Unmanned aerial vehicle electrical system simulation verification method based on digital twinning

Abstract

The application relates to the technical field of data processing, and discloses a simulation verification method for an unmanned aerial vehicle (UAV) electrical system based on digital twinning. The application constructs a digital twinning architecture of the UAV electrical system and deploys an adaptive order reduction solver, maps an electrical network topology structure into a static adjacency matrix, and maps attitude angular velocity, environmental temperature and voltage and current sequences into graph node feature vectors. Spatial topology features are extracted through a graph convolution layer, time sequence coupling features of attitude changes and electrical parameters are extracted through a long short-term memory network layer, high-dimensional partial differential equation sets describing multi-physical field coupling are mapped into low-dimensional discrete state space equations for forward deduction. Voltage and current residuals returned by a physical entity at a previous moment are taken as feedback quantities to dynamically correct boundary conditions of the equations, so that the calculation resource cost during multi-physical field coupling simulation is reduced, and the calculation time delay caused by direct solving of the high-dimensional equations is eliminated.

Description

Technical Field

[0001] This invention relates to the field of data processing technology and discloses a simulation and verification method for the electrical system of a drone based on digital twins. Background Technology

[0002] Existing digital twin-based simulation and verification schemes for UAV electrical systems typically establish an electrical network model within a digital twin platform, including generators, power distribution control switches, electrical loads, and connecting cables. To achieve simulation verification, conventional methods acquire voltage and current sensing data from the UAV's electrical nodes as input, and then perform calculations using equivalent circuit models or lumped parameter models. When considering the electromagnetic field distribution within the electrical system, the interaction between device heating and structural stress, existing technologies directly deploy pre-established high-dimensional partial differential equations within the digital twin platform, using the sensing data as initial conditions for forward extrapolation. Since the UAV's attitude continuously changes during flight, the temperature and stress state of the electrical equipment's environment also change accordingly. Therefore, when solving high-dimensional equations, existing technologies directly substitute attitude data collected at different times as static parameters into the coefficient terms of the high-dimensional partial differential equations for calculation.

[0003] Based on the above-mentioned existing technology, directly solving a set of high-dimensional partial differential equations containing attitude parameters in the digital twin platform will cause the amount of computation to exceed the platform's computing power limit, resulting in computational delay, which makes it impossible for the digital twin to synchronize the electrical state changes of the physical entity in real time. Summary of the Invention

[0004] The purpose of this invention is to provide a simulation and verification method for the electrical system of unmanned aerial vehicles based on digital twins, which can effectively solve the problems in the background art mentioned above.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: The simulation and verification method for UAV electrical systems based on digital twins includes: constructing a digital twin architecture for UAV electrical systems that includes a power supply topology layer, a power distribution network layer, and a power load layer, and deploying an adaptive order reduction solver based on a spatiotemporal graph neural network on the digital twin platform; The electrical network topology is mapped to a static adjacency matrix of a spatiotemporal graph neural network, and the three-axis attitude angular rate, ambient temperature, and voltage and current sequences of electrical nodes collected in real time by the UAV sensor system are mapped to graph node feature vectors. Spatial topological features are extracted by processing the static adjacency matrix and graph node feature vectors through graph convolutional layers in a spatiotemporal graph neural network, and temporal coupling features of attitude change and electrical parameters are extracted by processing the spatial topological features through long short-term memory network layers. The high-dimensional partial differential equations describing the electromagnetic-thermal-stress multiphysics coupling are mapped to low-dimensional discrete state-space equations. The adaptive order reduction solver performs forward derivation based on the low-dimensional discrete state space equations and uses the voltage and current residuals returned by the physical entity at the previous time step as feedback to dynamically correct the boundary conditions of the low-dimensional discrete state space equations.

[0006] Preferably, the construction of the digital twin architecture of the UAV electrical system, which includes a power supply topology layer, a power distribution network layer, and a power load layer, includes: defining the generator node and the battery node as the starting node of the power supply topology layer, defining the solid-state power controller node as the intermediate node of the power distribution network layer, defining the motor node, the servo node, and the avionics node as the ending node of the power load layer, and defining the physical cable connecting the starting node, the intermediate node, and the ending node as a directed edge. The process of mapping the electrical network topology to a static adjacency matrix of a spatiotemporal graph neural network includes: extracting the cable impedance characteristics and cable spatial direction length of directed edges, generating a static adjacency matrix with asymmetric weight values ​​based on the connection relationship between the start node, intermediate node, and end node, and inputting the static adjacency matrix into the spatiotemporal graph neural network.

[0007] Preferably, the step of mapping the three-axis attitude angular rate, ambient temperature, and voltage and current sequence of electrical nodes collected in real time by the UAV sensing system into graph node feature vectors includes: synchronously acquiring the UAV's roll rate, pitch rate, yaw rate, ambient temperature of the compartment where the electrical node is located, and the real-time voltage and current values ​​of the corresponding electrical node at a fixed sampling frequency. The voltage change rate and current change rate are obtained by performing first-order difference calculation on the real-time voltage and real-time current values. The roll rate, pitch rate, yaw rate, ambient temperature, real-time voltage value, real-time current value, voltage change rate, and current change rate are aligned and stitched together according to the timestamp to generate an initial feature tensor containing multi-channel data. The initial feature tensor is then normalized to its maximum and minimum values ​​to generate graph node feature vectors.

[0008] Preferably, the step of processing the static adjacency matrix and graph node feature vectors through the graph convolutional layer in the spatiotemporal graph neural network to extract spatial topological features includes: performing matrix multiplication on the static adjacency matrix and graph node feature vectors in the graph convolutional layer to obtain the first-order neighbor node feature information of the current node; Perform a feature dimension concatenation operation between the feature information of the first-order neighbor nodes and the graph node feature vector of the current node. The concatenated features are weighted by a linear transformation layer, and a bias term parameter is introduced into the linear transformation layer. A nonlinear activation function is introduced to perform nonlinear processing on the output after weight mapping, filtering out data components below the preset activation threshold. The multi-node feature vectors after nonlinear processing are combined into a matrix form to generate spatial topology features containing the electrical relationships between the current node and its first-order neighbor nodes.

[0009] Preferably, the step of processing spatial topological features through a long short-term memory network layer to extract temporal coupling features between attitude changes and electrical parameters includes: expanding the spatial topological features output by the graph convolutional layer into sequential data according to time steps and inputting it into the long short-term memory network layer; In the forget gate of the Long Short-Term Memory network layer, the hidden state of the previous time step and the spatial topological features of the current time step are concatenated and sigmoid activation is applied to generate forget weights. In the input gate, the concatenated features are subjected to sigmoid activation to generate updated weights, and then subjected to tanh activation to generate candidate state vectors. The cell states from the previous time step are removed based on the forgetting weight, and the candidate state vectors are superimposed based on the update weight. The output gate then undergoes sigmoid activation and tanh activation to generate temporally coupled features.

