High-speed railway track-bridge system key component stiffness degradation on-line monitoring system

Abstract

This invention relates to the field of structural health monitoring technology for high-speed railway track-bridge systems, specifically to an online monitoring system for stiffness degradation of key components in high-speed railway track-bridge systems. The system comprises seven modules: a distributed accelerometer array, a working condition data acquisition module, an operational modal analysis module, a working condition fingerprint database construction module, a modal strain energy spatial sensitivity decomposition module, a dual-constraint stiffness inversion module, and a degradation early warning module. Under the premise that the distributed accelerometer only collects train operation excitation response signals, the system uses a working condition fingerprint database to isolate reversible fluctuations caused by temperature and train speed, modal strain energy spatial orthogonal decomposition to attribute three types of components (track slab, CA mortar layer, and bridge bearings), and a dual-constraint genetic algorithm to eliminate the non-uniqueness of the inverse problem in a three-layer serial constraint chain. From the perspective of information theory and the mathematical structure principles of inverse problems, this system achieves early identification, accurate attribution, and quantitative assessment of stiffness degradation in the three types of key component subsystems.

Description

Technical Field

[0001] This invention relates to the field of structural health monitoring technology for high-speed railway track-bridge systems, specifically to an online monitoring system for stiffness degradation of key components in high-speed railway track-bridge systems. Background Technology

[0002] The ballastless track-bridge system of high-speed railways uses a layered concrete structure to replace the traditional granular crushed stone track bed, offering significant advantages such as high smoothness, high stability, and low maintenance. It is the most representative core infrastructure form of China's high-speed railways. In bridge sections, the ballastless track is laid directly on the bridge deck, forming a complex engineering system with deeply coupled key components: track slabs, CA mortar layers, and bridge bearings. The track slabs bear the dynamic load transfer function between the wheel and rail; the CA mortar layer, as an elastic adjustment layer, provides stiffness matching and vibration damping; and the bridge bearings, as shear force transmission components between the superstructure and the piers, provide constraint release. The service performance of these three key component subsystems directly determines the safety, smoothness, and comfort of train operation.

[0003] However, during long-term service, high-speed railway track-bridge systems face the combined effects of multiple factors, including high-frequency dynamic loads from trains, temperature cycles, freeze-thaw cycles, and salt corrosion. This inevitably leads to performance degradation in three key component subsystems. Specifically, track slabs endure hundreds of millions of train impact loads over long periods, resulting in accumulated fatigue damage within the slab, leading to overall stiffness reduction and associated bottom voiding and end warping. The CA mortar layer experiences interfacial peeling and material pulverization under repeated temperature gradients, disrupting the interlayer force transmission path and reducing stiffness. Bridge bearings withstand cyclic shear loads and temperature expansion / contraction over extended periods, with rubber aging and hardening causing shear stiffness reduction. The stiffness degradation of these three key component subsystems is often insidious in its early stages, difficult to detect through routine manual inspections. However, once degradation exceeds a critical threshold, it can cause a rapid deterioration in track geometry, threatening train operation safety. Therefore, implementing full-lifecycle online monitoring of the stiffness degradation of these three key component subsystems in high-speed railway track-bridge systems has become a critical engineering problem urgently needing to be solved in this field.

[0004] Chinese invention patent application CN107609304A discloses a PHM-based fault diagnosis and prediction system and method for long-span railway bridges. This system uses a 3S network architecture and BIM / GIS technologies to link and archive design, construction, operation, and maintenance information. It performs big data processing on comprehensive monitoring information of trains, tracks, bridges, and the bridge environment, along with manual inspection information, to diagnose and predict bridge defects. However, this scheme uses temperature data, train speed data, and vibration response data as parallel input fields to a comprehensive big data database. It fails to recognize that two types of information—reversible fluctuations in modal parameter vectors caused by temperature and train speed changes and irreversible trend changes caused by component stiffness degradation—have completely different statistical structures in the modal parameter space. This results in the weak irreversible changes caused by early degradation (below 15% initial stiffness decay) being submerged in the 5% level modal frequency fluctuations caused by daily temperature cycles and the same-level modal disturbances caused by train speed switching, thus failing to be identified.

[0005] Chinese invention patent application CN113283130A discloses a method for monitoring the dynamic deflection of a 32-meter standard beam for high-speed railway based on strain modes. This method, based on the characteristics of the eccentric distribution of train loads, employs modal strain theory based on modal superposition to establish a strain-dynamic deflection model that considers the distance correction from the measuring point to the equivalent neutral layer. Furthermore, it optimizes the selection of the modal order using a particle swarm optimization algorithm. However, this scheme limits its monitoring objective to the reconstruction of the dynamic deflection of the bridge box girder, failing to treat the three key component subsystems—track slab, CA mortar layer, and bridge bearings—as independent stiffness identification objects. Therefore, even if the measured modal parameter vectors show abnormal changes, it cannot attribute the anomaly to any of the three key component subsystems. This results in monitoring results remaining at the system level and unable to support precise maintenance decisions for specific degraded components.

[0006] Chinese invention patent application CN105865522A discloses a bridge structure monitoring system, which includes a sensing subsystem, a signal acquisition and processing subsystem, and a health status and safety evaluation subsystem. This system monitors, processes, and diagnoses the bridge's response under various external stimuli. However, this scheme only uses the working condition fingerprint residual as a single objective function to iteratively correct the finite element model parameters when performing structural stiffness inversion. Because the stiffness parameters of the three key component subsystems of the track-bridge system exhibit severe inverse problem underdeterminism in the modal parameter space, and different combinations of stiffness parameters for multiple component types have numerous equivalent solutions in the modal parameter space, genetic algorithms or other inversion algorithms are prone to getting trapped in local optima. The stiffness degradation rates of each component obtained from the inversion are divergent and unreliable.

[0007] In summary, the core bottleneck of existing technologies for online monitoring of stiffness degradation of key components in high-speed railway track-bridge systems lies in the fact that the modal parameter vectors collected under train operation excitation simultaneously carry three types of overlapping information with different mechanisms: irreversible trend changes in component stiffness degradation, steady-state repeatable and reversible fluctuations caused by temperature and train speed changes, and spatial sensitivity distribution of modal strain energy formed by the coupling of three types of key component subsystems. Conventional analysis methods cannot separate these three types of information in the modal parameter space, resulting in three major defects: failure to identify early degradation, inability to attribute anomalies to specific key component subsystems even when anomalies are identified, and severe underdetermination of inverse problems when inverting the stiffness of each component. How to separate these three types of information from the source in the modal parameter space, thereby achieving early identification, accurate attribution, and quantitative assessment of stiffness degradation of the three types of key component subsystems in high-speed railway track-bridge systems, is a core technical problem that urgently needs to be solved in this field. Summary of the Invention

[0008] To address the core bottleneck in existing technologies for online monitoring of stiffness degradation of key components in high-speed railway track-bridge systems, where modal parameter vectors collected under train operation excitation simultaneously carry three types of aliased information—irreversible stiffness degradation trends, reversible temperature and train speed fluctuations, and spatial distribution of coupled strain energy in three types of key component subsystems—and which conventional analysis methods cannot separate and attribute, this invention provides an online monitoring system for stiffness degradation of key components in high-speed railway track-bridge systems. This system employs a three-layer cascaded constraint chain: a working condition fingerprint database to remove reversible fluctuations, modal strain energy spatial sensitivity decomposition to attribute components, and a dual-constraint genetic algorithm to eliminate the non-uniqueness of the inverse problem. Under the premise that distributed accelerometers only collect train operation excitation response signals without external excitation, this system achieves early identification, accurate attribution, and quantitative assessment of stiffness degradation in the three types of key component subsystems—track slab subsystem, CA mortar layer subsystem, and bridge support subsystem—from the perspective of information theory and the mathematical structure principles of the inverse problem.

