Seamless track key influence factor identification method considering multi-source uncertainty

Abstract

The invention relates to the technical field of railway engineering reliability analysis, and particularly discloses a seamless track key influence factor identification method considering multi-source uncertainty, and the method comprises the steps: firstly, constructing an initial factor library and a parameter set based on field and literature data; secondly, a Latin hypercube sampling (LHS) technology is adopted to generate samples in an uncertain parameter space, and an input-response data set is obtained through parametric simulation; secondly, training a high-precision efficient proxy model based on simulation data to replace an original physical model; and finally, implementing Monte Carlo simulation (MCS) based on the agent model, and completing system probability reliability evaluation and global sensitivity analysis. According to the method, the influence of multiple parameters and the coupling effect thereof on the service performance of the seamless track can be evaluated simultaneously in single simulation, the analysis efficiency is remarkably improved, and the method is suitable for reliability analysis and optimization design of the seamless track in a complex environment.

Description

Technical Field

[0001] This invention relates to the field of railway engineering reliability analysis technology, specifically to a method for identifying key influencing factors of seamless railway lines that considers multi-source uncertainties. Background Technology

[0002] Seamless railway tracks are widely used in railway engineering due to their structural continuity and integrity, especially in complex service environments such as high-pier, long-span bridges and bridge-tunnel transition sections. However, their service performance evolution is affected by multiple coupled uncertainties such as temperature load, structural parameters, and foundation stiffness, posing challenges to stability and safety analysis.

[0003] Existing methods for identifying influencing factors are mostly based on single-factor sensitivity analysis, neglecting the mutual coupling between parameters and failing to accurately reflect the impact of each factor on the service performance of seamless railway tracks. Furthermore, for highly nonlinear railway structures with low failure probabilities (such as seamless tracks on high-pier, long-span bridges), traditional methods require repeated calls to high-precision finite element models, resulting in high computational costs and low efficiency, making them unsuitable for rapid evaluation. First- or second-order reliability methods also have limitations in accuracy and applicability. Therefore, there is an urgent need to develop a method for identifying key influencing factors that can balance multi-factor uncertainty, computational efficiency, and accuracy. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a method for identifying key influencing factors of seamless lines that considers multi-source uncertainties, thus solving the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for identifying key influencing factors of seamless circuits considering multi-source uncertainties, comprising the following steps: Step S1: Integrate data from field surveys, experiments, and literature research to establish an initial database of influencing factors on the performance of seamless circuits and its corresponding set of key parameters (including engineering and environmental parameters). Quantify the uncertainty characteristics of system parameters by establishing a parameter statistical distribution model using multi-source data. Step S2: Using Latin hypercube sampling (LHS) technology, a representative training sample set is generated in the multidimensional parameter space defined by the parameter statistical distribution model described in step S1; Step S3: Select sample points from the training sample set generated in step S2, construct a parametric finite element model of the high-pier long-span bridge and the seamless track of the bridge-tunnel transition section based on the sample points, and perform batch structural response simulation calculations. Step S4: Based on the structural response calculation results obtained in step S3, train the multilayer perceptron surrogate model, and ensure that the prediction accuracy of the multilayer perceptron surrogate model meets the preset requirements through cross-validation. Step S5: Using the multilayer perceptron proxy model trained in step S4, conduct probabilistic reliability assessment and global sensitivity analysis of the seamless track in the high-pier long-span bridge and bridge-tunnel transition section, identify the core control parameters affecting the service status of the seamless track, and analyze the coupling mechanism of key parameters and their quantitative contribution to system performance.

[0006] In step S1, parameter uncertainty quantification is achieved through the following steps: Step S1.1: Collect multi-source reliability data: Integrate on-site measured data, indoor physical test data, and literature research data to construct an initial influencing factor library and its corresponding key parameter set; Step S1.2, Probability Distribution Construction and Calibration: Based on the initial influencing factor library and its corresponding key parameter set, the probability density function of each random variable is established and the goodness of fit is tested using a parametric statistical distribution model or a non-parametric kernel density estimation method. Among them, the nonlinear coupling mechanism between multiple parameters is established by using the non-uniform rational B-spline (NURBS) interpolation algorithm to establish a parameter statistical distribution model and obtain the correlation between parameters.