[0010] Preferably, the step of mapping the high-dimensional partial differential equations describing the electromagnetic-thermal-stress multiphysics coupling to low-dimensional discrete state-space equations includes: extracting the spatial discrete grid coefficients and temporal discrete difference coefficients from the high-dimensional partial differential equations, and converting the spatial discrete grid coefficients and temporal discrete difference coefficients into one-dimensional vector form. The fully connected layer maps the spatial discrete grid coefficients and time discrete difference coefficients in one-dimensional vector form to the state transition matrix and control input matrix in the low-dimensional discrete state space equation. The boundary conditions for dynamically correcting the low-dimensional discrete state space equations include: calculating the difference between the predicted voltage and current sequence output by the digital twin platform and the actual voltage and current sequence transmitted back by the physical entity to obtain the voltage and current residuals, and superimposing the voltage and current residuals into the control input matrix of the low-dimensional discrete state space equations as boundary condition correction terms.

[0011] Preferably, the static adjacency matrix has asymmetric weight values, including: when the power supply topology layer includes a primary power supply node and a backup power supply node, introducing a state indicator variable into the static adjacency matrix; When the main power node is in normal power supply state, the state indicator variable corresponding to the directed edge from the main power node to the intermediate node of the power distribution network layer is set to the first value, and the state indicator variable corresponding to the directed edge from the backup power node to the intermediate node is set to the second value. When the main power node fails and is disconnected, the state indicator variable corresponding to the directed edge from the main power node to the intermediate node is switched from the first value to the second value, and the state indicator variable corresponding to the directed edge from the backup power node to the intermediate node is switched from the second value to the first value. The asymmetric weight value of the static adjacency matrix is ​​updated according to the value of the state indicator variable.

[0012] Preferably, the weight mapping of the concatenated features through the linear transformation layer includes: embedding a multi-head self-attention calculation layer in the linear transformation layer; In the multi-head self-attention computation layer, the concatenated features are mapped to the query matrix, key matrix, and value matrix, respectively. Calculate the product of the query matrix and the transpose of the key matrix to obtain the attention score matrix between nodes; The absolute value of the rate of change of voltage at the current node is used as a scaling factor to perform dot product scaling on the attention score matrix; The attention score matrix after scaling is normalized by softmax to obtain the attention weight coefficients. The attention weight coefficients are multiplied by the value matrix to output the node features after attention weight allocation. The node features are then input into a linear transformation layer that introduces bias term parameters.

[0013] Preferably, the step of expanding the spatial topological features output by the graph convolutional layer into sequential data according to time steps and inputting it into the long short-term memory network layer includes: separating the spatial topological features into electrical fast-changing feature components and attitude slow-changing feature components; The electrical fast change feature components are input into the first long short-term memory network layer, and the attitude slow change feature components are input into the second long short-term memory network layer. The first long short-term memory network layer uses a short time step for forward computation, while the second long short-term memory network layer uses a long time step for forward computation. The first hidden state output by the first long short-term memory network layer and the second hidden state output by the second long short-term memory network layer are concatenated and fused along the feature channel dimension. The concatenated and fused feature vector is then used as the input data for the current time step and input into the forget gate of the long short-term memory network layer.

[0014] Preferably, the step of superimposing the voltage and current residuals into the control input matrix of the low-dimensional discrete state space equation as boundary condition correction terms includes: establishing a sliding window queue containing a preset time window length; At each simulation time step, the voltage and current residuals calculated at the current time are stored at the tail of the sliding window queue, and the voltage and current residuals at the head of the sliding window queue at the earliest time are removed. Extract the variance and mean of all voltage and current residuals in the sliding window queue; Construct the process noise covariance matrix and observation noise covariance matrix of the Kalman filter based on the variance and mean values; The coefficients of the state transition matrix in the low-dimensional discrete state-space equation are recursively calculated and updated using a Kalman filter, and the updated state transition matrix is ​​used for forward extrapolation in the next simulation time step.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention maps the electrical network topology to a static adjacency matrix, and maps the three-axis attitude angular rate, ambient temperature, and electrical node voltage and current sequences to graph node feature vectors. It utilizes graph convolutional layers to extract spatial topological features and long short-term memory (LSTM) network layers to extract the temporal coupling features between attitude changes and electrical parameters. This maps the high-dimensional partial differential equations describing multi-physics coupling to low-dimensional discrete state-space equations. This approach reduces the computational resource overhead of the digital twin platform during multi-physics coupling simulation, eliminates the computational delay caused by directly solving high-dimensional partial differential equations, and achieves real-time synchronous updates of the electrical state features of the digital twin and the physical entity. By introducing the voltage and current residuals returned by the physical entity as feedback, the boundary conditions of the low-dimensional discrete state-space equations are dynamically corrected, thus correcting state deviations during the forward derivation of the low-dimensional equations.

[0016] 2. This invention generates a static adjacency matrix with asymmetric weights by extracting cable impedance characteristics and cable spatial routing length. During primary / backup power switching, the matrix weights are updated using state indicator variables, reflecting the actual physical routing and on / off status of the power supply redundancy architecture in a digital twin platform. The absolute value of the node voltage change rate is used as a scaling factor for the multi-head self-attention computation layer. Electrically fast-changing characteristic components and attitude-slow-changing characteristic components are separated and computed using networks with different time steps, reducing the characteristic interference of attitude-slow-changing data on electrically fast-changing data. A sliding window queue is used to extract the variance and mean of voltage and current residuals to construct the coefficients of the filter used to update the state transition matrix, suppressing the influence of random fluctuations in sensor data on the forward derivation process of the low-dimensional discrete state space equations. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the construction of the digital twin architecture and the generation of the static adjacency matrix for the UAV electrical system of this invention. Figure 2 This is a flowchart of the graph node feature vector generation process of the present invention; Figure 3 This is a flowchart of the spatial topology feature extraction process of the present invention; Figure 4 This is a flowchart of the temporal coupling feature extraction process of the present invention; Figure 5 This is a flowchart of the order reduction mapping of the multiphysics coupling equations in this invention; Figure 6 This is a flowchart of the dynamic correction of boundary conditions and Kalman update of the present invention. Detailed Implementation

[0018] Please refer to the attached document. Figure 1 This embodiment provides a digital twin simulation verification scenario for the entire electrical system of a fixed-wing UAV in a digital twin-based UAV electrical system simulation verification method. The UAV electrical system includes a generator, battery, solid-state power controller, propulsion motor, servo motor, avionics equipment, and connecting cables. The digital twin platform adopts a distributed real-time simulation architecture, possessing multi-source sensor data access, real-time model calculation, and status visualization capabilities. A digital twin architecture for the UAV electrical system is constructed, comprising a power supply topology layer, a power distribution network layer, and an electrical load layer. The power supply topology layer is the energy input unit of the UAV electrical system, containing power supply equipment that provides power to the entire aircraft. The power distribution network layer is the intermediate link for energy transmission and distribution, containing core devices for controlling the on / off and distribution of power. The electrical load layer is the energy consumption unit, containing various electrical devices required for UAV flight and mission execution. The three layers interact with each other through standardized data interfaces to fully map the hierarchical structure and energy transmission path of the physical entity electrical system. In the real-time computing nodes of the digital twin platform, an adaptive order reduction solver based on a spatiotemporal graph neural network is deployed in a threaded manner. The input interface of the solver is connected to the output interface of the spatiotemporal graph neural network, and the output interface of the solver is connected to the state update interface of the three-layer model of the digital twin architecture, so as to realize the real-time synchronization of simulation results.

