Continuous measurement method for track regularity based on inertial navigation data

Abstract

This invention discloses a continuous measurement method for track ride comfort based on inertial navigation data, belonging to the field of track inspection technology. The method first acquires time-stamped MEMS-IMU three-dimensional attitude acceleration data and ground-penetrating radar electromagnetic echo data during the operation of a track inspection vehicle; it extracts inherent frequency features through time-domain identification of track structure modal parameters, constructs target-free correction constraints using standard design modal parameters, and compensates for inertial navigation drift errors through online self-calibration of multi-source errors across the entire temperature domain; it establishes a mapping correlation model between ride comfort parameters and substructure deformation parameters, outputting a comprehensive evaluation result of track ride comfort over the entire mileage. This invention achieves long-distance continuous high-precision measurement without discrete targets, can correlate apparent deformation and substructure defects in a unified coordinate system, accurately locates the root cause of ride comfort anomalies, and is suitable for track lifecycle health inspection in scenarios without GNSS signals.

Description

Technical Field

[0001] This invention discloses a method for continuous measurement of track smoothness based on inertial navigation data, which relates to the field of track detection technology. Background Technology

[0002] Current track smoothness measurements typically employ inertial measurement units (IMUs) to collect attitude and acceleration data of the inspection vehicle during operation, and then calculate the track geometry parameters through integration. In scenarios without GPS signals, such as long tunnels, the drift error of the IMU accumulates with the mileage. Conventional solutions rely on discrete fixed targets deployed along the track for position correction. Absolute coordinates are acquired as the inspection vehicle passes over the targets to reset the error, and inertial navigation is used to maintain the calculation within the interval between adjacent targets. For the inspection of the track substructure, electromagnetic echo data is typically collected independently by ground-penetrating radar (GPR). The dielectric constant of the substructure is then inverted based on simple ray tracing or empirical formulas. These two types of data are processed independently in time and space.

[0003] The aforementioned existing technology relies on discrete fixed targets to correct inertial navigation drift errors, which causes the smoothness calculation within adjacent target intervals to be disturbed by residual drift and thus cannot maintain continuous high accuracy. Furthermore, this data decoupling mechanism that relies on discrete position correction severs the continuous spatial mapping relationship between the apparent geometric parameters of the track and the parameters of the substructure, making it impossible to associate smoothness anomalies and substructure defects in the same continuous coordinate system, and thus making it impossible to locate the structural root cause of smoothness anomalies. Summary of the Invention

[0004] The purpose of this invention is to provide a solution that can effectively address the problems described in the background section.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: Continuous measurement methods for track smoothness based on inertial navigation data include: Acquire time-stamped MEMS-IMU three-dimensional attitude acceleration data and ground-penetrating radar electromagnetic echo data during the operation of the track inspection vehicle; Based on the time-domain identification of track structure modal parameters, the inherent frequency characteristics of the track in acceleration data are extracted. A targetless correction constraint term is constructed based on the standard design modal parameters. Combined with online self-calibration of multi-source errors in the full temperature domain, the inertial navigation drift error is compensated. The trajectory continuity and smoothness parameters are calculated based on the compensated three-dimensional attitude data. Using the compensated spatial location data as spatial coordinate constraints, the deformation parameters of the lower structure of the track are calculated by inputting electromagnetic wave travel time tomography inversion solution; Establish a mapping relationship model between continuous ride comfort parameters and substructure deformation parameters, and output the comprehensive evaluation results of track ride comfort over the entire mileage.

[0006] Preferably, the construction of target-free correction constraints includes: The orbital dynamics equations are transformed into state-space form. A genetic algorithm is introduced to perform parallel optimization of the initial state vector and damping ratio matrix in the state-space model. The deviation between the globally optimal modal parameters obtained by optimization and the standard design modal parameters is used as the virtual observation of Kalman filtering to generate modal constraint equations that suppress low-frequency drift of the inertial navigation system.

[0007] Preferably, the input electromagnetic wave travel time tomography inversion includes: By abandoning the ray tracing path assumption, the Maxwell curl equation under spatial coordinate constraints is discretized into a velocity-stress staggered grid form. The electromagnetic wave forward modeling operator is constructed by introducing the perfectly matched layer absorption boundary condition in the seismic wave field and solving the adjoint field backpropagation error by combining the conjugate gradient method.

[0008] Preferably, establishing a mapping association model includes: The apparent smoothness parameters and the dielectric constant distribution obtained by full waveform inversion are constructed into a heterogeneous graph structure, in which the smoothness measurement points and the lower spatial grid are used as nodes, and the spatial topological adjacency relationship is used as edges. The feature representations of cross-scale nodes are aggregated through graph convolutional networks to extract the topological transmission path of apparent geometric deformation and latent defects.

