Post-earthquake driving performance evaluation method, driving operation method, medium and device

Abstract

This invention relates to the field of post-earthquake bridge traffic capacity technology, and particularly to a method for evaluating post-earthquake train performance, a train operation method, a medium, and equipment. The post-earthquake train performance evaluation method includes: calculating post-earthquake residual irregularities based on a numerical model of a high-speed railway track-bridge system, and introducing a root mean square rate of change index for track irregularities to quantify the level of post-earthquake track residual irregularities; obtaining a multi-dimensional mapping model based on a weighted comprehensive scoring and whale optimization adaptive function mapping method; constructing a rapid post-earthquake train performance evaluation model based on a 95% guarantee rate according to the multi-dimensional mapping model; solving for the speed thresholds corresponding to various train performance indicators under different structural damping ratios based on the rapid post-earthquake train performance evaluation model, and using the lowest speed threshold under different structural damping ratios as the post-earthquake train performance evaluation result for the track-bridge system under different structural damping ratios. This invention enables rapid evaluation of post-earthquake train performance through the rapid post-earthquake train performance evaluation model.

Description

Technical Field

[0001] This invention relates to the field of post-earthquake bridge traffic capacity assessment technology, and in particular to a post-earthquake vehicle performance assessment method, vehicle operation method, medium and equipment. Background Technology

[0002] While significant progress has been made in the field of earthquake resistance for high-speed railway bridges, studies on earthquake-induced track irregularities and post-earthquake traffic safety have all set the structural damping ratio as a fixed parameter. This approach fails to consider the inherent differences in the damping ratios of different bridges during the design phase, nor does it take into account the characteristic that damping will change during actual service. Therefore, certain limitations still exist.

[0003] The structural damping ratio, as a core parameter affecting the dynamic response of a track-bridge system, is not only influenced by the pre-set damping during the bridge design phase, but also undergoes significant random variations due to material aging, construction deviations, and environmental loads (such as temperature cycling and long-term train impacts) during service. These variations in the damping ratio further amplify the uncertainty of track irregularities on the bridge after an earthquake, leading to deviations in traffic safety assessments. Therefore, in-depth research on post-earthquake traffic safety on bridges, considering the randomness of the structural damping ratio, is urgently needed. Existing technologies have revealed the significant impact of the damping ratio on track irregularities by establishing power spectral density curves for the CRTS II type slab track system and proposed a simplified calculation method. Furthermore, the effects of damping ratio and seismic intensity on track irregularities have been further analyzed using amplitude response spectra and structural random adjustment coefficients. While both studies have to some extent overcome the limitation of fixed damping ratio parameters and improved the accuracy of post-earthquake track condition prediction, they both target CRST II type slab track and have not established the relationship between damping ratio uncertainty and train operation safety, making it difficult to provide effective guidance for post-earthquake train operation.

[0004] Current research on post-earthquake bridge traffic capacity has the following key shortcomings: 1. Research on the impact of damping ratio on track-bridge systems mainly focuses on CRTS II type slab track, while research on CRTS III type slab track still needs to be supplemented; 2. The adaptability of quantitative indicators is poor. The velocity spectrum intensity index ignores the train vibration effect induced by post-earthquake traffic speed, leading to a deviation between the assessment results and actual safety risks. The seismic intensity parameter, on the other hand, fails to consider the spatial geometric characteristics of track irregularities and the dynamic coupling relationship between train operation, thus failing to accurately reflect its direct impact on wheel-rail contact and train vibration; 3. Traffic safety assessment methods generally rely on complex coupling models, requiring the integration of multi-dimensional data, resulting in cumbersome calculation processes and low efficiency; 4. Existing research has not combined with actual operational scenarios to clarify post-earthquake bridge traffic maintenance plans and emergency rescue speed-limited operation strategies, lacking universality and strong engineering operability, making it difficult to meet the actual needs of rapid and accurate post-earthquake decision-making.

[0005] Therefore, it is necessary to provide a new method for evaluating post-earthquake vehicle performance, a new method for vehicle operation, a new medium, and new equipment to solve the above-mentioned technical problems. Summary of the Invention

[0006] The main objective of this invention is to provide a method for evaluating post-earthquake train performance, a train operation method, a medium, and equipment, aiming to solve the problem that existing methods have not established the correlation between damping ratio uncertainty and train operation safety, making it difficult to provide effective guidance for post-earthquake train operation.

[0007] To achieve the above objectives, the present invention proposes a post-earthquake vehicle performance evaluation method, comprising the following steps: S1: Taking a certain track-bridge system as the research object, a numerical model of a high-speed railway track-bridge system with stochastic structural damping ratio is established based on the research object. S2: Calculation of post-earthquake residual irregularities based on a numerical model of a high-speed railway track-bridge system, introducing the root mean square rate of change of track irregularities. Indicators quantify the level of residual track irregularities after the earthquake; S3: An adaptive function mapping method based on the weighted comprehensive score (WCS) and whale-optimized WOA is used to fit the quantitative relationship between the root mean square rate of change of track irregularities and train performance indicators, obtaining information on structural damping ratio and root mean square rate of change of track irregularities. A multidimensional mapping model of vehicle speed and driving performance; S4: Construct a rapid evaluation model for post-earthquake driving performance based on a 95% guarantee rate using a multi-dimensional mapping model; S5: Based on the relevant limits of the driving performance indicators in the normative documents and the rapid post-earthquake driving performance evaluation model, solve the speed thresholds corresponding to each driving performance indicator under different structural damping ratios, and take the lowest speed threshold under different structural damping ratios as the post-earthquake driving performance evaluation results of the track-bridge system under different structural damping ratios.

[0008] Optionally, S2 includes: S2.1. Use the MR method to select N uniformly distributed ground motions from the PEER strong earthquake database; S2.2 Input the selected seismic motion into the numerical model of the high-speed railway track-bridge system to calculate the seismic-induced track residual irregularities of the track-bridge system under different structural damping ratios. S2.3 Calculate the root mean square rate of change of track irregularities corresponding to each earthquake-induced track residual irregularity. The specific formula is as follows: ; in: This represents the total mileage of the rails. X Mileage location, The earthquake caused residual irregularities in the track.

[0009] Optionally, S3 includes: S3.1. Based on the train sub-model and the numerical model of the high-speed railway track-bridge system, a coupled model of the train-track-bridge system is built; S3.2. Using the seismic track residual irregularities calculated in S2.2 as the external excitation input of the train-track-bridge system coupling model, the system dynamic response analysis under different vehicle speed conditions is carried out to obtain the vehicle performance index dataset, which includes the derailment coefficient, wheel load reduction rate, wheel set lateral horizontal force, vehicle body lateral acceleration and Spearing index. S3.3. Using different typical function models as candidate function models, the Whale Optimized WOA algorithm is used to solve the structural parameters of each candidate function model based on the driving performance index dataset. A multi-evaluation index weighted comprehensive scoring mechanism is then used to automatically select the candidate function model with the highest comprehensive score, taking into account vehicle speed and damping ratio. A multidimensional mapping model between driving performance indicators and driving performance indicators.

[0010] Optionally, S3.3 includes: S3.3.1 Initialize the whale pod, including: Initialize the candidate function model set and its parameter boundaries; For a candidate function model in the candidate function model set Randomly generate num_whales whales, each whale corresponding to a set of parameter configurations for a candidate function model. ;in: Number the candidate function models; The candidate function model requiring logarithmic operations is preprocessed using the following formula: ; in: Represent the logarithmic transformation index, express index, Represents the smallest floating-point integer in a computer. S3.3.2, Assess the whale, including: ① Based on the parameter configuration of each whale, a pre-trained model is built. The pre-trained model is trained on the training set of the driving performance index dataset. Each pre-trained model is trained for 10 epochs. The MSE is used as the fitness function to calculate the fitness of each whale, that is, the MSE calculated on the validation set of each pre-trained model after training. The current best whale and its fitness are recorded. ② Update the whale positions, specifically: update the position of each whale according to the update formula of the WOA algorithm, and apply boundary constraints. This means updating to obtain the new parameter configuration; where: For model parameter vectors, For parameter boundaries; ③ Repeat steps ① and ② until the fitness converges, or until the maximum number of iterations is reached (limited by the code), and output the optimal parameters. Calculate the predicted value ; S3.3.3 Constructing Optimal Parameters The corresponding optimal candidate function model is identified, and its fit index is calculated, including the coefficient of determination. Root mean square error RMSE and mean absolute error MAE ; S3.3.4 Normalize the fitting index and calculate the comprehensive score based on the normalized fitting index; S3.3.4 Repeat S3.3.1 to S3.3.3 to traverse all candidate function models and obtain the comprehensive score corresponding to different candidate function models; S3.3.5 Select the candidate function model with the highest comprehensive score as the multidimensional mapping model.