[0019] The electrical network topology of the UAV electrical system is mapped to a static adjacency matrix of a spatiotemporal graph neural network. The electrical network topology includes the physical connection relationships of all electrical devices in the entire aircraft. Each electrical device corresponds to an independent node in the graph structure, and the physical connection cables between devices correspond to the edges in the graph structure. The direction of the edges is determined according to the transmission direction of electrical energy in the electrical system, and a corresponding directed graph structure is generated. The node connection relationship of the directed graph structure is converted into a two-dimensional static adjacency matrix. The rows and columns of the matrix correspond to the nodes in the directed graph, and the element values ​​in the matrix correspond to the connection relationship and physical connection attribute between the nodes.

[0020] The three-axis attitude angular rate, ambient temperature, and voltage and current sequences of electrical nodes collected in real time by the UAV sensing system are mapped into graph node feature vectors. The UAV sensing system includes an inertial measurement unit, a temperature sensor, a voltage sensor, and a current sensor. The inertial measurement unit collects the three-axis attitude angular rate during the UAV's flight, the temperature sensor collects the ambient temperature of the compartment where each electrical node is located, and the voltage and current sensors collect the real-time voltage and current values ​​of the corresponding electrical nodes, respectively. All sensing data have a unified hardware timestamp. Based on the timestamp, the multi-source sensing data at the same moment are time-aligned and converted into multi-dimensional feature data of the corresponding nodes. These are then combined to generate graph node feature vectors that meet the input requirements of a spatiotemporal graph neural network.

[0021] Spatial topological features are extracted by processing the static adjacency matrix and graph node feature vectors through graph convolutional layers in a spatiotemporal graph neural network. The spatiotemporal graph neural network contains at least one graph convolutional layer. The input of the graph convolutional layer is the static adjacency matrix and graph node feature vectors. The graph convolutional layer aggregates the feature information of the current node's neighboring nodes to mine the electrical relationships between nodes in the electrical network, including the power supply relationship between the power supply node and the distribution node, the power distribution relationship between the distribution node and the load node, and the electrical coupling relationship between peer nodes. After processing by the graph convolutional layer, spatial topological features containing the topological relationship information of the entire network are generated.

[0022] The spatial topological features are processed by a Long Short-Term Memory (LSTM) network layer to extract the temporal coupling features between attitude changes and electrical parameters. The spatiotemporal graph neural network also contains at least one LSM network layer. The input of the LSM network layer is the spatial topological features output by the graph convolutional layer. The spatial topological features are arranged in chronological order as a continuous temporal sequence. The LSM network layer processes the temporal sequence in terms of temporal dimension to capture the temporal correlation characteristics between UAV attitude changes and electrical parameters. This includes the impact of ambient temperature changes caused by attitude changes on the impedance characteristics of electrical nodes, the impact of load power fluctuations caused by attitude changes on node voltage and current, and the impact of cable stress changes caused by attitude changes on cable transmission characteristics. Finally, a temporal coupling feature containing temporal correlation information is generated.

[0023] This paper maps a set of high-dimensional partial differential equations describing the coupling of electromagnetic, thermal, and stress multiphysics fields into low-dimensional discrete state-space equations. The high-dimensional partial differential equations describing this coupling include the electromagnetic field distribution described by Maxwell's equations, the device temperature field distribution described by the heat conduction equations, the structural stress field distribution described by the elasticity equations, and the coupling equations between these three physical fields. The dimension of the equation set is determined by the number of discrete spatial grids, ranging from thousands to tens of thousands of dimensions. Through order reduction mapping, the high-dimensional partial differential equations are transformed into low-dimensional discrete state-space equations with dimensions ranging from tens to hundreds of dimensions. The reduced-order state-space equations retain the core physical properties of the original high-dimensional equations while significantly reducing the computational cost of solving them.

[0024] Please refer to the attached document. Figure 6 The adaptive order reduction solver performs forward deduction based on the low-dimensional discrete state-space equations and uses the voltage and current residuals returned by the physical entities at the previous time step as feedback to dynamically correct the boundary conditions of the low-dimensional discrete state-space equations. The adaptive order reduction solver uses the low-dimensional discrete state-space equations as its core computational model, takes the temporal coupling characteristics of the current time step as initial conditions, performs forward deduction of the electrical state at the next time step, and generates the predicted voltage and current sequences for the corresponding electrical nodes.

[0025] The actual voltage and current sequences transmitted back from the sensing system of the physical entity at the same moment are obtained. The difference between the predicted voltage and current sequences and the actual voltage and current sequences is calculated to obtain the voltage and current residuals. The voltage and current residuals are used as feedback quantities and superimposed on the boundary conditions of the low-dimensional discrete state-space equations to dynamically correct the boundary conditions. The corrected boundary conditions are used for forward extrapolation at the next moment to eliminate state deviations generated during the extrapolation process.

[0026] Table 1. Hierarchical Node Definition Table for Digital Twin Architecture of UAV Electrical System

[0027] The table above defines the node types, core functions, and quantity configuration examples for each level in the digital twin architecture. It provides a standardized node definition basis for the graph structure mapping of electrical network topology, ensuring that nodes and physical entities correspond during the topology mapping process, avoiding node omissions or mapping errors, and guaranteeing the consistency between the digital twin architecture and the physical entity electrical system.

[0028] In this embodiment, a three-layer digital twin architecture is constructed to fully map the physical structure and energy transmission path of the UAV's electrical system. The spatial topology features and attitude-electrical temporal coupling features of the electrical network are extracted through a spatiotemporal graph neural network. The order reduction mapping of the multi-physics coupling equation system significantly reduces the computational load of simulation. The dynamic correction of boundary conditions through residual feedback achieves real-time synchronization of the electrical state between the digital twin and the physical entity, eliminating the computational delay caused by directly solving high-dimensional equations.