[0009] Preferably, the online self-calibration of multi-source errors across the entire temperature range includes: A partial differential heat conduction equation is established between the internal heat source and the outer shell environment of the inertial navigation system. The lattice Boltzmann method in fluid mechanics is used to simulate the internal air convection heat transfer process. A real-time temperature field digital twin is constructed, and thermodynamic state variables are injected as prior inputs into the self-calibration model to decouple the coupling error between temperature and zero partial scaling factor.

[0010] Preferably, the injected self-calibration model includes: A deep reinforcement learning framework is constructed, using the residuals of thermodynamic state variables and modal constraint equations as the state space, the step size of the filter covariance matrix in the self-calibration model as the action space, and the minimization of long-term drift cumulative error as the reward function. The adaptive update of calibration parameters is achieved through the interaction between the agent and the dynamic temperature environment.

[0011] Preferably, adaptive updating of calibration parameters includes: In the calculation of the reward function, the Fisher information matrix from communication sensing is introduced. The information matrix is ​​constructed by obtaining the second derivative of the log-likelihood function of the state space parameter. The determinant value of the information matrix is ​​used to quantify the state observability under the current temperature and modal constraint combination, and redundant observation data with observability below the preset threshold are dynamically eliminated.

[0012] Preferably, the dynamic removal of redundant observation data includes: The observation data selection is transformed into a nonlinear binary combinatorial optimization problem. A Hamiltonian corresponding to the Fisher information matrix is ​​constructed. The ground state of the Hamiltonian is found by using a quantum approximation optimization algorithm through parameterized quantum gate circuit evolution. The bit string corresponding to the ground state represents the optimal observation data retention strategy.

[0013] Preferably, the comprehensive evaluation results of track smoothness across the entire track length include: The continuous dielectric constant distribution sequence of the entire track, calculated by the optimal observation data preservation strategy, is regarded as a spatial marker. The spatiotemporal Transformer architecture in natural language processing is introduced, and long-distance dependencies are captured through a multi-head self-attention mechanism to predict the spatiotemporal evolution trend of the deformation of the lower structure of the track within a preset time step.

[0014] Preferably, the predicted spatiotemporal evolution trends include: By setting apparent smoothness degradation, substructure deformation aggravation, and residual inertial navigation drift error as players in the game, and using the robustness of the smoothness evaluation result as the payoff function, the Nash equilibrium point of the non-cooperative dynamic game is solved, and the policy space boundary corresponding to the equilibrium point is used as the confidence interval of the comprehensive evaluation result.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention utilizes time-domain identification of track structure modal parameters to extract inherent frequency features, combines a genetic algorithm to optimize state-space model parameters, uses standard modal parameter deviations as Kalman filter virtual observations to construct targetless correction constraints, and employs a full-temperature-domain multi-source error online self-calibration algorithm to eliminate dependence on discrete fixed targets and maintain continuous accuracy of long-distance smoothness measurements. By using the corrected spatial position data as spatial coordinate constraints for tomographic inversion, and employing heterogeneous graph structures and graph convolutional networks to aggregate cross-scale features of apparent smoothness measurement points and lower spatial grids, a topological transmission path for apparent geometric deformation and latent defects is established in a continuous coordinate system, realizing the structural root cause localization of smoothness anomalies.

[0016] 2. This invention abandons ray tracing in electromagnetic wave travel-time tomography, constructs a velocity-stress staggered grid forward modeling operator using Maxwell's curl equation, introduces perfectly matched layer absorption boundary conditions and combines the conjugate gradient method to solve the adjoint field backpropagation error, thus improving the resolution of the dielectric constant inversion of the lower structure. In the online self-calibration of multi-source errors across the entire temperature domain, the lattice Boltzmann method is used to simulate air convection to construct a digital twin of the temperature field, and deep reinforcement learning is combined to adjust the step size using the covariance matrix as the action space to achieve adaptive updating of calibration parameters. The Fisher information matrix is ​​introduced to quantify state observability and eliminate redundant observation data. The optimal data retention strategy is solved by constructing a Hamiltonian and using a quantum approximation optimization algorithm. The multi-head self-attention mechanism in the space-time converter architecture is used to predict the spatiotemporal evolution trend of the lower structure deformation, and the confidence interval of the comprehensive evaluation result is defined by solving the Nash equilibrium point using non-cooperative dynamic game theory. Attached Figure Description