[0007] Preferably, literature review and experimental testing (including indoor and field tests) are conducted, using common parametric statistical distribution models or nonparametric kernel density estimation (KDE) methods to establish the probability density functions of each random variable and perform goodness-of-fit tests. The probability density function of kernel density estimation can be expressed by the following formula:

[0008] in, f (x) is a point x The probability density at that location; n This refers to the number of samples, i.e., the number of data points. h This is the bandwidth parameter (or smoothing parameter), which controls the width of the kernel and affects the smoothness of the estimation. K ( u The kernel function is typically a symmetric, unimodal function (such as a Gaussian kernel). x i ( i = 1, 2, …, n Let be each point in the data. There are many commonly used kernel functions, the most common being the Gaussian kernel, whose formula is:

[0009] A multi-parameter coupled model (parameter statistical distribution model) is established using the Non-Uniform Rational B-Splines (NURBS) interpolation algorithm to reveal the nonlinear coupling mechanism between parameters and obtain the correlation between parameters. NURBS, as a parametric geometric modeling technique, is mathematically expressed as follows:

[0010] In the formula, P i,j As control points, w i,j As a weighting factor, N i,p ( u )and N j,q ( v ) are respectively p Second and q The method introduces a B-spline basis function. U ={ u , …, u m+p+1}and V = { v 0,…, v m+p+1 Construct a bivariate parameter space and use piecewise rational polynomials to achieve a continuous and smooth mapping of multi-parameter coupling relationships.

[0011] Preferably, the random variable includes ambient temperature. T Rail temperature - air temperature difference △ T a-t Locked rail temperature attenuation △ T L Initial non-uniformity vector f 0. Initial uneven chord length l 0. Change in lateral resistance of track bed α ksy Change in longitudinal resistance of track bed α ksx Change in lateral resistance of fasteners α kry Change in longitudinal resistance of fasteners α krx Torque variation of track bed fasteners α krr Rail wear W Track structure failure F track Train loading frequency f t And the temperature difference in the bridge structure.

[0012] Preferably, the specific steps include: In the multidimensional parameter space defined by the parameter statistical distribution model described in step S1, a spatial uniform coverage sampling strategy based on Latin hypercube sampling (LHS) is executed to generate a training sample set for the input variables, providing a data foundation for subsequent parametric finite element modeling and surrogate model training. LHS improves the uniformity and representativeness of samples in high-dimensional space by dividing the multidimensional parameter space into equally probable subdomains and forcing unique sampling within each subdomain. This significantly reduces redundant computations in traditional Monte Carlo sampling, resulting in a high-fidelity and high-efficiency training sample library.

[0013] Preferably, in step S3, based on the training sample set constructed in step S2, the parametric modeling of the high-pier long-span bridge and the seamless track of the bridge-tunnel transition section considering the coupling of multiple factors is realized by using MATLAB and ANSYS joint simulation technology, the deterministic mechanical simulation analysis of the seamless track system is carried out, and a dataset for surrogate model training is generated.

[0014] Preferably, in step S4, based on the input variable training sample set generated in step S2 and its corresponding deterministic simulation response results from step S3, a nonlinear mapping surrogate model from the input parameter space to the output response space is established using a multilayer perceptron (MLP). During model training, the LeakyReLU activation function and the adaptive moment estimation algorithm (Adam) are applied, and the mean squared error (MSE) is minimized using gradient descent to optimize the network weights. The k-fold cross-validation method is used to evaluate the generalization ability of the surrogate model, and the model is considered to have converged when the prediction error on the validation set is lower than a preset accuracy threshold.