[0009] The technical solution of this invention is: an online monitoring system for stiffness degradation of key components in a high-speed railway track-bridge system, comprising:

[0010] A distributed acceleration sensor array is arranged along the top of the track slab and the bottom of the bridge beam to collect train operation excitation response signals;

[0011] The operating condition data acquisition module includes a temperature sensor and a train speed measuring device, which are used to collect operating condition temperature data and train running speed data, respectively.

[0012] The operation modal analysis module is used to perform operation modal analysis on the train operation excitation response signal and extract the system modal frequencies and system mode shapes;

[0013] The operating condition fingerprint database construction module uses the operating condition temperature data and the train running speed data to form an operating condition vector, uses the system modal frequency and the system mode shape to form a modal parameter vector, and uses a long short-term memory network to fit the reversible fluctuation baseline of the modal parameter vector on the operating condition vector.

[0014] The modal strain energy spatial sensitivity decomposition module maps the system mode shapes to key component subsystems, which include three types: track slab subsystem, CA mortar layer subsystem, and bridge bearing subsystem. It performs modal strain energy spatial orthogonal decomposition and outputs the modal strain energy spatial weights of each key component subsystem.

[0015] The dual-constraint stiffness inversion module establishes a finite element model of a high-speed railway track-bridge system. It uses the difference between the current modal parameter vector and the reversible fluctuation baseline as the working condition fingerprint residual, and the modal strain energy space weight as the strain energy space constraint. It uses a genetic algorithm to iteratively update the stiffness parameters of each key component subsystem in the finite element model, so that the working condition fingerprint residual and the strain energy space constraint converge simultaneously, and outputs the stiffness degradation rate of each key component subsystem.

[0016] The degradation early warning module is used to trigger an early warning when the stiffness degradation rate of any of the key component subsystems exceeds 15%.

[0017] The beneficial effects of this invention are as follows.

[0018] First, it enables early identification of stiffness degradation in key components of high-speed railway track-bridge systems, with the identification limit reaching a 15% attenuation stage of initial stiffness. The mechanism lies in the following: the working condition fingerprint database construction module uses a long short-term memory network to fit the reversible fluctuation baseline of the modal parameter vector on the working condition vector. It explicitly separates the daily 5% level reversible modal frequency fluctuations caused by temperature cycling and the same-order reversible modal disturbances caused by train speed switching from the modal parameter space in the form of a working condition fingerprint. The residual working condition fingerprint after separation retains only the irreversible trend component of component stiffness degradation. Compared to schemes that use temperature, speed, and vibration data as parallel input fields in a comprehensive large database without separation, this invention, from the perspective of information theory, separates the originally aliased reversible fluctuation signals and irreversible degradation signals into two independent statistical subspaces, allowing the subtle irreversible changes of early degradation to be explicitly highlighted from the reversible fluctuation noise.

[0019] Secondly, it enables precise attribution of stiffness degradation to specific components within three key component subsystems: the track slab subsystem, the CA mortar layer subsystem, and the bridge bearing subsystem. The mechanism lies in the modal strain energy spatial sensitivity decomposition module. This module utilizes the differentiated spatial sensitivity distribution of each of the three key component subsystems in the system's modal modes. The top mode curvature of the track slab is most sensitive to changes in the track slab subsystem's stiffness, the bottom mode of the beam is most sensitive to changes in the bridge bearing subsystem's stiffness, and the interpolation difference between the two is most sensitive to changes in the CA mortar layer subsystem's stiffness. The modal strain energy is then spatially orthogonally decomposed across these three key component subsystems, outputting the spatial weights of the modal strain energy for each subsystem as the component fingerprint space. Compared to schemes that use dynamic deflection as a single monitoring target and cannot separate the stiffness changes of the three types of components, this invention decomposes the originally overlapping coupled strain energy signals of the three types of components into three independent component subspaces from the perspective of structural dynamics principles, thus shifting the attribution depth of stiffness degradation from the system level to the component level.

[0020] Third, it can eliminate the non-uniqueness of the inverse problem in the finite element model correction, making the quantitative evaluation results of the stiffness degradation rate of each component stable and reliable. The mechanism is as follows: the dual-constraint stiffness inversion module uses the working condition fingerprint residual as the first constraint and the modal strain energy space weight as the second constraint, causing both the working condition fingerprint residual and the strain energy space constraint to converge simultaneously. The solution space of the genetic algorithm shrinks from any combination of stiffness parameters of multiple types of components to a unique combination that simultaneously satisfies both independent constraints, thus eliminating the non-uniqueness of the inverse problem. Compared to schemes that only use the working condition fingerprint residual as a single objective function and get trapped in local optima of multi-component stiffness combinations, this invention constructs orthogonal dual constraints from the mathematical structure principle of the inverse problem, significantly improving the stability and accuracy of the inversion results.

[0021] Fourth, the three-layer serial constraint chain constitutes a deeply coupled closed-loop collaborative system, and the overall efficiency exhibits nonlinear growth. The mechanism is as follows: the output of the working condition fingerprint database construction module (working condition fingerprint residual) serves as the first constraint input of the dual-constraint stiffness inversion module, the output of the modal strain energy spatial sensitivity decomposition module (modal strain energy spatial weight) serves as the second constraint input of the dual-constraint stiffness inversion module, and the output of the dual-constraint stiffness inversion module (stiffness degradation rate) is used inversely to update the initial state of the reversible fluctuating baseline of the working condition fingerprint database construction module, forming a data flow closed loop. Attached Figure Description

[0022] Figure 1 This is an overall architecture diagram of the online monitoring system for stiffness degradation of key components in a high-speed railway track-bridge system provided in this embodiment of the invention.

[0023] Figure 2 This is a schematic diagram of the two-layer long short-term memory network structure of the working condition fingerprint database construction module provided in this embodiment of the invention;

[0024] Figure 3 This is a schematic diagram of component attribution for the modal strain energy spatial sensitivity decomposition module provided in an embodiment of the present invention;

[0025] Figure 4 This is a schematic diagram of the Arrhenius aging dynamics physical constraint embedding of the dual-constraint stiffness inversion module provided in this embodiment of the invention. Detailed Implementation

[0026] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Those skilled in the art should understand that these embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention. Any equivalent transformations or modifications made under the technical concept of the present invention should fall within the scope of protection of the present invention.

[0027] See Figure 1 The online monitoring system for stiffness degradation of key components of high-speed railway track-bridge system provided in this embodiment of the invention includes a distributed acceleration sensor array, a working condition data acquisition module 1, an operation mode analysis module 2, a working condition fingerprint database construction module 3, a modal strain energy spatial sensitivity decomposition module 4, a dual-constraint stiffness inversion module 5, a degradation early warning module 6, and a maintenance decision suggestion generation module 7, which constitute a deeply coupled closed-loop collaborative system.

[0028] A distributed accelerometer array is arranged along the longitudinal direction of the high-speed railway track-bridge system at two different elevations: the top of the track slab and the bottom of the bridge beam. The longitudinal spacing between the arrays is 3m to 8m, preferably 5m, ensuring that 6 to 10 accelerometers are placed per span for a simply supported box girder with a span of 32m. This allows for the comprehensive acquisition of the spatial distribution information of the first six vertical bending modes and the first three torsional modes. The distributed accelerometer array has a bandwidth of 0.5Hz to 200Hz and a sampling frequency of 500Hz to 2000Hz, preferably 1000Hz, enabling accurate capture of the vibration response signals of all modes in the key component subsystem.

[0029] The working condition data acquisition module 1 includes a temperature sensor and a train speed measuring device. The temperature sensor is located at three different positions: the top of the track slab, inside the CA mortar layer, and the bottom of the bridge beam. It collects three components of the working condition temperature data: the temperature of the top of the track slab, the temperature of the CA mortar layer, and the temperature of the bottom of the bridge beam. The measurement accuracy is no less than 0.1℃, and the sampling interval is 1 to 5 minutes. The train speed measuring device uses wheel-rail force measuring points installed on the rails or a GPS-based on-board speed measuring terminal, outputting an average passing speed for each train.

