Waveguide electromagnetic wave transmission loss dynamic prediction method and device

Abstract

The application discloses a waveguide electromagnetic wave transmission loss dynamic prediction method and device. A directed attribute graph is constructed according to the physical connection structure of a waveguide network. After port radio frequency observation data and environmental sensor data are coded, the posterior distribution of the degradation state of each node is inferred by combining a graph variational inference network with an electromagnetic propagation attenuation model constraint. The degradation state is predicted by a multi-scale time sequence evolution prediction through a double-channel neural state space model. The link total transmission loss prediction value is obtained by aggregation along the directed attribute graph through a loss mapping network, and the future evolution trend is extrapolated. The application can accurately infer the degradation state of each node and predict the dynamic evolution of the transmission loss under incomplete observation conditions.

Description

Technical Field

[0001] This application relates to artificial intelligence, deep learning, and signal processing, specifically to a method and apparatus for dynamic prediction of electromagnetic wave transmission loss in waveguides. Background Technology

[0002] Metal waveguides are key components for electromagnetic energy transmission in the microwave and millimeter-wave bands, widely used in scenarios with extremely high transmission reliability requirements, such as satellite communication feed networks, high-power radar transmission systems, and microwave power supply systems for particle accelerators. In these systems, waveguides typically form transmission networks in a multi-segment cascade configuration, including straight waveguide sections, bends, transition sections, and flange connection nodes. The transmission loss of each waveguide segment collectively determines the signal attenuation characteristics of the entire link. As microwave systems evolve towards higher frequency bands, higher power, and longer service lives, the need for loss assessment of waveguide transmission networks has expanded from static calculations in the design phase to real-time dynamic monitoring during operation.

[0003] During the design phase, engineers typically calculate the theoretical attenuation constants of each waveguide segment based on the wall conductor loss formula and mode cutoff conditions from classical electromagnetic theory, and estimate the total loss of the entire link by simply superimposing the losses of each segment. While numerical simulation methods such as the finite element method and the finite-difference time-domain method can handle electromagnetic field solutions for complex geometries, a single steady-state simulation usually takes several hours to several days. However, these analytical methods are all based on the assumption that waveguide geometry, material conductivity, and surface roughness are constant, and can only provide steady-state loss values ​​under specific parameter configurations, failing to reflect the dynamic changes in transmission loss over time during operation.

[0004] Waveguide systems face the continuous effects of multiple physical degradation mechanisms during actual operation. Thermal cycling causes microscopic dimensional changes in the waveguide cross-section and differential thermal expansion at flange connections; mechanical vibration leads to transient micro-displacements and intermittent contact defects at flange joints; the cumulative oxidation and corrosion of the metal inner wall surface over service time results in continuously increasing surface roughness and gradual degradation of conductor conductivity; and fluctuations in ambient humidity in pressurized waveguide systems alter the dielectric properties of the medium inside the tube. These degradation mechanisms are complexly coupled. For example, thermal cycling accelerates the relaxation of flange bolt preload, amplifying the micro-displacements caused by vibration; temperature changes alter the kinetic rate of oxidation reactions on the metal surface, making the degradation rate of conductor loss a function of temperature. These multi-physics coupled degradation effects propagate and superimpose at each stage in a multi-segment cascaded waveguide network, causing the transmission loss of the entire link to exhibit nonlinear, spatially non-uniform, and temporally non-stationary dynamic evolution characteristics, which traditional steady-state analysis methods cannot effectively describe. Meanwhile, the timescales of different degradation mechanisms vary greatly. The loss changes caused by temperature fluctuations and mechanical vibrations occur on timescales of seconds to minutes, while the accumulation of surface oxidation and the degradation of conductor conductivity are slow processes that span months to years. Currently, there is a lack of technical means to simultaneously capture the degradation dynamics of different timescales and model their mutual coupling effects.

[0005] In recent years, machine learning-based methods have been preliminarily applied in the design and optimization of waveguide devices. For example, neural networks are used to predict the effective refractive index of optical waveguides to accelerate parameter scanning, convolutional neural networks are used to predict the transmission characteristics of plasma waveguides, and physical information neural networks are used to solve the waveguide eigenvalue problem. However, these studies all deal with the static mapping relationship between design parameters and steady-state performance indicators, completely neglecting the time-series dynamic prediction of transmission loss during the degradation process. In the field of equipment degradation prediction, although some studies have used graph neural networks and variational inference for degradation monitoring and remaining lifetime prediction, respectively, these methods are geared towards vibration signal analysis of rotating machinery such as aero-engines, which are fundamentally different from the degradation mechanism and observation mode of metal waveguides and cannot be directly applied. Currently, there are no dynamic prediction methods for transmission loss of metal waveguides during operation, nor has any work attempted to model the spatial distribution of loss and cascade transmission effects from the perspective of the topological structure of multi-segment cascaded waveguide networks.

[0006] The aforementioned problems are particularly prominent in closed deployment platforms such as spaceborne microwave payloads and airborne radar. In these platforms, once the waveguide network is deployed, it cannot be disassembled for inspection or measured segment by segment. The entire link operates as a closed system, with limited RF signal observations obtainable only from the feed port. Simultaneously, environmental sensors are sparsely distributed, and their sampling locations cannot cover all waveguide segments. Under the constraint of highly incomplete observational information, how to infer the transmission loss distribution and dynamic evolution trend of each segment and node of the entire waveguide network from limited global RF observations and sparse local environmental monitoring data is a pressing technical problem that has yet to be effectively addressed. Summary of the Invention

[0007] To address the technical problems in existing technologies, such as the lack of a dynamic prediction method for transmission loss in multi-segment cascaded metallic waveguide networks during operation and the inability to infer the transmission loss distribution and temporal evolution trend of each segment and node under conditions of highly incomplete observation information, this invention provides a method and apparatus for dynamic prediction of electromagnetic wave transmission loss in waveguides. By constructing a directed attribute graph topology model of the waveguide network, introducing a graph variational inference mechanism based on electromagnetic propagation attenuation model constraints, and a dual-channel multi-scale temporal coupled evolution network, this invention enables the inference of the degradation state of each node and the prediction of the dynamic evolution of link transmission loss from limited port RF observations and sparse environmental sensor data.

[0008] In one aspect, the present invention provides a method for dynamically predicting electromagnetic wave transmission loss in a waveguide, comprising the following steps.

[0009] Step S1: Construct a directed attribute graph based on the physical connection structure of the waveguide network. Each waveguide segment is modeled as a transmission node, and each flange connection is modeled as a connection node. Port RF observation data and environmental sensor data are encoded into a global observation embedding vector and an initial feature vector for each node, respectively. Specifically, for a cascaded network consisting of N waveguide segments and M flange connections, each straight waveguide segment, bend, and transition segment is modeled as a transmission node, and each flange connection is modeled as a connection node. Directed edges are established between adjacent nodes according to the propagation direction of the electromagnetic wave signal. The constructed directed attribute graph contains N+M nodes and a corresponding set of directed edges. Each transmission node in the directed attribute graph carries the cross-sectional type, cross-sectional size, length, and design operating frequency of the corresponding waveguide segment as static attributes. Each connection node carries the flange type and design clearance tolerance of the corresponding flange as static attributes. A multilayer perceptron is used to jointly encode the static attributes and local environmental features of each node to generate the initial feature vector. Furthermore, the port RF observation data includes the overall transmission coefficient amplitude, overall transmission coefficient phase, port reflection coefficient amplitude, and port reflection coefficient phase obtained from the input and output ports of the waveguide network. These RF observations form a global RF feature vector at each sampling time. Another multilayer perceptron encodes this global RF feature vector into a global observation embedding vector, which serves as the global conditional input for subsequent inference. Environmental sensor data includes measurements from temperature, vibration, and humidity sensors distributed locally within the waveguide network. Since the environmental sensors are sparsely distributed in the closed platform, only some node locations have direct environmental observations. The readings of each sensor are associated with the nearest node in the directed attribute graph as the local environmental feature of that node. For nodes without sensor coverage, their local environmental features are set as missing features.

[0010] Step S2: On the directed attribute graph, a graph variational inference network is used. Taking the initial feature vector and the global observation embedding vector as input, and passing through multiple layers of graph attention message passing, the posterior distribution parameters of the degradation state vectors of each node are output. Based on the electromagnetic propagation attenuation model, the degradation states of each node are aggregated along the directed attribute graph to form an estimate of the total link transmission loss. The deviation between this estimate and the measured RF values ​​at the port is used to construct a physical consistency constraint loss. Specifically, a degradation state vector is defined for each node. Each component of this vector represents the current cross-sectional thermal deformation, surface roughness increment, conductor conductivity attenuation rate, and flange alignment offset of the node, respectively. Due to the constraints of the closed platform, the degradation state of each node cannot be directly measured. Therefore, the degradation state vector of each node is modeled as a latent variable, and its posterior distribution is inferred from observables using variational inference methods. The graph attention message passing layer of the graph variational inference network employs a multi-head attention mechanism to calculate attention weights. The global observation embedding vector is fused into the feature update process of each node through an attention gating mechanism. After multiple layers of message passing, the feature vectors of each node output the mean vector and log-variance vector of the posterior distribution of the degradation state through a linear mapping layer. The degradation state estimate is obtained by sampling from the posterior distribution using a reparameterization technique. Furthermore, in each layer of message passing, the features of each node exchange information with neighboring nodes through directed edges, enabling nodes with direct environmental observations to propagate degradation information along the waveguide network topology to nodes without sensor coverage. The global observation embedding vector distributes the end-link loss information contained in the port RF observations to each node through an attention gating mechanism.