[0011] Optional, overall score The specific calculation formula is as follows: ; in: To determine the coefficient weights, The root mean square error weight is used. The average absolute error weighting, The normalized coefficient of determination This is the normalized root mean square error. The normalized mean absolute error; The expression for the multidimensional mapping model is as follows: ; in: This is a number representing the structural damping ratio. For the first Derailment coefficient under a structural damping ratio For the first Wheel load reduction rate under structural damping ratio For the first Lateral horizontal force under a structural damping ratio For the first Lateral acceleration of the vehicle body under a given structural damping ratio For the first The Spelling index under structural damping ratio , and These are the three model parameter values ​​corresponding to the derailment coefficient. , and These are the three model parameter values ​​corresponding to the wheel load reduction rate. , and These are the three model parameter values ​​corresponding to the lateral horizontal force. , and The three model parameter values ​​corresponding to the lateral acceleration of the vehicle body , and These are the three model parameter values ​​corresponding to the Spelling index.

[0012] Optionally, S4 includes: S4.1 Calculate the unbiased estimator of the error variance The specific formula is as follows: ; In the formula, The number of samples; Number the sample; The number of model parameters; S4.2, The error variance construction based on the multidimensional mapping model follows a set of degrees of freedom. of The test statistic for the distribution is as follows: ; In the formula, For the first Group samples Sample values ​​of the indicator; For the first Sample values ​​of driving performance indicators in the group sample. for The sample mean of the indicator; yes index variance ; S4.3, Based on the test statistic at the confidence level Make a decision The prediction interval is expressed as follows: ; In the formula, for One-sided upper quantile of the distribution; These are the two-tailed quantiles of the standard normal distribution; for The predicted value; S4.4 Expression for determining the 95% one-sided guarantee rate curve based on the prediction interval The details are as follows: ; in: for index Corresponding driving performance indicators The predicted value; S4.5, Based on the multidimensional mapping model, the 95% one-sided guarantee rate curve is obtained. The indicators and various driving performance indicators are based on a mapping model with a 95% guarantee rate; S4.6. Using the weighted comprehensive score WCS and the adaptive function mapping method of whale optimization WOA in S3, the mapping relationship between the mapping model parameters and the train running speed based on the 95% guarantee rate is solved to obtain the rapid evaluation model of post-earthquake train performance.

[0013] In addition, the present invention also provides a post-earthquake vehicle operation method, including: Based on the extent of the earthquake's impact, the study area was divided into a post-earthquake operation and maintenance area and a post-earthquake emergency rescue area. A tiered operation plan will be adopted for post-earthquake operation and maintenance in the affected areas. Specifically, this involves tiering the operation based on track dynamic response thresholds and train safety control standards. The numerical range of the indicators is divided into three categories of track conditions: slight deterioration, moderate deterioration, and severe deterioration. The track conditions are used as the basis for guiding the maintenance and repair of the line to formulate a graded operation plan. The post-earthquake operation and maintenance area is operated in accordance with the formulated graded operation plan. The post-earthquake driving performance assessment results obtained based on the post-earthquake driving performance assessment method described above are used to assess post-earthquake driving in the emergency rescue area.

[0014] Alternatively, the tiered operation plan is as follows: When the value is ≤0.4, it is considered a slightly deteriorated state. The existing conventional operation mode is adopted, and the first set threshold is used as the driving threshold for the current state. 0.4 < A value ≤0.9 indicates moderate degradation. Scheduled maintenance work should be carried out, and the degradation should be addressed within the specified timeframe. The indicator recovers to the range of slightly deteriorated state, and the driving threshold of the current state is set as the second set threshold. 0.9 < A reading of ≤4 indicates a severely deteriorated condition. In such cases, the emergency response plan will be activated, speed limits will be issued or the line will be closed, and a professional repair team with specialized equipment will be dispatched to the site for repairs until... Once the value falls back to a safe range and the wheel-rail dynamic response verification shows no abnormalities, the line will gradually resume normal operation, with the third set threshold as the current operating threshold. Among them, the first set threshold is greater than the second set threshold, which is greater than the third set threshold; Based on the post-earthquake driving performance assessment results obtained using the post-earthquake driving performance assessment method described above, post-earthquake driving operations will be carried out in the post-earthquake emergency rescue area, specifically as follows: ① The performance indicators of vehicles on bridges under seismic loading are divided into driving safety indicators and driving comfort indicators. Driving safety indicators include derailment coefficient, wheel load reduction rate and wheel set lateral horizontal force; driving comfort indicators include vehicle body lateral acceleration and Spearing index. ② Under the premise of meeting the relevant limit requirements of the design specification documents, according to different The post-earthquake driving performance evaluation results corresponding to the indicators are fitted with functions to obtain the speed threshold expressions for driving safety indicators and driving comfort indicators under different structural damping ratios: ; in: The speed threshold corresponding to the driving safety index. , and These are the three fitting parameters for the speed threshold expression corresponding to the driving safety index; The speed threshold corresponding to the driving comfort index. 、 and These are the three fitting parameters for the speed threshold expression corresponding to the driving comfort index; ③ Fit the parameters of the velocity threshold expression with the structural damping ratio to obtain the corresponding fitting curve; ④ Determine the speed threshold under different structural damping ratios based on the fitted curves. Use the speed threshold corresponding to the driving safety index to limit the speed of post-earthquake vehicles transporting disaster relief materials, and use the speed threshold corresponding to the driving comfort index to limit the speed of post-earthquake vehicles transporting disaster relief personnel.

[0015] In addition, the present invention also provides a readable storage medium, characterized in that it stores computer program instructions thereon, which, when executed by a processor, implement the post-earthquake driving performance evaluation method as described above.

[0016] In addition, the present invention also provides an electronic device, including: at least one processor, at least one memory, and computer program instructions stored in the memory, wherein the computer program instructions are executed by the processor to perform the post-earthquake driving performance evaluation method as described above.

