Parameter design method and system for business class seats of railway train

Abstract

The application discloses a business seat parameter design method and system for a railway train and belongs to the technical field of man-machine engineering of railway vehicles. A multi-element joint probability distribution model of multiple sitting postures of human bodies is established, and seat geometric size parameters are determined based on interval coverage and sensitivity analysis; a weighted body pressure distribution entropy index is constructed by introducing human body part sensitivity weight to optimize cushion surface parameters; a four-degree-of-freedom human body-seat coupled vibration model is established, and vibration damping performance is evaluated in combination with typical train operation conditions; three indexes are taken as objective functions, a multi-objective genetic algorithm is used for collaborative optimization, and an end scheme is output through an approximate ideal solution sorting method. The application solves the problems of low multi-dimensional adaptation rate, ignoring part sensitivity in body pressure evaluation, not considering human-chair coupling effect in vibration evaluation and lacking collaborative optimization of parameters in the prior art, and comprehensive optimal seat parameter design is obtained.

Description

Technical Field

[0001] This invention belongs to the field of railway vehicle equipment ergonomics technology, specifically relating to the design method and system for the parameters of business class seats for railway trains. Background Technology

[0002] With the continuous improvement of my country's high-speed railway network and the increasing demand for travel quality from passengers, the design quality of business class seats on railway trains, as the core carrier of the high-end passenger experience, directly affects passenger comfort and the market competitiveness of railway operations. The parametric design of business class seats involves multiple dimensions, including seat geometry, seat cushion and backrest surface curvature, and vibration reduction performance. It is a typical multi-constraint, multi-objective coupled optimization problem. Seat geometry needs to be determined based on the anthropometric characteristics of the target passenger group; the seat cushion surface curvature needs to balance the uniformity of body pressure distribution and pressure control in key load-bearing areas; and vibration reduction performance needs to consider the multi-frequency vibration excitation generated by the train under different operating conditions. Furthermore, there are mutual coupling and constraints between these design dimensions, thus placing high demands on the systematic and scientific nature of the design methodology.

[0003] In determining seat geometry, current technologies typically refer to percentile data from anthropometric standards, independently taking the extreme value of a percentile for each anthropometric parameter as the basis for seat design. However, there are statistical correlations between various human sitting posture parameters; for example, taller individuals usually have greater seat depth. The method of taking individual percentiles ignores this multidimensional correlation, leading to a situation where individual parameters show high coverage, but the combined coverage of multiple parameters is significantly low. This results in potential inadequate size matching when the seat is designed to accommodate passengers of different body types. Regarding seat cushion surface parameter design, current technologies primarily rely on the single indicator of body pressure distribution uniformity for comfort evaluation. This indicator only reflects the overall dispersion of pressure distribution and does not distinguish the differentiated sensitivity of different parts of the body to contact pressure. When minimizing this indicator is the optimization objective, the algorithm may tend to transfer high pressure from highly sensitive areas such as the ischial tuberosity to less sensitive areas such as the anterior thigh. Although the overall statistical dispersion is reduced, the highly sensitive areas are subjected to excessive concentrated pressure, making it difficult to truly reflect the actual feeling of seating comfort. In evaluating seat vibration comfort, existing methods typically treat the seat as a rigid support, neglecting the frequency response characteristics of the seat's own elastic structure and the coupled vibration effect between the human body and the seat. The vibrations generated by railway trains during operation are multi-directional, broadband, and time-varying. When the natural frequency of the seat falls within the frequency range sensitive to vertical vibrations of the human body, a resonance amplification effect may occur, a risk that traditional methods treating the seat as a rigid body cannot identify.