[0017] Figure 1 This is the overall flowchart of the method of the present invention; Figure 2 This is a flowchart illustrating the construction of the targetless correction constraint term in this invention. Figure 3 This is a flowchart of the electromagnetic wave travel time tomography inversion process of the present invention; Figure 4 This is a flowchart illustrating the mapping and association process between heterogeneous graphs and graph convolutional networks in this invention. Figure 5 This is a flowchart of the online self-calibration process for multi-source errors across the entire temperature range, as described in this invention. Figure 6 This is a flowchart of the confidence interval for spatiotemporal prediction and comprehensive evaluation in this invention. Detailed Implementation

[0018] The continuous track smoothness measurement method based on inertial navigation data described in this specific embodiment operates on a track smoothness integrated measurement system mounted on a track inspection vehicle. The system includes a MEMS-IMU module, a ground-penetrating radar module, a time synchronization unit, an onboard computing unit, and a storage unit. The MEMS-IMU module and the ground-penetrating radar module are both coupled to the onboard computing unit via the time synchronization unit. The time synchronization unit is configured to output a sub-microsecond unified timestamp signal, achieving strict alignment of the time dimensions of the two types of acquired data. The onboard computing unit is configured to execute the various data processing steps of this method, and the storage unit is configured to store the raw data, intermediate processed data, and the final output results.

[0019] Example 1: Refer to Appendix Figure 1The time synchronization unit employs the PTP precision time protocol to provide the MEMS-IMU module and the ground-penetrating radar module with a common source of synchronization trigger signal and timestamp. The sampling frequency of the MEMS-IMU module is configured to be 1kHz to 10kHz, and the output three-dimensional attitude acceleration data includes linear acceleration α along the X, Y, and Z axes of the carrier coordinate system. x a y a z and angular velocities around the X, Y, and Z axes. Each set of data is bound to a synchronization timestamp t. The sampling frequency of the ground-penetrating radar module is matched to the sampling frequency of the MEMS-IMU module by an integer multiple. The output electromagnetic wave echo data includes the echo amplitude sequence within a preset time window. Each set of echo data is bound to a synchronization timestamp t that is from the same source as the acceleration data. The two types of data with timetamp alignment are then transmitted to the on-board computing unit.

[0020] The onboard computing unit extracts the natural frequency characteristics of the track from the acceleration data based on the time-domain identification of the track structure modal parameters. Specifically, after performing detrending and zero-mean preprocessing on the acceleration data, a Hankel matrix is ​​constructed using the random subspace method, and singular value decomposition is performed to extract the system state matrix, identifying the natural frequencies, damping ratios, mode shapes, and other modal parameters of the track structure. Using the standard design modal parameters given in the track design documents as a benchmark, a targetless correction constraint term is constructed. Simultaneously, a full-temperature-domain multi-source error online self-calibration model is established, which, combined with the targetless correction constraint term, compensates for the inertial navigation drift error of the MEMS-IMU, including zero bias error, scaling factor error, installation error, and low-frequency cumulative drift error.

[0021] Based on the compensated three-dimensional attitude data, the onboard computing unit calculates the track continuous ride comfort parameters. Specifically, the compensated vehicle attitude angles (roll, pitch, and heading) and linear acceleration are projected onto the track coordinate system through a transformation matrix from the vehicle coordinate system to the track coordinate system. The projected linear acceleration is integrated once to obtain a velocity sequence, and then integrated twice to obtain a displacement sequence. Based on the displacement sequence, five types of ride comfort parameters—elevation, orientation, level, gauge, and torsion—are calculated continuously across the entire track mileage. Each mileage point corresponds to a set of continuous ride comfort parameters.

[0022] Using the compensated three-dimensional spatial location data as spatial coordinate constraints, the onboard computing unit maps the time-domain electromagnetic wave echo data to a unified spatial coordinate system, inputs the electromagnetic wave travel-time tomography inversion process, and calculates the deformation parameters of the track substructure. These deformation parameters include the dielectric constant and conductivity distribution of different depth layers in the track bed, subgrade, and roadbed. Abnormal changes in the dielectric constant correspond to deformation defects in the substructure such as voids, loosening, abnormal moisture content, and insufficient compaction.

[0023] The onboard computing unit establishes a mapping and correlation model between continuous ride comfort parameters and substructure deformation parameters. Under a unified spatial coordinate system, it completes the spatial registration of apparent ride comfort parameters and substructure deformation parameters at the same mileage point, extracts the correlation between ride comfort anomalies and substructure defects, and finally outputs the comprehensive evaluation results of track ride comfort for the entire mileage, including ride comfort level, over-limit location, root cause location of defects, defect type and severity.

[0024] As a preferred embodiment, refer to Figure 2 The onboard computing unit transforms the multi-degree-of-freedom vibration dynamics equations of the track structure into a state-space form. The expression for the track dynamics equations is as follows: ; Where M is the mass matrix of the track structure, C is the damping ratio matrix, K is the stiffness matrix, and x(t) is the structural displacement response vector. For the velocity response vector, F(t) is the acceleration response vector, corresponding to the three-dimensional attitude acceleration data collected by the MEMS-IMU, and F(t) is the wheel-rail excitation vector generated by the movement of the detection vehicle.