[0029] In one optional embodiment, when constructing a digital twin architecture for the UAV electrical system that includes a power supply topology layer, a power distribution network layer, and a power load layer, the generator node and the battery node are defined as the starting nodes of the power supply topology layer. The generator node is the main power supply unit of the UAV, driven by the aircraft engine, outputting three-phase AC power, which is converted into 270V high-voltage DC power by a rectifier and filter module to provide the main power supply for the entire aircraft. The battery node is the backup power supply unit, using a high-rate lithium battery pack and a battery management system. It is in a float charging state when the generator node is working normally, and provides emergency power for the entire aircraft when the generator node fails, thus achieving power supply redundancy backup.

[0030] Solid-state power controller nodes are defined as intermediate nodes in the power distribution network layer. These nodes are all-solid-state contactless switching devices with microsecond-level on / off control capabilities, high-precision electrical parameter acquisition capabilities, and comprehensive fault protection functions. They are divided into main distribution solid-state power controller nodes and secondary distribution solid-state power controller nodes. The main distribution solid-state power controller node connects to the starting node of the power supply topology layer to realize the power distribution and on / off control of the main power supply bus. The secondary distribution solid-state power controller node connects to the main distribution solid-state power controller node and the terminal node of the load layer to realize refined power distribution control of each load.

[0031] The motor node, servo node, and avionics node are defined as the terminal nodes of the electrical load layer. The motor node is the UAV's propulsion motor, which uses a permanent magnet synchronous motor to provide flight power for the UAV and is the highest power load of the entire aircraft. The servo node includes the UAV's aileron servo, elevator servo, directional servo, and landing gear servo, which are used to control the UAV's flight attitude and landing gear retraction and extension, and have a lower power level. The avionics node includes the flight control computer, inertial navigation equipment, satellite navigation equipment, and data link communication equipment, which provide core support for the UAV's flight control and mission execution, and have a medium power level. The physical cables connecting the start node, intermediate nodes, and end node are defined as directed edges. The cables connecting the start node and intermediate nodes are power supply bus cables, using large-section aviation cables to carry the total power supply current of the entire machine. The cables connecting the intermediate nodes and end nodes are power distribution branch cables, using aviation cables with corresponding cross-sectional areas according to the power level of the corresponding load. The direction of all directed edges of the cables is consistent with the direction of power transmission, that is, from the start node to the intermediate node and from the intermediate node to the end node. The resulting graph structure is a directed acyclic graph.

[0032] When mapping the electrical network topology to a static adjacency matrix of a spatiotemporal graph neural network, the cable impedance characteristics and cable spatial length of the directed edges are extracted. The cable impedance characteristics include the DC resistance, series inductance, and parallel capacitance of the cable, which are calculated using the cable type, cross-sectional area, length, and material parameters. The cable spatial length is the actual length of the cable laid in the UAV's airframe structure, which is consistent with the UAV's airframe structure layout.

[0033] A static adjacency matrix with asymmetric weights is generated based on the connection relationships between the start node, intermediate nodes, and end node. The dimension of the static adjacency matrix is ​​N×N, where N is the total number of nodes in the entire electrical network. The elements in the matrix... This represents the weight of the directed edge from node i to node j. The weight is positively correlated with the DC resistance, series inductance, parallel capacitance, and spatial length of the corresponding cable. If there is no directed edge from node i to node j, then... The value of is 0. Since the direction of the directed edges is fixed, there is no symmetrical connection between the directed edge from node i to node j and the directed edge from node j to node i. Therefore, the static adjacency matrix is ​​an asymmetric matrix. The generated static adjacency matrix is ​​input into the graph convolutional layer of the spatiotemporal graph neural network.

[0034] When the power supply topology layer includes primary power supply nodes and backup power supply nodes, a state indicator variable is introduced into the static adjacency matrix. State indicator variable This corresponds to the on / off state of the directed edge from node i to node j, with a value ranging from 0 to 1. When the main power node is in a normal power supply state, the state indicator variable corresponding to the directed edge from the main power node to the intermediate node of the distribution network layer is set. Set the value to the first value, where the first value is 1, and set the state indicator variable corresponding to the directed edge from the backup power node to the intermediate node. Set to the second value, which is 0; at this time, the corresponding element in the static adjacency matrix ,in The basic weight value of this directed edge is calculated from the impedance characteristics and spatial length of the cable. The effective weight of the directed edge corresponding to the main power node is... The effective weight of the directed edge corresponding to the backup power node is 0, indicating that the backup power branch is in an open state. When the primary power node fails and is disconnected, the state indicator variable corresponding to the directed edge from the primary power node to the intermediate node is... Switching from the first value to the second value changes the state indicator variable corresponding to the directed edge from the backup power node to the intermediate node. When switching from the second value to the first value, the effective weight of the directed edge corresponding to the primary power node is 0, and the effective weight of the directed edge corresponding to the backup power node is... This indicates that the main power supply branch is disconnected and the backup power supply branch is connected. The asymmetric weight value of the static adjacency matrix is ​​updated according to the value of the status indicator variable.

[0035] Please refer to the attached document. Figure 2 When mapping the real-time collected three-axis attitude angular rate, ambient temperature, and voltage and current sequences of electrical nodes from the UAV sensor system into graph node feature vectors, a fixed sampling frequency is used. Simultaneously acquire the roll rate of the drone Pitch rate yaw rate The ambient temperature T of the compartment where the electrical node is located, and the real-time voltage value u(t) and real-time current value i(t) of the corresponding electrical node, and the sampling frequency. The value is 5kHz, and the sampling period is... This ensures the complete capture of the rapid transient characteristics of electrical parameters. A first-order difference calculation is performed on the real-time voltage value u(t) and the real-time current value i(t) to obtain the voltage change rate. With the rate of change of current The formula for calculating the first-order difference is: in The sampling period is the same as the sampling interval of the sensor data.

[0036] Roll rate Pitch rate yaw rate Ambient temperature T, real-time voltage u(t), real-time current i(t), voltage change rate Current change rate The data is aligned and concatenated according to timestamps to generate an initial feature tensor X(t) containing 8 channels of data. The initial feature tensor X(t) has a dimension of 1×8, and each channel of data corresponds to a physical quantity. The timestamp alignment error does not exceed one sampling period. The initial feature tensor X(t) is then subjected to max-min normalization to generate graph node feature vectors. The formula for normalization is: in Let be the value of the k-th channel of the graph node feature vector. This represents the value of the k-th channel of the initial feature tensor. This is the preset minimum value for the k-th channel data. The preset maximum value for the k-th channel data is defined, where k ranges from 1 to 8. The preset maximum and minimum values ​​for each channel are determined based on the actual working range of the corresponding physical quantity. After normalization, all channel values ​​of the graph node feature vector are within the range of 0 to 1, eliminating the influence of data with different dimensions on subsequent network processing. The generated graph node feature vector is then input into the graph convolutional layer of the spatiotemporal graph neural network.