[0004] Furthermore, in existing seat design processes, geometric dimensions, surface shapes, and vibration damping parameters are typically determined independently at different stages, without adequately considering the coupling effects and interrelationships between these parameters. For example, while increasing the depth of the seat cushion's concavity can improve the uniformity of body pressure distribution, it also alters the contact area between the body and the cushion, as well as the effective load-bearing thickness of the cushion, thus affecting the cushion's equivalent stiffness and vibration transmission performance. The lack of a collaborative optimization method that incorporates multiple parameters into a unified optimization framework and establishes the coupling relationships between them means that while independent optimization may yield good results in one performance dimension, significant degradation occurs in other dimensions, making it difficult to achieve a globally optimal design outcome.

[0005] Therefore, there is an urgent need for a design method and system for railway train business class seats that can comprehensively consider human body size coverage, body pressure distribution comfort, vibration transmission performance, and achieve parameter synergistic optimization. Summary of the Invention

[0006] To address the problems existing in the background art, the present invention provides a method for designing parameters of business class seats for railway trains, comprising the following steps: S1. Joint distribution modeling of human body dimensions: Collect multiple seated human body dimension data of the target passenger group, conduct distribution characteristic tests and correlation analysis on each dimension data, and establish a multivariate joint probability distribution model of multiple dimension parameters. S2. Determination of seat geometric dimension parameters based on interval coverage: Based on the multivariate joint probability distribution model, the joint probability of multiple dimension parameters falling into their respective design adaptation intervals is used as the interval coverage. Under the constraint that the interval coverage is not lower than the preset target value, the interval allocation is adjusted by sensitivity analysis of the adaptation intervals of each parameter to determine the seat geometric dimension parameters. S3. Optimization of seat cushion surface parameters based on body pressure distribution entropy: Establish a parameterized seat cushion surface model, obtain body pressure distribution data of the seat cushion contact area through finite element simulation, introduce part sensitivity weights based on human body pressure perception characteristics to calculate weighted body pressure distribution entropy, and optimize the seat cushion surface shape parameters with the goal of maximizing the weighted body pressure distribution entropy and satisfying the pressure constraints of key load-bearing areas. S4. Evaluation of seat-human body coupled vibration transmissibility: Establish a multi-degree-of-freedom human body-seat coupled equivalent linear lumped parameter vibration model, use the car body vibration signal under typical train operating conditions as excitation input, calculate the frequency-weighted vibration transmissibility, evaluate and optimize the seat's vibration reduction performance. S5. Multi-objective parameter collaborative optimization: The interval coverage, the weighted body pressure distribution entropy and the frequency-weighted vibration transmissibility are used as the optimization objective functions. The seat geometric parameters, surface shape parameters and vibration reduction parameters are uniformly encoded as design variables. The coupling constraint relationship between surface parameters and vibration reduction parameters is established. A multi-objective genetic algorithm based on non-dominated sorting is used for collaborative optimization. Infeasible solutions are handled through the constraint dominance principle to obtain the Pareto optimal solution set. S6. Optimal Solution Output: The candidate solutions in the Pareto optimal solution set are standardized by objective function value, the minimization objective is transformed into a positive transformation, and the final seat parameter design scheme is output by comprehensively sorting the candidate solutions according to the design priority weight using the approximation ideal solution sorting method.

[0007] In a preferred embodiment, step S1 includes the following sub-steps: S11. Human body size data collection: Obtain sample data of the sitting human body size of the target passenger group from the human body size standard database or actual survey data. The sample data includes six sitting posture size parameters: sitting height, sitting depth, hip width, shoulder width, calf plus foot height and thigh thickness. S12. Distribution characteristic test and preprocessing: The six sitting posture size parameters are subjected to Shapiro-Wilk normality test respectively; when a parameter fails the test, it is subjected to Box-Cox transformation and then retested; if the normality requirement is still not met after transformation, the kernel density estimation method is used to nonparametrically model the marginal distribution of the parameter. S13. Joint distribution modeling: Calculate the correlation coefficients between each pair of the six sitting posture size parameters; when all parameters meet the normality requirement, construct the mean vector and covariance matrix to establish a multivariate normal joint probability distribution model; when there are parameters that do not meet the normality requirement, use the Copula function to combine the marginal distributions of each parameter to establish a joint probability distribution model; the established joint probability distribution model is used for interval coverage calculation in the subsequent step S2.