[0017] This invention establishes a numerical model of a high-speed railway track-bridge system with stochastic structural damping ratio, revealing the influence of structural damping ratio on seismically induced track residual irregularities; and introduces the root mean square rate of change of track irregularities (RMS). The post-earthquake track residual irregularity level was quantified, and an adaptive function mapping method based on weighted comprehensive scoring and whale optimization was constructed. A quantitative fitting relationship between the damping ratio and driving performance indicators was established, and the "damping ratio- A multi-dimensional mapping model of "indicators-train speed-train performance" is used to achieve rapid assessment of post-earthquake train performance. Finally, based on the post-earthquake functional recovery needs of high-speed railways, two typical scenarios are distinguished: post-earthquake operation and maintenance, and post-earthquake emergency rescue. Separate plans are developed for each scenario. The graded post-earthquake track-bridge system operation plan and the post-earthquake train speed limit operation strategy based on performance targets determine the safe speed threshold for post-earthquake train operation under different damping ratios, providing accurate theoretical support and engineering reference for the operation restoration, emergency maintenance and disaster relief speed limit decision-making of high-speed railway bridges after earthquakes. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0019] Figure 1 This is a schematic diagram of the geometric distribution of track irregularities caused by earthquakes under a 5% structural damping ratio in an embodiment of the present invention. Figure 2 This is a schematic diagram of the geometric distribution of track irregularities caused by earthquakes under a 10% structural damping ratio in an embodiment of the present invention. Figure 3 This is a schematic diagram of the geometric distribution of track irregularities caused by earthquake under a 20% structural damping ratio in an embodiment of the present invention. Figure 4 This is a schematic diagram of the geometric distribution of track irregularities caused by earthquakes under a 30% structural damping ratio in an embodiment of the present invention. Figure 5 As described in the embodiments of the present invention A diagram illustrating the calculation results of the indicator; Figure 6Different speeds in the embodiments of the present invention A diagram illustrating the correlation strength between the indicators and the derailment coefficient; Figure 7 Different speeds in the embodiments of the present invention A diagram illustrating the correlation strength between the indicator and the Spelling indicator; Figure 8 This is based on a 95% guarantee rate at a 2% structural damping ratio in an embodiment of the present invention. A schematic diagram of the mapping model between indicators and derailment coefficients; Figure 9 This is based on a 95% guarantee rate at a 2% structural damping ratio in an embodiment of the present invention. A schematic diagram of the mapping model between indicators and wheel load reduction rate; Figure 10 This is based on a 95% guarantee rate at a 2% structural damping ratio in an embodiment of the present invention. Schematic diagram of the mapping model between the index and the lateral horizontal force of the wheelset; Figure 11 This is based on a 95% guarantee rate at a 5% structural damping ratio in the embodiments of the present invention. A schematic diagram of the mapping model between indicators and derailment coefficients; Figure 12 This is based on a 95% guarantee rate at a 5% structural damping ratio in the embodiments of the present invention. A schematic diagram of the mapping model between indicators and wheel load reduction rate; Figure 13 This is based on a 95% guarantee rate at a 5% structural damping ratio in the embodiments of the present invention. Schematic diagram of the mapping model between the index and the lateral horizontal force of the wheelset; Figure 14 This is based on a 95% guarantee rate at a 10% structural damping ratio in this embodiment of the invention. A schematic diagram of the mapping model between indicators and derailment coefficients; Figure 15 This is based on a 95% guarantee rate at a 10% structural damping ratio in this embodiment of the invention. A schematic diagram of the mapping model between indicators and wheel load reduction rate; Figure 16 This is based on a 95% guarantee rate at a 10% structural damping ratio in this embodiment of the invention. Schematic diagram of the mapping model between the index and the lateral horizontal force of the wheelset; Figure 17 This is based on a 95% guarantee rate at a 20% structural damping ratio in an embodiment of the present invention. A schematic diagram of the mapping model between indicators and derailment coefficients; Figure 18 This is based on a 95% guarantee rate at a 20% structural damping ratio in an embodiment of the present invention. A schematic diagram of the mapping model between indicators and wheel load reduction rate; Figure 19 This is based on a 95% guarantee rate at a 20% structural damping ratio in an embodiment of the present invention. Schematic diagram of the mapping model between the index and the lateral horizontal force of the wheelset; Figure 20 This is based on a 95% guarantee rate at a structural damping ratio of 30% in this embodiment of the invention. A schematic diagram of the mapping model between indicators and derailment coefficients; Figure 21 This is based on a 95% guarantee rate at a structural damping ratio of 30% in this embodiment of the invention. A schematic diagram of the mapping model between indicators and wheel load reduction rate; Figure 22 This is based on a 95% guarantee rate at a structural damping ratio of 30% in this embodiment of the invention. Schematic diagram of the mapping model between the index and the lateral horizontal force of the wheelset; Figure 23 This is based on a 95% guarantee rate at a 2% structural damping ratio in an embodiment of the present invention. A schematic diagram of the mapping model between the index and the lateral acceleration of the vehicle body; Figure 24 This is based on a 95% guarantee rate at a 5% structural damping ratio in the embodiments of the present invention. A schematic diagram of the mapping model between the index and the lateral acceleration of the vehicle body; Figure 25 This is based on a 95% guarantee rate at a 10% structural damping ratio in this embodiment of the invention. A schematic diagram of the mapping model between the index and the lateral acceleration of the vehicle body; Figure 26 This is based on a 95% guarantee rate at a 20% structural damping ratio in an embodiment of the present invention. A schematic diagram of the mapping model between the index and the lateral acceleration of the vehicle body; Figure 27 This is based on a 95% guarantee rate at a structural damping ratio of 30% in this embodiment of the invention. A schematic diagram of the mapping model between the index and the lateral acceleration of the vehicle body; Figure 28 This is based on a 95% guarantee rate at a 2% structural damping ratio in an embodiment of the present invention. A schematic diagram illustrating the mapping model between the indicator and the Spelling indicator; Figure 29 This is based on a 95% guarantee rate at a 5% structural damping ratio in the embodiments of the present invention. A schematic diagram illustrating the mapping model between the indicator and the Spelling indicator; Figure 30 This is based on a 95% guarantee rate at a 10% structural damping ratio in this embodiment of the invention. A schematic diagram illustrating the mapping model between the indicator and the Spelling indicator; Figure 31 This is based on a 95% guarantee rate at a 20% structural damping ratio in an embodiment of the present invention. A schematic diagram illustrating the mapping model between the indicator and the Spelling indicator; Figure 32 This is based on a 95% guarantee rate at a structural damping ratio of 30% in this embodiment of the invention. A schematic diagram illustrating the mapping model between the indicator and the Spelling indicator; Figure 33 Parameters in the embodiments of the present invention A i3 A schematic diagram of the fitting curve with driving speed; Figure 34 Parameters in the embodiments of the present invention C i3 A schematic diagram of the fitting curve with driving speed; Figure 35 This is a schematic diagram of the post-earthquake operation and maintenance area in an embodiment of the present invention; Figure 36 This is a schematic diagram of a post-earthquake emergency rescue area in an embodiment of the present invention; Figure 37 Parameters in the embodiments of the present invention With damping ratio A schematic diagram of the fitted curve; Figure 38 Parameters in the embodiments of the present invention With damping ratio A schematic diagram of the fitted curve; Figure 39 Parameters in the embodiments of the present invention With damping ratio A schematic diagram of the fitted curve; Figure 40 Parameters in the embodiments of the present invention With damping ratio A schematic diagram of the fitted curve; Figure 41 Parameters in the embodiments of the present invention With damping ratio A schematic diagram of the fitted curve; Figure 42 Parameters in the embodiments of the present invention With damping ratio A schematic diagram of the fitted curve; Figure 43 This is a schematic diagram of the speed threshold curves for the vehicle safety index under different structural damping ratios in an embodiment of the present invention. Figure 44 This is a schematic diagram of the speed threshold curves for driving comfort indicators under different structural damping ratios in an embodiment of the present invention.

[0020] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0022] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indication will also change accordingly.

[0023] Furthermore, in this invention, descriptions involving "first," "second," etc., are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0024] In this invention, unless otherwise explicitly specified and limited, the terms "connection," "fixed," etc., should be interpreted broadly. For example, "fixed" can mean a fixed connection, a detachable connection, or an integral part; it can mean a mechanical connection or an electrical connection; it can mean a direct connection or an indirect connection through an intermediate medium; it can mean the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0025] Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are feasible for those skilled in the art. If the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0026] This invention proposes a post-earthquake train performance evaluation method, train operation method, medium, and equipment, aiming to solve the problem that existing methods have not established the correlation between damping ratio uncertainty and train operation safety, making it difficult to provide effective guidance for post-earthquake train operation.

[0027] Example 1: This embodiment provides a method for evaluating vehicle performance after an earthquake, including the following steps: S1: Taking a certain track-bridge system as the research object, a numerical model of a high-speed railway track-bridge system with stochastic structural damping ratio is established based on the research object. This embodiment uses the CRTSⅢ type slab track-bridge system as the research object. The bridge section adopts a prestressed concrete simply supported box girder with a span of 32.6m and a height of 3.052m. 0.1m expansion joints are provided between adjacent beam segments and between the beam and the abutment to buffer deformation caused by temperature changes and loads. The piers are solid piers with a height of 14m. The pier cap adopts a 1:45 variable cross-section design, with a height of 3m and a top cross-section size of 7.8m × 3.0m; the pier body adopts a uniform cross-section arrangement, with a height of 11m and a cross-section size of 6.0m × 2.0m. Four PZ-5000 pot bearings are arranged under each main beam span, including one fixed bearing, one bidirectional sliding bearing, and two unidirectional sliding bearings. Their longitudinal distance from the beam end is 0.75m, and their transverse center distance is 2.25m. The maximum vertical bearing capacity of the support is 5000kN, of which the horizontal yield force of the fixed support is 1079.4kN and the horizontal yield force of the sliding support is 107.74kN, thus ensuring the vertical bearing capacity while achieving reasonable horizontal deformation coordination.

[0028] The track section adopts a CRTSⅢ type structure, whose key components include CHN60 type steel rails, WJ-8 type fasteners, precast track slabs, U-shaped reinforcing bars, a self-compacting concrete layer, a geotextile isolation layer, an elastic cushion layer, and a grooved reinforced concrete base slab. The track slab and the self-compacting concrete filling layer are fixed together by two rows of interlaced U-shaped reinforcing bars, forming a composite structure with high integrity and high bending stiffness. A 4mm thick geotextile is placed between the self-compacting concrete layer and the base slab as an isolation layer to buffer the stress and deformation transmitted from the superstructure. At the groove of the base slab, the self-compacting concrete bosses interlock with the grooves to achieve longitudinal and lateral restraint, and an 8mm thick elastic cushion layer is laid between the bosses and grooves to improve the stress performance. The base slab is connected to the simply supported beams by pre-embedded reinforcing bars, thereby ensuring the overall coordination between the track and the bridge.

[0029] This embodiment establishes a CRTS Ⅲ numerical model based on existing finite element software. Beam 188 elements are used to simulate components such as the rails, track slabs, self-compacting concrete layers, base plates, box girders, and piers. The connections between the track slab and the self-compacting concrete layer, and between the base plate and the box girder, are simulated using MPC 184 rigid arm elements. The rotational degrees of freedom of the geotextile, friction plates, supports, and fasteners, as well as the elastic padding layer on the inner wall of the groove, are simulated using Combin 40 elements. The translational degrees of freedom of the friction plates, sliding supports, fixed supports, and fasteners are simulated using Combin 40 spring elements. The geometric lengths of all elements used in the modeling strictly match the actual structural dimensions of the project, and fixed constraint boundaries are set at both ends of the track subsystem. The constitutive relationship of the interlayer nonlinear spring elements is the core of accurately simulating the interlayer contact mechanical properties of the track-bridge system.

[0030] S2: Calculation of post-earthquake residual irregularities based on a numerical model of a high-speed railway track-bridge system, introducing the root mean square rate of change of track irregularities. Indicators quantify the level of residual track irregularities after the earthquake; S2 includes: S2.1. Use the MR method to select N uniformly distributed ground motions from the PEER strong earthquake database; In this embodiment, to consider the randomness and widespread nature of ground motions, the MR method is used to select ground motions. Considering the engineering realities involved in the study, the earthquake magnitude M is set to a range of 5-8; simultaneously, considering the dynamic response characteristics of the bridge under study, the epicentral distance R is set to a range of 0-100 km. Forty evenly distributed ground motions are selected from the PEER strong earthquake database. Given that rails generally maintain their initial smoothness under frequent earthquakes, their impact on post-earthquake train operation is relatively limited. Therefore, this embodiment only considers two peak ground acceleration (PGA) levels: 0.3 g (design earthquake) and 0.57 g (rare earthquake). Different PGA levels are achieved by amplitude modulation of the selected ground motion peak values.