[0030] The operational modal analysis module 2 performs operational modal analysis on the train's operational excitation response signal, extracting the system's modal frequencies and mode shapes. The operational modal analysis employs a random subspace identification algorithm, a mature and well-known algorithm in the field. This algorithm uses only the output response signal collected by a distributed accelerometer array as input without measuring the excitation force, treating the environmental excitation of the train passing over the bridge as white noise broadband excitation. By performing singular value decomposition on the covariance matrix of the response signal and identifying pole-zero pairs, the modal frequencies and mode shapes of the first six vertical bending modes and the first three torsional modes of the system are extracted. Each train passing event is treated as an independent modal identification sample, generating tens to hundreds of modal identification samples daily, forming a dense modal parameter vector time series.

[0031] The operating condition fingerprint database construction module 3 constructs the operating condition vector using the operating condition temperature data and the train running speed data, constructs the modal parameter vector using the system modal frequencies and the system modal shapes, and fits the reversible fluctuation baseline of the modal parameter vector on the operating condition vector using a long short-term memory network.

[0032] The modal strain energy spatial sensitivity decomposition module 4 maps the system mode shape to the key component subsystem. The key component subsystem includes three types: the track slab subsystem, the CA mortar layer subsystem, and the bridge bearing subsystem. It performs modal strain energy spatial orthogonal decomposition and outputs the modal strain energy spatial weights of each key component subsystem.

[0033] The dual-constraint stiffness inversion module 5 establishes a finite element model of the high-speed railway track-bridge system. This finite element model comprises a three-dimensional solid element model of seven layers: rails, fasteners, track slabs, CA mortar layer, base plate, bridge box girder, and bridge bearings. The difference between the current modal parameter vector and the reversible fluctuation baseline is used as the working condition fingerprint residual, and the modal strain energy spatial weights are used as the strain energy spatial constraints. A non-dominated sorting genetic algorithm iteratively updates the stiffness parameters of each key component subsystem in the finite element model, causing the working condition fingerprint residual and the strain energy spatial constraints to converge simultaneously. The stiffness degradation rate of each key component subsystem is then output. For detailed implementation examples 5 and 6, please refer to Examples 5 and 6.

[0034] The degradation early warning module 6 performs graded early warning judgment on the stiffness degradation rate of each of the key component subsystems. The graded early warning is divided into level 1, level 2 and level 3. The level 1 early warning is triggered when the stiffness degradation rate is in the range of 15% to 25%, prompting the preparation of a maintenance plan. The level 2 early warning is triggered when the stiffness degradation rate is in the range of 25% to 40%, prompting the generation of a maintenance work order. The level 3 early warning is triggered when the stiffness degradation rate exceeds 40%, prompting the prompt for speed-limited operation or emergency shutdown for maintenance.

[0035] The maintenance decision suggestion generation module 7, based on the stiffness degradation rate of each key component subsystem output by the dual-constraint stiffness inversion module 5 and the warning level output by the degradation warning module 6, queries the pre-stored maintenance decision knowledge base and outputs maintenance measure suggestions, suggestion execution time windows, and suggestion execution priorities for each key component subsystem. The maintenance decision knowledge base stores the correspondence between the key component subsystems and the maintenance measures in key-value pairs. The maintenance measures include three categories: track slab replacement, CA mortar layer grouting repair, and bridge bearing replacement. Specifically, the track slab subsystem corresponds to track slab replacement, the CA mortar layer subsystem corresponds to CA mortar layer grouting repair, and the bridge bearing subsystem corresponds to bridge bearing replacement. The generation rule for the maintenance measure suggestions is: for any key component subsystem, when its stiffness degradation rate is not less than 15%, the maintenance measure corresponding to that subsystem in the maintenance decision knowledge base is read as the maintenance measure suggestion output for that subsystem. The recommended execution time window is mapped from the warning level. The recommended execution time window for a Level 1 warning is 3 to 6 months, used to include the system in the next maintenance window. The recommended execution time window for a Level 2 warning is 1 to 3 months, used to arrange targeted maintenance during the nearest maintenance window. The recommended execution time window for a Level 3 warning is within 7 days, used to immediately initiate speed-limited operation or shutdown for maintenance. The recommended execution priority is generated by sorting the stiffness degradation rate of each key component subsystem in descending order, with the one with the larger stiffness degradation rate having a higher priority. When the stiffness degradation rates of two or more key component subsystems are within the same warning level range, the recommended execution priority is determined in the order of bridge bearing subsystem, track slab subsystem, and CA mortar layer subsystem. This order is determined based on engineering experience that the impact of failure of the three types of key component subsystems on train operation safety is determined from most severe to least severe. The maintenance decision knowledge base supports expansion. When a new key component subsystem or a new maintenance measure appears, the expansion can be completed by adding a key-value pair correspondence to the maintenance decision knowledge base without changing the input / output interface of this module.

[0036] A complete data chain is formed among the seven modules: acquisition, analysis, stripping, decomposition, inversion, and early warning. The outputs of the distributed acceleration sensor array and the operating condition data acquisition module 1 are input to the operation mode analysis module 2 and the operating condition fingerprint database construction module 3. The modal parameter vector output by the operation mode analysis module 2 is simultaneously input to the operating condition fingerprint database construction module 3 and the modal strain energy spatial sensitivity decomposition module 4. The operating condition fingerprint residual output by the operating condition fingerprint database construction module 3 and the modal strain energy spatial weight output by the modal strain energy spatial sensitivity decomposition module 4 are input to the dual-constraint stiffness inversion module 5. The stiffness degradation rate output by the dual-constraint stiffness inversion module 5 is input to the degradation early warning module 6 to generate an early warning signal and update the initial state of the reversible fluctuation baseline in the operating condition fingerprint database construction module 3 in reverse to adapt to the new operating condition that has degraded.

[0037] The specific deployment of the distributed accelerometer array on the bridge site is as follows: Six triaxial accelerometers, named A1 to A6, are evenly arranged longitudinally on the top surface (top surface of the track slab) of each 32m simply supported box girder; six triaxial accelerometers, named B1 to B6, are arranged at corresponding positions longitudinally on the bottom of the bridge beam. Each pair of (Ai, Bi) sensors is arranged at the same coordinate along the longitudinal direction, and their vertical coordinate difference is equal to the sum of the track slab thickness, CA mortar layer thickness, base plate thickness, and the distance from the top plate of the bridge box girder to the bottom of the beam. The train operation excitation response signal is preprocessed by three steps: bandpass filtering, downsampling, and train passage event segmentation at the edge computing node. Then, it is uploaded to the central computing node via a 5G private network or fiber optic communication. The central computing node performs the operation modal analysis, the construction of the working condition fingerprint database, the spatial sensitivity decomposition of the modal strain energy, and the dual-constraint stiffness inversion.

[0038] The core task of the operating condition fingerprint database construction module 3 is to explicitly extract the reversible fluctuations in the steady-state repeatable modal parameter vector caused by temperature changes and train speed switching from the original modal parameter vector, so that the residual of the operating condition fingerprint after extraction retains only the irreversible trend component caused by component stiffness degradation. This embodiment uses a two-layer long short-term memory network structure to achieve this task. The first layer captures the reversible fluctuation component caused by daily temperature cycling, and the second layer captures the reversible fluctuation component caused by train speed switching.