[0011] Furthermore, the physical consistency constraint loss comprises two parts: the first part is the deviation between the estimated single-segment transmission loss of each waveguide segment and the estimated mismatch loss at each flange connection, calculated using the electromagnetic propagation attenuation model based on the degradation state vectors of each node, and aggregated along the directed attribute graph according to the cascaded transmission relationship to obtain the total link transmission loss estimate and the measured overall transmission coefficient at the port; the second part is the deviation between the estimated reflection component at each connection node, calculated based on the cross-sectional thermal deformation and flange alignment offset in the degradation state vectors of each node and the measured reflection coefficient at the port, aggregated along the directed attribute graph. The joint optimization of the physical consistency constraint loss and the evidence lower bound loss of variational inference ensures that the inferred degradation state statistically fits the observed data while physically satisfying the constraints of the electromagnetic transmission equation.

[0012] Step S3 involves predicting the temporal evolution of the degradation state of each node using a dual-channel neural state-space model. The first channel employs a gated recurrent unit (GRU) to capture short-period degradation changes, while the second channel uses a neural ordinary differential equation (Neural ODE) to model long-period degradation trends. Specifically, the first channel of the dual-channel neural state-space model takes the estimated degradation state of each node at the current moment and the environmental observation at the current moment as input, and outputs the rapid change increment of the degradation state at the next moment through the gated recurrent unit. The second channel obtains the slow evolution trajectory of the degradation state by numerically integrating the parameterized ordinary differential equation in the time dimension. Monotonicity constraints are introduced into the ordinary differential equation to ensure that the evolution directions of the surface roughness increment and the conductor conductivity decay rate conform to physical monotonicity. Furthermore, in the dual-channel neural state-space model, the output of the first channel is used to extract the cumulative driving effect on the slow evolution trajectory of the second channel through a weighted cumulative operation within a time window, serving as an additional input to the second channel. The current state of the second channel adjusts the state transition parameters of the gated loop unit in the first channel through a modulation function. When the slow variable channel indicates that the accumulated thermal fatigue at a flange connection has led to a significant decrease in preload, the micro-displacement response amplitude of that connection node to vibration excitation in the fast variable channel will increase accordingly.

[0013] Furthermore, the dual-channel neural state-space model performs a round of graph message passing after each state update, allowing the degradation state of each node to exchange information with neighboring nodes along the topology of the directed attribute graph. Changes in the degradation state of the upstream waveguide segment influence the degradation trajectory of downstream nodes through this graph message passing operation. Through this spatial transmission mechanism, the spatial propagation characteristics of degradation effects in cascaded networks are captured.

[0014] Step S4: The degradation state of each node is mapped to the predicted transmission loss value of each segment through a loss mapping network. This is then aggregated along the directed attribute graph to obtain the predicted total transmission loss value of the link, and the future loss evolution trend is extrapolated using an autoregressive approach. Specifically, the loss mapping network adopts a residual structure, using the calculation result of the theoretical attenuation constant formula as a benchmark value. The neural network learns the loss deviation caused by degradation, and under no degradation conditions, the prediction result of the loss mapping network regresses to the classical theoretical value. Further, the loss mapping network takes the degradation state vector of each node and static design parameters as input, and combines the functional relationship between the attenuation constant and waveguide geometric parameters, material conductivity, and surface roughness in the electromagnetic propagation model to output the predicted insertion loss value of each waveguide segment. The predicted loss values ​​of each waveguide segment and each connecting node are then aggregated sequentially along the propagation direction of the directed graph to obtain the current predicted total transmission loss value of the entire link. For extrapolating and predicting the future loss evolution trend, the dual-channel neural state-space model in step S3 is expanded forward in an autoregressive manner. At each prediction time step, the predicted value of the degradation state in the previous step and the predicted value or preset value of the environmental stress are used as inputs to output the predicted value of the degradation state in the next time step. Then, the loss mapping network is used to convert it into the predicted value of transmission loss. By gradually expanding, the evolution trend curve of transmission loss within the preset time interval can be obtained. Preferably, the predicted value of environmental stress can be obtained by using a time series prediction model trained based on historical environmental data. For periodic environmental stress, the extrapolated value of its periodic pattern can also be directly used.

[0015] The training loss function of the method consists of a weighted sum of three parts: the evidence lower bound loss from variational inference, the physical consistency constraint loss, and the mean square error between the predicted and measured values ​​of the total transmission loss of the link at each time step. The training data is generated by multi-physics coupling simulation of the waveguide network under different environmental conditions. Specifically, the evidence lower bound loss includes the reconstruction loss and the Kullback-Leibler (KL) divergence term between the posterior and prior distributions. The three parts of the loss are weighted and summed to form the total loss function for end-to-end joint optimization. Preferably, the training data can be obtained by performing finite element thermodynamic and electromagnetic field simulations on the transmission loss evolution process of the waveguide network under different environmental conditions. This generates a simulation dataset containing environmental parameters, port RF observations, and actual loss values ​​for each segment at each time step for pre-training the model, followed by fine-tuning using actual online monitoring data.

[0016] In another aspect, the present invention provides a waveguide electromagnetic wave transmission loss dynamic prediction device, comprising:

[0017] The waveguide network topology modeling module is used to construct a directed attribute graph based on the physical connection structure of the waveguide network, model each waveguide segment as a transmission node, model each flange connection as a connection node, and encode port RF observation data and environmental sensor data into a global observation embedding vector and an initial feature vector of each node, respectively.

[0018] The degradation state variational inference module is used to perform graph variational inference on the directed attribute graph, taking the initial feature vector and the global observation embedding vector as input, and outputting the posterior distribution parameters of the degradation state vector of each node through multi-layer graph attention message passing. According to the electromagnetic propagation attenuation model, the degradation state of each node is aggregated along the directed attribute graph into an estimated value of the total transmission loss of the link. The deviation between the estimated value and the measured value of port radio frequency is used to construct the physical consistency constraint loss.

[0019] The multi-scale temporal evolution module is used to predict the temporal evolution of the degradation state of each node through a dual-channel neural state space model. The first channel uses a gated recurrent unit to capture short-period degradation changes, and the second channel uses neural ordinary differential equations to model long-period degradation trends.

[0020] The link loss prediction module is used to map the degradation state of each node to the predicted transmission loss value of each segment through the loss mapping network, aggregate along the directed attribute graph to obtain the predicted total transmission loss value of the link, and extrapolate the future loss evolution trend in an autoregressive manner.

[0021] The present invention provides a method and apparatus for dynamic prediction of electromagnetic wave transmission loss in waveguides. By modeling a multi-segment cascaded waveguide network as a directed attribute graph and performing variational inference on the graph structure, it can infer the degradation state distribution of each waveguide segment and flange connection under conditions relying only on limited port RF observations and sparse environmental sensor data. This solves the problem of observational incompleteness in closed deployment platforms where segment-by-segment disassembly and detection of the waveguide network is impossible. By introducing a physical consistency constraint loss based on the electromagnetic propagation attenuation model and mode coupling theory, the inference process is explicitly constrained by the electromagnetic transmission equation, improving the physical rationality and accuracy of degradation state estimation. By designing a dual-channel neural state-space model to capture short-period rapid changes and long-period slow evolution and achieve cross-scale coupling, it can accurately model the interaction of multiple physical degradation mechanisms such as thermal cycling, mechanical vibration, and surface oxidation at different time scales. By embedding graph message passing operations during the temporal evolution process, it can capture the spatial transmission characteristics of degradation effects along the propagation path in the cascaded network. Through the residual structure design of the loss mapping network, the prediction results naturally regress to classical electromagnetic theory values ​​under degradation-free conditions, ensuring physical interpretability. Attached Figure Description

[0022] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0023] Figure 1 This is a schematic diagram of the overall process of the waveguide electromagnetic wave transmission loss dynamic prediction method provided in the embodiment of the present invention.

[0024] Figure 2 This is a schematic diagram of the structure of the directed attribute graph construction and graph variational inference network of the waveguide network provided in the embodiment of the present invention.

[0025] Figure 3 This is a schematic diagram of the structure of the dual-channel neural state space model provided in an embodiment of the present invention.

[0026] Figure 4 This is a structural block diagram of the waveguide electromagnetic wave transmission loss dynamic prediction device provided in an embodiment of the present invention.

[0027] Figure 5 This is a schematic diagram of the information propagation in graphical variational inference under sparse observation conditions according to the present invention.

[0028] Figure 6 This is a cross-sectional view of the physical structure of the multi-segment cascaded waveguide network of the present invention.

[0029] Figure 7 This is a comparison curve of MAPE for different methods under different prediction spans in this invention.