[0031] S2.2 Input the selected seismic motion into the numerical model of the high-speed railway track-bridge system to calculate the seismic-induced track residual irregularities of the track-bridge system under different structural damping ratios. To ensure the broad applicability of this embodiment and to fully reveal the influence of different damping ratios on the dynamic response of the track-bridge system, the damping ratio was set to five gradient values: 2%, 5%, 10%, 20%, and 30%. System parametric analysis was conducted, resulting in 500 seismically induced residual track irregularities in the track-bridge system under different structural damping ratios. (See also...) Figures 1 to 4It can be seen that the structural damping ratio has a significant regulatory effect on the amplitude of earthquake-induced track irregularities. As the structural damping ratio gradually increases, the peak response of the track irregularities under seismic excitation shows a gradual decreasing trend. This is because increasing damping effectively enhances the system's ability to dissipate vibrational energy, weakens the dynamic amplification effect of the structure under seismic loading, and thus significantly reduces the deformation amplitude of the track irregularities. Therefore, the larger the structural damping ratio, the smaller the amplitude of earthquake-induced track irregularities. Appropriately improving the structural damping characteristics has a positive effect on improving the dynamic response of the track structure under seismic loading.

[0032] S2.3 Calculate the root mean square rate of change of track irregularities corresponding to each earthquake-induced track residual irregularity based on the track residual deformation function. The specific formula is as follows: ; in: This represents the total mileage of the rails. Mileage location, The earthquake caused residual irregularities in the track.

[0033] The evaluation of train operation on the bridge requires a vehicle-bridge coupled dynamic analysis based on the actual operating conditions of the train, and the performance indicators must meet the corresponding limits. From a dynamic mechanism perspective, the residual track deformation after an earthquake serves as the core geometric input. When the train passes at a speed v, it is mapped to a time-domain excitation through wheel-rail contact. The sensitivity of the wheel-rail dynamic system to this excitation is not solely determined by the track displacement amplitude, but rather depends more on the "intensity of change" characterized by the geometric change rate. This intensity is further amplified with the train speed, directly dominating the response characteristics of performance indicators such as wheel-rail lateral force, derailment coefficient, wheel load reduction rate, and car acceleration. These performance indicators are essentially a scalarized extraction of the dynamic response time history intensity. Their evaluation logic is highly consistent with the dynamic mechanism of "excitation intensity-system response." Therefore, constructing a single-valued indicator that is consistent with the performance evaluation logic and can accurately characterize the intensity of track geometric change is crucial for achieving a quantitative correlation between track geometry, train speed, and vehicle dynamic response. Based on this, this embodiment introduces... The core design of this indicator closely adheres to the dynamic essence and engineering practicality, using the spatial derivative of the track residual deformation function as the basic parameter to accurately capture the intensity of track geometric changes. Through squaring, it eliminates the interference of positive and negative directions on the evaluation of excitation intensity and nonlinearly amplifies localized severe changes such as post-earthquake faults and steep slopes, highlighting the contribution of key risk points. Spatial integration and averaging of the entire track path achieve a statistical representation of the overall track degradation intensity, avoiding the random bias of single-point data. Finally, square root calculation restores the physical dimensions consistent with the original geometric change rate, improving the indicator's engineering comparability and intuitiveness. Compared to the limitations of traditional static indicators that only focus on displacement amplitude, By quantifying the "intensity of change" and incorporating the dynamic amplification effect of train speed on the excitation, this not only provides a scientific basis for establishing a direct quantitative correlation between "track smoothness deterioration - train speed - train performance," but also lays a reliable theoretical foundation for post-earthquake safety control of trains on high-speed railway bridges from a mechanistic perspective. In this embodiment, the seismic-induced residual track irregularities under different structural damping ratios are corresponding... See the value calculation results. Figure 5 Therefore, it can be seen that the PGA has... It has a significant impact when PGA is increased from 0.3 g to 0.57 g. The increasing trend indicates that track smoothness deteriorates more severely under strong ground motion. Meanwhile, The overall damping ratio decreases with increasing structural damping ratio, especially in low structural damping ratio conditions. The curve essentially encloses the condition of high structural damping ratio. The curve. This is because the increase in structural damping ratio can effectively absorb the vibration energy of the track system under seismic loading through energy dissipation effects, reduce the vibration amplitude, and thus suppress the development of seismic-induced track irregularities.

[0034] S3: An adaptive function mapping method based on the weighted comprehensive score (WCS) and whale-optimized WOA is used to fit the quantitative relationship between the root mean square rate of change of track irregularities and train performance indicators, obtaining information on structural damping ratio and root mean square rate of change of track irregularities. A multidimensional mapping model of vehicle speed and driving performance; S3 includes: S3.1. Based on the train sub-model and the numerical model of the high-speed railway track-bridge system, a coupled model of the train-track-bridge system is built; This embodiment uses existing software to build a coupled model of a high-speed railway train-track-bridge system. The model employs a modular subsystem construction and precise definition of the coupling interface, decomposing the complex coupled system into two independent parts: a train sub-model and a track-bridge sub-model. Power transmission between the two subsystems is then achieved through wheel-rail contact, ultimately forming a complete excitation-response analysis link. This provides model support for subsequent analysis of the impact of earthquake-induced track irregularities on train operation.

[0035] The train sub-model uses the ICE3 high-speed train as the research object, adopting an 8-car formation, including 2 motor cars and 6 trailer cars. Each car is modeled as a rigid body system, consisting of 1 car body, 2 bogies, and 4 wheelsets. The car body, bogies, and wheelsets are all considered rigid components, and their elastic deformation is not considered. The components are connected by a primary suspension system and a secondary suspension system. The suspension system is simulated using spring-damped elements, where the primary suspension system is responsible for power transmission between the bogies and wheelsets, and the secondary suspension system is responsible for vibration damping between the car body and bogies. This train sub-model contains a total of 31 degrees of freedom, specifically distributed as follows: 5 degrees of freedom for the car body, 5 degrees of freedom for each bogie, and 4 degrees of freedom for each wheelset. The stiffness and damping parameters of the suspension system are determined with reference to the design parameters of the actual train to ensure that the model can realistically reflect the dynamic characteristics of the train.

[0036] In this embodiment, wheel-rail contact is a key component in achieving dynamic coupling between the train sub-model and the track-bridge sub-model. Knife-edge contact constraints are used to simulate the geometric contact relationship between the wheel and rail. The wheelset tread is set as a 1 / 40 conical surface, the lateral clearance between the wheel and rail is set to 10 mm, and the contact stiffness is taken as 1.6 × 10⁻⁶ mm. 7 N / m. In the tangential direction of wheel-rail contact, the lateral creep force is solved using the Kalker linear creep model. When the creep rate between the wheel and rail exceeds the critical value, the Shen-Hedrick-Euristic nonlinear model is introduced to correct the creep force to ensure the accuracy of the wheel-rail force transmission calculation.

[0037] S3.2. Using the seismic track residual irregularities calculated in S2.2 as the external excitation input of the train-track-bridge system coupling model, the system dynamic response analysis under different vehicle speed conditions is carried out to obtain the vehicle performance index dataset, which includes the derailment coefficient, wheel load reduction rate, wheel set lateral horizontal force, vehicle body lateral acceleration and Spearing index. This embodiment uses 400 seismically induced track residual irregularities as external excitation inputs to a coupled train-track-bridge system model to conduct system dynamic response analysis under multiple speed conditions. Six speed gradients are set: train speeds of 100, 150, 200, 250, 300, and 350 km / h. For each speed condition, the derailment coefficient, wheel load reduction rate, wheelset lateral force, car body lateral acceleration, and Spearing index are calculated, ultimately forming a complete dataset of 2400 sets of train performance indicators.

[0038] Based on 2400 sets of driving performance indicators and The data was first obtained by calculating the Pearson correlation coefficient. r Correlation coefficient with Spearman For each driving performance index and The correlation strength is quantified and judged. and The calculation formula is as follows: ; In the formula, For the first Group Sample values ​​of the indicator; For the first Sample values ​​of the group's driving performance indicators; and They are respectively The sample mean of the indicators and driving performance indicators; This represents the number of samples.

[0039] ; In the formula, for index, For driving performance indicators, For the first Group samples in Rank in a sequence; For the first Group samples in Rank in a sequence; and These are the mean values ​​of the ranks.

[0040] At different speeds The correlation strength with the derailment coefficient and the Spelling index is as follows: Figure 3 As shown, it can be seen that The Pearson and Spearman correlation coefficients with indicators such as derailment coefficient, wheel load reduction rate, wheelset lateral horizontal force, and vehicle body lateral acceleration are all greater than 0.9, showing extremely strong correlations. The Pearson correlation coefficient with the Spearing index is approximately 0.8, but its Spearman correlation coefficient is greater than 0.9, exhibiting a significant non-linear correlation. This result validates... The rationality and applicability of the indicators in the evaluation of the geometric state of bridge tracks after an earthquake.