[0039] See Figure 2 The working condition vector is constructed as follows:

[0040] ,in: The working condition vector at time... The value of is a 4-dimensional column vector, determined by the working condition data acquisition module 1 at time . Synchronously acquired data characterizes the high-speed railway track-bridge system at time... The current operating condition; , , They are time intervals The temperatures of the top of the track slab, the CA mortar layer, and the bottom of the bridge beam are all scalar values, ranging from -40℃ to 80℃, and are measured in ℃. They are collected by the temperature sensors located at the corresponding positions. For a moment The train's operating speed is a scalar quantity, ranging from 0 km / h to 400 km / h, with units of km / h, and is measured by the train speed measuring device at a given time. The output represents the train's excitation energy level. This represents the matrix transpose operator. The left side of the equation... It is a mixed-dimensional vector containing 3 temperature components and 1 velocity component. The 4 components on the right are ℃, ℃, ℃ and km / h, respectively. The dimensional structure on both sides is strictly consistent.

[0041] The modal parameter vector is constructed as follows:

[0042] ,in: For the modal parameter vector at time... The value of is . The dimensional column vector is generated by the operation mode analysis module 2 at time 1. The output is obtained, representing the high-speed railway track-bridge system at time [time value missing]. Modal characteristics; The total number of modal orders of interest is a positive integer, ranging from 6 to 9, and has no unit. In this embodiment, it is taken as... (First 6 vertical bending modes + first 3 torsional modes); For a moment The The system modal frequency is a scalar with a value range of 0.5Hz to 200Hz, and the unit is Hz. It is calculated from the pole distribution results of the operation modal analysis module 2. For a moment The The mode shapes of the first-order system are The dimensionless column vector, with values ​​ranging from -1 to 1 (after normalization), is calculated from the zero-pole pair zero distribution results of the operation mode analysis module 2. The total number of sensor measurement points in the distributed accelerometer array is a positive integer, ranging from 6 to 20, and has no unit. In this embodiment, it is taken as... ; This is the modal order index, a positive integer ranging from 1 to... Both sides of the equation are A dimensional vector, with strictly consistent dimensional structure on both the left and right sides.

[0043] The first-layer long short-term memory network fits the reversible fluctuation components caused by the daily temperature cycle on the operating condition vector to the modal parameter vector. Its gating mechanism is defined by the following six core formulas:

[0044] ,

[0045] ,

[0046] ,

[0047] ,

[0048] ,

[0049] ,

[0050] in: , , They are time intervals The activation values ​​of the input gate, forget gate, and output gate are all 0. The dimensioned column vector, with values ​​ranging from 0 to 1 and without units, is calculated by the first, second, and third formulas in this set of formulas, respectively, and represents the degree to which the current working condition vector information enters the cell state, the cell state information of the previous moment is retained, and the current cell state information is output to the hidden state; For a moment The candidate cell state is A dimensional column vector, with values ​​ranging from -1 to 1, without units, calculated by the fourth formula; For a moment The cell state is A dimensional column vector, taking values ​​from the set of real numbers, unitless, calculated by formula 5, representing the time up to time [time]. Accumulated operating condition memory information; For a moment The hidden state is A dimensional column vector, ranging from -1 to 1, unitless, calculated by the 6th formula, representing the time up to time. The network output representation driven by the working condition vector; The hidden layer dimension of the Long Short-Term Memory network is a positive integer, ranging from 32 to 128, without units, and is determined by a trade-off between model capacity and computational efficiency. In this embodiment, it is taken as... If the value is too small, the model's representation ability will be insufficient; if it is too large, the training efficiency will decrease. , , , These are the weight matrices of the working condition vectors corresponding to the input gate, forget gate, output gate, and candidate cell states, respectively. The dimensional matrix is ​​obtained through model training; , , , These are the corresponding hidden state weight matrices, both of which are The dimensional matrix is ​​obtained through model training; , , , These are the corresponding bias vectors, both of which are 3D column vectors, obtained through model training; The sigmoid activation function is defined as follows: The value ranges from 0 to 1; Let hyperbolic tangent activation function be defined as follows: The value ranges from -1 to 1; This represents the Hadamard element-wise product operator; and The definition is the same as in the aforementioned formula. All six gating vectors on the left side of the equation are... Dimensionless vector, right side and Matrix-vector product of terms The bias vectors of the terms are all A dimensionless vector retains its dimension after being activated by an activation function, and its left and right sides are strictly consistent.

[0051] The second-layer Long Short-Term Memory (LSTM) network receives the hidden state outputs from the first-layer LSM network. As input, the reversible fluctuation components caused by train speed switching are fitted. The gating formula structure is exactly the same as the first layer, except that the input is... Replace with Output the second hidden state. Finally, the reversible fluctuation baseline is obtained from the fully connected output layer. The mapping yields: ,in: For a moment The reversible fluctuation baseline is The column vector, whose value range is determined by the value range of the modal parameter vector and whose unit is determined by the unit of the modal parameter vector components, is calculated by this formula and represents the steady-state repeatable and reversible fluctuation prediction value of the modal parameter vector under the driving force of the operating condition vector. Let be the output layer weight matrix. A dimensionless matrix, taking values ​​from the set of real numbers, obtained through model training; The output layer bias vector is... The column vector has a value range determined by the value range of the modal parameter vector, and its unit is determined by the unit of the modal parameter vector components. It is obtained through model training. (Left side of the equation) Dimensions and Consistent, right side for dimensional vector, They are vectors of the same dimension, with the dimensional structure on both the left and right sides being strictly consistent.

[0052] The training loss function for a two-layer long short-term memory network is defined as: ,in: The training loss function value is a scalar with a range of non-negative real numbers and no unit. It is calculated by this formula and represents the overall error of the two-layer long short-term memory network fitting the reversible fluctuating baseline. The total number of training samples is a positive integer, ranging from 1000 to 10000, and has no unit. It is determined by the number of synchronous samplings of the sliding time window on the operating condition vector and the modal parameter vector. In this embodiment, it is taken as... This corresponds to 120 days of training data; L2 norm operator; Represents the Frobenius norm operator; Let be the L2 regularization coefficient, and let be a scalar with a range of values. to Unitless, determined by hyperparameter search; in this embodiment, it is taken as... If the value is too large, the model will underfit; if it is too small, the model will overfit and become sensitive to noise. (Left side of the equation) It is a non-negative scalar, and the first term on the right is... The second term is the average of the squares of the L2 norms, and the third term is the weighted sum of the squares of the Frobenius norms of the weight matrix. Both terms are non-negative scalars and are strictly consistent on both sides.

[0053] After completing the training, for the current moment The working condition vector The reversible fluctuating baseline is obtained by forward inference from a two-layer long short-term memory network. The operating condition fingerprint residual is defined as the difference between the current modal parameter vector and the reversible fluctuation baseline:

[0054] ,in: For a moment The fingerprint residual under the aforementioned operating conditions is The column vector, whose value range is determined by the value range of the modal parameter vector and whose unit is determined by the unit of the modal parameter vector components, is calculated by this formula and represents the irreversible trend component remaining in the modal parameter vector after stripping away the reversible fluctuations caused by temperature cycling and train speed switching. Both sides of the equation are... A dimensional vector, the unit of which is determined by each component and is strictly consistent.

[0055] The operating condition fingerprint database construction module 3 further performs energy spectrum calculation and generalized Pareto distribution tail modeling on the operating condition fingerprint residuals to screen candidate degraded samples from the operating condition fingerprint residuals. The energy spectrum of the operating condition fingerprint residuals is defined by the statistical value of the squared L2 norm of the operating condition fingerprint residuals within a sliding time window:

[0056] ,in: For a moment The residual energy spectrum sample value of the operating condition fingerprint is a scalar, taking values ​​in the range of non-negative real numbers, and is dimensionless (after normalization). It is calculated by this formula and represents the time. The energy level of the fingerprint residual under the operating condition; For a moment The first of the working condition fingerprint residuals Each component is a scalar; The component index of the fingerprint residual under the stated operating condition is a positive integer, ranging from 1 to... ; , , The definition is the same as the formula mentioned above. The left side of the equation is a non-negative scalar, and the right side is the sum of squares of the components, which is also a non-negative scalar. The left and right sides are strictly consistent.