[0030] Figure 8 This is a dual-axis graph comparing the time series prediction of total link transmission loss and the effect of temperature in this invention. Detailed Implementation

[0031] To make the objectives and technical solutions of this invention clearer, the embodiments of this invention will be further described in detail below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of this invention and should not be construed as limiting the scope of protection of this invention.

[0032] Example 1

[0033] This embodiment provides a method for dynamically predicting electromagnetic wave transmission loss in waveguides, such as... Figure 1 As shown, the method includes steps S1 to S4. The following example uses a cascaded transmission network consisting of 12 waveguide segments and 11 flange connections. This network comprises 8 standard WR-90 rectangular straight waveguide segments, 2 E-plane elbow segments, and 2 rectangular-to-circular transition segments. The operating frequency band is the X-band, from 8.2 GHz to 12.4 GHz. The segments are connected via UG-39 / U-shaped flanges. This waveguide network is deployed inside a closed platform. During operation, it is impossible to disassemble and inspect each segment individually; only limited radio frequency observations can be obtained from the input and output ports. Environmental sensors are deployed only at some node locations.

[0034] like Figure 6As shown, a typical multi-segment cascaded waveguide network consists of various types of waveguide segments connected sequentially via flanges. The straight waveguide segment employs a rectangular cross-section tube structure with an inner wall width dimension of 'a' and a narrow side dimension of 'b'. It transmits the TE10 fundamental mode internally, exhibiting a sinusoidal electric field distribution that peaks at the center of the cross-section. The E-plane bend segment achieves the conversion of electromagnetic wave propagation direction through a bent tube with a specific bending radius 'R'. The rectangular-to-circular transition section uses a gradually changing cross-section to achieve matching connections between waveguides of different cross-sectional shapes. The circular waveguide segment employs a circular cross-section tube structure for matching connections with equipment using circular waveguide interfaces.

[0035] The waveguide sections are connected by flanges, which include bolt fastening structures and sealing surfaces, with a small gap between the two flanges. During long-term operation, the inner surface of the pipe wall degrades, gradually changing from an initial smooth state to a rough surface. Electromagnetic waves propagate along a directional path from the input to the output, experiencing transmission losses as they pass through the waveguide sections and flange connections.

[0036] Step S1: Construct a directed attribute graph based on the physical connection structure of the waveguide network, model each waveguide segment as a transmission node, model each flange connection as a connection node, and encode the port RF observation data and environmental sensor data into a global observation embedding vector and the initial feature vector of each node, respectively.

[0037] In this embodiment, the 12 waveguide segments and 11 flange connections are modeled separately, forming a directed property graph containing 23 nodes. Each straight waveguide segment, bend, and transition segment is modeled as a transmission node, and each flange connection is modeled as a connection node. Directed edges are established between adjacent nodes according to the direction of electromagnetic wave propagation from the input port to the output port. Specifically, the first transmission node represents the first straight waveguide segment at the network entrance, followed by the first connection node representing the first flange connection, and so on, alternating between transmission nodes and connection nodes according to the physical cascading order, ultimately forming a chain-like directed property graph consisting of 23 nodes and 22 directed edges. For waveguide networks with branching structures, the directed property graph will present a tree-like or mesh topology; the cascaded network in this embodiment corresponds to a linear chain topology.

[0038] The static attributes carried by each node in the directed attribute graph are defined as follows. For transmission nodes, static attributes include cross-section type (rectangular or circular, represented by one-hot encoding), cross-section dimensions (width a and narrowness b of a rectangular waveguide, diameter d of a circular waveguide, in millimeters), waveguide segment length (in millimeters), and design operating frequency (with the center frequency of the frequency band at 10.3 GHz as a reference, and the operating bandwidth recorded as 4.2 GHz). For connection nodes, static attributes include flange type (represented by discrete encoding) and design clearance tolerance (in micrometers, the design clearance tolerance for UG-39 / U-type flanges is 25.4 micrometers). After numerical normalization, the above static attributes are concatenated into the design parameter vector of each node. The design parameter vector of transmission nodes has a 7-dimensional dimension, and the design parameter vector of connection nodes has a 3-dimensional dimension. After being padded with zeros to the same dimension, the vectors are fed into the encoding network.

[0039] The acquisition and encoding process of port RF observation data is as follows. A directional coupler and a power detector are installed at each of the input and output ports of the waveguide network. A set of RF observations is acquired at each sampling interval (60 seconds in this embodiment), including four scalar values: the amplitude and phase of the overall transmission coefficient S21, and the amplitude and phase of the input port reflection coefficient S11. These four values ​​form a 4-dimensional global RF feature vector at each sampling time. A multilayer perceptron with two hidden layers (32-dimensional and 64-dimensional) is used to encode this global RF feature vector. The activation function is the Gaussian Error Linear Unit (GELU) function, outputting a 64-dimensional global observation embedding vector. This global observation embedding vector represents the overall transmission state information of the entire link at the current time and will serve as the global conditional input for feature updates of each node during subsequent inference.

[0040] The environmental sensor data processing procedure is as follows. In this embodiment, environmental sensors are deployed at 7 out of the 23 nodes in the waveguide network. Four of these locations simultaneously install temperature sensors (platinum resistance thermometers, accuracy 0.1 degrees Celsius) and vibration acceleration sensors (triaxial microelectromechanical systems (MEMS) accelerometers), while the remaining three locations install humidity sensors. The readings of each sensor are associated with the nearest node as the local environmental feature vector for that node. Temperature values ​​are in degrees Celsius, vibration acceleration is in g, and humidity is in relative humidity percentage. For the remaining 16 nodes without sensor coverage, all components in their local environmental feature vectors are set as missing components (marked with negative infinity). The encoding network ignores the input components corresponding to these missing components using a masking mechanism. The design parameter vectors and local environmental feature vectors of each node are concatenated and input into a node-encoded multilayer perceptron with two hidden layers, each 64-dimensional. The GELU activation function is used, and the output is the initial feature vector of each node, also 64-dimensional.

[0041] Step S2: On the directed attribute graph, a graph variational inference network is used. The initial feature vector and the global observation embedding vector are used as inputs. The posterior distribution parameters of the degradation state vectors of each node are output through multi-layer graph attention message passing. According to the electromagnetic propagation attenuation model, the degradation state of each node is aggregated along the directed attribute graph to form an estimate of the total transmission loss of the link. The deviation between the estimate and the measured value of the port radio frequency is used to construct the physical consistency constraint loss.

[0042] like Figure 2 As shown, in this embodiment, the degradation state vector of each node is defined as a 4-dimensional vector, whose four components represent: cross-sectional thermal deformation (in micrometers, representing the deviation of the cross-sectional dimensions from the design value), surface roughness increment (in micrometers, representing the increase in surface roughness of the conductor's inner wall relative to the initial processing state), conductor conductivity attenuation rate (a dimensionless proportional value, ranging from 0 to 1, representing the attenuation ratio of the current conductivity to the initial conductivity), and flange alignment offset (in micrometers, representing the lateral alignment deviation at the flange connection; this component is fixed at zero for transmission nodes). Each component of the degradation state vector is a latent variable that cannot be directly measured.

[0043] The graph variational inference network comprises three layers of graph attention message passing. In each message passing layer, each node first receives messages from its upstream and downstream neighboring nodes according to the direction of the directed edges. Message computation employs a four-head attention mechanism, with each attention head having a 16-dimensional dimension. For node i and its neighboring node j, the attention coefficient aij is obtained by calculating the dot product similarity of the feature vectors of node i and node j after query transformation and key transformation, respectively, and then normalizing it using softmax. Based on attention aggregation, the global observation embedding vector is fused into the feature update process of each node through an attention gating mechanism. Specifically, the global observation embedding vector is linearly mapped and then multiplied element-wise with the aggregated message of each node. The gating coefficient before the product is calculated by a gating network with a sigmoid function as the output layer, whose input is the concatenation of the current feature vector of each node and the global observation embedding vector. Through this gating mechanism, the end-link loss information contained in the port RF observations can be adaptively distributed to each node, allowing nodes with a strong correlation to global loss changes to obtain larger gating coefficients. After three layers of graph attention message passing, the 64-dimensional feature vector of each node is output to a 4-dimensional mean vector and a 4-dimensional log-variance vector through a linear mapping layer. These two vectors jointly parameterize the posterior Gaussian distribution of the degradation state of each node. During the sampling process, a reparameterization technique is used to scale and shift the standard normal noise through the mean and standard deviation of the posterior distribution, thereby obtaining the degradation state estimate from the posterior distribution while ensuring differentiability.