[0041] S3.3. Using different typical function models as candidate function models, the Whale Optimized WOA algorithm is used to solve the structural parameters of each candidate function model based on the driving performance index dataset. A multi-evaluation index weighted comprehensive scoring mechanism is then used to automatically select the candidate function model with the highest comprehensive score, taking into account vehicle speed and damping ratio. A multidimensional mapping model between driving performance indicators and driving performance indicators.

[0042] To establish The quantitative correlation between indicators and train performance indicators enables a direct mapping from quantitative indicators of track irregularities to train performance response. This embodiment proposes WCS-WOA (an adaptive function mapping method based on weighted comprehensive scoring and whale optimization). This method is based on multiple candidate function models, uses WOA to achieve global optimization of model parameters, and combines a weighted comprehensive scoring mechanism of multiple evaluation indicators to automatically select the optimal quantitative mapping model.

[0043] Considering To investigate the correlation between indicators and driving performance indicators, candidate function models were selected, encompassing typical functions such as multinomial, exponential, power, and logarithmic functions. These models comprehensively cover common variable mapping relationships in engineering while also considering model simplicity and fitting ability. The mathematical forms of each candidate function model are shown in Table 1. for index, For driving performance indicators, , , These are the parameters to be optimized for each model.

[0044] Table 1 Candidate function models and their mathematical forms

[0045] To unify the parameter identification framework for various models, reduce the dependence of nonlinear estimation on initial values, and improve the global optimization capability of the parameter optimization process, this embodiment uses WOA (While Optimization of Mapping Functions) to solve for the structural parameters of the mapping function. WOA is a swarm intelligence-based metaheuristic optimization method. Its basic idea is to treat each candidate solution as an "individual whale," and by simulating the bubble-net feeding behavior of humpback whales, it adaptively switches between global exploration and local exploitation to approximate the optimal solution of the objective function. WOA includes three stages: shrinking and surrounding the prey, attacking the prey with the bubble-net, and randomly searching for prey. The specific steps are as follows: S3.3.1 Initialize the whale pod, including: Initialize the candidate function model set and its parameter boundaries; For a candidate function model in the candidate function model set Randomly generate num_whales whales, each whale corresponding to a set of parameter configurations for a candidate function model. ; Since logarithmic models require independent variables to be greater than 0, to avoid calculation failures caused by Ln(0) or Ln(negative numbers), candidate function models requiring logarithmic operations are preprocessed. The specific formula is as follows: ; in: Represent the logarithmic transformation TCR index, express TCR index, It represents the smallest floating-point integer in a computer, used to ensure the stability and validity of numerical calculations.

[0046] S3.3.2, Assess the whale, including: ① Based on the parameter configuration of each whale, a pre-trained model is built. The pre-trained model is trained on the training set of the driving performance index dataset. Each pre-trained model is trained for 10 epochs. The MSE is used as the fitness function to calculate the fitness of each whale, that is, the MSE calculated on the validation set of each pre-trained model after training. The current best whale and its fitness are recorded. ② Update the whale positions (surrounding prey / spiral update / random search), specifically: update the position of each whale according to the update formula of the WOA algorithm, and apply boundary constraints. This means updating to obtain the new parameter configuration; where: Parameter boundaries.

[0047] The specific update formula for the WOA algorithm is as follows: ; in: ; ; ; ; ; ; In the formula, D 1 represents the distance between the optimal position at the current moment and the actual position of the humpback whale; C 1 represents the vector coefficient; This is the optimal position at the current moment; and These are the positions of the humpback whale at the current moment and the next moment, respectively. It is a vector that changes continuously with the iteration process; As a variable, it decreases linearly from 2 to 0; A random number within the range [0,1]; This represents the maximum number of iterations. This represents the current iteration number. This represents the distance between the humpback whale and its prey at the current moment. A random number within the range [-1, 1]; The constant used to define the shape of the helix is ​​set to 1. During the random prey search phase, when When the value is not less than 1, the model expands the search range by randomly selecting a location to achieve a global search. for The absolute value of is a key criterion controlling global exploration and local development; its calculation formula is: ; ; In the formula, This represents the current random position of the humpback whale; This represents the distance between the optimal position at the current moment and the position of the humpback whale. These are the coefficients of a random vector.

[0048] ③ Repeat steps ① and ② until the fitness converges, or until the maximum number of iterations is reached (limited by the code), and output the optimal parameters. Calculate the predicted value ; This embodiment, based on the regression parameter estimation principle of WOA, uniformly describes regression parameter estimation as an optimization problem of minimizing the sum of squared residuals. The model prediction value is defined as... The residual is: ; Using the sum of squared residuals as the objective function : ; In the formula, the linear model parameter vector Power function model parameter vector WOA performs global optimization of the objective function through collaborative search, outputting a result that optimizes the objective function. The smallest parameter is taken as the fitting result.

[0049] To objectively and comprehensively evaluate the fitting effect of each candidate model and avoid the one-sidedness of evaluation by a single indicator, the coefficient of determination, root mean square error, and mean absolute error are selected as the core evaluation indicators. Each indicator quantifies the model fitting accuracy from different dimensions, forming a complementary evaluation system.

[0050] Coefficient of determination The ability of a model to explain the inherent relationships in the original data is a core indicator for measuring the goodness of fit of the model; the closer it is to 1, the better the model's performance. The stronger the explanatory power of the relationship with driving performance indicators, the better the fit. The calculation formula is as follows: ; In the formula, SSE It is the sum of squared residuals, i.e. , = ; TSS It is the total sum of squares, that is .

[0051] The root mean square error (RMSE) is obtained by taking the square root of the mean square error, eliminating the dimensional amplification effect of squaring. Its dimensions are completely consistent with the original driving performance indicators, and it can directly quantify the dimensional average deviation between the model's predicted values ​​and the measured values. This meets the need for extreme deviation control in driving safety research. The smaller the index value, the smaller the model's average prediction deviation. The calculation formula is: ; Mean absolute error ( MAE The index represents the average absolute deviation between the model's predicted values ​​and the measured values. Using absolute error calculation avoids the cancellation of positive and negative deviations and is insensitive to outliers, robustly reflecting the overall fit stability of the model. A smaller index value indicates stronger model fit stability and less susceptibility to extreme values. The calculation formula is as follows: ; A weighted comprehensive scoring method was used to comprehensively screen the candidate models that had completed parameter optimization, and finally determine the final model. The optimal quantitative mapping model between indicators and driving performance indicators. First, Equation 1-2 is used. Standard normalization is performed using Equation 2. RMSE and MAE Perform positive normalization. Then, assign differentiated weights to the evaluation indicators based on research needs, and set... With a weight of 0.6, the focus is on highlighting the core role of goodness of fit in model selection. RMSE and MAE All weights were set to 0.2 to balance the magnitude of the model's prediction bias and its fitting stability.

[0052] Formula 1 is: ; in: The maximum coefficient of determination for each candidate model. The minimum coefficient of determination for each candidate model; Formula 2 is: ; ; Where: is the normalized root mean square error or mean absolute error. The maximum root mean square error of each candidate model. The minimum root mean square error of each candidate model is given. The maximum mean absolute error of each candidate model. This represents the minimum mean absolute error of each candidate model.

[0053] S3.3.3 Constructing Optimal Parameters The corresponding optimal candidate function model is identified, and its fit index is calculated, including the coefficient of determination. Root mean square error RMSE and mean absolute error MAE ; S3.3.4 Normalize the fitting index and calculate the comprehensive score based on the normalized fitting index; Overall score The specific calculation formula is as follows: ; in: To determine the coefficient weights, The root mean square error weight is used. The average absolute error weighting, The normalized coefficient of determination This is the normalized root mean square error. The normalized mean absolute error; In this embodiment, the comprehensive score The formula is: .

[0054] S3.3.4 Repeat S3.3.1 to S3.3.3 to traverse all candidate function models and obtain the comprehensive score corresponding to different candidate function models; S3.3.5 Select the candidate function model with the highest comprehensive score as the multidimensional mapping model.

[0055] In this embodiment, the specific expression of the multidimensional mapping model is as follows: ; in: This is a number representing the structural damping ratio. For the first Derailment coefficient under a structural damping ratio For the first Wheel load reduction rate under structural damping ratio For the first Lateral horizontal force under a structural damping ratio For the first Lateral acceleration of the vehicle body under a given structural damping ratio For the first The Spelling index under structural damping ratio , and These are the three model parameter values ​​corresponding to the derailment coefficient. , and These are the three model parameter values ​​corresponding to the wheel load reduction rate. , and These are the three model parameter values ​​corresponding to the lateral horizontal force. , and The three model parameter values ​​corresponding to the lateral acceleration of the vehicle body , and These are the three model parameter values ​​corresponding to the Spelling index.

[0056] In this embodiment, under the intermediate vehicle speed of 200 km / h, The parameter values ​​for the mapping model between the indicators and various driving performance indicators are shown in Table 2. A , B , C These correspond to the three parameters of the multidimensional mapping model.