[0008] In a preferred embodiment, step S2 includes the following sub-steps: S21. Fit Range Setting: Set a design fit range for each of the six sitting posture size parameters. Each fit range is determined by the lower limit of the design range for that parameter. and design limit Composition, in which This is the parameter number; the initial value is taken from the 5th percentile to the 95th percentile of the corresponding parameter. S22. Interval Coverage Calculation: Randomly sample from the joint probability distribution model established in step S13. One sample point, No less than 10,000; determine whether the six parameter values ​​of each sample point simultaneously fall within their respective fit intervals; count the number of sample points that simultaneously satisfy all six interval constraints. Calculate the interval coverage using the following formula. : ; in, For interval coverage, dimensionless, it represents the joint probability that all dimensional parameters are simultaneously adapted by the seat design scheme; The number of sample points that simultaneously satisfy all six adaptation interval constraints; This represents the total number of sample points drawn from the joint distribution model; S23. Sensitivity-based range adjustment: Set the target coverage value. Apply a unit perturbation to the adaptation interval width for each size parameter and recalculate the interval coverage. The sensitivity coefficients of interval coverage to the interval width of each parameter are obtained; in descending order of sensitivity coefficients, the parameter intervals with high sensitivity are expanded first, while the parameter intervals with low sensitivity are contracted, while satisfying the condition... Not less than To minimize the overall size increment of the seat under constraints; S24. Geometric Dimension Parameter Mapping and Output: Based on the correspondence between human sitting posture dimensions and seat structural dimensions, the optimized adaptation ranges are converted into seat structural parameters: the seat depth design value is taken as the upper limit of the seat depth adaptation range. The seat width design value is taken as the upper limit of the hip width adaptation range. Upper limit of the shoulder width matching range The larger of the values ​​is taken, plus a lateral margin; the seat height design value is the seat surface height corresponding to the median value of the lower leg plus foot height adaptation range; the backrest height is the upper limit value of the seat height adaptation range. Subtract the seat height; take the initial backrest angle as the midpoint between 100° and 110°; thus obtain the initial geometric dimensions of the seat.

[0009] In a preferred embodiment, step S3 includes the following sub-steps: S31. Parametric seat cushion surface modeling: Using the seat reference point as the origin of the coordinate system, define the shape parameters of the seat cushion surface, including the height of the front edge of the seat cushion, the depth of the ischial tuberosity region, the height of the side wing of the seat cushion, the longitudinal radius of curvature of the seat cushion, and the lateral radius of curvature of the seat cushion; using the above shape parameters as control quantities, generate a parametric seat cushion surface geometric model through B-spline interpolation. S32. Body Pressure Distribution Simulation and Normalization: Import the geometric model of the seat cushion surface into finite element software to establish a contact analysis model including the seat cushion material layer and the human buttock-thigh contact area; discretize the seat cushion contact area into... OK A rectangular mesh is used; after applying a seated human body gravity load, contact simulation is performed to solve the problem, and the normal contact pressure value at each mesh node is extracted. Divide the pressure value at each node by the sum of all node pressure values ​​to obtain the normalized pressure value. This makes the sum of the normalized pressure values ​​of all nodes equal to 1; S33. Weighted Body Pressure Distribution Entropy Calculation: Based on the corresponding anatomical location of each grid node on the cushion, and drawing on experimental data on human pressure perception sensitivity or published human factors engineering literature, assign a pressure sensitivity weight coefficient to each node. The weighting coefficient for the ischial tuberosity region is higher than that for the mid-thigh region, and the weighting coefficient for the mid-thigh region is higher than that for the anterior thigh region. The weighted body pressure distribution entropy is calculated using the following formula. : ; in, is the weighted volume pressure distribution entropy, which is dimensionless and ranges from 0 to 1; For the first Line number The pressure sensitivity weighting coefficients of the human body parts corresponding to the grid nodes are dimensionless. For the first Line number The normalized pressure value of the column grid node, dimensionless; The natural logarithm operator; The number of grid rows; Number of grid columns; Indicates all Sum of the nodes; The closer the value is to 1, the more uniform the body pressure distribution is after considering site sensitivity; S34. Surface parameter optimization: using the weighted volume pressure distribution entropy... Maximizing the desired effect, the seat cushion surface shape parameters defined in step S31 are used as optimization variables. Constraints include ensuring the maximum contact pressure in the ischial tuberosity region does not exceed the human body's pressure comfort threshold and the total contact area of ​​the seat cushion is not less than a preset minimum. The solution is obtained within the manufacturing process allowable range of each shape parameter to achieve the desired effect. The optimal combination of surface parameters that yields the maximum value.