[0044] The physical consistency constraint loss is constructed based on the electromagnetic propagation attenuation model and mode coupling theory. For each transmission node, the estimated single-segment transmission loss of each waveguide segment is calculated based on the cross-sectional thermal deformation, surface roughness increment, and conductor conductivity attenuation rate in its degraded state vector, combined with the conductor loss formula for a rectangular waveguide wall with transverse electric TE10 mode transmission. In this formula, the attenuation constant alpha_c is related to the waveguide cross-sectional size, operating frequency, and conductor surface resistivity Rs, while the surface resistivity Rs has a functional relationship described by the modified Hammerstad formula with respect to conductor conductivity sigma and surface roughness Rq. For each connection node, the estimated mismatch loss and reflection component at the connection point are calculated using mode coupling theory based on the flange alignment offset and cross-sectional thermal deformation. The single-segment transmission loss of each waveguide segment is accumulated segment by segment along the propagation direction of the directed graph in decibels, and the estimated total transmission loss of the link is obtained by adding the mismatch loss of each connection node. The first part of the physical consistency constraint loss is defined as the mean square deviation between the estimated total link transmission loss and the amplitude of the measured overall transmission coefficient S21 at the port; the second part is defined as the mean square deviation between the estimated equivalent port reflection coefficient after network topology aggregation of the reflection components of each connected node and the amplitude of the measured port reflection coefficient S11. The two parts are weighted and summed with weights of 1.0 and 0.5, respectively. Joint optimization of the physical consistency constraint loss and the evidence lower bound loss of variational inference ensures that the inference results simultaneously meet the dual requirements of statistical fitting and physical equation constraints.

[0045] Step S3: The temporal evolution of the degradation state of each node is predicted by a dual-channel neural state space model. The first channel uses a gated recurrent unit to capture short-cycle degradation changes, and the second channel uses neural constant differential equations to model long-cycle degradation trends.

[0046] like Figure 3 As shown, the dual-channel neural state-space model includes a fast variable channel and a slow variable channel. During the model inference phase, the gated recurrent unit of the fast variable channel takes the 4-dimensional degradation state estimate of each node at the current time t and the environmental observation at the current time as input, and outputs the rapid change increment of the degradation state at the next time t+1. The hidden layer dimension of the gated recurrent unit is 128-dimensional, and the parameters of its reset gate and update gate are shared among all nodes. The fast variable channel mainly captures the degradation changes of time constants on the order of minutes to hours, such as the thermal expansion and contraction of waveguide cross-sections caused by diurnal temperature fluctuations and the transient micro-displacements of flange joints caused by mechanical vibrations during equipment operation.

[0047] The slow variable channel evolves continuously over time using a neural ordinary differential equation. Specifically, an ordinary differential equation dx_slow / dt = f_theta(x_slow, t) parameterized by a three-layer multilayer perceptron is defined, where f_theta is a parameterized vector field function, each hidden layer has a 64-dimensional dimension, and the activation function is a softplus function. A fourth-order adaptive step-size Runge-Kutta integrator (Dormand-Prince method) is used to integrate this ordinary differential equation from time t to time t+1 to obtain the slow evolution trajectory of the degenerate state. Monotonicity constraints are introduced into the slow variable channel. For the two irreversible degradation indices, surface roughness increment and conductor conductivity decay rate, a softplus nonlinear transformation is applied to the output of the ordinary differential equation to ensure that their time derivatives are always non-negative, thus guaranteeing that these two degradation indices monotonically do not decrease over time.

[0048] The cross-scale coupling mechanism between the two channels is implemented as follows. The fast variable channel performs an exponentially weighted accumulation of its output rapid change increments within a sliding window of length W time steps, extracting the cumulative driving effect vector of the fast variable on the evolution of the slow variable. This vector serves as an additional input to the neural ordinary differential equation of the slow variable channel. In this embodiment, the sliding window length W is 24, corresponding to a 24-hour observation window, and the exponential decay coefficient is 0.92. Conversely, the current state of the slow variable channel adjusts the update gate bias parameter of the gated recurrent unit in the fast variable channel through a modulation function, so that when the long-term cumulative degradation of a node is high, its short-term dynamic response sensitivity increases accordingly. The modulation function adopts an affine transformation form, and its slope and bias are obtained from the slow variable state through a single-layer linear mapping.

[0049] After each state update step in the dual-channel neural state-space model, a round of graph message passing is performed. This round of message passing occurs on the directed attribute graph constructed in step S1, employing a single-layer graph attention mechanism. This allows each node to exchange information with its upstream and downstream neighboring nodes along the topology regarding its evolved and degenerate states. Through this spatial transmission mechanism, the additional scattering energy changes caused by the increased surface roughness of the upstream waveguide segment can be transmitted to the downstream connected nodes and affect their degradation evolution trajectory due to mismatch loss. This allows for the explicit capture of the spatial propagation characteristics of degradation effects in cascaded waveguide networks during time-series prediction.

[0050] Step S4: The degradation state of each node is mapped to the predicted transmission loss value of each segment through the loss mapping network. The total transmission loss prediction value of the link is obtained by aggregating along the directed attribute graph, and the future loss evolution trend is extrapolated in an autoregressive manner.

[0051] The loss mapping network takes the concatenated 4D degraded state vectors of each node and static design parameters as input, and outputs the predicted insertion loss values ​​for each waveguide segment using a residual structure. Specifically, the baseline branch of the loss mapping network calculates the theoretical value of the attenuation constant alpha_c0 based on the wall conductor loss formula in classical electromagnetic theory and the waveguide cross-sectional geometric parameters; this calculation process does not contain learnable parameters. The residual branch consists of a 3-layer multilayer perceptron, with each hidden layer having a 64-dimensional dimension. The GELU function is used as the activation function, and the output is a scalar loss deviation delta_alpha. The final single-segment insertion loss prediction value equals the baseline value of the theoretical attenuation constant multiplied by the waveguide segment length, plus the deviation output by the residual branch. Under the ideal condition that the degraded state vector is zero, the residual branch approaches zero after training, allowing the overall prediction result of the loss mapping network to naturally regress to the classical theoretical value, ensuring physical interpretability. For the connection node, another output branch of the loss mapping network takes the flange alignment offset and cross-sectional thermal deformation as input, and outputs the mismatch loss prediction value at that connection.

[0052] By summing the predicted insertion loss of each transmission node and the predicted mismatch loss of each connection node along the propagation direction of the directed graph, in decibels, the total predicted transmission loss of the entire link at the current moment can be obtained. This total predicted transmission loss can be used for online comparison with operating thresholds to determine whether the link performance meets the system performance requirements.

[0053] For extrapolating and predicting the future loss evolution trend, the dual-channel neural state-space model in step S3 is switched to autoregressive prediction mode. Starting from the current time t0, at each prediction time step, the degradation state prediction value output from the previous step is used to replace the current degradation state estimate as the input of the dual-channel model. The environmental stress input uses the prediction value of the periodic extrapolation model trained based on historical environmental data (for the diurnal periodic components of temperature and vibration, the observation value at the same time on the previous day is directly used as an approximation), gradually expanding to the target prediction time point. The degradation state prediction value output at each prediction time step is converted into the transmission loss prediction value at that time step through the loss mapping network. By arranging the loss prediction values ​​of all prediction time steps in chronological order, the evolution trend curve of transmission loss within the future preset time interval can be obtained. In this embodiment, the prediction time interval is set to the next 72 hours, and the prediction time step is consistent with the sampling interval of 60 seconds, generating a total of 4320 prediction value loss predictions at prediction time points.

[0054] The training process of each network module in the above method adopts an end-to-end joint optimization strategy. Training data is generated through multiphysics coupling simulation. Specifically, a thermo-coupled finite element model and a full-wave electromagnetic field simulation model of the same scale as the cascaded network consisting of the 12 waveguide segments and 11 flange connections are established in finite element simulation software. Eight typical environmental condition sequences are set in the simulation, including isothermal steady-state condition, temperature periodic fluctuation condition (fluctuation amplitudes of 5K, 15K, and 30K), random vibration condition (power spectral densities of 0.01g^2 / Hz and 0.04g^2 / Hz), and two combined conditions of temperature and vibration. The simulation time span for each condition sequence is 720 hours, and the actual degradation state vector of each node at each time point, the actual transmission loss value of each segment, port RF observations, and environmental parameters of each sensor location are output with a time step of 60 seconds. A total of approximately 345,600 simulation samples were generated from 8 different operating conditions. The first 80% of these samples were divided into a training set and the last 20% into a validation set based on the time dimension.

[0055] The total loss function during model training consists of a weighted sum of three parts. The first part is the evidence lower bound loss of the variational inference module, including the mean squared reconstruction loss calculated using the simulated true values ​​of the degraded states of each node as the reconstruction target, and the KL divergence term between the posterior distribution and the standard normal prior distribution. The weight coefficient of the KL divergence term is set to 0.01 to avoid posterior collapse. The second part is the physical consistency constraint loss described in step S2, with a weight coefficient of 0.5. The third part is the mean squared error between the predicted total transmission loss of the link at each time step and the simulated true value, with a weight coefficient of 1.0. The training process uses the AdamW optimizer, with an initial learning rate of 2.3 × 10^-4. A cosine annealing strategy is used to gradually decay the learning rate from the initial value to 1.0 × 10^-6 over 500 training epochs. The batch size is set to 16 sequences (each sequence is 128 time steps long), and the weight decay coefficient is set to 1.0 × 10^-4. Training was performed in data parallelism on four GPUs, with a total training time of approximately 36 hours. During training, every 10 epochs, the relative root mean square error of the predicted total link transmission loss and the mean absolute error of the estimated degradation state of each node were evaluated on the validation set. An early stopping mechanism was triggered when the relative root mean square error of the predicted total link transmission loss on the validation set no longer decreased for 30 consecutive evaluation epochs. After training, fine-tuning was performed using actual online monitoring data at a learning rate of 1.0 × 10⁻⁵ for 50 epochs to reduce the distribution offset between the simulation and experimental domains.