[0057] Table 2 Parameter values ​​of the mapping model between the indicators and various driving performance indicators

[0058] S4: Construct a rapid evaluation model for post-earthquake driving performance based on a 95% guarantee rate using a multidimensional mapping model.

[0059] To meet the requirements for driving safety margin in post-earthquake engineering applications, this embodiment constructs a rapid evaluation model for post-earthquake driving performance based on a 95% guarantee rate.

[0060] S4.1 Calculate the error variance Unbiased estimator: random error variance The error variance reflects the magnitude of the model error. unbiased estimator for: S4.1 Calculate the unbiased estimator of the error variance The specific formula is as follows: ; In the formula, The number of samples; Number the sample; The number of model parameters; Since predicted values ​​are affected not only by the variance of random errors but also by the degree of deviation of the independent variable from the sample mean, a test statistic can be constructed to measure the difference between predicted and true values.

[0061] S4.2, The error variance construction based on the multidimensional mapping model follows a set of degrees of freedom. of The test statistic for the distribution is as follows: ; In the formula, For the first Group samples Sample values ​​of the indicator; For the first Sample values ​​of driving performance indicators in the group sample. for The sample mean of the indicator; yes index variance .

[0062] S4.3. Based on the expression of the test statistic, at the confidence level... Down, The prediction interval can be expressed as: ; In the formula, for One-sided upper quantile of the distribution; These are the two-tailed quantiles of the standard normal distribution; for The predicted value.

[0063] When the number of samples Large enough (in this embodiment) M (30) and prediction points close to the sample mean When the prediction interval is such that it can be approximately simplified to: ; The expression for the S4.4, 95% one-sided guarantee rate curve is: ; in: for index Corresponding driving performance indicators The predicted value; S4.5, Based on the multidimensional mapping model, the 95% one-sided guarantee rate curve is obtained. The indicators and various driving performance indicators are based on a mapping model with a 95% guarantee rate; as shown below: ; In this embodiment, the analysis is conducted using a vehicle speed of 200 km / h as an example, and the relevant results are as follows: Figures 8 to 32 As shown.

[0064] S4.6. Using the weighted comprehensive score WCS and the adaptive function mapping method of whale optimization WOA in S3, the mapping relationship between the mapping model parameters and the train running speed based on the 95% guarantee rate is solved to obtain the rapid evaluation model of post-earthquake train performance.

[0065] Using WCS-WOA to apply a 95% guarantee rate The parameters of the mapping model between the indicators and various train performance indicators are adaptively optimized and solved based on the train speed. Taking the lateral horizontal force of the wheelset as an example, the solution results are as follows: Figure 33 and Figure 34 As shown.

[0066] Depend on Figure 33 and Figure 34 It can be seen that the parameters of the wheelset lateral horizontal force mapping model are significantly correlated with the vehicle speed, and the goodness of fit is close to 1. Based on a 95% guarantee rate... In the mapping model between the indicators and various train performance indicators, the parameters of the mapping models for the remaining train performance indicators all show a significant correlation with train speed. This correlation is obtained using a quadratic polynomial fitting. All are greater than 0.9.

[0067] In this embodiment, the quantitative relationship between the parameters of the mapping model and the driving speed for five different structural damping ratio conditions is listed in Table 3.

[0068] Table 3. Quantitative relationship between the parameters of the mapping model and driving speed.

[0069] S5: Based on the relevant limits of the driving performance indicators in the normative documents and the rapid post-earthquake driving performance evaluation model, solve the speed thresholds corresponding to each driving performance indicator under different structural damping ratios, and take the lowest speed threshold under different structural damping ratios as the post-earthquake driving performance evaluation results of the track-bridge system under different structural damping ratios.

[0070] In this embodiment, WCS-WOA adaptive filtering is used to select the most suitable match. A functional model mapping the relationship between the vehicle's performance indicators and its corresponding parameters was developed, and these parameters were accurately calculated. The derailment coefficient, wheel load reduction rate, wheelset lateral force, and vehicle body lateral acceleration indicators were compared with... The best fit is a univariate linear function model, and the Sperling index is... The power function model provides the best fit.

[0071] Example 2 This embodiment provides a method for post-earthquake operation of high-speed railway bridges under random damping ratios, including: See Figure 35 and Figure 36 Based on the earthquake's impact range, the study area was divided into a post-earthquake operation and maintenance area and a post-earthquake emergency rescue area. The post-earthquake operation and maintenance area refers to remote areas far from urban centers where the earthquake occurred. Its impact is limited to the high-speed railway line itself passing through the area, without involving densely populated areas or emergency rescue needs. In this case, a comprehensive and systematic inspection is required. After completing targeted repairs and verifying that the line meets safe operation standards, operation can be resumed according to the established plan, with the core focus on ensuring the line's traffic capacity; precise determination of train speed thresholds is not necessary. The post-earthquake emergency rescue area refers to densely populated urban areas and surrounding areas where the earthquake occurred. In this case, the high-speed railway... As a core transportation lifeline after the earthquake, facing emergency rescue needs, it is necessary to quickly repair and eliminate major safety hazards on the line to ensure that driving safety and basic comfort meet the established operating limits, thereby efficiently carrying out the transfer of disaster relief materials (such as food, medicine, rescue equipment, etc.) and professional rescue forces (firefighters, medical personnel, armed police, etc.). In this scenario, the restoration and operation of the line must achieve a dynamic balance between safety constraints and transportation efficiency. Through technical means such as accurately calculating driving speed thresholds, scientifically controlling operating speed, and optimizing transportation scheduling plans, the efficiency of disaster relief resource delivery can be maximized, providing key support for the smooth implementation of post-earthquake emergency rescue work.

[0072] A tiered operation plan will be adopted for post-earthquake operation and maintenance areas. Specifically, this involves: adjusting the operation plan based on track dynamic response thresholds and train operation safety control standards. The numerical range of the indicators is divided into three categories of track conditions: slight deterioration, moderate deterioration, and severe deterioration. The track conditions are used as the basis for guiding the maintenance and repair of the line to formulate a graded operation plan. The post-earthquake operation and maintenance area is operated in accordance with the formulated graded operation plan. The tiered operation plan is as follows: A track strength of ≤0.4 indicates a slightly deteriorated condition. Under this condition, the existing conventional operating mode is adopted, with the first set threshold serving as the current operating threshold. The track geometry is good, residual deformation is within the excellent range, and all operating performance indicators meet the specified limits, allowing trains to pass smoothly and comfortably. Therefore, for the first-level standard track condition, the conventional operating mode is adopted, focusing on daily maintenance and conducting periodic track condition inspections, with a focus on monitoring the connection stability between fasteners and track slabs to maintain the basic conditions for track smoothness.

[0073] 0.4 < A value ≤0.9 indicates moderate degradation. Scheduled maintenance work should be carried out, and the degradation should be addressed within the specified timeframe. The indicators have recovered to the range of slightly deteriorated state, with the second set threshold as the current operating threshold. The track geometry has deteriorated to a certain extent, with minor irregularities in some areas. Although these do not exceed safety limits, they can easily lead to increased vehicle vibration and decreased comfort. If left untreated for a long period, the condition may continue to worsen, requiring trains to operate at reduced speeds. Emergency repairs can be carried out according to the line's operational needs. Therefore, for track conditions meeting the secondary standard, they are included in the key monitoring scope. Inspections are conducted to locate concentrated irregularities and planned maintenance operations are arranged. Through targeted repair plans, these issues will be addressed within the specified timeframe. The value is restored to the first-level standard range. In this embodiment, the specified time limit is determined based on the actual situation.

[0074] 0.9 < A reading of ≤4 indicates a severely deteriorated condition. In such cases, the emergency response plan will be activated, speed limits will be issued or the line will be closed, and a professional repair team with specialized equipment will be dispatched to the site for repairs until... Once the value returns to a safe range and the wheel-rail dynamic response verification shows no abnormalities, normal line operation will be gradually restored, with the third set threshold serving as the current operating threshold. If the track geometry is severely deteriorated, with significant residual deformation or abrupt irregularities, the risk of wheel-rail contact increases dramatically, directly threatening train safety, and immediate remedial measures are required. Therefore, if the track condition reaches Level III, the emergency response plan will be immediately activated, speed limits will be issued or the line will be closed, and a professional repair team with specialized equipment will be dispatched to the site to conduct large-scale repairs. A review is required after the repairs are completed. Once the value returned to a safe range and the wheel-rail dynamic response verification showed no abnormalities, the line gradually resumed normal operation.

[0075] Among them, the first set threshold is greater than the second set threshold, which is greater than the third set threshold; the first set threshold, the second set threshold, and the third set threshold are respectively: 350km / h -1 250km / h -1 and 100km / h -1。

[0076] In this embodiment The graded intervals and their corresponding post-earthquake driving speed thresholds are listed in Table 4.

