughly determining the area of ​​abnormal vibration by comparing spectral energy or amplitude. While this method is relatively simple to implement, it is based on the fundamental characteristics of vibration signals and has several shortcomings. First, it is susceptible to load fluctuations and background noise interference, making the extraction of effective signals extremely difficult in complex field environments. Second, the lack of detailed modeling of the vibration propagation path results in low positioning accuracy and weak spatial resolution. In practical applications, it often only allows for a general assessment of the fault area, failing to pinpoint the exact location of the fault, which significantly complicates subsequent maintenance work.

[0005] In summary, existing technologies generally suffer from problems such as ambiguous positioning, separation of mechanisms, and poor anti-interference capabilities. Most methods can only achieve status warning and area judgment, but cannot output the three-dimensional coordinates of the fault source, resulting in a lack of targeted maintenance decisions. Summary of the Invention

[0006] To address the aforementioned shortcomings in the prior art, the transformer internal fault source localization method based on vibration signal propagation characteristics analysis provided by this invention solves the problem that the prior art cannot output the three-dimensional coordinates of the fault source, resulting in a lack of targeted maintenance decisions.

[0007] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0008] A method for locating internal fault sources in transformers based on the analysis of vibration signal propagation characteristics is provided, characterized by the following steps:

[0009] S1. Construct a finite element model of the transformer and use modal analysis and vibration transmission path simulation to determine the optimal sensor placement scheme with the optimization objective of maximizing the determinant of the Fisher information matrix.

[0010] S2. In the finite element model, virtual sensors are arranged according to the optimal layout scheme, and multiple different mechanical fault excitations are applied at all possible fault source locations to obtain the vibration signal of each virtual sensor.

[0011] S3. For each mechanical fault excitation, a sample pair is formed by using the corresponding fault source location and the vibration signals of all virtual sensors, and all sample pairs are used to form a simulation dataset.

[0012] S4. The deep learning localization network is trained using a simulation dataset to obtain a deep learning model for locating internal fault sources in transformers.

[0013] S5. Obtain the vibration signals of the sensors of the transformer under test according to the optimal layout scheme, and input them into the deep learning model after preprocessing and feature extraction to predict the location of the fault source of the transformer.

[0014] Furthermore, step S1 further includes:

[0015] S11. Construct a finite element model of a transformer that includes windings, core, insulating oil, and tank, and discretize the outer surface of the transformer tank into N candidate measurement points to form the design space S for sensor layout.

[0016] S12. Within the space where a fault may occur inside the transformer, define a set of fault source locations that includes several fault source locations;

[0017] S13. For each fault source location, apply a unit pulse excitation simulating mechanical fault in the finite element model, and calculate the vibration response time history of all candidate measurement points through transient dynamic analysis.

[0018] S14. Calculate the sensitivity matrix of the vibration response time history of candidate measuring points to the location of the fault source, for any layout scheme containing n sensors. Based on the sensitivity matrix, calculate the location of the kth fault source. Fisher's information matrix at n < N;

[0019] S15. Based on the Fisher information matrix, construct an optimization problem for sensor layout. Then, use a global optimization method to solve the optimization problem and obtain the optimal sensor layout scheme including n sensors. .

[0020] Furthermore, the expression for the sensitivity matrix is:

[0021] ;

[0022] in, For candidate test point i, the location of the kth fault source The sensitivity matrix below; To set the disturbance amount; Let t be the vibration response time history of candidate measurement point i; t is time.

[0023] The expression for the Fisher information matrix is:

[0024] ;

[0025] in, For any layout scheme containing n sensors At the location of the fault source Fisher's information matrix at the location; T is the transpose; The noise variance of the sensor arranged at candidate measurement point i;

[0026] The expression for the optimization problem is:

[0027] ,subject to ;

[0028] ;

[0029] in, For any layout scheme including n sensors; K is the total number of fault source locations; for The value of the determinant in the middle row; Location of the fault source Fisher's information matrix at the location; The optimal sensor deployment scheme; for The number of elements in the text.

[0030] Furthermore, the deep learning localization network adopts an encoder-decoder structure, and its loss function L is expressed as follows:

[0031] ;

[0032] in, Predicted by deep learning models The Middle The location of the fault source corresponding to each sensor; for The Middle The actual fault source locations corresponding to each sensor; [M], [C], and [K] are the mass matrix, damping matrix, and stiffness matrix obtained after discretizing the finite element model; F represents the displacement field inferred by the deep learning model; F represents the mechanical fault excitation.