[0025] Define state vector The dynamic equations are transformed into state-space expressions: ; Y(t) = CX(t) + DF(t); Where A is the system matrix, I is the identity matrix, B is the input matrix, C is the output matrix, D is the direct transmission matrix, and Y(t) is the observed acceleration data.

[0026] A genetic algorithm is introduced to perform parallel optimization of the initial state vector X0 and the damping ratio matrix C in the state-space model. Specifically, real-number encoding is used, with elements of the initial state vector X0 and the damping ratio matrix C serving as individual genes; the population size is set to 50–200, the crossover probability to 0.6–0.9, and the mutation probability to 0.01–0.1; the fitness function is set as the reciprocal of the deviation between the optimized modal parameters and the standard design modal parameters, with the fitness value negatively correlated with the deviation value. Through iterative operations of selection, crossover, and mutation, the globally optimal initial state vector and damping ratio matrix are obtained, and then the globally optimal modal parameters are solved. This includes the optimal natural frequency, damping ratio, and mode shape parameters.

[0027] The globally optimal modal parameters are compared with the standard design modal parameters. The deviation is used as a virtual observation for Kalman filtering to generate modal constraint equations that suppress low-frequency drift of the inertial navigation system. The expression for the virtual observation is: ; The state vector of the Kalman filter includes the inertial navigation system's position error, velocity error, attitude angle error, zero bias error, and scaling factor error. The virtual observations are incorporated into the observation equation of the Kalman filter, and the expression of the observation equation is: Z K =H K X K +V K ; Among them, Z K The observation vector includes the inertial navigation raw observation and the virtual observation Z. virtual H K Let X be the observation matrix. K V is the state error vector. K The observed noise vector is represented by the modal constraint equations, which are constructed based on virtual observations and used to constrain the state estimation process of the Kalman filter, suppressing low-frequency cumulative drift of the inertial navigation system in GNSS-free scenarios.

[0028] As a preferred embodiment, refer to Figure 3 The onboard computing unit abandons the ray-tracing path assumption and discretizes the Maxwell curl equation under spatial coordinate constraints into a velocity-stress staggered mesh form. In a lossless, isotropic medium, the time-domain Maxwell curl equation is expressed as: ; ; Where E is the electric field intensity vector and H is the magnetic field intensity vector. The permeability of the medium, The dielectric constant of the medium, The dielectric conductivity is denoted as .

[0029] An interleaved grid is constructed using the Yee grid format, with electric and magnetic field components arranged alternately on the spatial grid. Interleaved sampling is used in the time dimension, with the electric field component sampled at integer time steps and the magnetic field component sampled at half-integer time steps; the spatial grid step size... Based on the center frequency setting of the ground-penetrating radar, the value is less than 1 / 20 of the minimum wavelength in the medium; time step The Courant-Friedrichs-Lewy stability condition is satisfied, and its expression is: ; Among them, c max σ is the maximum electromagnetic wave propagation speed in the medium.

[0030] An electromagnetic wave forward modeling operator is constructed by introducing a perfectly matched layer absorbing boundary condition in the seismic wavefield. The perfectly matched layer is set around the computational domain with a thickness of 5 to 20 grid steps. A complex stretching coordinate transformation is introduced within the perfectly matched layer region to replace the spatial derivative in Maxwell's equations with the derivative in complex stretching coordinates, thereby achieving non-reflective absorption of the emitted electromagnetic waves and eliminating the interference of boundary reflections on the forward modeling results. The output of the forward modeling operator is simulated electromagnetic wave echo data, which is compared with the measured radar echo data to form residuals.

[0031] By combining the conjugate gradient method to solve for the backpropagation error of the adjoint field, high-resolution full-waveform inversion of the dielectric constant of the lower structure is achieved. The inversion objective function is defined as the measured echo data d. obs With forward simulation data d cal The L2 norm of the residual is expressed as: ; in, The dielectric constant distribution to be inverted is shown.

[0032] The gradient of the objective function with respect to the dielectric constant is obtained by using the adjoint state method. The gradient expression is: ; Among them, E adj The accompanying field is obtained by backpropagation of the residual data as the accompanying source. The dielectric constant distribution is updated iteratively using the conjugate gradient method, with the iteration step size determined by linear search, until the change in the objective function is less than a preset threshold, thus obtaining the final dielectric constant distribution, i.e., the deformation parameters of the track substructure; T is the total acquisition time window (total observation time) of the ground-penetrating radar electromagnetic wave echo data, and the integration interval is from the electromagnetic wave emission start time t=0 to the echo acquisition termination time t=T. This time window is consistent with the preset echo data acquisition time window of the ground-penetrating radar module of this patent.