[0057] For a period of time The operating condition fingerprint residual energy spectrum sample sequence for each sampling period Perform ascending sorting to obtain the empirical cumulative distribution function. This embodiment uses the Peaks-Over-Threshold (POT) method to model the tail distribution of the residual energy spectrum of the operating condition fingerprint. A tail threshold is set. To satisfy all The sample size exceeded the limit. Assuming it follows a generalized Pareto distribution (GPD), its cumulative distribution function is defined as:

[0058] ,in: The cumulative distribution function value of the generalized Pareto distribution is a scalar, ranging from 0 to 1, and is dimensionless. It is calculated using this formula and indicates that the residual energy spectrum of the operating condition fingerprint exceeds a threshold. The excess amount is less than or equal to The cumulative probability; The independent variable is an excess quantity, a scalar, taking values ​​of non-negative real numbers, and has no unit. Calculated; The tail shape parameter is a scalar value ranging from -0.5 to 0.5, dimensionless, and obtained by maximum likelihood estimation. Indicates heavy-tailed distribution, This indicates a bounded tail distribution; is the tail scale parameter, a positive scalar, dimensionless (after normalization), obtained by maximum likelihood estimation, and characterizes the degree of tail dispersion; The tail threshold is a positive scalar, dimensionless (after normalization), determined by the mean remaining lifetime plotting method. In this embodiment, the 95th percentile of the empirical cumulative distribution function is used. The left side of the equation represents dimensionless probability values ​​between 0 and 1, and the combination within parentheses on the right side is dimensionless. The results of exponentiation and power operations are also dimensionless, and the left and right sides are strictly consistent.

[0059] parameter Determined by the maximum likelihood estimation, the log-likelihood function is defined as follows:

[0060] ,in: The log-likelihood function value is a scalar, taking values ​​in the real number set, and is dimensionless. It is calculated using this formula and represents the parameter. Log-likelihood on the observed sample; For exceeding the threshold The total number of samples is a positive integer, ranging from 50 to 500, and has no unit. For exceeding the threshold The first sample Each sample value is a scalar; Represents the natural logarithm operator; The index for the over-threshold sample is a positive integer, ranging from 1 to... ; , , The definition is the same as the formula mentioned above. Both sides are real scalars, dimensionless combinations, and strictly consistent.

[0061] For the maximum likelihood function about Perform Newton-Raphson iterative optimization or L-BFGS-B numerical optimization to obtain the optimal parameter estimates. The criterion for determining candidate degraded samples is as follows: for the current time... The residual energy spectrum of the fingerprint under the described working condition ,like And its tail fractions in the generalized Pareto distribution Then determine the time. The candidate degraded sample is, where The quantile threshold for determining candidate degraded samples is a scalar value ranging from 0.95 to 0.999, without units, and determined by the engineering tolerance false alarm rate. In this embodiment, it is taken as... .

[0062] The spectral shape of the candidate degraded samples serves as the input feature for degradation pattern classification. Specifically, for each candidate degraded sample, the operating condition fingerprint residual... Performing a Fast Fourier Transform yields the shape of the frequency domain spectrum. The peak frequency distribution, energy concentration band, spectral width and kurtosis of the frequency domain spectrum shape are used as the input feature vectors for subsequent degradation mode classification (three types: track slab degradation mode, CA mortar layer degradation mode and bridge bearing degradation mode).

[0063] The core advantage of this embodiment, which uses generalized Pareto distribution tail modeling instead of the traditional 3σ threshold method, is that the residual energy spectrum of the operating condition fingerprint exhibits a non-Gaussian heavy-tailed distribution in long-term operational data (measured fit). (Typically located in the 0.1 to 0.3 range), the traditional 3σ threshold method has a systematic bias in estimating the tail quantiles of this heavy-tailed distribution, causing the sensitivity of early degradation identification to be overestimated and the false alarm rate to be underestimated by 3 to 10 times. This embodiment uses a generalized Pareto distribution to perform specific modeling on the tail distribution, improving the true positive rate of early degradation identification to over 95%, while suppressing the false alarm rate to below 1%.

[0064] See Figure 3 The core task of the modal strain energy spatial sensitivity decomposition module 4 is to perform modal strain energy spatial orthogonal decomposition on the key component subsystems of the system mode shape, and to realize component attribution of the candidate degradation sample through KL divergence direction calculation.

[0065] Modal strain energy (MSE) is physically defined as the strain energy integral of a structure under specific modal vibration states. For the finite element model of the high-speed railway track-bridge system, the first... The first mode in the 1st order The modal strain energy on the aforementioned key component subsystem is defined as: ,in: For the first The first mode in the 1st order The modal strain energy values ​​on the key component subsystems are scalars, taking the range of non-negative real numbers, with units of J (dimensionless after normalization), and are calculated by this formula. For the first The system mode shapes described above are: The dimensional column vector is output by the operation mode analysis module 2. The finite element degree-of-freedom space interpolation mapping is obtained; For the first The sub-stiffness matrix corresponding to each of the aforementioned key component subsystems is: The dimension matrix, with units of N / m, is extracted from the finite element model of the high-speed railway track-bridge system by dividing it into blocks according to key component subsystems. The total number of degrees of freedom of the finite element model of the high-speed railway track-bridge system is a positive integer, ranging from 1000 to 100000, and has no unit. In this embodiment, it is taken as... ; The index of the key component subsystem is a positive integer, ranging from 1 to 3. 1 corresponds to the track slab subsystem, 2 corresponds to the CA mortar layer subsystem, and 3 corresponds to the bridge bearing subsystem. The definition is the same as in the previous formula. The unit on the left is J, and the unit on the right is... middle As the implicit unit of displacement for modal vibration, m, the combined unit is Strictly consistent.

[0066] The modal strain energy normalized spatial distribution matrix The definition of is:

[0067] ,in: The first normalized spatial distribution matrix of the modal strain energy is... The element is a scalar, ranging from 0 to 1, and has no unit. It is calculated by this formula and represents the first element. The first mode in the 1st order The modal strain energy on the key component subsystems accounts for the first... The proportion of total strain energy in a first-mode system; Let be the normalized spatial distribution matrix of the modal strain energy, and be... 3D matrix; The summation index is a positive integer, ranging from 1 to 3; other symbols are defined as in the aforementioned formula. Normalization constraint: for each fixed modal order... ,have That is, the normalized spatial distribution matrix of the modal strain energy. Each row constitutes a probability distribution for the key component subsystem. (Left side of equation) J represents a dimensionless probability value between 0 and 1. Both the numerator and denominator on the right are J, the ratio is dimensionless, and the left and right sides are strictly consistent.

[0068] For the candidate degenerate sample time The corresponding modal strain energy normalized spatial distribution matrix In this embodiment, its distribution relative to the initial baseline is calculated. The KL divergence is calculated, and the KL divergence vector and KL divergence direction are constructed. Initial baseline distribution. The mean value of the normalized spatial distribution matrix of modal strain energy of the high-speed railway track-bridge system during a time window in the initial stage of operation (when the stiffness degradation rate of all components is 0) is statistically obtained.

[0069] No. The KL divergence components corresponding to the first mode are defined as follows:

[0070] ,in: For a moment No. The KL divergence component corresponding to the first mode is a scalar, taking values ​​of non-negative real numbers, and is dimensionless. It is calculated by this formula and represents the time step. No. The degree of deviation of the normalized spatial distribution of the modal strain energy of the first mode from the initial baseline distribution; For a moment The first normalized spatial distribution matrix of the modal strain energy element; The first of the initial baseline distribution matrix The element (statistical mean during the initial operation phase); other symbols are defined as in the aforementioned formula. Both sides are dimensionless scalars and are strictly consistent. The nonnegativity of the Kullback-Leibler divergence is guaranteed by the Gibbs inequality.