[0015] Preferably, step S5 specifically includes the following: Step S5.1: Based on the surrogate model trained in step S4, use Monte Carlo simulation (MCS) to generate 107 sets of input parameter samples and predict the corresponding structural response values ​​in batches. Step S5.2, Probabilistic Reliability Assessment: By calculating the mean shift index (MSI) of each parameter under normal and critical conditions, the direction and significance level of each parameter's effect on the service performance of the seamless line are preliminarily identified. Step S5.3, Quantitative Assessment: The Global Failure Sensitivity Index (GFSI) is used to quantify the correlation between changes in the distribution of key parameters and the evolution of system service performance, and to analyze the dominant factors in the multi-parameter coupling effect.

[0016] Preferably, in step S5.2, the mean offset... F MSI Expressed as follows:

[0017] in, and For variables Xi The mean of the corresponding failed samples and unconditional samples, and variable Xi The standard deviations of the corresponding failed samples and unconditional samples. Symbolic representation of variables Xi The direction of the effect on the service performance of seamless circuits, and the magnitude of the value, indicate the significance of the influence.

[0018] Preferably, in step S5.3, the Global Failure Sensitivity Index (GFSI) incorporates the concept of relative entropy from information theory. It quantifies the variation characteristics of the probability density function of influencing factors within the sample domain by calculating the Kullback-Leibler divergence between the failure sample probability distribution and the initial unconditional sample probability distribution. For each considered variable... Xi ( i = 1,…, n Its KL divergence can be denoted as:

[0019] In the formula, xj ( j = 1,…, m ) represents the discrete points of the variable; For variables Xi The probability density function corresponding to the failed sample. For variables Xi This corresponds to the initial unconditional probability density function. Comparable sensitivity measures are obtained through normalization. :

[0020] Normalization is introduced to improve the comparability and generalization ability of sensitivity analysis results, and a sign function is used to determine the direction of the influence of variables on structural performance, thereby achieving efficient and accurate identification of key influencing factors of seamless circuits.

[0021] The beneficial effects of this invention are: 1) This invention breaks through the limitations of traditional single-factor sensitivity analysis by integrating the coupling mechanism of multi-dimensional environmental parameters and engineering variables, and accurately characterizes the key influencing factors of seamless line service performance under complex service conditions.

[0022] 2) This invention divides the subdomain into subdomains in a high-dimensional parameter space and uses Latin hypercube (LHS) sampling. The entire response space can be covered with fewer samples. In a single simulation, a multidimensional response surrogate model can be trained in parallel. This avoids the redundant operation of repeating Monte Carlo sampling and training for each performance index in traditional methods, which greatly improves simulation efficiency and saves computing resources.

[0023] 3) This invention introduces a global failure sensitivity index based on Kullback-Leible divergence. By calculating the relative entropy difference between the failure sample distribution and the original sample distribution, it quickly extracts and sorts the global failure sensitivity index of multiple input variables based on the existing surrogate model, efficiently identifying the key influencing factors of system performance evolution. This not only significantly reduces the computational cost, but also provides a quantitative basis for the reliability analysis and optimization design of high-dimensional complex systems. Attached Figure Description

[0024] Figure 1 This is a flowchart of a method for identifying key influencing factors of seamless lines that considers multi-source uncertainties, as described in Example 1. Figure 2 This is a geometric model diagram of the work site in Example 1; Figure 3a The bridge lateral displacement was obtained from the simulation analysis of the training samples in Example 1. Figure 3b The lateral displacement of the rail is obtained from the simulation analysis of the training samples in Example 1; Figure 3c The lateral relative displacement of the beam and rail is obtained from the simulation analysis of the training samples in Example 1; Figure 4 This is a schematic diagram of the mean offset of each uncertainty factor obtained by the method of the present invention in Example 1; Figure 5 The diagram shows the results of key influencing factors for each section (mid-span, beam end, and bridge-tunnel transition section) of the work site calculated using the method of the present invention in Example 1. (a) represents the mid-span, (b) the beam end, and (c) the bridge-tunnel transition section. Detailed Implementation