[0033] As a preferred embodiment, refer to Figure 4 The onboard computing unit constructs a heterogeneous graph structure G=(V,E) by combining the apparent ride comfort parameters with the dielectric constant distribution obtained from full waveform inversion. The node set V includes two types of heterogeneous nodes: the first type is the ride comfort measurement point node V. S Each smoothness measurement point node corresponds to a continuous smoothness parameter of a mileage point. The node features are a multi-dimensional feature vector composed of the elevation, direction, level, gauge, and torsion parameters of that mileage point; the second type is the lower spatial grid node V. g Each lower spatial grid node corresponds to the dielectric constant of the three-dimensional spatial grid obtained by full waveform inversion. The node features are a multi-dimensional feature vector composed of the dielectric constant, conductivity, and spatial coordinates of the grid.

[0034] The edge set S includes two types of edges: the first type is spatial topological adjacency edges, which connect nodes that are spatially adjacent, including adjacency edges between smoothness measurement point nodes and adjacency edges between lower spatial grid nodes. The adjacency relationship is determined by the Euclidean distance of spatial coordinates, and adjacency edges are established between nodes whose distance is less than a preset threshold; the second type is cross-scale associated edges, which connect smoothness measurement point nodes with lower spatial grid nodes within the coverage area directly below the measurement point, and establish a spatial mapping relationship between apparent smoothness parameters and deformation parameters of the lower structure.

[0035] The graph convolutional network aggregates feature representations of nodes across scales to extract the topological transmission paths of apparent geometric deformations and latent defects. The graph convolutional network consists of two sequentially connected convolutional layers. The first layer is a same-scale feature aggregation layer, which performs same-scale neighborhood feature aggregation on smoothness measurement point nodes and lower spatial grid nodes. The aggregation formula is as follows: ; ; in, Let be the feature matrix of the smoothness measurement points in the l-th layer. The characteristic matrix of the lower spatial grid nodes in the l-th layer is... This is the normalized form of the adjacency matrix of the smoothness measurement points. This is the normalized form of the adjacency matrix of the lower spatial grid nodes. Let L be the trainable weight matrix of the l-th layer. It is the ReLU nonlinear activation function.

[0036] The second layer is a cross-scale feature aggregation layer, which uses the cross-scale adjacency matrix corresponding to the cross-scale associated edges. Cross-scale aggregation is performed on the features of the two types of nodes. The aggregation formula is as follows: ; ; in, For cross-scale aggregated weight matrix, The self-eigenmap weight matrix, This is the transpose of the cross-scale adjacency matrix.

[0037] The aggregated features are decoded through a fully connected layer to obtain the correlation between smoothness anomalies and substructure defects. The topological transmission path from substructure dielectric constant anomalies to apparent smoothness exceedances is extracted, thus realizing the structural root cause localization of smoothness anomalies.

[0038] As a preferred embodiment, refer to Figure 5The onboard computing unit establishes a partial differential heat conduction equation for the internal heat source and the surrounding environment of the inertial navigation system. The internal heat source of the inertial navigation system includes the driving circuit and sampling circuit of the MEMS accelerometer and gyroscope. The expression of the heat conduction equation is as follows: ; in, Let be the density of the medium, c be the specific heat capacity of the medium, T be the temperature, t be the time, k be the thermal conductivity of the medium, and q be the heat flux density of the heat source.

[0039] The air convection heat transfer process inside the inertial navigation system cavity is simulated using the lattice Boltzmann method in fluid mechanics. A three-dimensional discrete velocity model (D3Q19) is adopted, and the evolution equation of the distribution function is as follows: ; Among them, f i Let c be the particle distribution function in the i-direction. i Let be the discrete velocity in the i-direction. For time step, The relaxation time is dimensionless. This is the equilibrium distribution function.

[0040] The equilibrium distribution function adopts the discrete form of the Maxwell-Boltzmann distribution, and its expression is: ; Among them, w i Here are the weighting coefficients, u is the macroscopic velocity of the fluid, and c is the weighting coefficient. S The velocity of sound in a crystal lattice.

[0041] The temperature and velocity distributions of the air inside the inertial navigation system are obtained using the lattice Boltzmann method. Combined with the solution to the heat conduction equation, a real-time temperature field digital twin is constructed. The output of this digital twin is the real-time temperature T of each sensitive element inside the inertial navigation system. S With temperature gradient , that is, thermodynamic state variables.