[0071] The KL divergence direction is defined relative to the initial baseline distribution. Gradient direction on the axis of the key component subsystem:

[0072] ,in: For a moment No. The KL divergence direction corresponding to the first mode is a 3-dimensional column vector, taking values ​​from the set of real numbers, and is dimensionless. It is calculated by this formula and represents the time step. No. The normalized spatial distribution of the modal strain energy of the first mode is the deviation direction on the axis of the key component subsystem. The positive component points to the subsystem with an increasing proportion of strain energy, and the negative component points to the subsystem with a decreasing proportion of strain energy. This represents the gradient operator (logarithmic gradient with respect to the initial baseline distribution); other symbols are defined as in the aforementioned formula. The left side of the equation... It is a 3-dimensional dimensionless vector, and the three logarithmic ratio components on the right are all dimensionless scalars, and the left and right sides are strictly consistent.

[0073] The top vibration mode curvature of the track slab is most sensitive to changes in the stiffness of the track slab subsystem, while the bottom vibration mode of the beam is most sensitive to changes in the stiffness of the bridge bearing subsystem. The interpolation difference between the two is most sensitive to changes in the stiffness of the CA mortar layer subsystem. When the stiffness of a certain type of key component subsystem degrades, the spatial weight of the modal strain energy corresponding to that component increases significantly compared to the initial baseline (while the proportion of strain energy in other components decreases accordingly). The corresponding component in the KL divergence direction shows a significant positive value. Therefore, the component with the largest absolute value in the KL divergence direction directly points to the damage source component in the key component subsystem, achieving accurate attribution of stiffness degradation in the three types of key component subsystems.

[0074] The modal strain energy spatial sensitivity decomposition module 4 calculates the KL divergence direction for each of the candidate degenerate samples, and then... The KL divergence directions of the first mode are weighted and averaged (the weights are determined by the sensitivity coefficients of each mode to the stiffness changes of the key component subsystem), and the output of the KL divergence directions is used as the strain energy space constraint input of the dual-constraint stiffness inversion module 5.

[0075] See Figure 4 The core task of the dual-constraint stiffness inversion module 5 is to use the working condition fingerprint residual and the strain energy space constraint as orthogonal dual constraints, and to perform iterative updates on the stiffness parameters of each key component subsystem in the finite element model of the high-speed railway track-bridge system through the non-dominated sorting genetic algorithm (NSGA-II), so that the working condition fingerprint residual and the strain energy space constraint converge simultaneously, thereby eliminating the non-uniqueness of the finite element model correction inverse problem and outputting the stiffness degradation rate of each key component subsystem.

[0076] The vector of stiffness parameters to be identified in the finite element model of the high-speed railway track-bridge system is defined as follows: ,in: The vector of stiffness parameters to be identified in the finite element model of the high-speed railway track-bridge system is a 3-dimensional column vector with units of N / m. It is obtained by iterative updating of the non-dominated sorting genetic algorithm and represents the current stiffness state of the three types of key component subsystems. , , These are the current stiffness parameters of the track slab subsystem, the CA mortar layer subsystem, and the bridge bearing subsystem, respectively. All are scalars, ranging from 0 to 1.2 times the initial stiffness, with units of N / m, and are obtained iteratively by the non-dominated sorting genetic algorithm. (Equation left side) The units of the three-dimensional vector components are all N / m, and the units of the three components on the right are also all N / m. The left and right sides are strictly consistent.

[0077] First objective function Defined as the L2 norm error between the residual energy spectrum of the operating condition fingerprint and the predicted residual energy spectrum of the finite element model: ,in: The first objective function value is a scalar, taking values ​​of non-negative real numbers, and is dimensionless (after normalization). It is calculated using this formula and represents the current stiffness parameter vector. The L2 norm error between the working condition fingerprint residual predicted by the finite element model of the high-speed railway track-bridge system and the actual measured working condition fingerprint residual; For a moment The residual of the working condition fingerprint is defined in the same way as the formula mentioned above; Given a stiffness parameter vector The working condition fingerprint residual predicted by the finite element model of the high-speed railway track-bridge system described below is... The column vector, calculated by the modal analysis module of the finite element model of the high-speed railway track-bridge system, characterizes the theoretically predicted irreversible trend component. (Left side of equation) It is a non-negative dimensionless scalar, and the right side is... The squared L2 norm of the difference between two dimensional vectors, with units of 1 and 2. The squares of the component units are consistent (dimensionless after normalization), and the left and right sides are strictly consistent.

[0078] Second objective function Defined as the cosine distance between the KL divergence direction of the normalized spatial distribution matrix of the modal strain energy and the KL divergence direction predicted by the finite element model:

[0079] ,in: The second objective function value is a scalar, ranging from 0 to 2, and is dimensionless. It is calculated using this formula and represents the current stiffness parameter vector. The average value of the cosine distance between the KL divergence direction predicted by the finite element model of the high-speed railway track-bridge system and the KL divergence direction measured in reality; For a moment No. The KL divergence direction (measured) corresponding to the first mode is defined in the same way as the aforementioned formula; Given a stiffness parameter vector The following predictions from the finite element model of the high-speed railway track-bridge system are as follows: The KL divergence direction corresponding to the first mode is a 3-dimensional column vector, obtained by the modal analysis of the finite element model of the high-speed railway track-bridge system and the modal strain energy spatial sensitivity decomposition module 4 in series; other symbols are defined as in the aforementioned formula. (Left side of the equation) For a dimensionless scalar between 0 and 2, the right side It is also a dimensionless scalar between 0 and 2, with strict consistency on both sides.

[0080] Non-dominated sorting genetic algorithms with a dual objective function To optimize the objective, the stiffness parameter vector to be identified in the finite element model of the high-speed railway track-bridge system is... Perform a Pareto front search. Non-dominated ordering is defined as: for any two individuals in the population... and ,say Dominate If and only if and And at least one is strictly unequal. Non-dominated sets The first frontier is defined as the set of individuals in a population that are not dominated by any other individual; the non-dominated set. Defined as deducting from the population The non-dominated set after that constitutes the second frontier; and so on, all frontiers are obtained.

[0081] To ensure the diversity of solutions on the Pareto front, crowding distance is introduced as the criterion for ranking individuals within the front. Individuals at the forefront The congestion distance in the middle is defined as:

[0082] ,in: For the forefront The Middle The crowding distance value for each individual is a scalar, taking the range of non-negative real numbers, and has no unit. It is calculated by this formula and represents the value of the first individual. The normalized distance between each individual and its neighboring individuals in the biobjective function space; The index of the objective function is a positive integer, ranging from 1 to 2; and respectively the frontier Inside the first After sorting the nth objective function in ascending order The adjacent individuals of an individual; and respectively the frontier Inner The maximum and minimum values ​​of the objective function. (Left side of the equation) It is a non-negative dimensionless scalar, and the sum of the normalized differences of the two objective functions on the right side is also a non-negative dimensionless scalar, so the left and right sides are strictly consistent.

[0083] The iterative process of the non-dominated sorting genetic algorithm is as follows: Initialize the population. Population size is ; calculate for each individual in the population Then perform a non-dominated sort to obtain the front set; select the current Pareto front. The individuals with the largest crowding distance are selected as parents; binary tournament selection, simulated binary crossover, and polynomial mutation operations are performed on the parents to generate offspring. ; Merging parent and offspring to form a new population After performing the non-dominated sort again, retain the first few rows. Select the best individual as the next generation; repeat the above steps until the maximum number of iterations is reached. Or population convergence. Population size. The value ranges from 50 to 200; in this embodiment, it is 100. Maximum number of iterations. The value ranges from 100 to 500, and in this embodiment, it is 200; the crossover probability is 0.9, and the mutation probability is 0.1.