[0037] Table 2. Correspondence between asymmetric weight values ​​and node connectivity in the static adjacency matrix.

[0038] The table above clarifies the node connection relationships, weight calculation methods, state control logic, and physical connection descriptions corresponding to each element in the static adjacency matrix. This provides a quantitative basis for the graph structure mapping of electrical network topology. At the same time, the real-time mapping of the switching state of the main and backup power supplies is realized through state indicator variables, ensuring that the static adjacency matrix can accurately reflect the actual on / off state of the electrical system.

[0039] In this embodiment, a standardized construction of the digital twin architecture of the UAV electrical system is achieved through explicit node and directed edge definitions, ensuring complete consistency between the hierarchical structure of the digital twin and the physical entity. A static adjacency matrix with asymmetric weights accurately maps the topology of the electrical network and the physical properties of the cables. Dynamic mapping of the on / off states of the power supply redundancy architecture is achieved through state indicator variables, enabling real-time response to the switching actions of the primary and backup power supplies. Time alignment, first-order difference, and maximum / minimum value normalization of multi-channel data generate graph node feature vectors that meet the input requirements of a spatiotemporal graph neural network, eliminating the influence of data with different dimensions and providing accurate input data for subsequent feature extraction and simulation.

[0040] Please refer to the attached document. Figure 3 In another optional embodiment, when processing the static adjacency matrix and graph node feature vectors through the graph convolutional layer in the spatiotemporal graph neural network to extract spatial topological features, the static adjacency matrix A and the graph node feature vector matrix are processed in the graph convolutional layer. Perform matrix multiplication to obtain the feature information of the first-order neighbor nodes of the current node, and the graph node feature vector matrix. The dimension is N×D, where N is the total number of nodes in the entire network, and D is the feature dimension of a single node. The value of D is 8, which is consistent with the number of channels in the feature vector of a graph node. The formula for matrix multiplication is: in The first-order neighbor node feature matrix has dimensions N×D. Each row in the matrix corresponds to the feature aggregation result of all first-order neighbor nodes of a node, and the aggregation weight is determined by the asymmetric weight value in the static adjacency matrix.

[0041] The first-order neighbor node feature matrix The graph node eigenvector matrix of the current node Perform a concatenation operation along the feature dimension to obtain the concatenated feature matrix. The dimension is N×2D, and the calculation formula for the splicing operation is: in This represents a concatenation operation on the feature dimension, which merges the features of each node with the aggregated features of its neighboring nodes on the feature channel dimension.

[0042] The concatenated feature matrix is ​​processed through a linear transformation layer. Weight mapping is performed, and a bias term parameter b is introduced into the linear transformation layer. The linear transformation layer contains a trainable weight matrix. Weight matrix The dimension is , The output feature dimension of the linear transformation layer. The value is 16, and the dimension of the bias term parameter b is 1× The formula for calculating the weight mapping is: in The feature matrix after weight mapping has a dimension of N× .

[0043] The output after weight mapping is modified by introducing a non-linear activation function. Nonlinear processing is performed using the ReLU activation function to filter out data components below a preset activation threshold of 0. The calculation formula for nonlinear processing is as follows: in The feature matrix is ​​obtained after nonlinear processing, with a dimension of N× The multi-node feature vectors, after nonlinear processing, are combined into a matrix to generate a spatial topology feature containing the electrical relationships between the current node and its first-order neighbor nodes. Spatial topological features That is The dimension is N× .

[0044] A multi-head self-attention computation layer is embedded in the linear transformation layer. Within this multi-head self-attention computation layer, the concatenated feature matrix is... Each matrix is ​​mapped to a query matrix Q, a key matrix K, and a value matrix V through three independent linear transformation layers. The dimensions of the query matrix Q, key matrix K, and value matrix V are all N× ,in The feature dimension is for single-head attention, the number of multi-head attention is h, and the value of h is 4. The total feature dimension is... , The value of is 4. The product of the query matrix Q and the transpose of the key matrix K is calculated to obtain the attention score matrix S between nodes. The calculation formula is: Where S has dimensions N×N, and the elements in S... This represents the attention score of the i-th node to the j-th node. A higher score indicates a higher degree of feature correlation between the two nodes.

[0045] The absolute value of the rate of change of voltage at the node at the current moment. The attention score matrix S is scaled using a dot product as a scaling factor. The scaling formula is as follows: in This is a standard scaling factor for the attention score, used to avoid the vanishing gradient problem of the softmax function caused by excessively large inner product values. The absolute value of the voltage change rate is also included. As a dynamic scaling factor, when the voltage change rate of a node is large, the scaling factor increases, reducing the fluctuation range of the attention score and suppressing feature interference caused by voltage abrupt changes.

[0046] Scaling of the attention score matrix Perform softmax normalization to obtain the attention weight coefficient matrix α. The formula for softmax normalization is: in Let α be the attention weight coefficient between the i-th node and the j-th node, and the sum of all attention weight coefficients for each node is 1. Multiply the attention weight coefficient matrix α by the value matrix V to output the node features after attention weight allocation. The calculation formula is: The dimension is N× The features output by h attention heads are concatenated to obtain the final output features of the multi-head self-attention computation layer. The dimension is N×2D, and the The input is fed into a linear transformation layer that introduces bias term parameters for subsequent weight mapping processing.

[0047] Please refer to the attached document. Figure 4 When processing spatial topological features through a Long Short-Term Memory (LSTM) network layer to extract the temporal coupling features between attitude changes and electrical parameters, the spatial topological features F_spa output from the graph convolutional layer are expanded into sequential data at time steps and input into the LSM network layer. The length of the sequential data is T, where T is 32. The input at each time step is... The value of t ranges from 1 to T. Long Short-Term Memory (LSTM) network layers include a forget gate, an input gate, cell state update units, and an output gate. In the forget gate, the spatial topological features of the hidden state h(t-1) from the previous time step and the current time step are compared. By splicing the pieces together, we can obtain the splicing features. splicing features Perform sigmoid activation to generate the forgetting weight f(t), calculated as follows: Where σ is the sigmoid activation function, with an output value ranging from 0 to 1. Here is the weight matrix for the forget gate. For the forgetting gate bias parameter, the closer the value in the forgetting weight f(t) is to 0, the more corresponding information from the cell state in the previous time step is removed.

[0048] In the input gate, splicing features are... Perform sigmoid activation to generate updated weights i(t), calculated using the following formula: in Here is the weight matrix of the input gate. The bias term parameters are the input gate parameters; simultaneously, the splicing features are... Perform tanh activation to generate candidate state vectors. The calculation formula is: in Here is the weight matrix for the candidate states. The bias term parameter represents the candidate state, and the output value of the tanh activation function ranges from -1 to 1.