[0033] Furthermore, the expressions for the mass matrix, damping matrix, and stiffness matrix are as follows:

[0034] , ;

[0035] , ;

[0036] , ;

[0037] in, For the mass matrix Units; Stiffness matrix Units; Damping matrix Units; The density of the materials of each component in the transformer; It is a unit shape function matrix; For the unit integration field; The strain-displacement matrix is ​​composed of the gradients of shape functions. The constitutive matrix is ​​composed of the material's elastic modulus E and Poisson's ratio. Confirmed; T stands for transpose; and is the Rayleigh damping coefficient.

[0038] Furthermore, the coefficient , With modal damping ratio Relationship satisfaction ,in Let be the i-th natural frequency; by experimentally determining the damping ratio corresponding to two different natural frequencies, we obtain... , The value.

[0039] Furthermore, the finite element model is constructed based on solid mechanics and acoustic theory, and includes the elastic wave equation in solid medium and the acoustic wave equation in insulating oil; after discretization, the finite element model yields the mass matrix, damping matrix, and stiffness matrix, and the dynamic equation of the finite element model is formed through these three matrices.

[0040] The expression for the elastic wave equation in the solid medium is:

[0041] ;

[0042] in, The density of the materials of each component in the transformer; For displacement vector field, Describe every point inside the solid exist The vibration displacement at any given moment; For gradient operators, Let F be the divergence of the displacement field, and F be the mechanical fault excitation. For the Laplace operator; and All are Mela constants;

[0043] The expression for the acoustic wave equation in the insulating oil is as follows:

[0044] ;

[0045] in, For sound pressure field, Describe each point of the insulating oil exist The sound pressure fluctuation value at any given moment; Let be the speed at which sound waves propagate in oil.

[0046] The expression for the dynamic equation is:

[0047] ;

[0048] in, and They are respectively The second and first derivatives.

[0049] Furthermore, the method for preprocessing and feature extraction of the vibration signal in step S5 includes:

[0050] Bandpass filtering was performed on the vibration signals of all sensors, and then time-domain statistical features, frequency-domain spectral features, time-frequency joint features, and array spatial relationship features were extracted from the bandpass filtered signals.

[0051] The time-domain statistical features include at least the root mean square value, peak value, kurtosis, and impulse factor of the signal; the frequency-domain spectral features are obtained by performing a fast Fourier transform on the signal, and at least the peak frequency, centroid frequency, and energy proportion of the preset characteristic frequency band are extracted.

[0052] The time-frequency joint features are obtained by acquiring the time spectrum of the signal through short-time Fourier transform or wavelet transform and extracting it from there; the array spatial relationship features are obtained by calculating the cross-correlation function, coherence function and generalized cross-power spectrum phase difference between signals from different sensor channels, which are used to characterize the propagation time difference and phase relationship of vibration signals between sensor arrays.

[0053] Furthermore, the method for locating internal fault sources in transformers also includes converting the probability distribution of all fault source locations into a three-dimensional heat map:

[0054] The confidence score of each fault source location output by the deep learning model is normalized to obtain the probability value of each fault source location.

[0055] Based on the probability values ​​of all fault source locations, the color and opacity of the fault source locations are calculated using a transfer function, the expression of which is:

[0056] ;

[0057] in, This represents the probability value of the fault source location; To map the probability value s to a transfer function of optical properties (color and opacity); It is an exponential function; This is a preset focus probability threshold; To surround The control parameter for the width of the probability value range that is prominently displayed during visualization; This is the scaling factor for the overall opacity;

[0058] Based on the color and opacity corresponding to all fault source locations, the data is accumulated and mixed according to the volume drawing integral formula to obtain a color three-dimensional heat map showing the probability of faults at each fault source location.

[0059] The beneficial effects of this invention are as follows: This solution combines finite element model with deep learning, which can directly output the precise coordinates (x, y, z) and probability heat map of the fault source in the three-dimensional space of the transformer. Its positioning accuracy can reach the centimeter level in both theory and experimental verification, thereby transforming the maintenance instruction from "inspecting a certain area" to "inspecting specific coordinate points", achieving a qualitative change.