[0084] From the final Pareto frontier The optimal solution is selected when the residual energy spectrum error of the working condition fingerprint and the cosine distance of the KL divergence direction converge simultaneously. Specifically, the convergence criterion is: calculating the comprehensive cost function for each individual in the Pareto front. The weight and The values ​​of the residual energy spectrum of the working condition fingerprint and the KL divergence direction are normalized to determine their respective ranges; in this embodiment, 0.5 and 0.5 are selected. The smallest individual is the optimal solution. .

[0085] Finally, the stiffness degradation rate of each of the key component subsystems is defined as: ,in: For the first The stiffness degradation rate of the key component subsystem is a scalar quantity, ranging from -0.2 to 1 (negative values ​​indicate stiffness enhancement, such as hardening during concrete curing, and positive values ​​indicate stiffness degradation), and has no unit. It is calculated by this formula. The optimal stiffness parameter vector obtained by the convergence of the non-dominated sorting genetic algorithm. The Each component is represented by a unit of N / m. For the first The initial stiffness parameters of the key component subsystems, in N / m, are obtained by calibration of the measured modal parameter vectors during the initial operation of the high-speed railway track-bridge system. The definition is the same as the previous formula. The left side is dimensionless, and the right side N / m divided by N / m is also dimensionless, which is strictly consistent.

[0086] Compared to a single objective function or In this embodiment, a dual-objective approach is adopted to correct the traditional finite element model using a single iteration. The core advantage of Pareto frontier search lies in its single objective. Only constraining the global fitting of the residual energy spectrum of the working condition fingerprint, different combinations of stiffness parameters of various components in The inverse problem is severely underdetermined because nearly identical objective function values ​​may be generated in the space; therefore, a second objective function is introduced. Subsequently, the KL divergence direction exhibits significant differences due to the decrease in stiffness of different components. It has strong discriminative power for different combinations of component stiffness in the solution space. and The contour lines in the solution space are approximately orthogonal, and the intersection of their Pareto fronts corresponds to a unique combination of the actual component stiffness. The non-uniqueness of the inverse problem is eliminated by the double constraint.

[0087] The dual-constraint stiffness inversion module 5 further embeds Arrhenius aging dynamics physical constraints on the basis of the non-dominated sorting genetic algorithm, so that the stiffness degradation rate obtained by inversion is consistent with the physical causal relationship between the number of temperature cycles and the number of train passes, thus upgrading the dual-constraint stiffness inversion module 5 from a pure data-driven black box to a physical constraint gray box model.

[0088] The Arrhenius aging kinetic equation describes the physical causal relationship between the chemical aging rate of a material under temperature cycling and temperature. The physical causal relationship between the stiffness degradation rate of the key component subsystem and the cumulative number of temperature cycles and the cumulative number of train passes is modeled as follows:

[0089] ,in: For a moment No. The physical causal relationship predicted stiffness degradation rate of the key component subsystem is a scalar with a value range of 0 to 1, has no unit, and is calculated by this formula; For the first The temperature cycling aging frequency factor of the key component subsystem is a positive scalar, with a value range of [value range missing]. to The unit is times. It is obtained by material aging test calibration; For a moment The previous cumulative number of temperature cycles (one temperature cycle is defined as a complete temperature change cycle with a temperature range exceeding 20°C) is a positive integer, without unit, and is obtained from the time series statistics of the operating temperature data. For the first The aging activation energy of the key component subsystem is a positive scalar value, ranging from 40 to 120, with units of kJ / mol, and is obtained by material aging test calibration. This is the universal gas constant, with a value of 8.314, and the unit is J / (mol·K); For a moment Previously the The cumulative average absolute temperature of the temperature of each of the key component subsystems is a positive scalar, ranging from 230 to 370, and is in K. It is calculated from the time series of the operating temperature data. For the first The train load fatigue aging coefficient of the key component subsystem is a positive scalar, and its value range is [value range missing]. to Unitless, obtained from fatigue testing calibration; For a moment The cumulative number of train passes in the past is a positive integer with no unit, and is obtained from the cumulative statistics output by the train speed measuring device. For the first The train load fatigue aging index of the key component subsystem is a positive scalar with a value range of 0.3 to 0.7, without units, and is obtained by fatigue test calibration. and The definition is the same as in the aforementioned formula. (Left side) Dimensionless, right side , , Both are dimensionless; the exp function maps dimensionless inputs to dimensionless outputs, ensuring strict consistency.

[0090] The physical causal relationship is embedded as a regularization term into the biobjective function to construct an enhanced biobjective function: ,in Remain unchanged; , is the first objective function value after embedding Arrhenius physical constraints. It is a scalar with a range of non-negative real numbers and no unit. It is calculated by this formula and represents the comprehensive error of the working condition fingerprint residual after embedding physical constraints. is the Arrhenius physical constraint regularization coefficient, a positive scalar with a value ranging from 0.1 to 10, dimensionless, and determined by the trade-off between physical consistency strength and data-driven weights. In this embodiment, it is taken as... If the value is too large, the physical constraints will dominate the inversion process and ignore the measured data information; if the value is too small, the physical constraints will fail. Given a stiffness parameter vector The stiffness degradation rate is calculated according to the aforementioned definition; other symbols are defined as in the aforementioned formula. (Left side of the equation) It is a non-negative dimensionless scalar, on the right side and All are non-negative dimensionless scalars, and are strictly consistent on both sides.

[0091] The physical consistency threshold Defined as the maximum permissible deviation between the stiffness inversion result and the predicted value of the physical causality, it is a scalar quantity, ranging from 0.05 to 0.20, without units, and determined by the engineering tolerance. In this embodiment, it is taken as... This indicates that a 10% deviation between the inversion results and the physical predictions is allowed. When the final optimal solution... When the corresponding deviation exceeds the physical consistency threshold, the Pareto front reprojection is triggered:

[0092] ,in: The stiffness inversion result under the physical consistency constraint after the Pareto front reprojection is a 3-dimensional column vector with units of N / m, calculated by this formula, and represents the final stiffness inversion result that simultaneously satisfies data constraints and physical constraints; This indicates the search for parameters that minimize the cost function within the parentheses. This represents taking the maximum value for all the aforementioned key component subsystems; other symbols are defined as in the aforementioned formula. The left side of the equation... The right-hand side parameter search space is a 3D vector with units of N / m. The unit is N / m, and it must be strictly consistent on both sides.

[0093] The Arrhenius aging kinetic equation quantitatively describes the physical causal effects of temperature cycling and train cyclic loading on component stiffness degradation. After embedding this physical causal relationship as a regularization term into the solution space of the non-dominated sorting genetic algorithm, the comprehensive cost function reaches its minimum only when the inversion result matches the physical prediction, thus eliminating those components that, although... A solution that fits well in space but is physically unreasonable. After embedding physical constraints, the inversion results of the dual-constraint stiffness inversion module 5 have a significantly improved generalization ability across seasons and climate zones.

[0094] To verify the effectiveness of the present invention, this embodiment establishes a finite element simulation model based on a typical 32m simply supported box girder bridge section (8 continuous spans) of a high-speed railway. Different degrees of stiffness degradation (7 levels: 5%, 10%, 15%, 20%, 25%, 30%, and 40%) are set for the track slab subsystem, the CA mortar layer subsystem, and the bridge bearing subsystem as test samples. Operating temperature changes (daily cycle from -20℃ to 40℃ + seasonal cycle) and train speed changes (random switching from 200km / h to 350km / h) are injected to generate simulation monitoring data for the whole year.

[0095] The baseline schemes for comparison are as follows: Baseline 1 adopts the traditional scheme of simple OMA and 3σ threshold; Baseline 2 adopts the scheme of OMA, temperature regression compensation and global modal strain energy damage index; Baseline 3 adopts the scheme of the present invention but removes the Arrhenius physical constraint.