[0049] The cell state C(t-1) from the previous time step is removed according to the forgetting weight f(t), and the candidate state vector C~(t) is superimposed according to the update weight i(t) to update the cell state C(t) at the current time step. The calculation formula is as follows: Where ⊙ represents the Hadamard product, which is the multiplication of corresponding elements in the matrix.

[0050] In the output gate, splicing features are... Perform sigmoid activation to generate output weight o(t), calculated using the following formula: in This is the weight matrix of the output gate. The bias term parameters for the output gate are used; then, the cell state C(t) at the current time step is activated by tanh activation, and a Hadamard product is performed with the output weight o(t) to generate the hidden state h(t) at the current time step, which is the temporal coupling feature. The calculation formula is: Temporal coupling characteristics It includes the temporal coupling relationship between UAV attitude changes and electrical parameters, which is used for subsequent low-dimensional state-space equation mapping and forward derivation.

[0051] Spatial topological features output by graph convolutional layers When the data is expanded into sequential data according to time steps and input into the Long Short-Term Memory (LSTM) network layer, the spatial topological features are... Separate into electrical fast-changing characteristic components With pose-slowly changing feature components Among them, the electrical fast-changing characteristic components This includes characteristic data corresponding to real-time voltage values, real-time current values, voltage change rate, and current change rate. This type of data changes frequently and responds quickly, reflecting the transient characteristics of the electrical system; attitude-slow-varying characteristic components. It includes characteristic data such as roll rate, pitch rate, yaw rate, and ambient temperature. This type of data changes at a low frequency and has a slow response speed, reflecting the gradual changes in the UAV's flight state and environment.

[0052] Electrical fast-transformation characteristic components The input is fed into the first Long Short-Term Memory network layer to process the slowly changing pose feature components. The input is fed into the second Long Short-Term Memory (LSTM) network layer. The first LSM network layer uses a short time step Δt1 for forward computation, where Δt1 is equal to the sampling period Δt, i.e., 200μs, consistent with the sampling frequency of the electrical parameters, ensuring the capture of the fast-changing characteristics of the electrical parameters. The second LSM network layer uses a long time step Δt2 for forward computation, where Δt2 is 50 times Δt1, i.e., 10ms, reducing the computation frequency of slowly changing features and minimizing computational resource overhead. The first hidden state h1(t) output from the first LSM network layer and the second hidden state h2(t) output from the second LSM network layer are concatenated and fused along the feature channel dimension. The resulting feature vector is... The concatenated and merged feature vectors The input data for the current time step is fed into the forget gate of the Long Short-Term Memory network layer for subsequent temporal coupling feature extraction.

[0053] Table 3. Input / output parameters and computational logic definitions for each layer of the spatiotemporal graph neural network.

[0054] The table above clarifies the input and output parameters, core computational logic, and trainable parameters of each layer in the spatiotemporal graph neural network, providing a standardized implementation basis for the construction, training, and deployment of the network, ensuring the reproducibility and accuracy of the feature extraction process, and clarifying the differentiated processing logic of the dual long short-term memory network layers, providing a clear implementation path for the separation of fast-changing and slow-changing features.

[0055] In this embodiment, neighbor aggregation of electrical network node features is achieved through first-order graph convolution operations, accurately extracting the spatial topological features of the electrical network and fully reflecting the electrical relationships between nodes. By embedding a multi-head self-attention computation layer, adaptive weight allocation of node features is achieved. Using the absolute value of the voltage change rate as a dynamic scaling factor, feature interference caused by voltage abrupt changes is suppressed, improving the stability of feature extraction. Through the gating mechanism of the long short-term memory network layer, the long-term temporal dependency between attitude changes and electrical parameters is effectively captured, and accurate temporal coupling features are extracted. By separating the fast-changing electrical features and the slow-changing attitude features, and using dual long short-term memory network layers with different time steps for differentiated processing, the feature interference of slow-changing data on fast-changing data is reduced, while reducing computational resource overhead, providing high-quality feature data for subsequent order reduction mapping and simulation inference.

[0056] Please refer to the attached document. Figure 5 In another optional embodiment, when mapping the high-dimensional partial differential equations describing the electromagnetic-thermal-stress multiphysics coupling to low-dimensional discrete state-space equations, the spatial discrete grid coefficients and temporal discrete difference coefficients in the high-dimensional partial differential equations are extracted. The high-dimensional partial differential equations include electromagnetic field control equations, thermal field control equations, stress field control equations, and inter-field coupling equations. The electromagnetic field control equations adopt the low-frequency approximation form of Maxwell's equations, neglecting displacement current, and describe the current distribution and electromagnetic field distribution in the electrical system. The equation form is: in The magnetic vector potential, For scalar potential, The magnetic permeability of the material, Let be the electrical conductivity of the material, and J be the current density. The thermal field governing equation uses the heat conduction equation to describe the temperature field distribution of the electrical device, considering Joule heating as the main heat source. The equation is in the form of: in For material density, Here, k is the specific heat capacity at constant pressure, k is the thermal conductivity of the material, and T is the device temperature, in J·J / This represents the Joule heating source term. The stress field governing equations employ linear elasticity equilibrium equations to describe the stress and strain distribution of the device structure, considering the influence of thermal stress. The equation form is: Where C is the elastic stiffness tensor, ε is the strain tensor, and u is the displacement vector. For volume forces, The coefficient of thermal expansion of the material. Here, I is the reference temperature and the unit tensor. The inter-field coupling relationships include: material conductivity. It changes with temperature T. ,in The conductivity at the reference temperature, σ is the temperature coefficient of electrical conductivity; parameters such as the elastic modulus and coefficient of thermal expansion of a material change with temperature T; structural stress and strain can cause changes in the resistivity of a material, which in turn affects the electrical conductivity σ.

[0057] The aforementioned high-dimensional partial differential equation system is spatially discretized using the finite element method and temporally discretized using the finite difference method. The resulting equation system has the same dimension as the number of spatial discretization grids, ranging from several thousand to tens of thousands of dimensions. The spatial discretization grid coefficients K and the temporal discretization difference coefficients M are extracted from the discretized high-dimensional partial differential equation system and converted into one-dimensional vector forms, respectively. and By using two fully connected layers, the one-dimensional vector form is transformed... and The mapping is represented by the state transition matrix Φ and the control input matrix Γ in the low-dimensional discrete state-space equation. The fully connected layer contains a linear transformation layer and a ReLU nonlinear activation layer, mapping the high-dimensional coefficient vector to low-dimensional matrix parameters. The form of the low-dimensional discrete state-space equation is: Where x(t) is an n-dimensional system state vector, n is the dimension of the low-dimensional state space, and n takes the value 64, which is much smaller than the dimension of the high-dimensional partial differential equation system; u(t) is an m-dimensional control input vector, corresponding to the temporal coupling characteristics. The value of m is 16; y(t) is a p-dimensional system output vector, corresponding to the predicted voltage and current values ​​of the electrical nodes, where the value of p is 16. Γ is an n×n dimensional state transition matrix, describing the time-domain evolution of the system state; Γ is an n×m dimensional control input matrix, describing the influence of the control input on the system state; H is a p×n dimensional output matrix, describing the mapping relationship between the system state and the output quantity; v(t) is the observation noise vector, corresponding to the random noise of the sensor data.