[0060] This solution introduces an optimization deployment criterion based on maximizing the Fisher information matrix. Given a certain number of sensors, it automatically optimizes the deployment scheme with the strongest information acquisition capability by using sensitivity information calculated through a finite element model. This ensures that the entire system possesses the highest theoretical positioning accuracy potential and cost-effectiveness from the source of data acquisition, achieving a leap from empirical design to theoretically optimal design.

[0061] The finite element model of this scheme is constructed based on solid mechanics and acoustic theory. It integrates the basic physical laws of solid mechanics and acoustics. The three discretized matrices are incorporated into the loss function of deep learning. This is equivalent to embedding the hard constraints of the finite element model into the deep learning training process. This makes the model's learning and prediction not only rely on the statistical laws of data, but also strictly follow the basic physical laws of solid mechanics and acoustics. As a result, it can more accurately reverse-calculate the true source of the signal in complex paths, which significantly improves the positioning reliability in complex heterogeneous media. Attached Figure Description

[0062] Figure 1 A flowchart of a method for locating internal fault sources in transformers based on the analysis of vibration signal propagation characteristics;

[0063] Figure 2 This is a detailed flowchart of a method for locating internal fault sources in transformers based on the analysis of vibration signal propagation characteristics. Detailed Implementation

[0064] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0065] refer to Figure 1 , Figure 1 A flowchart of a method for locating internal fault sources in transformers based on the analysis of vibration signal propagation characteristics is shown; for example... Figure 1 As shown, the method S includes steps S1 to S5.

[0066] In step S1, a finite element model of the transformer is constructed, and modal analysis and vibration transmission path simulation are used to determine the optimal sensor placement scheme with the maximization of the determinant of the Fisher information matrix as the optimization objective.

[0067] In one embodiment of the present invention, the detailed implementation method of step S1 includes steps S11 to S15:

[0068] S11. Construct a finite element model of a transformer that includes windings, core, insulating oil, and tank, and discretize the outer surface of the transformer tank into N candidate measurement points to form the design space S for sensor layout.

[0069] The finite element model is constructed based on solid mechanics and acoustic theory, and includes the elastic wave equation in solid media and the acoustic wave equation in insulating oil. After discretization, the finite element model yields the mass matrix, damping matrix, and stiffness matrix, and the dynamic equation of the finite element model is formed through these three matrices.

[0070] The expression for the elastic wave equation in the solid medium is:

[0071] ;

[0072] in, The density of the materials of each component in the transformer; For displacement vector field, Describe every point inside the solid exist The vibration displacement at any given moment; For gradient operators, Let F be the divergence of the displacement field, and F be the mechanical fault excitation. For the Laplace operator; and All are Mela constants;

[0073] The expression for the acoustic wave equation in the insulating oil is as follows:

[0074] ;

[0075] in, For sound pressure field, Describe each point of the insulating oil exist The sound pressure fluctuation value at any given moment; Let be the speed at which sound waves propagate in oil.

[0076] The expression for the dynamic equation is:

[0077] ;

[0078] in, and They are respectively The second and first derivatives.

[0079] In implementation, the preferred expressions for the mass matrix, damping matrix, and stiffness matrix in this scheme are as follows:

[0080] , ;

[0081] , ;

[0082] , ;

[0083] in, For the mass matrix Units; Stiffness matrix Units; Damping matrix Units; The density of the materials of each component in the transformer; It is a unit shape function matrix; For the unit integration field; The strain-displacement matrix is ​​composed of the gradients of shape functions. The constitutive matrix is ​​composed of the material's elastic modulus E and Poisson's ratio. Confirmed; T stands for transpose; and is the Rayleigh damping coefficient.

[0084] coefficient , With modal damping ratio Relationship satisfaction ,in Let be the i-th natural frequency; by experimentally determining the damping ratio corresponding to two different natural frequencies, we obtain... , The value.

[0085] S12. Within the spatial range where a fault may occur inside the transformer, define a set of fault source locations that includes several fault source locations. Each fault source location is represented by a three-dimensional vector. .

[0086] S13. For each fault source location, apply a unit pulse excitation simulating mechanical fault in the finite element model, and calculate the vibration response time history of all candidate measurement points through transient dynamic analysis.