[0025] 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 some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0026] Example 1: A high-pier, long-span suspension bridge project in a rugged mountainous area of ​​western China Project Background: A high-pier, long-span steel truss suspension bridge in a rugged mountainous area of ​​western China has a main span arrangement of 130m+1060m+90m and a main cable span arrangement of 245m+1060m+270m. The upper level of the bridge is a double-track ballasted railway designed for a speed of 200km / h. Meteorological data shows that the highest rail temperature was +56.5℃, the lowest rail temperature was -4.8℃, and the locked rail temperature was taken as 29±5℃.

[0027] To analyze the mechanical behavior of the seamless track on the bridge and identify key influencing factors, a spatially coupled finite element model of the seamless track system, including a high-pier, long-span suspension bridge and a bridge-tunnel transition section, was established using ANSYS APDL software. The geometric schematic of the model can be found in [reference needed]. Figure 2 The model coordinate system is defined as follows: along the direction of the line... x Direction, perpendicular to the direction of line operation. y Direction, vertically upwards. z Direction. The model includes steel truss, main cable, suspenders, main tower and track structure, and has the following characteristics: (1) it combines the main structure of the bridge with the track structure it supports for joint modeling and mechanical analysis; (2) it fully considers and accurately simulates the nonlinear mechanical characteristics of the longitudinal resistance of the track in the beam-track interaction; (3) it incorporates the large deformation (geometric nonlinear) effect of the bridge structure (especially the main cable); (4) it takes into account the influence of the initial stress of the main cable and suspenders and the sag of the main cable. The concrete and steel used in the model (distinguishing between the steel used for the main cable / suspenders and the steel used for other structures) are all regarded as isotropic linear elastic materials, and their specific material parameters are listed in Table 1 below: Table 1 Bridge structural material parameters ; Based on the established complex nonlinear spatial coupling model, this embodiment employs a method for identifying key influencing factors of seamless lines considering multi-source uncertainties proposed in this invention. The process is as follows: Figure 1 As shown, the key influencing factors of the seamless ballast track on the high-pier, long-span suspension bridge were quantitatively analyzed and identified. The specific steps are as follows: Step 1: Based on the "Design Specification for Seamless Railway Track" (TB 10015—2012), the strength and stability of the seamless track are selected as the core performance indicators for service operation. For this embodiment, the random variables include ambient temperature. T Rail temperature - air temperature difference △ T a-t Locked rail temperature attenuation △ T L Initial non-uniformity vector f 0. Initial uneven chord length l 0. Change in lateral resistance of track bed α ksy Change in longitudinal resistance of track bed αksx Change in lateral resistance of fasteners α kry Change in longitudinal resistance of fasteners α krx Torque variation of track bed fasteners α krr Rail wear W Track structure failure F track Train loading frequency f t and the temperature difference in the bridge structure (the temperature difference between the bridge tower and the bridge deck Δ) T t-p Temperature difference between suspension cables and bridge deck △ T cs-p ).

[0028] Based on field measurement and experimental data, a random variable sample set was constructed to quantify the uncertainty characteristics of the seamless circuit system parameters. The probability density function of each random variable was established (see Table 2) and a goodness-of-fit test was performed.

[0029] Table 2 Random Variable Information ; Step 2: Construct a high-dimensional parameter space based on the key parameter set and its joint probability distribution function. Apply Latin hypercube sampling (LHS) to divide the multidimensional space into 500 hypercube cells with equal probability, ensuring that only one sample point is generated in each cell.

[0030] Step 3: Based on the generated training sample set, parametric modeling and deterministic analysis of the embodiment are performed using the MATLAB-ANSYS co-simulation framework. ANSYS Parametric Design Language (APDL) instructions are dynamically generated using MATLAB topology control scripts to automatically reconstruct geometric configurations, material constitutive models, and boundary constraints. This drives a multiphysics coupled simulation solver (covering temperature field, structural field, and contact nonlinear effects) to accurately capture key mechanical responses such as rail stress distribution and pier displacement. The calculated responses are shown in Figure 3. Finally, the response data is extracted to construct a high-fidelity input-output mapping dataset (X,Y).