[0010] In a preferred embodiment, step S4 includes the following sub-steps: S41. Establishment of a four-degree-of-freedom equivalent linear vibration model: The human-seat system is simplified into an equivalent linear lumped parameter model of four mass-spring-damping subsystems connected in series vertically; the first mass block represents the seat base, with a mass of... Through stiffness and damping Connected to the vehicle floor; the second mass block represents the seat cushion, with a mass of Through stiffness and damping Connected to the seat base; the third mass block represents the lower torso of the human body, with a mass of Through stiffness and damping Connected to the seat cushion; the fourth mass block represents the upper torso of the human body, with a mass of Through stiffness and damping It is connected to the lower torso of the human body; the mass value of each mass block is determined according to the structural design parameters of the seat and the biomechanical parameters of the human body. S42. Frequency Domain Solution: Based on the four-degree-of-freedom equivalent linear model, write a set of differential equations of motion for the four mass blocks in the vertical direction, using the vertical vibration displacement of the vehicle floor as the system excitation input; perform a Fourier transform on the set of equations of motion to obtain the transfer function between the human torso displacement response and the vehicle floor excitation. ; S43. Operational Excitation Acquisition: Typical train operating conditions are divided into three categories: straight-line uniform speed operation, curve passing operation, and turnout or bridge passing operation; the power spectral density of the vertical vibration of the car body floor is acquired for each type of operating condition. The data is obtained through fitting actual measured data of the line or vehicle dynamics simulation. S44. Calculation of frequency-weighted vibration transmissibility: Combining the transfer function obtained in step S42 and the power spectral density of each operating condition obtained in step S43, the frequency-weighted vibration transmissibility is calculated using the following formula. : ; in, The frequency-weighted transmissivity is dimensionless. The magnitude of the transfer function; The vertical frequency weighting function specified in ISO 2631-1 standard; The power spectral density of the vertical vibration of the vehicle body floor; Angular frequency; A value less than 1 indicates that the seat system has a vibration damping effect; the frequency-weighted vibration transmissibility corresponding to each of the three working conditions is obtained by substituting the corresponding power spectral density into the calculation.