[0056] Example 2

[0057] In a preferred embodiment of the present invention, the graph variational degradation state inference process under electromagnetic physical constraints in step S2 is described in detail. This embodiment addresses a cascaded network consisting of 12 waveguide segments and 11 flange connections, with a directed property graph containing 23 nodes. Only 6 of these nodes are covered by environmental sensors, and the degradation state of the remaining 17 nodes must be obtained entirely through the inference mechanism.

[0058] The graph attention message passing layer of the graph variational inference network is set to 4 layers, with each layer employing an 8-head attention mechanism. In the message passing of the l-th layer, the feature update process of node i is as follows: First, the attention weight alpha_ij^(l) between node i and its neighbor node j is calculated. This weight is obtained by concatenating the feature vector h_i^(l) of node i, the feature vector h_j^(l) of neighbor node j, and the attribute vector e_ij of the connecting edge, and then calculating it through a two-layer perceptron and softmax normalization. Each attention head independently calculates a set of attention weights and generates an intermediate representation vector. The intermediate representation vectors of the 8 heads are concatenated and linearly projected to obtain the neighbor aggregation information m_i^(l). The global observation embedding vector g is fused into the feature update through an attention gating mechanism. Specifically, g and the current feature h_i^(l) of node i are input into a gating unit, which outputs a scalar gating value gamma_i^(l), ranging from 0 to 1. The updated feature of node i is calculated as h_i^(l+1) = h_i^(l) + gamma_i^(l) * m_i^(l) + (1 - gamma_i^(l)) * W_g * g, where W_g is a learnable linear transformation matrix. Through this gating mechanism, when the local neighborhood information of a node is sufficient, the gating value tends to 1, thus relying on neighborhood aggregation; when the local information is insufficient, the gating value tends to 0, thus making better use of global port observation information.

[0059] Preferably, the feature dimension of each attention head is set to 32, and the aggregated feature dimension after splicing 8 heads is 256. After linear projection, it is reduced to 128 dimensions as the updated feature dimension of the node. The initial feature vector dimension of each node is 128, and the global observation embedding vector dimension is 64. The dimension of the degradation state vector is set to 6, and each component corresponds to the cross-sectional thermal deformation, surface roughness increment, conductor conductivity attenuation rate, flange alignment offset, sealing degradation index (dimensionless value, ranging from 0 to 1, characterizing the aging degree of the gas-pressurized waveguide sealing structure, which participates in the attenuation constant calculation by adjusting the equivalent dielectric loss tangent of the medium inside the tube), and contact resistance increment (in milliohms, characterizing the additional ohmic loss caused by oxidation of the metal contact surface at the flange connection, which is added to the mismatch loss calculation of the connection node). After four layers of message passing, the 128-dimensional feature vectors of each node are output as 6-dimensional mean vectors mu_i and 6-dimensional log-sigma_i^2 respectively through two parallel linear mapping layers. The degradation state estimate is obtained by sampling from the posterior distribution using the reparameterization technique z_i = mu_i + sigma_i * epsilon, where epsilon is a random vector sampled from the standard normal distribution.

[0060] Specifically, the first part of the physical consistency constraint loss is calculated according to the following process. For the waveguide segment corresponding to transmission node i, the degraded equivalent surface resistance Rs_eff_i = Rs_0_i * (1 + pi * delta_Rq_i / delta_s)^2 * (1 / (1 - eta_sigma_i))^0.5 is calculated based on the surface roughness increment delta_Rq_i and the conductor conductivity attenuation rate eta_s in its degraded state vector, where Rs_0_i is the surface resistance under the design state and delta_s is the skin depth. Further, the degraded attenuation constant alpha_i is calculated based on the cross-sectional type and dimensions of the waveguide segment. For the TE10 mode of a rectangular waveguide, the attenuation constant alpha_i = Rs_eff_i / (a ​​* b * beta * k * eta) * (2 * b * pi^2 / a + a * k^2), where a and b are the inner dimensions of the wide and narrow sides of the waveguide (corrected for cross-sectional thermal deformation), beta is the propagation constant, k is the wave number, and eta is the wave impedance of the filling medium. The single-segment transmission loss of each waveguide segment is L_seg_i = alpha_i * length_i (in neppers), where length_i is the length of the waveguide segment. For the flange connection corresponding to node j, the mismatch loss L_flange_j = -10 * log10(|C_00|^2) is calculated based on the mode coupling theory according to the flange alignment offset delta_d_j in its degraded state, where C_00 is the mode coupling coefficient of the fundamental mode. This coefficient is calculated by the mode field overlap integral of the waveguide sections on both sides under the condition of offset delta_d_j. The transmission loss of each segment and the mismatch loss of each connection are cascaded and summed along the propagation direction of the directed graph to obtain the estimated total transmission loss L_total_est of the link. The first part of the physical consistency constraint loss is L_phys_1 = |L_total_est- L_total_meas|^2, where L_total_meas is the total loss value corresponding to the measured overall transmission coefficient of the port.

[0061] The second part of the physical consistency constraint loss involves the constraint of the reflection components. The thermal deformation of the cross-section at each connection node causes differences in the cross-sectional dimensions of adjacent waveguide segments, and the flange alignment offset causes misalignment of the cross-sectional centers; both contribute to mode mismatch reflection. For connection node j, its reflection coefficient Gamma_j is calculated based on mode coupling theory under the small reflection approximation condition. The deviation between the reflection components of each connection node, aggregated step-by-step along the network topology, and the measured value of the port reflection coefficient constitutes the second part of the loss, L_phys_2. Preferably, when the reflection coefficients at each connection in the cascaded network are small, a step-by-step cascaded approximation method can be used to superimpose the reflection components.

[0062] Furthermore, this embodiment introduces multi-band joint physical constraints to enhance the identifiability of each component of the degradation state. The operating frequency band of the waveguide typically covers a certain frequency range. Within this frequency range, 3 to 5 discrete frequency sampling points f_1 to f_K are selected, and the aforementioned physical consistency constraint loss is calculated at each frequency sampling point. Since the sensitivity of the attenuation constant alpha to each degradation parameter varies with frequency—the effect of surface roughness increment on the attenuation constant is more prominent at the high-frequency end, while the effect of cross-sectional thermal deformation is dominant at the low-frequency end near the cutoff frequency—the physical constraint loss at different frequency points applies gradient constraints in different directions to each component of the degradation state vector, thereby breaking the parameter coupling and indistinguishability problems that may exist between the components of the degradation state under single-frequency constraints. The multi-band joint physical constraint loss is L_phys_multi = sum_{k=1}^{K} w_k * (L_phys_1(f_k) + L_phys_2(f_k)), where w_k is the constraint weight of each frequency point, preferably set to be proportional to the Fisher information of the degradation parameter of the attenuation constant at that frequency point.

[0063] In the overall training loss function, the weight coefficient lambda_phys of the physical consistency constraint loss term adopts a progressively increasing strategy during training. Initially, a small weight value is set (preferably, an initial value of 0.01) to allow the variational inference network to first learn the statistical patterns of degenerate states from the data. Subsequently, the weight is linearly increased to the target weight value (preferably, a target value of 1.0) during training. The strengthening of physical constraints in the later stages of training ensures that the inference results converge to a physically consistent solution space while satisfying statistical fitting. The weight of the KL divergence term also employs an annealing strategy, progressively increasing from 0 to 1, to avoid posterior collapse.

[0064] This implementation offers the following advantages in terms of degradation state inference accuracy. By combining graph attention message passing with global observation gating, degradation information from sensor-covered nodes can propagate directionally along the waveguide network topology to sensorless nodes. Simultaneously, end-to-end loss information from port RF observations can be adaptively allocated to each node. Compared to purely data-driven variational inference methods without physical constraints, the electromagnetic propagation attenuation model constraint confines the degradation state search space to the physically feasible domain, avoiding non-physical interpretations that violate the electromagnetic propagation equations. Multi-band joint constraints further reduce the confusion of each degradation component, enabling the separate identification of degradation indicators such as surface roughness increment and conductor conductivity attenuation rate, which are difficult to distinguish under single-frequency observations. When the proportion of sensorless nodes in the waveguide network exceeds 80%, the above inference mechanism maintains the effectiveness of degradation state estimation. However, when this proportion approaches 95% and the network topology diameter is large, the inference accuracy for distant nodes with a topological distance exceeding four hops from the nearest sensor-covered node may decrease.