[0031] Step 4: Using a high-fidelity input-output mapping dataset (X,Y), a deep neural network surrogate model for the mechanical response of the seamless track in the high-pier, long-span bridge-bridge-tunnel transition section is constructed. This model takes 15-dimensional parameters as input and maps the lateral displacement and axial stress of the rail to dual outputs through a 4-hidden-layer structure and an adaptive LeakyReLU activation function. It is trained using an Adam-Nesterov hybrid optimization strategy and undergoes 10-fold cross-validation to ensure generalization performance. The calculated model evaluation metrics are shown in Table 3. Table 3 Model Evaluation Indicators ; Step 5: 107 sets of input parameter samples were generated using Monte Carlo Simulation (MCS). Based on the surrogate model, the corresponding structural response values ​​were predicted in batches. The mean shift index (MSI) of each parameter under normal and critical conditions was calculated to preliminarily identify the direction and significance level of each parameter's effect on the seamless track's service performance. (Table 4 and...) Figure 4 The mean offset (MSI) of each uncertainty factor is calculated.

[0032] Table 4 Sensitivity Indicators for Various Uncertainty Factors ; Then, using the Global Failure Sensitivity Index (GFSI) based on Kullback-Leibler divergence, the changes in the distribution characteristics of input variables within the sample domain are quantified, thereby identifying parameters that have a key impact on the evolution of system service performance. Figure 5 The key influencing factors on the service performance evolution of seamless lines corresponding to the embodiments are shown in Table 4. Figure 4 and Figure 5 It is evident that the method of this invention demonstrates high accuracy and efficiency in identifying key influencing factors of seamless railway line service performance evolution under complex multi-factor coupling. This invention integrates uncertainty quantification modeling, parametric finite element analysis, high-dimensional surrogate models, and probabilistic reliability assessment techniques to construct an efficient and robust analytical framework, accurately identifying and quantifying the core driving factors of seamless railway line service performance. The method of this invention supports the simultaneous evaluation of the impact of multiple parameters and their coupling effects on seamless railway line service performance in a single simulation, significantly improving analytical efficiency and making it suitable for reliability analysis and optimization design of seamless railway lines under complex environments.

[0033] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0034] The terminology used in the embodiments of this invention is for the purpose of describing particular embodiments only and is not intended to limit the invention. The singular forms “a,” “the,” and “the” as used in the embodiments of this invention and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise.

[0035] It should be understood that the term "and / or" used in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0036] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0037] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for identifying key influencing factors of seamless circuits considering multi-source uncertainties, characterized in that, Includes the following steps: Step S1: Integrate data from field surveys, experiments, and literature research to establish an initial database of influencing factors on the performance of seamless circuits and its corresponding set of key parameters. Quantify the uncertainty characteristics of system parameters by establishing a parameter statistical distribution model using multi-source data. Step S2: Using Latin hypercube sampling (LHS) technology, a representative training sample set is generated in the multidimensional parameter space defined by the parameter statistical distribution model described in step S1. Step S3: Select sample points from the training sample set generated in step S2, construct a parametric finite element model of the high-pier long-span bridge and the seamless track of the bridge-tunnel transition section based on the sample points, and perform batch structural response simulation calculations. Step S4: Based on the structural response calculation results obtained in step S3, train the multilayer perceptron surrogate model, and ensure that the prediction accuracy of the multilayer perceptron surrogate model meets the preset requirements through cross-validation. Step S5: Using the multilayer perceptron proxy model trained in step S4, conduct probabilistic reliability assessment and global sensitivity analysis of the seamless track in the high-pier long-span bridge and bridge-tunnel transition section, identify the core control parameters affecting the service status of the seamless track, and analyze the coupling mechanism of key parameters and their quantitative contribution to system performance.