[0087] S14. Calculate the sensitivity matrix of the vibration response time history of candidate measuring points to the location of the fault source:

[0088] ;

[0089] in, For candidate test point i, the location of the kth fault source The sensitivity matrix below; To set the disturbance amount; Let t be the vibration response time history of candidate measurement point i; t is time.

[0090] For any layout scheme containing n sensors Based on the sensitivity matrix, calculate the location of the kth fault source. The Fisher information matrix at point n < N; the expression for the Fisher information matrix is:

[0091] ;

[0092] in, For any layout scheme containing n sensors At the location of the fault source Fisher's information matrix at the location; T is the transpose; Let i be the noise variance of the sensor placed at candidate measurement point i.

[0093] S15. Based on the Fisher information matrix, construct an optimization problem for sensor layout. Then, use a global optimization method to solve the optimization problem and obtain the optimal sensor layout scheme including n sensors. .

[0094] This scheme preferentially uses a genetic algorithm for global optimization. During initialization, multiple layout schemes with m sensors are generated from the candidate measurement point set S. Then, selection, crossover, and mutation operations are performed to generate different sensor layout schemes, and the objective function value corresponding to each scheme is iteratively calculated. Ultimately, it converges to the theoretically optimal sensor deployment scheme. .

[0095] In this scheme, the optimal sensor deployment includes 48 high-sensitivity vibration accelerometers. The sensors adopt a PXIe synchronous acquisition system with a sampling frequency of 5000Hz to meet the complete acquisition of vibration signals below 2500Hz.

[0096] In one embodiment of the present invention, the expression of the optimization problem is:

[0097] ,subject to ;

[0098] ;

[0099] in, For any layout scheme including n sensors; K is the total number of fault source locations; for The value of the determinant in the middle row; Location of the fault source Fisher's information matrix at the location; The optimal sensor deployment scheme; for The number of elements in the text.

[0100] In step S2, virtual sensors are deployed in the finite element model according to the optimal layout scheme, and multiple different mechanical fault excitations are applied at all possible fault source locations to obtain the vibration signal of each virtual sensor.

[0101] In step S3, for each mechanical fault excitation, a sample pair is formed using the corresponding fault source location and the vibration signals of all virtual sensors, and all sample pairs are used to form a simulation dataset.

[0102] In step S4, the deep learning localization network is trained using a simulation dataset to obtain a deep learning model for locating internal fault sources in the transformer.

[0103] In this scheme, the deep learning localization network adopts an encoder-decoder structure. The encoder part consists of a multi-channel one-dimensional convolutional neural network and a long short-term memory network connected in parallel, which is responsible for extracting deep time-frequency features from the array vibration signal. The decoder part combines the extracted features with the physical constraints of the finite element simulation model and maps the features to the three-dimensional spatial coordinates of the fault source through the inverse solution mechanism.

[0104] Furthermore, the multi-channel one-dimensional convolutional neural network contains five convolutional layers with kernel sizes of 64, 32, 16, 8, and 4, employing the ReLU activation function; the long short-term memory network consists of a three-layer bidirectional LSTM network with 128 units each. The decoder contains four fully connected layers with 256, 128, 64, and 3 neurons.

[0105] In implementation, this scheme preferably uses the following expression for the loss function L of the deep learning localization network:

[0106] ;

[0107] in, Predicted by deep learning models The Middle The location of the fault source corresponding to each sensor; for The Middle The actual fault source locations corresponding to each sensor; [M], [C], and [K] are the mass matrix, damping matrix, and stiffness matrix obtained after discretizing the finite element model; F represents the displacement field inferred by the deep learning model; F represents the mechanical fault excitation.

[0108] In step S5, vibration signals from sensors deployed according to the optimal layout scheme of the transformer under test are acquired, preprocessed, and feature extracted before being input into a deep learning model to predict the location of the transformer's fault source. Detailed steps can be found in [reference needed]. Figure 2 .

[0109] In implementation, the preferred method for preprocessing and feature extraction of the vibration signal in step S5 includes:

[0110] Bandpass filtering was performed on the vibration signals of all sensors, and then time-domain statistical features, frequency-domain spectral features, time-frequency joint features, and array spatial relationship features were extracted from the bandpass filtered signals.

[0111] The time-domain statistical features include at least the root mean square value, peak value, kurtosis, and impulse factor of the signal; the frequency-domain spectral features are obtained by performing a fast Fourier transform on the signal, and at least the peak frequency, centroid frequency, and energy proportion of the preset characteristic frequency band are extracted.