[0065] From a theoretical perspective, the graph variational inference mechanism can effectively infer the degenerate state of each node under conditions of incomplete observations due to the synergistic effect of three aspects. First, the topological structure of the directed attribute graph provides structured path constraints for information propagation. The propagation direction of degenerate information is consistent with the actual propagation direction of electromagnetic waves, allowing the impact of the degenerate state of upstream nodes on downstream nodes to be naturally modeled. The multi-head design in the graph attention mechanism allows different attention heads to focus on different types of degenerate dependencies, such as thermal conduction coupling between adjacent transmission nodes and mechanical coupling between a connecting node and the transmission nodes on both sides. Second, the physical consistency constraint establishes a deterministic mapping relationship between the latent variables of the degenerate state and the observables. Even if a node does not have direct local observations, its degenerate state still indirectly affects the port observations through the cascaded transmission equations. The gradient of the physical constraint loss can propagate back along the cascaded path to the node, thus providing an effective monitoring signal. Third, multi-band constraints utilize the differences in the interaction modes between electromagnetic fields and waveguide walls at different frequencies. High-frequency electromagnetic waves have a shallower skin depth and are therefore more sensitive to surface roughness. Low-frequency electromagnetic waves respond more violently to changes in the propagation constant of cross-sectional dimensions when approaching the cutoff frequency. This frequency-dependent difference provides identification conditions for the independent components of the degenerate state vector, similar to multi-view observation.

[0066] like Figure 5As shown, under the condition that the sensor coverage is less than 30%, this invention achieves the effective propagation of limited local observation information in the waveguide network topology through a graph attention message passing mechanism. The upper part of the figure shows a chain-like directed attribute graph containing 23 nodes, in which transmission nodes and connection nodes are arranged alternately, only 6 nodes are equipped with sensors (coverage of about 26%), and the remaining 17 nodes have no sensor coverage.

[0067] The central part of the diagram illustrates the layer-by-layer diffusion of information during the three-layer graph attention message passing process. After the first layer of message passing, information only propagates to the direct neighbors of nodes with sensors; after the second layer, the information expands to nodes within a two-hop range; and after the third layer, the information covers all network nodes. The lower part of the diagram illustrates the role of the global observation gating mechanism: RF observation data from the input and output ports are incorporated into the state updates of each node through gating parameters. In areas with sufficient local information, the gating value approaches 1 to rely on neighborhood information, while in areas far from sensors, the gating value approaches 0 to rely on global observation compensation. The confidence heatmap at the bottom visually reflects the confidence distribution of the degradation state estimates for each node; nodes with sensors and their neighboring areas have high confidence, while the confidence of nodes far from sensors gradually decreases.

[0068] Example 3

[0069] In another embodiment of the present invention, a method for dynamic prediction of waveguide transmission loss based on a frequency domain piecewise linearized state space model is provided. This method adopts a different technical path from the above-described embodiments in characterizing and modeling the degradation state.

[0070] In this embodiment, the construction method of the directed attribute graph of the waveguide network in step S1 is the same as in the previous embodiment, but the processing of the port RF observation data adopts a frequency domain transformation method. Specifically, the port RF observation data is sampled in the frequency domain within the working frequency band according to a preset frequency resolution to obtain the frequency domain response curves of the transmission coefficient and reflection coefficient. A one-dimensional convolutional network is used to extract multi-scale frequency domain features along the frequency axis of the frequency domain response curve. The one-dimensional convolutional network contains three convolutional layers with kernel sizes of 7, 5, and 3, and the number of output channels of each layer are 32, 64, and 128, respectively. By progressively reducing the kernel size, wideband trend features, mid-band structural features, and narrowband detail features are extracted sequentially. The outputs of the three layers are adaptively averaged and concatenated to generate a frequency domain observation embedding vector. Compared with the previous embodiment where RF observations are encoded into a single global embedding vector, frequency domain convolutional encoding retains the structured information in the frequency dimension, which is beneficial for subsequent modeling of frequency dependence in physical constraints.

[0071] In the degradation state inference stage, this implementation does not employ a variational inference framework, but instead uses a deterministic state estimation method based on the extended Kalman filter concept. The degradation state vector of each node is considered as the latent state of the dynamic system. Using the environmental observations and frequency domain observation embedding vectors of each node as observation inputs, a prediction-update step is iteratively executed on the directed attribute graph. In the prediction step, a parameterized state transition network predicts the prior estimate of the degradation state at the next time step and its diagonal approximation of the covariance matrix based on the current degradation state estimates of each node and the environmental inputs. In the update step, the frequency domain observation embedding vectors are mapped to the observed estimates of the degradation state through a physical constraint layer, and the posterior degradation state estimate is obtained through a weighted fusion of the prior and observed estimates. The advantage of this method is that it generates deterministic point estimates rather than distributed estimates at each step, resulting in lower computational overhead in the inference stage compared to the sampling process of variational inference.

[0072] In the temporal evolution prediction stage, this implementation adopts a piecewise linearization strategy to replace the dual-channel architecture of GRU and Neural ODE in the previous implementation. Specifically, the degradation process is divided into several stages on the time axis. The evolution of the degradation state within each stage is approximated as a linear dynamic system, and the transition between stages is controlled by the degradation state triggering conditions. The linearized evolution equation of the degradation state is z_i(t+1) = A_p * z_i(t) + B_p * u_i(t) + c_p, where A_p, B_p, and c_p are the system matrix and bias term of the p-th stage. A stage identification network determines the stage index p based on the value range of the current degradation state z_i(t) and outputs the corresponding parameters. u_i(t) is an external input vector containing environmental stress and neighborhood degradation information. The stage identification network uses a lightweight multilayer perceptron, and its output is the soft-assignment probability of each candidate stage. Differentiable discrete stage selection is achieved through the Gumbel-Softmax technique. The physical meaning of this piecewise linearization strategy is that the degradation process exhibits different dynamic characteristics at different stages. For example, the degradation of waveguides in the early stage of service is mainly slow oxidation and approximately linear. In the middle stage of degradation, the degradation rate may jump after the surface roughness accumulates to a certain extent. The piecewise linear model can approximate this staged degradation behavior with low model complexity.

[0073] In the loss mapping and trend extrapolation stages, this implementation also utilizes the theoretical formula of the electromagnetic propagation attenuation model to calculate the baseline loss value and learns the bias through a lightweight correction network. This correction network employs a two-layer fully connected structure, with the input being a concatenation of the degraded state vector and waveguide segment static parameters, a hidden layer dimension of 64, and the output being a scalar loss correction. During the autoregressive extrapolation process, since the state transition matrix A_p of the piecewise linearized model is constant within each stage, the predicted degraded state value from the current moment to the T-th future step can be directly calculated using matrix exponentiation A_p^T without step-by-step expansion, thus offering computational efficiency advantages in long-term trend extrapolation. Preferably, when the extrapolation time steps exceed the stage length, the possibility of stage switching needs to be considered. In this case, stage identification is re-executed at the stage boundary, and the corresponding system matrix parameters are switched to connect the predicted trajectories of multiple stages.

[0074] In this implementation, the graph-based message passing operation is also embedded in each state update step to ensure that the spatial propagation characteristics of degradation effects in the cascaded network are captured. After the prediction phase of the prediction-update step is completed, the prior degradation state estimates of each node are exchanged with the topologically adjacent nodes through a round of graph attention message passing, enabling the accelerated degradation trend of the upstream waveguide segment to transmit early warning information to the downstream nodes. In each update step, the frequency domain observation embedding vector selectively utilizes information from different frequency bands through a frequency attention mechanism. This mechanism calculates the attention weights in the frequency dimension based on the current estimated value of the degradation state of each node, adaptively emphasizing the frequency band information most sensitive to the degradation parameters of that node. When the estimated value of the surface roughness increment of a transmission node is large, the frequency attention mechanism will automatically increase the weight corresponding to the high-frequency sampling points to obtain more sensitive observation constraints. When the stage division is inappropriate or the actual degradation process frequently switches near the stage boundary, the prediction accuracy of the piecewise linearization method may not be as good as that of the continuous nonlinear model. Under the application conditions where the degradation process exhibits obvious stage characteristics and the degradation behavior within each stage is relatively stable, this method can serve as a computationally efficient alternative to the aforementioned implementation method.

[0075] Example 4

[0076] This embodiment provides a waveguide electromagnetic wave transmission loss dynamic prediction device, such as... Figure 4 As shown, the device includes a waveguide network topology modeling module, a degradation state variational inference module, a multi-scale temporal evolution module, and a link loss prediction module. The device is deployed on a general-purpose computing server equipped with a multi-core processor and graphics processing unit for performing deep learning inference operations. It is connected to the port RF detection equipment and environmental sensor network of the waveguide network via a data acquisition interface.

[0077] The waveguide network topology modeling module constructs a directed property graph based on the physical connection structure of the waveguide network. It models each waveguide segment as a transmission node and each flange connection as a connection node. Port RF observation data and environmental sensor data are encoded into a global observation embedding vector and initial feature vectors for each node, respectively. During system initialization, this module generates the topology of the directed property graph and the static attributes of each node based on the waveguide network design drawings and deployment information. During operation, it periodically receives and encodes port RF observation data and environmental sensor data. Specifically, this module includes an RF feature encoding subunit and a node feature encoding subunit. The RF feature encoding subunit uses a multilayer perceptron to encode the overall transmission coefficient amplitude, overall transmission coefficient phase, port reflection coefficient amplitude, and port reflection coefficient phase at each sampling moment into a global observation embedding vector. The node feature encoding subunit uses another multilayer perceptron to jointly encode the static attributes and local environmental features of each node to generate initial feature vectors. For nodes without sensor coverage, the node feature encoding subunit sets their local environmental features as missing identifiers and processes them using a masking mechanism. The waveguide network topology modeling module passes the structural information of the directed attribute graph, the global observation embedding vector, and the initial feature vectors of each node to the degradation state variational inference module.