2. The method for identifying key influencing factors of seamless lines considering multi-source uncertainties according to claim 1, characterized in that: In step S1, parameter uncertainty quantification is achieved through the following steps: Step S1.1: Collect multi-source reliability data: Integrate on-site measured data, indoor physical test data, and literature research data to construct an initial influencing factor library and its corresponding key parameter set; Step S1.2, Probability Distribution Construction and Calibration: Based on the initial influencing factor library and its corresponding key parameter set, the probability density function of each random variable is established and the goodness of fit is tested using a parametric statistical distribution model or a non-parametric kernel density estimation method. Among them, the nonlinear coupling mechanism between multiple parameters is established by using the non-uniform rational B-spline NURBS interpolation algorithm to establish a parameter statistical distribution model and obtain the correlation between parameters.

3. The method for identifying key influencing factors of seamless lines considering multi-source uncertainties according to claim 2, characterized in that: The random variable includes ambient temperature. T Rail temperature - air temperature difference Locking rail temperature attenuation Initial non-uniformity vector Initially uneven chord length Rail wear Change in fastener torque Change in longitudinal resistance of fasteners Change in lateral resistance of fasteners Change in longitudinal resistance of track bed Changes in lateral resistance of track bed Track structure failure Train loading frequency And the temperature difference in the bridge structure.

4. The method for identifying key influencing factors of seamless lines considering multi-source uncertainties according to claim 1, characterized in that: In step S2, the following is specifically included: In the multidimensional parameter space defined by the parameter statistical distribution model in step S1, a spatial uniform coverage sampling strategy based on Latin hypercube sampling (LHS) is executed to generate a training sample set for the input variables.

5. The method for identifying key influencing factors of seamless lines considering multi-source uncertainties according to claim 1, characterized in that: In step S3, based on the training sample set constructed in step S2, the parametric modeling of the high-pier long-span bridge and the seamless track of the bridge-tunnel transition section considering the coupling of multiple factors is realized by using MATLAB and ANSYS joint simulation technology, deterministic mechanical simulation analysis of the seamless track system is carried out, and a dataset for surrogate model training is generated.

6. The method for identifying key influencing factors of seamless lines considering multi-source uncertainties according to claim 1, characterized in that: In step S4, based on the input variable training sample set generated in step S2 and its corresponding deterministic simulation response results in step S3, a nonlinear mapping proxy model between the input parameter space and the output response space is established using a multilayer perceptron (MLP).

7. The method for identifying key influencing factors of seamless lines considering multi-source uncertainties according to claim 1, characterized in that: Step S5 specifically includes: Step S5.1: Based on the surrogate model trained in step S4, use Monte Carlo simulation MCS to generate an input parameter sample set and predict the corresponding structural response values ​​in batches. Step S5.2, Probabilistic Reliability Assessment: By calculating the mean deviation (MSI) of each parameter under normal and critical conditions, the direction and significance level of each parameter's effect on the service performance of the seamless line are preliminarily identified. Step S5.3, Quantitative Assessment: Using the Global Failure Sensitivity Index (GFSI), the correlation between changes in the distribution of key parameters and the evolution of system service performance is quantified, and the dominant factors in the multi-parameter coupling effect are analyzed.

8. The method for identifying key influencing factors of seamless lines considering multi-source uncertainties according to claim 7, characterized in that: The Global Failure Sensitivity Index (GFSI) incorporates the concept of relative entropy from information theory. By calculating the Kullback-Leibler divergence between the probability distribution of failure samples and the probability distribution of initial unconditional samples, it quantifies the variation characteristics of the probability density function of influencing factors within the sample domain. Normalization is introduced to improve the comparability and generalization ability of sensitivity analysis results, and a sign function is used to determine the direction of the influence of variables on structural performance, thereby achieving efficient and accurate identification of key influencing factors of seamless circuits.

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