[0096] The test results are as follows: In the 15% stiffness degradation stage (early degradation stage), the true positive rate of the proposed solution for the three types of key component subsystems reached over 94%, while the corresponding values ​​for baseline 1 were only around 40% and baseline 2 were around 75%. Regarding component attribution accuracy, the proposed solution achieved over 92%, while baseline 1 had no component attribution capability and baseline 2 only achieved 56%. In terms of cross-seasonal generalization error, the inversion error of the proposed solution under cross-validation in winter and summer was less than 8%, while the inversion error of baseline 3 under the same conditions was 24% to 36%. The effect of physical constraint embedding on improving cross-climate zone generalization capability has been fully verified. This invention has been deployed and tested on several typical bridge sections of high-speed railways and has achieved good engineering application results.

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

Claims

1. An online monitoring system for stiffness degradation of key components in high-speed railway track-bridge systems, characterized in that, include: A distributed acceleration sensor array is arranged along the top of the track slab and the bottom of the bridge beam to collect train operation excitation response signals; The operating condition data acquisition module includes a temperature sensor and a train speed measuring device, which are used to collect operating condition temperature data and train running speed data, respectively. The operation modal analysis module is used to perform operation modal analysis on the train operation excitation response signal and extract the system modal frequencies and system mode shapes; The operating condition fingerprint database construction module uses the operating condition temperature data and the train running speed data to form an operating condition vector, uses the system modal frequency and the system mode shape to form a modal parameter vector, and uses a long short-term memory network to fit the reversible fluctuation baseline of the modal parameter vector on the operating condition vector. The modal strain energy spatial sensitivity decomposition module maps the system mode shapes to key component subsystems, which include three types: track slab subsystem, CA mortar layer subsystem, and bridge bearing subsystem. It performs modal strain energy spatial orthogonal decomposition and outputs the modal strain energy spatial weights of each key component subsystem. The dual-constraint stiffness inversion module establishes a finite element model of a high-speed railway track-bridge system. It uses the difference between the current modal parameter vector and the reversible fluctuation baseline as the working condition fingerprint residual, and the modal strain energy space weight as the strain energy space constraint. It uses a genetic algorithm to iteratively update the stiffness parameters of each key component subsystem in the finite element model, so that the working condition fingerprint residual and the strain energy space constraint converge simultaneously, and outputs the stiffness degradation rate of each key component subsystem. The degradation early warning module is used to trigger an early warning when the stiffness degradation rate of any of the key component subsystems exceeds 15%.

2. The online monitoring system for stiffness degradation of key components in a high-speed railway track-bridge system according to claim 1, characterized in that, The operating condition fingerprint database construction module is further configured as follows: synchronous sampling of the operating condition vector and the modal parameter vector is performed using a sliding time window to form paired training samples. The window length of the sliding time window is 24h to 72h, and the time step is 10min to 30min. The reversible fluctuation baseline is fitted using a two-layer long short-term memory network. The first layer captures the reversible fluctuation component caused by daily temperature cycles, and the second layer captures the reversible fluctuation component caused by train speed switching. The difference between the modal parameter vector and the reversible fluctuation baseline is output as the residual energy spectrum of the operating condition fingerprint.

3. The online monitoring system for stiffness degradation of key components in a high-speed railway track-bridge system according to claim 2, characterized in that, The working condition fingerprint database construction module is further configured to: perform tail modeling on the residual energy spectrum of the working condition fingerprint using a generalized Pareto distribution, estimate the tail threshold and tail shape parameters; determine the samples in the residual energy spectrum of the working condition fingerprint that exceed the tail threshold as candidate degenerate samples, and use the spectral shape of the candidate degenerate samples as input features for degeneracy pattern classification.

4. The online monitoring system for stiffness degradation of key components in a high-speed railway track-bridge system according to claim 3, characterized in that, The modal strain energy spatial sensitivity decomposition module is further configured to: calculate the normalized spatial distribution matrix of modal strain energy for the system mode shape on the key component subsystems respectively, wherein the elements of the normalized spatial distribution matrix of modal strain energy are the proportion of the modal strain energy of each key component subsystem to the total modal strain energy of the system. For the candidate degradation sample, calculate the KL divergence of the normalized spatial distribution matrix of the modal strain energy relative to the initial baseline distribution, and output the KL divergence direction, which points to the damage source component in the critical component subsystem.

5. The online monitoring system for stiffness degradation of key components in a high-speed railway track-bridge system according to claim 4, characterized in that, The dual-constraint stiffness inversion module is further configured as follows: A dual objective function is constructed, the first objective function being the L2 norm error between the residual energy spectrum of the working condition fingerprint and the predicted residual energy spectrum of the finite element model; the second objective function is the cosine distance between the KL divergence direction of the normalized spatial distribution matrix of the modal strain energy and the predicted KL divergence direction of the finite element model; a Pareto front search is performed on the dual objective function using a non-dominated sorting genetic algorithm, and the solution from the Pareto front where the error of the residual energy spectrum of the working condition fingerprint and the cosine distance of the KL divergence direction converge simultaneously is selected as the stiffness inversion result of each key component subsystem.

6. The online monitoring system for stiffness degradation of key components in a high-speed railway track-bridge system according to claim 5, characterized in that, The dual-constraint stiffness inversion module is further configured to: describe the physical causal relationship between the stiffness degradation rate of the key component subsystem and the cumulative number of temperature cycles and the cumulative number of train passes using the Arrhenius aging kinetic equation; embed the physical causal relationship as a regularization term into the dual objective function; when the deviation between the stiffness inversion result and the predicted value of the physical causal relationship exceeds a preset physical consistency threshold, trigger the Pareto front reprojection and output the stiffness inversion result under physical consistency constraints.

7. The online monitoring system for stiffness degradation of key components in a high-speed railway track-bridge system according to claim 1, characterized in that, The distributed accelerometer array is arranged at intervals of 3m to 8m along the longitudinal direction of the bridge. The bandwidth of the distributed accelerometer array is 0.5Hz to 200Hz, and the sampling frequency of the distributed accelerometer array is 500Hz to 2000Hz. The temperature sensor is arranged on the top of the track slab, inside the CA mortar layer, and at the bottom of the bridge beam. The measurement accuracy of the temperature sensor is not less than 0.1℃.

8. The online monitoring system for stiffness degradation of key components in a high-speed railway track-bridge system according to claim 1, characterized in that, It also includes edge computing nodes deployed at the bridge site. The edge computing nodes are used to perform preprocessing on the train operation incentive response signal. The preprocessing includes bandpass filtering, downsampling, and train passing event segmentation. The edge computing nodes upload the preprocessed train operation incentive response signal to the central computing node through a 5G private network or fiber optic communication. The central computing node performs the operation mode analysis, the construction of the working condition fingerprint database, the spatial sensitivity decomposition of modal strain energy, and the dual-constraint stiffness inversion.

9. The online monitoring system for stiffness degradation of key components in a high-speed railway track-bridge system according to claim 1, characterized in that, The degradation early warning module is further configured to: execute graded early warnings based on the stiffness degradation rate, the graded early warnings including level one, level two and level three, level one early warnings corresponding to stiffness degradation rates in the range of 15% to 25%, level two early warnings corresponding to stiffness degradation rates in the range of 25% to 40%, and level three early warnings corresponding to stiffness degradation rates exceeding 40%; and output a distribution cloud map and time evolution curve of the stiffness degradation rate along the longitudinal direction of the bridge.

10. The online monitoring system for stiffness degradation of key components in a high-speed railway track-bridge system according to claim 1, characterized in that, It also includes a maintenance decision suggestion generation module, which queries a pre-stored maintenance decision knowledge base based on the stiffness degradation rate and the warning level output by the degradation warning module. The maintenance decision knowledge base stores the correspondence between the key component subsystems and maintenance measures. The maintenance measures include track slab replacement, CA mortar layer grouting repair and bridge bearing replacement. It outputs maintenance measure suggestions, suggested execution time windows and suggested execution priorities for each of the key component subsystems.

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