[0042] The thermodynamic state variables are injected as prior inputs into the self-calibration model to decouple the coupling errors of temperature with zero bias and scaling factor. The temperature coupling model expression for the inertial navigation zero bias error b and scaling factor error s is as follows: ; ; Where b0~b4 are the temperature coefficients of zero bias, and S0~S4 are the temperature coefficients of scaling factors. The self-calibration model estimates the above temperature coefficients through Kalman filtering. Based on the prior input of thermodynamic state variables, it decouples the zero bias and scaling factor errors caused by temperature changes, and realizes online compensation for multi-source errors across the entire temperature range.

[0043] In a preferred embodiment, the onboard computing unit constructs a deep reinforcement learning framework and employs a proximal policy optimization algorithm to achieve adaptive updates of calibration parameters. The state space S of the deep reinforcement learning framework is composed of the thermodynamic state variable (real-time temperature T). S Temperature gradient The equation is composed of the residual *r* of the modal constraint equation, where the residual *r* of the modal constraint equation is the residual of the virtual observation in the Kalman filter, expressed as: The state-space expression is .

[0044] The action space A of the deep reinforcement learning framework represents the adjustment step size of the covariance matrix of the Kalman filter in the self-calibration model, including the adjustment step size of the process noise covariance matrix Q. And the adjustment step size of the observation noise covariance matrix R. The action space expression is , which is the space for continuous actions.

[0045] The reward function R of the deep reinforcement learning framework total The optimization objective is to minimize the long-term drift cumulative error, and the expression is: ; Among them, e pos e represents the cumulative position error of the inertial navigation system. vel For the velocity accumulation error, e att For the cumulative error of attitude angle, These are the weighting coefficients for the corresponding error terms.

[0046] The agent in the deep reinforcement learning framework, at each time step t, determines the current state S. t Output action A t Update the covariance matrix of the Kalman filter. The Kalman filter performs state estimation based on the updated covariance matrix, obtains new cumulative errors in position, velocity, and attitude, calculates the corresponding reward value, and updates the state S. t+1 The agent maximizes the cumulative reward through iterative training of the policy network and value network of the proximal policy optimization algorithm, thereby achieving adaptive updating of calibration parameters under dynamic temperature environment and modal constraints.

[0047] In a preferred embodiment, the onboard computing unit incorporates a Fisher information matrix in the reward function calculation, which is constructed by calculating the second derivative of the log-likelihood function of the state-space parameters. For the state-space parameters... This refers to the error state vector of the inertial navigation system, which includes position, velocity, attitude, zero bias, and scale factor errors. The log-likelihood function of the observed data is... , where \(Z\) is the observed data, including the original inertial navigation observed data and virtual observables; the expression of the Fisher information matrix \(F\) is: ; where \(E\) is the mathematical expectation, is the second-order partial derivative operator with respect to the state parameter , that is, the Hessian matrix.

[0048] Using the determinant value \(\det(F)\) of the Fisher information matrix, the state observability under the current temperature and modal constraint combination is quantified. The determinant value \(\det(F)\) is positively correlated with the state observability. A preset observability threshold \(Th\) is set. When \(\det(F)<Th\), it is determined that the current observed data has insufficient observability for the state parameter, and the corresponding observed data is redundant observed data, and dynamic rejection operations are performed. Specifically, for each group of observed data sequences \(Z\) i , calculate its corresponding Fisher information matrix \(F\) i and the determinant value \(\det(F\) i ). If \(\det(F\) i ) < Th, then this group of observed data is rejected and does not participate in the state update process of the Kalman filter.

[0049] As a preferred embodiment, the vehicle-mounted computing unit converts the observed data screening into a non-linear binary combinatorial optimization problem and constructs a Hamiltonian corresponding to the Fisher information matrix. Define the binary decision variable , where \(x\) i = 1 means to retain the \(i\)-th group of observed data, and \(x\) i = 0 means to reject the \(i\)-th group of observed data; the optimization objective is to maximize the determinant value of the Fisher information matrix corresponding to the retained observed data while minimizing the number of retained observed data. The optimization objective expression is: ; where is the regularization coefficient, is the \(L_0\) norm of the decision variable \(x\), that is, the number of groups of retained observed data.

[0050] Construct the cost Hamiltonian \(H\) corresponding to the above optimization problem C , and the expression is: ; where \(x\) i is the eigenvalue of the Pauli \(Z\) operator, corresponding to the state of the qubit [[ID=�2]] and , that is , \(Z\) i is the Pauli \(Z\) operator of the \(i\)-th qubit, A superposition state of a qubit is used to describe the quantum state during the evolution of a quantum circuit.