[0077] Table 4 Classification and post-earthquake driving speed threshold

[0078] To improve The applicability and flexibility of the grading standards need to be dynamically adjusted based on the actual operating conditions of the lines: for high-speed rail trunk lines with high transportation demand and strict safety standards, the threshold of the third-level standard can be appropriately tightened to strengthen track condition control; for high-speed rail lines that also serve conventional speeds, the threshold of the third-level standard can be appropriately relaxed to balance operating efficiency and maintenance costs. Meanwhile, under special climatic conditions (such as the frost heave period in winter or the roadbed softening period in the rainy season), the thresholds at each level can be temporarily tightened to provide early warning of track condition deterioration risks, ensuring that the grading standards always adapt to actual operating scenarios.

[0079] Based on the post-earthquake driving performance assessment results mentioned above, post-earthquake driving will be conducted in the emergency rescue area, specifically as follows: ① The performance indicators of vehicles on bridges under seismic loads are divided into driving safety indicators and driving comfort indicators. The driving safety indicators are used as the key control indicators for post-disaster material transportation. The driving safety indicators include the derailment coefficient, wheel load reduction rate, and wheel set lateral horizontal force. The driving comfort indicators are used as the key control indicators for post-disaster personnel transportation. The driving comfort indicators include the vehicle body lateral acceleration and the Spearing index.

[0080] ② Under the premise of meeting the relevant limit requirements of the "High-Speed ​​Railway Design Code", according to different The post-earthquake driving performance evaluation results corresponding to the indicators are fitted with functions to obtain the speed threshold expressions for driving safety indicators and driving comfort indicators under different structural damping ratios: ; in: The speed thresholds corresponding to each driving safety indicator are determined by selecting the minimum speed threshold for each indicator. , and These are the three fitting parameters for the speed threshold expression corresponding to the driving safety index; The speed threshold corresponding to each driving comfort index is determined by taking the minimum speed threshold corresponding to each driving comfort index. 、 and These are the three fitting parameters for the speed threshold expression corresponding to the driving comfort index; In this embodiment, the parameter values ​​of the velocity threshold expression under different structural damping ratios are shown in Table 5.

[0081] Table 5. Parameter values ​​for the velocity threshold calculation formula

[0082] ③ Fit the parameters of the velocity threshold expression to the structural damping ratio to obtain the corresponding fitting curve, see [link / reference]. Figures 37 to 42 .

[0083] This embodiment visualizes the velocity threshold curves under different structural damping ratios, such as... Figure 43 and Figure 44 As shown in the figure, the horizontal axis is The index and the vertical axis represent the speed threshold. V It can intuitively reflect the speed threshold distribution law corresponding to the driving safety and comfort after the earthquake under different structural damping ratios.

[0084] Depend on Figure 43 and Figure 44 It is evident that the structural damping ratio has a significant impact on both the post-earthquake driving safety and comfort speed thresholds. As the structural damping ratio increases, the safety speed threshold generally decreases, while the comfort speed threshold generally increases. The influence of the structural damping ratio on the safety speed threshold has… Level differences, in low The range has a relatively small impact, such as At a damping ratio of 2.5, the safety speed threshold under a 2% damping ratio condition is only about 1.8% lower than that under a 30% damping ratio condition. However, with... As the value increases, this effect is significantly amplified, and the safety velocity threshold of high-damping-ratio structures decreases more noticeably, such as... When the damping ratio is 4, the safety speed threshold of the track-bridge system under the 30% damping ratio condition is reduced by approximately 7% compared to the 2% damping ratio condition. This is because the high damping ratio... For more severe track irregularities, the overall operating speed threshold is lower, making safety performance indicators more sensitive to changes in damping ratio. Conversely, the structural damping ratio has a lower impact on the comfort speed threshold. The segments are more distinct, such as At a damping ratio of 2.5, the comfort speed threshold under a 2% damping ratio is approximately 4% lower than that under a 30% damping ratio, because the lower damping ratio... The speed threshold for inter-section driving is relatively high, and the comfort performance indicators are more sensitive to changes in vibration, with the damping ratio having a more significant impact; while when When the damping ratio is increased to 4, the comfort speed threshold under the 2% damping ratio condition is only reduced by about 1.6% compared to the 30% damping ratio condition. This is due to the higher... The speed threshold for inter-section train operation has been reduced to a low level, weakening the impact of damping ratio on the comfort speed threshold. Furthermore, vibration-induced track irregularities have a significant controlling effect on train performance; the more severe the track irregularities, the lower the permissible speed threshold. Moreover, comfort performance indicators are significantly more sensitive to vibration than safety performance indicators, a characteristic directly reflected in the differences in speed thresholds. When the damping ratio is 4, the minimum comfort speed threshold under full damping ratio conditions decreases by approximately 53% compared to the minimum safety speed threshold.

[0085] ④ Determine the speed threshold under different structural damping ratios based on the fitted curves. Use the speed threshold corresponding to the driving safety index to limit the speed of post-earthquake vehicles transporting disaster relief materials, and use the speed threshold corresponding to the driving comfort index to limit the speed of post-earthquake vehicles transporting disaster relief personnel.

[0086] This embodiment addresses the post-earthquake operational recovery needs of high-speed railway track-bridge systems, summarizing two typical application scenarios: post-earthquake operation and emergency rescue. Based on these scenarios, it establishes [a framework / system] for each. The track grading operation plan and the safety-oriented train speed limit operation plan provide important technical support for the rapid restoration of track operation and the efficient delivery of disaster relief resources after the earthquake.

[0087] Example 3: This embodiment provides a readable storage medium storing computer program instructions, which, when executed by a processor, implement the post-earthquake driving performance evaluation method described above.

[0088] It should be noted that the device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Furthermore, in the accompanying drawings of the device embodiments provided by this invention, the connection relationships between modules indicate that they have communication connections, which can be specifically implemented as one or more communication buses or signal lines. Those skilled in the art can understand and implement this without any creative effort.

[0089] Example 4: This embodiment also includes an electronic device, comprising: at least one processor, at least one memory, and computer program instructions stored in the memory, wherein the computer program instructions are executed by the processor to perform the post-earthquake driving performance evaluation method as described above.

[0090] For example, the computer program may be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention. The one or more modules / units may be a series of computer program instruction segments capable of performing a specific function, which describe the execution process of the computer program in the electronic device.

[0091] The electronic device can be a mobile phone, desktop computer, laptop, handheld computer, cloud server, or other computing device. The electronic device may include, but is not limited to, processors and memory. For example, the electronic device may also include input / output devices, network access devices, buses, etc.

[0092] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor. The processor is the control center of the electronic device, connecting all parts of the electronic device via various interfaces and lines.

[0093] The memory can be used to store the computer program and / or modules. The processor implements the computer program by running or executing the computer program and / or modules stored in the memory, and by calling data stored in the memory. The memory may mainly include a program storage area and a data storage area. The program storage area may store the operating system, at least one application program required for a function (such as sound playback function, image playback function, etc.), etc.; the data storage area may store data created according to the use of the mobile phone (such as audio data, phonebook, etc.). In addition, the memory may include high-speed random access memory, and may also include non-volatile memory, such as hard disk, memory, plug-in hard disk, smart media card (SMC), secure digital card (SD) card, flash card, at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0094] If the modules / units integrated in the electronic device are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of the present invention can also be implemented by a computer program instructing related hardware. The computer program can be stored in a readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0095] The above description is only a preferred embodiment of the present invention and does not limit the scope of the present invention. All equivalent structural transformations made under the inventive concept of the present invention using the contents of the present invention specification and drawings, or direct / indirect applications in other related technical fields, are included within the protection scope of the present invention.

Claims

1. A method for evaluating post-earthquake vehicle performance, characterized in that, Includes the following steps: S1: Taking a certain track-bridge system as the research object, a numerical model of a high-speed railway track-bridge system with stochastic structural damping ratio is established based on the research object. S2: Calculation of post-earthquake residual irregularities based on a numerical model of a high-speed railway track-bridge system, introducing the root mean square rate of change of track irregularities. Indicators quantify the level of residual track irregularities after the earthquake; S3: An adaptive function mapping method based on the weighted comprehensive score (WCS) and whale-optimized WOA is used to fit the quantitative relationship between the root mean square rate of change of track irregularities and train performance indicators, obtaining information on structural damping ratio and root mean square rate of change of track irregularities. A multidimensional mapping model of vehicle speed and driving performance; S4: Construct a rapid evaluation model for post-earthquake driving performance based on a 95% guarantee rate using a multi-dimensional mapping model; S5: Based on the relevant limits of the driving performance indicators in the normative documents and the rapid post-earthquake driving performance evaluation model, solve the speed thresholds corresponding to each driving performance indicator under different structural damping ratios, and take the lowest speed threshold under different structural damping ratios as the post-earthquake driving performance evaluation results of the track-bridge system under different structural damping ratios.

2. The method for evaluating post-earthquake vehicle performance according to claim 1, characterized in that, S2 includes: S2.

1. Use the MR method to select N uniformly distributed ground motions from the PEER strong earthquake database; S2.2 Input the selected seismic motion into the numerical model of the high-speed railway track-bridge system to calculate the seismic-induced track residual irregularities of the track-bridge system under different structural damping ratios. S2.3 Calculate the root mean square rate of change of track irregularities corresponding to each earthquake-induced track residual irregularity. The specific formula is as follows: ； in: This represents the total mileage of the rails. Mileage location, The earthquake caused residual irregularities in the track.