[0078] The degradation state variational inference module is used to perform graph variational inference on the directed attribute graph. Taking the initial feature vector and the global observation embedding vector as input, it outputs the posterior distribution parameters of the degradation state vectors of each node through a multi-layer graph attention message passing layer. Based on the electromagnetic propagation attenuation model, it aggregates the degradation states of each node along the directed attribute graph to obtain an estimate of the total link transmission loss. The deviation between this estimate and the port RF measured values ​​is used to construct the physical consistency constraint loss. After receiving the directed attribute graph structure information, global observation embedding vector, and initial feature vectors of each node from the waveguide network topology modeling module, this module achieves information interaction between nodes through a multi-layer graph attention message passing layer. Nodes with direct environmental observations propagate degradation information along the topology of the directed attribute graph to nodes without sensor coverage. The global observation embedding vector distributes the full-link loss information contained in the port RF observations to each node through an attention gating mechanism. This module outputs the posterior distribution parameters of the degradation state vectors of each node and passes the sampled degradation state estimates and physical consistency constraint losses to the multi-scale temporal evolution module and the model training and optimization process, respectively.

[0079] The multi-scale temporal evolution module predicts the temporal evolution of the degradation state of each node using a dual-channel neural state-space model. The first channel uses a gated recurrent unit to capture short-period degradation changes, while the second channel uses neural ordinary differential equations to model long-period degradation trends. This module receives the degradation state estimates of each node at the current time from the degradation state variational inference module, along with the current environmental observations. Through collaborative computation between the fast and slow variable channels, it outputs the predicted degradation state of each node at the next time step. The output of the fast variable channel extracts the cumulative driving effect on the slow variable channel through weighted accumulation within a time window. The current state of the slow variable channel adjusts the state transition parameters of the gated recurrent unit in the fast variable channel using a modulation function, forming a cross-scale bidirectional coupling. After each state update, the module performs a round of graph message passing, allowing each node to exchange information with neighboring nodes along the topology of the directed attribute graph, capturing the spatial propagation characteristics of degradation effects in cascaded networks. The multi-scale temporal evolution module then transmits the predicted degradation state values ​​of each node to the link loss prediction module.

[0080] The link loss prediction module maps the degradation state of each node to the predicted transmission loss value of each segment through a loss mapping network. It then aggregates these values ​​along the directed attribute graph to obtain the total predicted transmission loss value of the link and extrapolates the future loss evolution trend in an autoregressive manner. This module receives the degradation state prediction values ​​of each node from the multi-scale time-series evolution module and the static design parameters of each node provided by the waveguide network topology modeling module. Through the residual structure loss mapping network, it outputs the insertion loss prediction values ​​of each waveguide segment and the mismatch loss prediction values ​​of each connection node. All loss prediction values ​​are summed segment by segment along the propagation direction of the directed graph in decibels to obtain the total predicted transmission loss value of the link at the current moment. In extrapolation prediction mode, the link loss prediction module, in collaboration with the multi-scale time-series evolution module, proceeds forward in an autoregressive manner, progressively predicting the degradation state at each future time step and converting it into a predicted transmission loss value. This generates an evolution trend curve of the transmission loss within a preset future time interval and outputs it to the upper-level monitoring system for online alarms and maintenance decisions.

[0081] Example 5

[0082] This embodiment uses an X-band microwave signal transmission system inside a closed platform as an application scenario to demonstrate the specific implementation process and technical effects of the aforementioned waveguide electromagnetic wave transmission loss dynamic prediction method. The transmission system consists of a cascaded network of 16 waveguide segments and 15 flange connections, including 10 WR-90 rectangular straight waveguide segments, 3 E-plane elbow segments, 2 rectangular-to-circular transition segments, and 1 circular straight waveguide segment, operating in the 8.2GHz to 12.4GHz frequency band. Because this waveguide network is installed inside a closed enclosure and is surrounded by equipment and cables, it is impossible to disassemble and test each segment or insert intermediate test ports during operation. Only one set of radio frequency detection devices is installed at each of the network's input and output ports. Environmental sensors (5 combinations of temperature and vibration sensors, and 4 humidity sensors) are deployed at 9 of the 31 nodes, resulting in a sensor coverage of approximately 29%. During the mission, the platform experienced drastic temperature fluctuations (internal temperature ranged from 35°C to 78°C, with a daily temperature difference of up to 25K) and continuous broadband random vibrations (power spectral density ranging from 0.02 g² / Hz to 0.05 g² / Hz). The coupling effect of multiple degradation mechanisms caused the transmission loss of the waveguide network to continuously increase over hundreds of hours of operation. Conventional methods can only obtain the total transmission loss of the entire link through port RF measurements, and cannot distinguish the degradation contribution of each segment and connection point, nor can they predict the future evolution trend of the loss.

[0083] According to step S1 of the method of the present invention, a directed attribute graph containing 31 nodes and 30 directed edges is constructed based on the physical connection structure of the 16 waveguide segments and 15 flange connections. The sampling interval is set to 60 seconds. Port radio frequency observation data is collected and encoded into a 64-dimensional global observation embedding vector. The environmental data of 9 sensor-covered nodes and the missing identifiers of 22 sensorless nodes are jointly encoded to generate a 64-dimensional initial feature vector for each node.

[0084] According to step S2, variational inference is performed on the directed attribute graph through 3-layer graph attention message passing, outputting the posterior distribution parameters of the 4-dimensional degenerate state vector of each node, and constructing the physical consistency constraint loss through the electromagnetic propagation attenuation model.

[0085] According to step S3, the temporal evolution prediction of the degenerative state of each node is performed by a dual-channel neural state space model. The hidden layer dimension of the gated recurrent unit in the fast variable channel is 128-dimensional, and the neural ordinary differential equation of the slow variable channel adopts a fourth-order adaptive step-size integrator. The cross-scale coupling window length is 24 hours.

[0086] According to step S4, the predicted degradation state is mapped to the predicted transmission loss value of each segment through the loss mapping network and aggregated along the directed attribute graph to generate the transmission loss evolution trend prediction for the next 96 hours in an autoregressive manner.

[0087] During the model training phase, 10 environmental condition sequences generated by multiphysics coupling simulation were used for pre-training. The simulation time span for each sequence was 720 hours, resulting in approximately 432,000 simulation samples across time steps. After pre-training, 50 rounds of fine-tuning were performed using actual online monitoring data accumulated over the first 120 hours on the platform, with a fine-tuning learning rate of 1.0 × 10^-5.

[0088] To evaluate the technical effectiveness of the method of this invention, the following comparative and ablation experiments were designed. The comparative methods include: Method A, an end-to-end timing prediction method based on long short-term memory networks, directly predicts the total transmission loss of the link using the port RF observation sequence as input, without graph structure modeling or degradation state inference; Method B, a static prediction method based on standard graph neural networks, uses graph convolutional networks to model the waveguide network but does not include timing evolution prediction capabilities, independently inferring the current transmission loss from the current observation data at each time step. Ablation variants include: Variant C, the method of this invention after removing the physical consistency constraint loss, retaining only the evidence lower bound loss of variational inference and the mean square error of transmission loss prediction for training; Variant D, the method of this invention that replaces the dual-channel neural state-space model with a single-channel gated recurrent unit, removing slow variable channels and cross-scale coupling mechanisms.

[0089] The evaluation metrics used were the relative root mean square error (RRMSE) of the total link transmission loss prediction, the mean absolute error (MAE) of the degradation state estimation for each node (with the true value of the node degradation state in the simulation data as a reference), and the mean absolute percentage error (MAPE) of the extrapolated prediction for the next 72 hours. The test data consisted of actual monitoring data during 480 hours of continuous operation of the platform, with the first 120 hours used for fine-tuning and the last 360 hours used for evaluation.

[0090] In the task of predicting the total transmission loss of the link at the current moment, the RRMSE of the method of this invention is 3.27%, the RRMSE of method A is 8.94%, the RRMSE of method B is 6.51%, the RRMSE of variant C is 4.83%, and the RRMSE of variant D is 4.46%. In the task of estimating the degradation state of each node, the average MAE of the method of this invention is 1.82 μm for cross-sectional thermal deformation, 0.14 μm for surface roughness increment, 0.023 μm for conductor conductivity attenuation, and 2.37 μm for flange alignment offset. The corresponding MAEs of variant C are 2.71 μm, 0.22 μm, 0.038 μm, and 3.64 μm, respectively, indicating that the physical consistency constraint loss has a clear effect on improving the accuracy of degradation state estimation.