[0051] The ground state of a Hamiltonian is found through parameterized quantum gate circuit evolution using a quantum approximation optimization algorithm. The quantum circuit of this algorithm consists of p layers of alternating mixing Hamiltonians H. B With cost Hamiltonian H C The evolution gates are composed of the following, and the evolution operator expression is as follows: ; in, H is the parameter to be optimized. B For the mixing Hamiltonian, the expression is: X i Let X be the Pauli operator for the i-th qubit.

[0052] Optimize parameters using the classic optimizer Minimize the cost function ,in , For a superposition state of qubits, This represents a superposition of n qubits, where n is the number of qubits, consistent with the number of observation data sets. After optimization, the output of the quantum circuit is measured to obtain the bit string corresponding to the Hamiltonian ground state, i.e., the optimal decision variable x. i The combination of x represents the optimal observation data preservation strategy. i The observation data corresponding to =1 is retained, x i The observation data corresponding to =0 were removed.

[0053] In a preferred embodiment, the onboard computing unit treats the continuous dielectric constant distribution sequence of the entire mileage calculated by the optimal observation data preservation strategy as a spatial marker to construct a spatiotemporal sequence dataset. Where T is the historical time step, L is the number of measurement points for the entire mileage, and D is the feature dimension, including dielectric constant, ride comfort parameters, temperature data, and vehicle speed data.

[0054] A spatiotemporal Transformer architecture is introduced to capture long-range spatiotemporal dependencies through a multi-head self-attention mechanism. The spatiotemporal Transformer architecture includes a temporal attention layer, a spatial attention layer, and a feedforward network layer connected in sequence. The temporal attention layer is used to capture feature dependencies at different time steps of the same kilometer point, and the spatial attention layer is used to capture feature dependencies at different kilometer points of the same time step.

[0055] The calculation process of the multi-head self-attention mechanism is as follows: ; ; Where Q, K, and V are the query matrix, key matrix, and value matrix, respectively, obtained from the input features through a linear transformation, d k denoted as the dimension of the key matrix, h as the number of attention heads, and W0 as the output weight matrix.

[0056] The encoder of the spatiotemporal Transformer architecture performs feature encoding on historical spatiotemporal sequence data, and the decoder outputs the dielectric constant distribution sequence within a preset time step in the future, that is, the spatiotemporal evolution trend of the deformation of the lower structure of the track, so as to realize the advanced prediction of the future development of the disease.

[0057] As a preferred embodiment, refer to Figure 6 The onboard computing unit considers the apparent ride comfort degradation, increased substructure deformation, and residual inertial navigation drift error as three players in a non-cooperative dynamic game, denoted as player P1, player P2, and player P3. The strategy spaces of the three players are as follows: The strategy space S1 of player P1: smoothness degradation rate, with a value range of... ; The strategy space S2 of player P2: the deformation rate of the lower structure, with a value range of... ; The strategy space S3 of player P3: the cumulative rate of residual inertial navigation drift error, with a value range of [value missing]. .

[0058] Using the robustness of the smoothness evaluation results as the payoff function, U i (s1,s2,s3) represents the payoff for the i-th player under the strategy combination (s1,s2,s3), where The payoff function expressions for the three players are as follows: ; ; ; in, These are preset weighting coefficients.

[0059] Find the Nash equilibrium point of the non-cooperative dynamic game, where the Nash equilibrium point is a strategy combination. For any player i and any strategy, All have ,in Let be the equilibrium strategies of all players except player i. The Nash equilibrium and its corresponding combination of equilibrium strategies are obtained by solving the fixed-point iterative method.

[0060] The strategy space boundary corresponding to the equilibrium point is used as the confidence interval of the comprehensive evaluation result. That is, based on the smoothness deterioration boundary, substructure deformation boundary, and residual drift error boundary corresponding to the equilibrium strategy, the upper and lower limits of the comprehensive evaluation result of track smoothness over the entire mileage are determined, and the comprehensive evaluation result with confidence interval is output.

[0061] It should be noted that the various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Any technical solutions formed by combining the various embodiments are within the protection scope of this invention.

Claims

1. A method for continuous measurement of track smoothness based on inertial navigation data, characterized in that, include: Acquire time-stamped MEMS-IMU three-dimensional attitude acceleration data and ground-penetrating radar electromagnetic echo data during the operation of the track inspection vehicle; Based on the time-domain identification of track structure modal parameters, the inherent frequency characteristics of the track in acceleration data are extracted. A targetless correction constraint term is constructed based on the standard design modal parameters. Combined with online self-calibration of multi-source errors in the full temperature domain, the inertial navigation drift error is compensated. The trajectory continuity and smoothness parameters are calculated based on the compensated three-dimensional attitude data. Using the compensated spatial location data as spatial coordinate constraints, the deformation parameters of the lower structure of the track are calculated by inputting electromagnetic wave travel time tomography inversion solution; Establish a mapping relationship model between continuous ride comfort parameters and substructure deformation parameters, and output the comprehensive evaluation results of track ride comfort over the entire mileage.