[0112] The time-frequency joint features are obtained by acquiring the time spectrum of the signal through short-time Fourier transform or wavelet transform and extracting it from there; the array spatial relationship features are obtained by calculating the cross-correlation function, coherence function and generalized cross-power spectrum phase difference between signals from different sensor channels, which are used to characterize the propagation time difference and phase relationship of vibration signals between sensor arrays.

[0113] In one embodiment of the present invention, the method for locating internal fault sources in a transformer further includes converting the probability distribution of all fault source locations into a three-dimensional heat map:

[0114] The confidence score of each fault source location output by the deep learning model is normalized to obtain the probability value of each fault source location.

[0115] Based on the probability values ​​of all fault source locations, the color and opacity of the fault source locations are calculated using a transfer function, the expression of which is:

[0116] ;

[0117] in, This represents the probability value of the fault source location; To map the probability value s to a transfer function of optical properties (color and opacity); It is an exponential function; This is a preset focus probability threshold; To surround The control parameter for the width of the probability value range that is prominently displayed during visualization; This is the scaling factor for the overall opacity;

[0118] Based on the color and opacity corresponding to all fault source locations, the data is accumulated and mixed according to the volume drawing integral formula to obtain a color three-dimensional heat map showing the probability of faults at each fault source location.

[0119] In summary, this invention, by optimizing the deployment of vibration sensor arrays and combining a vibration propagation physical model with deep learning algorithms, achieves higher positioning accuracy and stronger anti-interference capabilities for internal mechanical fault sources. It can effectively identify early fault characteristics, provide important basis for predictive maintenance of transformers, significantly improve the accuracy of fault diagnosis and maintenance efficiency, and is of great significance for ensuring the safe and stable operation of power systems.

Claims

1. A method for locating internal fault sources in transformers based on the analysis of vibration signal propagation characteristics, characterized in that, Including the following steps: S1. Construct a finite element model of the transformer and use modal analysis and vibration transmission path simulation to determine the optimal sensor placement scheme with the optimization objective of maximizing the determinant of the Fisher information matrix. S2. In the finite element model, virtual sensors are arranged according to the optimal layout scheme, and multiple different mechanical fault excitations are applied at all possible fault source locations to obtain the vibration signal of each virtual sensor. S3. For each mechanical fault excitation, a sample pair is formed by using the corresponding fault source location and the vibration signals of all virtual sensors, and all sample pairs are used to form a simulation dataset. S4. The deep learning localization network is trained using a simulation dataset to obtain a deep learning model for locating internal fault sources in transformers. S5. Obtain the vibration signals of the sensors of the transformer under test according to the optimal layout scheme, and input them into the deep learning model after preprocessing and feature extraction to predict the location of the fault source of the transformer.

2. The method for locating internal fault sources in a transformer according to claim 1, characterized in that, Step S1 further includes: S11. Construct a finite element model of a transformer that includes windings, core, insulating oil, and tank, and discretize the outer surface of the transformer tank into N candidate measurement points to form the design space S for sensor layout. S12. Within the space where a fault may occur inside the transformer, define a set of fault source locations that includes several fault source locations; S13. For each fault source location, apply a unit pulse excitation simulating mechanical fault in the finite element model, and calculate the vibration response time history of all candidate measurement points through transient dynamic analysis. S14. Calculate the sensitivity matrix of the vibration response time history of candidate measuring points to the location of the fault source, for any layout scheme containing n sensors. Based on the sensitivity matrix, calculate the location of the kth fault source. Fisher's information matrix at n < N; S15. Based on the Fisher information matrix, construct an optimization problem for sensor layout. Then, use a global optimization method to solve the optimization problem and obtain the optimal sensor layout scheme including n sensors. .

3. The method for locating internal fault sources in a transformer according to claim 2, characterized in that, The expression for the sensitivity matrix is: ； in, For candidate test point i, the location of the kth fault source The sensitivity matrix below; To set the disturbance amount; Let t be the vibration response time history of candidate measurement point i; t is time. The expression for the Fisher information matrix is: ； in, For any layout scheme containing n sensors At the location of the fault source Fisher's information matrix at the location; T is the transpose; The noise variance of the sensor arranged at candidate measurement point i; The expression for the optimization problem is: ,subject to ; ； in, For any layout scheme including n sensors; K is the total number of fault source locations; for The value of the determinant in the middle row; Location of the fault source Fisher's information matrix at the location; The optimal sensor deployment scheme; for The number of elements in the middle.