[0058] When dynamically correcting the boundary conditions of the low-dimensional discrete state-space equations, the predicted voltage and current sequence y(t) output by the digital twin platform is compared with the actual voltage and current sequence transmitted back by the physical entity. The difference between them is used to obtain the voltage-current residual r(t), and the calculation formula is as follows: The voltage and current residuals r(t) are superimposed onto the control input matrix Γ of the low-dimensional discrete state-space equation as boundary condition correction terms. The corrected control input matrix ,in , The residual gain matrix is ​​a preset constant matrix, and the corrected control input matrix is ​​the control input matrix. Used for forward extrapolation to the next time step, enabling dynamic correction of boundary conditions.

[0059] A sliding window queue with a preset time window length L (200) is established. At each simulation time step, the voltage and current residuals r(t) calculated at the current time are stored at the tail of the sliding window queue, and the earliest voltage and current residuals r(tL) at the head of the queue are removed, ensuring that the sliding window queue always contains residual data from the most recent 200 time steps. The variance of all voltage and current residuals in the sliding window queue is extracted. with the mean The calculation formula is: Based on variance with the mean Construct the process noise covariance matrix Q and the observation noise covariance matrix R of the Kalman filter, where the process noise covariance matrix Q is an n×n dimensional diagonal matrix, and the elements on the diagonal are... Positive correlation, the observation noise covariance matrix R is a p×p dimensional diagonal matrix, and the elements on the diagonal are positively correlated with the observed noise. Positive correlation, mean The offset term used to correct the observation equation of the Kalman filter.

[0060] Using Kalman filters to analyze the state transition matrix in low-dimensional discrete state-space equations The coefficients are recursively calculated and updated. The recursive update process of the Kalman filter includes two stages: time update and measurement update. In the time update stage, based on the state estimate and state transition matrix of the previous time step, the prior state estimate and prior error covariance matrix of the current time step are calculated. The calculation formula is as follows: Where x(t|t-1) is the prior state estimate at the current time, x(t-1|t-1) is the posterior state estimate at the previous time, P(t|t-1) is the prior error covariance matrix at the current time, and P(t-1|t-1) is the posterior error covariance matrix at the previous time.

[0061] During the measurement update phase, based on the current observations, the Kalman gain is calculated, the posterior state estimate and the posterior error covariance matrix are updated, and the state transition matrix is ​​also updated. The coefficient is calculated using the following formula: Where K(t) is the Kalman gain, Let be the update gain matrix of the state transition matrix, be a preset constant matrix, and I be the identity matrix. The updated state transition matrix... Used for forward extrapolation in the next simulation time step to achieve dynamic correction of the system state evolution model.

[0062] Table 4. Mapping Relationship between Parameters of Low-Dimensional Discrete State-Space Equations and Coefficients of High-Dimensional Partial Differential Equations

[0063] The table above clarifies the mapping relationship, computational logic, and physical meaning between the parameters of the low-dimensional discrete state-space equations and the coefficients of the high-dimensional partial differential equations. It provides a quantitative basis for the reduction mapping of multi-physics coupled equations, ensuring that the reduced state-space equations can accurately retain the core physical characteristics of the original high-dimensional equations. At the same time, it provides a clear implementation path for boundary condition correction and model parameter update of residual feedback.

[0064] In this embodiment, a fully connected layer maps the high-dimensional multiphysics coupled partial differential equations into low-dimensional discrete state-space equations, significantly reducing the dimensionality and computational load of the simulation solution, eliminating the computational delay caused by directly solving high-dimensional equations, and ensuring the real-time simulation capability of the digital twin platform. By using voltage and current residuals as feedback quantities, the boundary conditions of the state-space equations are dynamically corrected, effectively correcting the state deviations in the forward extrapolation process of the low-dimensional model and improving the accuracy of the simulation results. By extracting the statistical characteristics of the residuals through a sliding window queue, a Kalman filter is constructed to recursively update the state transition matrix, suppressing the influence of random fluctuations in the sensor data on the forward extrapolation process and improving the robustness of the simulation model.

Claims

1. A simulation and verification method for the electrical system of an unmanned aerial vehicle (UAV) based on digital twins, characterized in that, include: A digital twin architecture for the electrical system of a drone, comprising a power supply topology layer, a power distribution network layer, and a power load layer, is constructed, and an adaptive order reduction solver based on a spatiotemporal graph neural network is deployed on the digital twin platform. The electrical network topology is mapped to a static adjacency matrix of a spatiotemporal graph neural network, and the three-axis attitude angular rate, ambient temperature, and voltage and current sequences of electrical nodes collected in real time by the UAV sensor system are mapped to graph node feature vectors. Spatial topological features are extracted by processing the static adjacency matrix and graph node feature vectors through graph convolutional layers in a spatiotemporal graph neural network, and temporal coupling features of attitude change and electrical parameters are extracted by processing the spatial topological features through long short-term memory network layers. The high-dimensional partial differential equations describing the electromagnetic-thermal-stress multiphysics coupling are mapped to low-dimensional discrete state-space equations. The adaptive order reduction solver performs forward derivation based on the low-dimensional discrete state space equations and uses the voltage and current residuals returned by the physical entity at the previous time step as feedback to dynamically correct the boundary conditions of the low-dimensional discrete state space equations.

2. The simulation and verification method for UAV electrical systems based on digital twins according to claim 1, characterized in that, The construction of the digital twin architecture of the UAV electrical system, which includes a power supply topology layer, a power distribution network layer, and a power load layer, includes: defining generator nodes and battery nodes as the starting nodes of the power supply topology layer, solid-state power controller nodes as the intermediate nodes of the power distribution network layer, motor nodes, servo nodes, and avionics nodes as the ending nodes of the power load layer, and defining the physical cables connecting the starting nodes, intermediate nodes, and ending nodes as directed edges. The process of mapping the electrical network topology to a static adjacency matrix of a spatiotemporal graph neural network includes: extracting the cable impedance characteristics and cable spatial direction length of directed edges, generating a static adjacency matrix with asymmetric weight values ​​based on the connection relationship between the start node, intermediate node, and end node, and inputting the static adjacency matrix into the spatiotemporal graph neural network.