[0091] In the extrapolation prediction task for the next 72 hours, the performance of the method of this invention under different prediction time spans is as follows: MAPE is 2.15% for predicting the next 12 hours, 3.48% for predicting the next 24 hours, 5.73% for predicting the next 48 hours, and 7.91% for predicting the next 72 hours. Method A's MAPEs for the same prediction span are 5.83%, 9.67%, 16.42%, and 23.15%, respectively. Method B cannot perform extrapolation prediction due to its lack of time-series prediction capabilities. Variant D has a MAPE of 11.64% for predicting the next 72 hours, which is 3.73 percentage points higher than the method of this invention, indicating the contribution of the dual-channel cross-scale coupling mechanism to the prediction accuracy over long time spans. During periods of large temperature fluctuations (daily temperature difference exceeding 20K), the prediction error of the method of this invention increases compared to periods of stable temperature, with the MAPE for predicting the next 72 hours rising from 6.53% during stable periods to 9.82% during periods of drastic temperature changes, but it is still better than the performance of the comparative methods during stable temperature periods.

[0092] To verify the extrapolation prediction accuracy of the method of the present invention under different prediction time spans, the test was conducted under the following conditions: based on 360 hours of continuous running data generated by the waveguide network simulation platform, the first 240 hours were used as training data, and extrapolation predictions were performed for the next 12 hours, 24 hours, 48 ​​hours and 72 hours respectively. The mean absolute percentage error (MAPE) was used as the evaluation index, and the comparison methods included the LSTM end-to-end method and the single-channel GRU variant.

[0093] like Figure 7 As shown, the MAPE of all methods increases with the increase of the prediction time span, but the growth rate of the method of this invention is significantly lower than that of the comparative methods. For a 12-hour prediction span, the MAPE of the method of this invention is 2.15%, method A is 5.83%, and variant D is 3.10%. For a 72-hour prediction span, the MAPE of the method of this invention is 7.91%, still below the acceptable performance threshold of 10%, while the MAPE of method A has increased to 23.15%, far exceeding the acceptable range. These results demonstrate that the dual-channel temporal evolution architecture and physical constraint mechanism of this invention effectively suppress the error accumulation of long-span extrapolation.

[0094] To verify the accuracy of the total link transmission loss prediction method under actual operating conditions and its robustness to temperature fluctuations, the method was evaluated on 360 hours of continuous operation test data. The relative root mean square error (RRMSE) was used as the overall accuracy index, and the temperature changes inside the cabin were recorded to analyze the impact of temperature on the prediction accuracy.

[0095] like Figure 8As shown, the predicted values ​​of the method of this invention are significantly better than those of method A, with an overall RRMSE of 3.27%, while the RRMSE of method A is 8.94%. Furthermore, during periods of stable temperature fluctuation, the MAPE of the method of this invention is 6.53%; during periods of drastic temperature change with a daily temperature difference exceeding 20K, the MAPE rises to 9.82%, but still remains within an acceptable range. In contrast, the prediction bias of method A increases significantly during periods of drastic temperature change. These results demonstrate that this invention, through explicit modeling of the temperature-driven long-term degradation trend by the slow variable channel in a dual-channel architecture, effectively improves the prediction robustness under complex thermal environments.

[0096] The experimental results above show that the method of the present invention, through the synergistic effect of directed attribute graph modeling, physical constraint graph variational inference, and dual-channel cross-scale temporal evolution prediction, can effectively infer the degradation state of each node and accurately predict the dynamic evolution trend of link transmission loss under highly incomplete observation conditions with sensor coverage of less than 30%.

[0097] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for dynamically predicting electromagnetic wave transmission loss in a waveguide, characterized in that, Includes the following steps: Step S1: Construct a directed attribute graph based on the physical connection structure of the waveguide network, model each waveguide segment as a transmission node, model each flange connection as a connection node, and encode the port RF observation data and environmental sensor data into a global observation embedding vector and an initial feature vector for each node, respectively. Step S2: On the directed attribute graph, a graph variational inference network is used. The initial feature vector and the global observation embedding vector are used as inputs. The posterior distribution parameters of the degradation state vectors of each node are output through multi-layer graph attention message passing. According to the electromagnetic propagation attenuation model, the degradation state of each node is aggregated along the directed attribute graph to form an estimate of the total transmission loss of the link. The deviation between the estimate and the measured value of the port radio frequency is used to construct the physical consistency constraint loss. Step S3: The degeneration state of each node is predicted in a temporal sequence using a dual-channel neural state space model. The first channel uses a gated recurrent unit to capture short-cycle degeneration changes, and the second channel uses neural constant differential equations to model long-cycle degeneration trends. Step S4: The degradation state of each node is mapped to the predicted transmission loss value of each segment through the loss mapping network. The total transmission loss prediction value of the link is obtained by aggregating along the directed attribute graph, and the future loss evolution trend is extrapolated in an autoregressive manner.

2. The method according to claim 1, characterized in that, In step S1, each transmission node in the directed attribute graph carries the cross-sectional type, cross-sectional size, length and design operating frequency of the corresponding waveguide segment as static attributes, and each connection node carries the flange type and design clearance tolerance of the corresponding flange as static attributes. The initial feature vector is generated by jointly encoding the static attributes and local environmental features of each node using a multilayer perceptron.

3. The method according to claim 1, characterized in that, In step S2, the physical consistency constraint loss includes two parts: the first part is the deviation between the estimated value of the single-segment transmission loss of each waveguide segment and the estimated value of the mismatch loss at each flange connection calculated by the electromagnetic propagation attenuation model based on the degradation state vector of each node, and the estimated value of the total transmission loss of the link calculated by the cascading transmission relationship along the directed attribute graph and the measured overall transmission coefficient of the port. The second part involves calculating the estimated reflection components at each connection node based on the cross-sectional thermal deformation and flange alignment offset in the degradation state vector of each node using mode coupling theory, and then aggregating these values ​​along the directed attribute graph to determine the deviation from the measured port reflection coefficient.

4. The method according to claim 1, characterized in that, In step S2, the graph attention message passing layer of the graph variational inference network uses a multi-head attention mechanism to calculate attention weights. The global observation embedding vector is fused into the feature update process of each node through an attention gating mechanism. After multiple layers of message passing, the feature vectors of each node output the mean vector and log-variance vector of the posterior distribution of the degenerate state through a linear mapping layer. The degenerate state estimate is obtained by sampling from the posterior distribution using a reparameterization technique.

5. The method according to claim 1, characterized in that, In step S3, the first channel of the dual-channel neural state space model takes the estimated degradation state of each node at the current moment and the environmental observation value at the current moment as input, and outputs the rapid change increment of the degradation state at the next moment through the gated loop unit; the second channel obtains the slow evolution trajectory of the degradation state by numerically integrating the parameterized ordinary differential equation in the time dimension. The ordinary differential equation introduces monotonicity constraints to ensure that the evolution direction of the surface roughness increment and the conductor conductivity decay rate conforms to physical monotonicity.

6. The method according to claim 5, characterized in that, In the dual-channel neural state-space model, the output of the first channel is used to extract the cumulative driving effect on the slow evolution trajectory of the second channel through a weighted cumulative operation within a time window, which is then used as an additional input to the second channel. The current state of the second channel is used to adjust the state transition parameters of the gated recurrent unit in the first channel through a modulation function.

7. The method according to claim 1, characterized in that, In step S4, the loss mapping network adopts a residual structure, using the calculation result of the theoretical attenuation constant formula as the benchmark value. The loss deviation caused by degradation is learned by the neural network, and the prediction result of the loss mapping network regresses to the classical theoretical value under the condition of no degradation.

8. The method according to claim 1, characterized in that, The training loss function of the method consists of a weighted sum of three parts: the evidence lower bound loss of variational inference, the physical consistency constraint loss, and the mean square error between the predicted and measured values ​​of the total transmission loss of the link at each time point. The training data is generated by multi-physics coupling simulation of the waveguide network under different environmental conditions.

9. The method according to claim 1, characterized in that, In step S3, the dual-channel neural state space model performs a round of graph message passing operation after each state update, so that the degradation state of each node exchanges information with adjacent nodes along the topology of the directed attribute graph. The degradation state change of the upstream waveguide segment affects the degradation evolution trajectory of the downstream node through the graph message passing operation.

10. A waveguide electromagnetic wave transmission loss dynamic prediction device, characterized in that, include: The waveguide network topology modeling module is used to construct a directed attribute graph based on the physical connection structure of the waveguide network, model each waveguide segment as a transmission node, model each flange connection as a connection node, and encode port RF observation data and environmental sensor data into a global observation embedding vector and an initial feature vector of each node, respectively. The degradation state variational inference module is used to perform graph variational inference on the directed attribute graph, taking the initial feature vector and the global observation embedding vector as input, and outputting the posterior distribution parameters of the degradation state vector of each node through multi-layer graph attention message passing. According to the electromagnetic propagation attenuation model, the degradation state of each node is aggregated along the directed attribute graph into an estimated value of the total transmission loss of the link. The deviation between the estimated value and the measured value of port radio frequency is used to construct the physical consistency constraint loss. The multi-scale temporal evolution module is used to predict the temporal evolution of the degradation state of each node through a dual-channel neural state space model. The first channel uses a gated recurrent unit to capture short-period degradation changes, and the second channel uses neural ordinary differential equations to model long-period degradation trends. The link loss prediction module is used to map the degradation state of each node to the predicted transmission loss value of each segment through the loss mapping network, aggregate along the directed attribute graph to obtain the predicted total transmission loss value of the link, and extrapolate the future loss evolution trend in an autoregressive manner.

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