2. The method for continuous measurement of track smoothness based on inertial navigation data according to claim 1, characterized in that, The construction of targetless calibration constraints includes: The orbital dynamics equations are transformed into state-space form. A genetic algorithm is introduced to perform parallel optimization of the initial state vector and damping ratio matrix in the state-space model. The deviation between the globally optimal modal parameters obtained by optimization and the standard design modal parameters is used as the virtual observation of Kalman filtering to generate modal constraint equations that suppress low-frequency drift of the inertial navigation system.

3. The method for continuous measurement of track smoothness based on inertial navigation data according to claim 2, characterized in that, Input electromagnetic wave travel time tomography inversion includes: By abandoning the ray tracing path assumption, the Maxwell curl equation under spatial coordinate constraints is discretized into a velocity-stress staggered grid form. The electromagnetic wave forward modeling operator is constructed by introducing the perfectly matched layer absorption boundary condition in the seismic wave field and solving the adjoint field backpropagation error by combining the conjugate gradient method.

4. The method for continuous measurement of track smoothness based on inertial navigation data according to claim 3, characterized in that, Establishing a mapping association model includes: The apparent smoothness parameters and the dielectric constant distribution obtained by full waveform inversion are constructed into a heterogeneous graph structure, in which the smoothness measurement points and the lower spatial grid are used as nodes, and the spatial topological adjacency relationship is used as edges. The feature representations of cross-scale nodes are aggregated through graph convolutional networks to extract the topological transmission path of apparent geometric deformation and latent defects.

5. The method for continuous measurement of track smoothness based on inertial navigation data according to claim 4, characterized in that, Full-temperature-range multi-source error online self-calibration includes: A partial differential heat conduction equation is established between the internal heat source and the outer shell environment of the inertial navigation system. The lattice Boltzmann method in fluid mechanics is used to simulate the internal air convection heat transfer process. A real-time temperature field digital twin is constructed, and thermodynamic state variables are injected as prior inputs into the self-calibration model to decouple the coupling error between temperature and zero partial scaling factor.

6. The method for continuous measurement of track smoothness based on inertial navigation data according to claim 5, characterized in that, The self-calibration model includes: A deep reinforcement learning framework is constructed, using the residuals of thermodynamic state variables and modal constraint equations as the state space, the step size of the filter covariance matrix in the self-calibration model as the action space, and the minimization of long-term drift cumulative error as the reward function. The adaptive update of calibration parameters is achieved through the interaction between the agent and the dynamic temperature environment.

7. The method for continuous measurement of track smoothness based on inertial navigation data according to claim 6, characterized in that, Achieving adaptive updates of calibration parameters includes: In the calculation of the reward function, the Fisher information matrix from communication sensing is introduced. The information matrix is ​​constructed by obtaining the second derivative of the log-likelihood function of the state space parameter. The determinant value of the information matrix is ​​used to quantify the state observability under the current temperature and modal constraint combination, and redundant observation data with observability below the preset threshold are dynamically eliminated.

8. The method for continuous measurement of track smoothness based on inertial navigation data according to claim 7, characterized in that, Dynamic removal of redundant observation data includes: The observation data selection is transformed into a nonlinear binary combinatorial optimization problem. A Hamiltonian corresponding to the Fisher information matrix is ​​constructed. The ground state of the Hamiltonian is found by using a quantum approximation optimization algorithm through parameterized quantum gate circuit evolution. The bit string corresponding to the ground state represents the optimal observation data retention strategy.

9. The method for continuous measurement of track smoothness based on inertial navigation data according to claim 8, characterized in that, The output of the comprehensive evaluation results of track smoothness over the entire mileage includes: The continuous dielectric constant distribution sequence of the entire track, calculated by the optimal observation data preservation strategy, is regarded as a spatial marker. The spatiotemporal Transformer architecture in natural language processing is introduced, and long-distance dependencies are captured through a multi-head self-attention mechanism to predict the spatiotemporal evolution trend of the deformation of the lower structure of the track within a preset time step.

10. The method for continuous measurement of track smoothness based on inertial navigation data according to claim 9, characterized in that, Predicting spatiotemporal evolution trends includes: By setting apparent smoothness degradation, substructure deformation aggravation, and residual inertial navigation drift error as players in the game, and using the robustness of the smoothness evaluation result as the payoff function, the Nash equilibrium point of the non-cooperative dynamic game is solved, and the policy space boundary corresponding to the equilibrium point is used as the confidence interval of the comprehensive evaluation result.

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