3. The method for evaluating post-earthquake vehicle performance according to claim 2, characterized in that, S3 includes: S3.

1. Based on the train sub-model and the numerical model of the high-speed railway track-bridge system, a coupled model of the train-track-bridge system is built; S3.

2. Using the seismic track residual irregularities calculated in S2.2 as the external excitation input of the train-track-bridge system coupling model, the system dynamic response analysis under different vehicle speed conditions is carried out to obtain the vehicle performance index dataset, which includes the derailment coefficient, wheel load reduction rate, wheel set lateral horizontal force, vehicle body lateral acceleration and Spearing index. S3.

3. Using different typical function models as candidate function models, the structural parameters of each candidate function model are solved using Whale Optimization (WOA) based on the driving performance index dataset. A multi-evaluation index weighted comprehensive scoring mechanism is then used to automatically select the candidate function model with the highest comprehensive score, taking into account vehicle speed and damping ratio. A multidimensional mapping model between driving performance indicators and driving performance indicators.

4. The method for evaluating post-earthquake vehicle performance according to claim 3, characterized in that, S3.3 includes: S3.3.1 Initialize the whale pod, including: Initialize the candidate function model set and its parameter boundaries; For a candidate function model in the candidate function model set Randomly generate num_whales whales, each whale corresponding to a set of parameter configurations for a candidate function model. ;in: Number the candidate function models; The candidate function model requiring logarithmic operations is preprocessed using the following formula: ； in: Represent the logarithmic transformation index, express index, Represents the smallest floating-point integer in a computer. S3.3.2, Assess the whale, including: ① Based on the parameter configuration of each whale, a pre-trained model is built. The pre-trained model is trained on the training set of the driving performance index dataset. Each pre-trained model is trained for 10 epochs. The MSE is used as the fitness function to calculate the fitness of each whale, that is, the MSE calculated on the validation set of each pre-trained model after training. The current best whale and its fitness are recorded. ② Update the whale positions, specifically: update the position of each whale according to the update formula of the WOA algorithm, and apply boundary constraints. This means updating to obtain the new parameter configuration; where: For model parameter vectors, For parameter boundaries; ③ Repeat steps ① and ② until the fitness converges, or until the maximum number of iterations is reached (limited by the code), and output the optimal parameters. Calculate the predicted value ; S3.3.3 Constructing Optimal Parameters The corresponding optimal candidate function model is identified, and its fit index is calculated, including the coefficient of determination. Root mean square error RMSE and mean absolute error MAE ; S3.3.4 Normalize the fitting index and calculate the comprehensive score based on the normalized fitting index; S3.3.4 Repeat S3.3.1 to S3.3.3 to traverse all candidate function models and obtain the comprehensive score corresponding to different candidate function models; S3.3.5 Select the candidate function model with the highest comprehensive score as the multidimensional mapping model.

5. The method for evaluating post-earthquake vehicle performance according to claim 4, characterized in that, Overall score The specific calculation formula is as follows: ； in: To determine the coefficient weights, The root mean square error weight is used. The average absolute error weighting, The normalized coefficient of determination This is the normalized root mean square error. The normalized mean absolute error; The expression for the multidimensional mapping model is as follows: ； in: This is a number representing the structural damping ratio. For the first Derailment coefficient under a structural damping ratio For the first Wheel load reduction rate under structural damping ratio For the first Lateral horizontal force under a structural damping ratio For the first Lateral acceleration of the vehicle body under a given structural damping ratio For the first The Spelling index under structural damping ratio , and These are the three model parameter values ​​corresponding to the derailment coefficient. , and These are the three model parameter values ​​corresponding to the wheel load reduction rate. , and These are the three model parameter values ​​corresponding to the lateral horizontal force. , and These are the three model parameter values ​​corresponding to the lateral acceleration of the vehicle body. , and These are the three model parameter values ​​corresponding to the Spelling index.

6. The method for evaluating post-earthquake vehicle performance according to any one of claims 1-5, characterized in that, S4 includes: S4.1 Calculate the unbiased estimator of the error variance The specific formula is as follows: ； In the formula, The number of samples; Number the sample; The number of model parameters; S4.2, The error variance construction based on the multidimensional mapping model follows a set of degrees of freedom. of The test statistic for the distribution is as follows: ； In the formula, For the first Group samples Sample values ​​of the indicator; For the first Sample values ​​of driving performance indicators in the group sample. for The sample mean of the indicator; yes index variance ; S4.3, Based on the test statistic at the confidence level Make a decision The prediction interval is expressed as follows: ； In the formula, for One-sided upper quantile of the distribution; These are the two-tailed quantiles of the standard normal distribution; for The predicted value; S4.4 Expression for determining the 95% one-sided guarantee rate curve based on the prediction interval The details are as follows: ； in: for index Corresponding driving performance indicators The predicted value; S4.5, Based on the multidimensional mapping model, the 95% one-sided guarantee rate curve is obtained. The indicators and various driving performance indicators are based on a mapping model with a 95% guarantee rate; S4.

6. Using the weighted comprehensive score WCS and the adaptive function mapping method of whale optimization WOA in S3, the mapping relationship between the mapping model parameters and the train running speed based on the 95% guarantee rate is solved to obtain the rapid evaluation model of post-earthquake train performance.

7. A post-earthquake vehicle operation method, characterized in that, include: Based on the extent of the earthquake's impact, the study area was divided into a post-earthquake operation and maintenance area and a post-earthquake emergency rescue area. A tiered operation plan will be adopted for post-earthquake operation and maintenance in the affected areas. Specifically, this involves tiering the operation based on track dynamic response thresholds and train safety control standards. The numerical range of the indicators is divided into three categories of track conditions: slight deterioration, moderate deterioration, and severe deterioration. The track conditions are used as the basis for guiding the maintenance and repair of the line to formulate a graded operation plan. The post-earthquake operation and maintenance area is operated in accordance with the formulated graded operation plan. The post-earthquake driving performance evaluation results obtained based on the post-earthquake driving performance evaluation method as described in any one of claims 1 to 6 are used to conduct post-earthquake driving in the post-earthquake emergency rescue area.

8. The post-earthquake vehicle operation method according to claim 7, characterized in that, The tiered operation plan is as follows: When the value is ≤0.4, it is considered a slightly deteriorated state. The existing conventional operation mode is adopted, and the first set threshold is used as the driving threshold for the current state. 0.4 < A value ≤0.9 indicates moderate degradation. Scheduled maintenance work should be carried out, and the degradation should be addressed within the specified timeframe. The indicator recovers to the range of slightly deteriorated state, and the driving threshold of the current state is set as the second set threshold. 0.9 < A reading of ≤4 indicates a severely deteriorated condition. In such cases, the emergency response plan will be activated, speed limits will be issued or the line will be closed, and a professional repair team with specialized equipment will be dispatched to the site for repairs until... Once the value falls back to a safe range and the wheel-rail dynamic response verification shows no abnormalities, the line will gradually resume normal operation, with the third set threshold as the current operating threshold. Among them, the first set threshold is greater than the second set threshold, which is greater than the third set threshold; The post-earthquake driving performance assessment results obtained based on the aforementioned post-earthquake driving performance assessment method are used to conduct post-earthquake driving operations in the post-earthquake emergency rescue area, specifically: ① The performance indicators of vehicles on bridges under seismic loading are divided into driving safety indicators and driving comfort indicators. Driving safety indicators include derailment coefficient, wheel load reduction rate and wheel set lateral horizontal force; driving comfort indicators include vehicle body lateral acceleration and Spearing index. ② Under the premise of meeting the relevant limit requirements of the design specification documents, according to different The post-earthquake driving performance evaluation results corresponding to the indicators are fitted with functions to obtain the speed threshold expressions for driving safety indicators and driving comfort indicators under different structural damping ratios: ； in: The speed threshold corresponding to the driving safety index. , and These are the three fitting parameters for the speed threshold expression corresponding to the driving safety index; The speed threshold corresponding to the driving comfort index. 、 and These are the three fitting parameters for the speed threshold expression corresponding to the driving comfort index; ③ Fit the parameters of the velocity threshold expression with the structural damping ratio to obtain the corresponding fitting curve; ④ Determine the speed threshold under different structural damping ratios based on the fitted curves. Use the speed threshold corresponding to the driving safety index to limit the speed of post-earthquake vehicles transporting disaster relief materials, and use the speed threshold corresponding to the driving comfort index to limit the speed of post-earthquake vehicles transporting disaster relief personnel.

9. A readable storage medium, characterized in that, It stores computer program instructions, which, when executed by a processor, implement the post-earthquake driving performance evaluation method as described in any one of claims 1 to 6.

10. An electronic device, characterized in that, include: The method for evaluating post-earthquake driving performance as described in any one of claims 1 to 6 includes at least one processor, at least one memory, and computer program instructions stored in the memory, which are executed by the processor when the computer program instructions are executed.

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