[0011] In a preferred embodiment, step S5 includes the following sub-steps: S51. Unified Coding of Design Variables: The geometric dimensions, seat surface shape parameters, and vibration damping parameters of the seat are uniformly coded into a single design variable vector. The geometric dimensions include seat width, seat depth, seat height, and backrest angle. The surface shape parameters include the height of the seat cushion front edge, the depth of the ischial tuberosity region indentation, the height of the seat cushion side wing bulge, the longitudinal radius of curvature of the seat cushion, and the lateral radius of curvature of the seat cushion. The vibration damping parameters include the base connection stiffness, the base connection damping, the equivalent stiffness of the seat cushion, and the equivalent damping of the seat cushion. S52. Establishing Coupling Relationships and Constructing Objective Functions: Establishing the coupling constraint relationship between surface shaping parameters and vibration reduction parameters, and setting the equivalent stiffness of the seat cushion. Expressed as the elastic modulus of the seat cushion foam material The actual contact area between the human body and the seat cushion and effective thickness of the seat cushion function ,in Determined jointly by surface modeling parameters and human body model. The cushion material is provided by the supplier, thus incorporating the impact of surface parameter variations on vibration transmission performance into the optimization framework; the three optimization objectives are constructed as follows: maximizing interval coverage, maximizing weighted body pressure distribution entropy, and minimizing the comprehensive operating condition frequency-weighted vibration transmission rate; the comprehensive operating condition frequency-weighted vibration transmission rate is the value of the vibration transmission rate of each of the three operating conditions weighted by the proportion of running time. S53, NSGA-II Solution and Constraint Handling: Population size, number of iterations, crossover probability, and mutation probability are set. Simulated binary crossover is used for the crossover operator, and polynomial mutation is used for the mutation operator. In each generation's fitness evaluation, infeasible individuals are handled using the constraint dominance principle, meaning feasible solutions dominate infeasible solutions, and infeasible solutions are ranked according to the degree of constraint violation. Constraints include: all geometric dimensions within the standard range for railway passenger car seats; all surface modeling parameters within the manufacturing process allowable range; the maximum contact pressure in the ischial tuberosity region not exceeding the human body pressure comfort threshold; the static sinking of the seat cushion within a reasonable range; and the peak amplitude of the transfer function of the seat system within the sensitive frequency range being lower than a preset threshold. Population diversity and convergence are maintained through fast non-dominated sorting and crowding distance calculation, outputting the Pareto optimal solution set.

[0012] In a preferred embodiment, step S6 includes the following sub-steps: S61. Target value standardization and forward transformation: The three objective function values ​​of each candidate scheme in the Pareto optimal solution set are standardized. The standardization method is to subtract the minimum value of the objective in the solution set from each objective function value and then divide by the difference between the maximum and minimum values ​​of the objective in the solution set. The minimum objective, namely the vibration transmissibility under the comprehensive working condition, is forward transformed by subtracting the standardized value of the objective from 1, so that after standardization, each objective is in the direction of being larger and better. S62. Weight Determination and Comprehensive Ranking: Based on the design priority of the business seats, the weights of the three objectives—interval coverage, weighted body pressure distribution entropy, and comprehensive working condition vibration transmissibility—are determined using the analytic hierarchy process (AHP) or entropy weight method. Positive and negative ideal solutions are constructed respectively. The positive ideal solution is a virtual scheme where the optimal value of each objective's positive standard value is taken from the solution set, and the negative ideal solution is a virtual scheme where the worst value of each objective's positive standard value is taken from the solution set. The weighted Euclidean distance from each candidate scheme to the positive and negative ideal solutions is calculated. The comprehensive proximity is calculated, which is equal to the distance to the negative ideal solution divided by the sum of the distances to the positive and negative ideal solutions. The comprehensive proximity is sorted from largest to smallest, and the values ​​of all design variables corresponding to the scheme with the best ranking are output as the final seat parameter design scheme.