4. The method for locating internal fault sources in a transformer according to claim 1, characterized in that, The deep learning localization network adopts an encoder-decoder structure, and its loss function L is expressed as follows: ； in, Predicted by deep learning models The Middle The location of the fault source corresponding to each sensor; for The Middle The actual fault source locations corresponding to each sensor; [M], [C], and [K] are the mass matrix, damping matrix, and stiffness matrix obtained after discretizing the finite element model; F represents the displacement field inferred by the deep learning model; F represents the mechanical fault excitation.

5. The method for locating internal fault sources in a transformer according to claim 4, characterized in that, The expressions for the mass matrix, damping matrix, and stiffness matrix are as follows: ， ； ， ； ， ； in, For the mass matrix Units; Stiffness matrix Units; Damping matrix Units; The density of the materials of each component in the transformer; It is a unit shape function matrix; For the unit integration field; The strain-displacement matrix is ​​composed of the gradients of shape functions. The constitutive matrix is ​​composed of the material's elastic modulus E and Poisson's ratio. Confirmed; T stands for transpose; and is the Rayleigh damping coefficient.

6. The method for locating internal fault sources in a transformer according to claim 5, characterized in that, coefficient , With modal damping ratio Relationship satisfaction ,in The i-th natural frequency; By experimentally determining the damping ratio corresponding to two different natural frequencies, we can obtain... , The value.

7. The method for locating internal fault sources in a transformer according to claim 1 or 5, characterized in that, The finite element model is constructed based on solid mechanics and acoustic theory, and includes the elastic wave equation in solid media and the acoustic wave equation in insulating oil. After discretization, the finite element model yields the mass matrix, damping matrix, and stiffness matrix, and the dynamic equation of the finite element model is formed through these three matrices. The expression for the elastic wave equation in the solid medium is: ； in, The density of the materials of each component in the transformer; It is a displacement vector field; For gradient operators, Let F be the divergence of the displacement field, and F be the mechanical fault excitation. For the Laplace operator; and All are Mela constants; The expression for the acoustic wave equation in the insulating oil is: ； in, For sound pressure field; Let be the speed at which sound waves propagate in oil. The expression for the dynamic equation is: ； in, and They are respectively The second and first derivatives.

8. The method for locating internal fault sources in a transformer according to claim 1, characterized in that, The method for preprocessing and feature extraction of the vibration signal in step S5 includes: Bandpass filtering was performed on the vibration signals of all sensors, and then time-domain statistical features, frequency-domain spectral features, time-frequency joint features, and array spatial relationship features were extracted from the bandpass filtered signals. The time-domain statistical features include at least the root mean square value, peak value, kurtosis, and impulse factor of the signal; the frequency-domain spectral features are obtained by performing a fast Fourier transform on the signal, and at least the peak frequency, centroid frequency, and energy proportion of the preset characteristic frequency band are extracted. The time-frequency joint features are obtained by acquiring the time spectrum of the signal through short-time Fourier transform or wavelet transform and extracting it from there; the array spatial relationship features are obtained by calculating the cross-correlation function, coherence function and generalized cross-power spectrum phase difference between signals from different sensor channels, which are used to characterize the propagation time difference and phase relationship of vibration signals between sensor arrays.

9. The method for locating internal fault sources in a transformer according to claim 1, characterized in that, It also includes converting the probability distribution of all fault source locations into a color 3D heatmap: The confidence score of each fault source location output by the deep learning model is normalized to obtain the probability value of each fault source location. Based on the probability values ​​of all fault source locations, the color and opacity of the fault source locations are calculated using a transfer function, the expression of which is: ； in, This represents the probability value of the fault source location; To map the probability value s to a transfer function of optical properties; It is an exponential function; This is a preset focus probability threshold; To surround The control parameter for the width of the probability value range that is prominently displayed during visualization; This is the scaling factor for the overall opacity; Based on the color and opacity corresponding to all fault source locations, the data is accumulated and mixed according to the volume drawing integral formula to obtain a color three-dimensional heat map showing the probability of faults at each fault source location.

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