3. The simulation and verification method for UAV electrical systems based on digital twins according to claim 1, characterized in that, The process of mapping the three-axis attitude angular rate, ambient temperature, and voltage and current sequences of electrical nodes collected in real time by the UAV sensing system into graph node feature vectors includes: synchronously acquiring the UAV's roll rate, pitch rate, yaw rate, ambient temperature of the compartment where the electrical node is located, and the real-time voltage and current values ​​of the corresponding electrical node at a fixed sampling frequency. The voltage change rate and current change rate are obtained by performing first-order difference calculation on the real-time voltage and real-time current values. The roll rate, pitch rate, yaw rate, ambient temperature, real-time voltage value, real-time current value, voltage change rate, and current change rate are aligned and stitched together according to the timestamp to generate an initial feature tensor containing multi-channel data. The initial feature tensor is then normalized to its maximum and minimum values ​​to generate graph node feature vectors.

4. The simulation and verification method for UAV electrical systems based on digital twins according to claim 1, characterized in that, The step of processing the static adjacency matrix and graph node feature vectors through the graph convolutional layer in the spatiotemporal graph neural network to extract spatial topological features includes: performing matrix multiplication on the static adjacency matrix and graph node feature vectors in the graph convolutional layer to obtain the first-order neighbor node feature information of the current node; Perform a feature dimension concatenation operation between the feature information of the first-order neighbor nodes and the graph node feature vector of the current node. The concatenated features are weighted by a linear transformation layer, and a bias term parameter is introduced into the linear transformation layer. A nonlinear activation function is introduced to perform nonlinear processing on the output after weight mapping, filtering out data components below the preset activation threshold. The multi-node feature vectors after nonlinear processing are combined into a matrix form to generate spatial topology features containing the electrical relationships between the current node and its first-order neighbor nodes.

5. The simulation and verification method for UAV electrical systems based on digital twins according to claim 1, characterized in that, The step of processing spatial topological features through a long short-term memory network layer to extract temporal coupling features between attitude changes and electrical parameters includes: expanding the spatial topological features output by the graph convolutional layer into sequential data according to time steps and inputting it into the long short-term memory network layer; In the forget gate of the Long Short-Term Memory network layer, the hidden state of the previous time step and the spatial topological features of the current time step are concatenated and sigmoid activation is applied to generate forget weights. In the input gate, the concatenated features are subjected to sigmoid activation to generate updated weights, and then subjected to tanh activation to generate candidate state vectors. The cell states from the previous time step are removed based on the forgetting weight, and the candidate state vectors are superimposed based on the update weight. The output gate then undergoes sigmoid activation and tanh activation to generate temporally coupled features.

6. The simulation and verification method for UAV electrical systems based on digital twins according to claim 1, characterized in that, The process of mapping the high-dimensional partial differential equations describing the electromagnetic-thermal-stress multiphysics coupling to low-dimensional discrete state-space equations includes: extracting the spatial discrete grid coefficients and temporal discrete difference coefficients from the high-dimensional partial differential equations, and converting the spatial discrete grid coefficients and temporal discrete difference coefficients into one-dimensional vector form. The fully connected layer maps the spatial discrete grid coefficients and time discrete difference coefficients in one-dimensional vector form to the state transition matrix and control input matrix in the low-dimensional discrete state space equation. The boundary conditions for dynamically correcting the low-dimensional discrete state space equations include: calculating the difference between the predicted voltage and current sequence output by the digital twin platform and the actual voltage and current sequence transmitted back by the physical entity to obtain the voltage and current residuals, and superimposing the voltage and current residuals into the control input matrix of the low-dimensional discrete state space equations as boundary condition correction terms.

7. The simulation and verification method for UAV electrical systems based on digital twins according to claim 2, characterized in that, The static adjacency matrix has asymmetric weight values, including: when the power supply topology layer includes a primary power supply node and a backup power supply node, introducing a state indicator variable into the static adjacency matrix; When the main power node is in normal power supply state, the state indicator variable corresponding to the directed edge from the main power node to the intermediate node of the power distribution network layer is set to the first value, and the state indicator variable corresponding to the directed edge from the backup power node to the intermediate node is set to the second value. When the main power node fails and is disconnected, the state indicator variable corresponding to the directed edge from the main power node to the intermediate node is switched from the first value to the second value, and the state indicator variable corresponding to the directed edge from the backup power node to the intermediate node is switched from the second value to the first value. The asymmetric weight value of the static adjacency matrix is ​​updated according to the value of the state indicator variable.

8. The simulation and verification method for UAV electrical systems based on digital twins according to claim 4, characterized in that, The weight mapping of the concatenated features through the linear transformation layer includes: embedding a multi-head self-attention calculation layer in the linear transformation layer; In the multi-head self-attention computation layer, the concatenated features are mapped to the query matrix, key matrix, and value matrix, respectively. Calculate the product of the query matrix and the transpose of the key matrix to obtain the attention score matrix between nodes; The absolute value of the rate of change of voltage at the current node is used as a scaling factor to perform dot product scaling on the attention score matrix; The attention score matrix after scaling is normalized by softmax to obtain the attention weight coefficients. The attention weight coefficients are multiplied by the value matrix to output the node features after attention weight allocation. The node features are then input into a linear transformation layer that introduces bias term parameters.

9. The simulation and verification method for UAV electrical systems based on digital twins according to claim 5, characterized in that, The step of expanding the spatial topological features output by the graph convolutional layer into sequential data according to time steps and inputting them into the long short-term memory network layer includes: separating the spatial topological features into electrical fast-changing feature components and attitude slow-changing feature components; The electrical fast change feature components are input into the first long short-term memory network layer, and the attitude slow change feature components are input into the second long short-term memory network layer. The first long short-term memory network layer uses a short time step for forward computation, while the second long short-term memory network layer uses a long time step for forward computation. The first hidden state output by the first long short-term memory network layer and the second hidden state output by the second long short-term memory network layer are concatenated and fused along the feature channel dimension. The concatenated and fused feature vector is then used as the input data for the current time step and input into the forget gate of the long short-term memory network layer.

10. The simulation and verification method for UAV electrical systems based on digital twins according to claim 6, characterized in that, The step of superimposing the voltage and current residuals into the control input matrix of the low-dimensional discrete state space equation as boundary condition correction terms includes: establishing a sliding window queue containing a preset time window length; At each simulation time step, the voltage and current residuals calculated at the current time are stored at the tail of the sliding window queue, and the voltage and current residuals at the head of the sliding window queue at the earliest time are removed. Extract the variance and mean of all voltage and current residuals in the sliding window queue; Construct the process noise covariance matrix and observation noise covariance matrix of the Kalman filter based on the variance and mean values; The coefficients of the state transition matrix in the low-dimensional discrete state-space equation are recursively calculated and updated using a Kalman filter, and the updated state transition matrix is ​​used for forward extrapolation in the next simulation time step.

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