[0013] This invention also provides a parameter design system for business class seats in railway trains, including a processor, a memory, and a computer program stored in the memory and executable by the processor. When the processor executes the computer program, it implements the following functional modules: The human body size data management module is connected to the interval coverage calculation module. It is used to receive and store multiple sitting human body size sample data of the target passenger group, perform distribution characteristic tests and correlation analysis on the sample data, establish a multivariate joint probability distribution model, and output the established model to the interval coverage calculation module. The interval coverage calculation module is connected to the human body size data management module and the multi-objective collaborative optimization module respectively. It is used to receive the multivariate joint probability distribution model and the adaptation interval of each size parameter, calculate the interval coverage through Monte Carlo sampling statistics and sensitivity analysis, and output the coverage value to the multi-objective collaborative optimization module. The body pressure distribution simulation and evaluation module is connected to the multi-objective collaborative optimization module. It is used to generate a parameterized surface geometric model based on the received cushion surface shape parameters, call the finite element simulation engine to calculate body pressure distribution data, normalize the body pressure distribution data and assign pressure sensitivity weights according to human body parts, calculate the weighted body pressure distribution entropy, and output the entropy value to the multi-objective collaborative optimization module. The vibration transmission analysis module is connected to the multi-objective collaborative optimization module. It is used to establish a four-degree-of-freedom human-seat coupling equivalent linear vibration model based on the received vibration reduction parameters, receive vibration excitation data of train operation conditions, calculate the frequency-weighted vibration transmission rate under each operation condition, and output the transmission rate results to the multi-objective collaborative optimization module. The multi-objective collaborative optimization module is connected to the interval coverage calculation module, the body pressure distribution simulation and evaluation module, and the vibration transmission analysis module, respectively. It is used to take interval coverage, weighted body pressure distribution entropy, and frequency-weighted vibration transmissibility as objective functions, and geometric dimension parameters, surface modeling parameters, and vibration reduction parameters as design variables. It establishes the coupling constraint relationship between surface parameters and vibration reduction parameters, executes a multi-objective genetic algorithm based on non-dominated sorting for collaborative optimization, handles infeasible solutions through constraint dominance principles, generates a Pareto optimal solution set, and outputs the final design scheme through the approximation ideal solution sorting method. The results output and reporting module is connected to the multi-objective collaborative optimization module to receive the parameter values ​​of the final design scheme and the evaluation results of each objective function, and to generate a design report containing seat parameters and performance evaluation.

[0014] In a preferred embodiment, the human body size data management module includes a data import submodule, a data preprocessing submodule, and a joint distribution modeling submodule. The data import submodule is used to read human body size sample data from external data sources and store it in a unified format. The data preprocessing submodule is connected to the data import submodule and is used to perform outlier removal and distribution characteristic testing on the imported sample data. The joint distribution modeling submodule is connected to the data preprocessing submodule and is used to establish a multivariate normal joint probability distribution model or a joint probability distribution model based on the valid sample data. The body pressure distribution simulation and evaluation module includes a parametric modeling submodule, a finite element simulation submodule, and an entropy calculation submodule. The parametric modeling submodule receives the seat cushion surface shape parameters and generates a three-dimensional curved surface geometric model through B-spline interpolation. The finite element simulation submodule is connected to the parametric modeling submodule and is used to perform seat cushion-human body contact simulation calculations on the three-dimensional curved surface geometric model and output contact pressure data for each node. The entropy calculation submodule is connected to the finite element simulation submodule and is used to normalize the contact pressure data and assign pressure sensitivity weighting coefficients based on experimental data or literature to different human body parts before calculating the weighted body pressure distribution entropy. The vibration transmission analysis module includes a dynamic modeling submodule, a vibration excitation input submodule, and a transmissibility calculation submodule. The dynamic modeling submodule is used to establish the mass matrix, stiffness matrix, and damping matrix of a four-degree-of-freedom equivalent linearly coupled vibration model based on seat structural parameters and human biomechanical parameters. The vibration excitation input submodule is used to store and manage the power spectral density data of the car body floor vibration under various operating conditions of the train. The transmissibility calculation submodule is connected to the dynamic modeling submodule and the vibration excitation input submodule, respectively, and is used to solve the vibration model in the frequency domain and calculate the frequency-weighted vibration transmissibility by combining the power spectral density of each operating condition and the ISO2631-1 standard frequency weighting function. The multi-objective collaborative optimization module includes a design variable encoding submodule, an NSGA-II optimization engine submodule, a Pareto solution set management submodule, and a TOPSIS decision submodule. The design variable encoding submodule encodes geometric parameters, surface modeling parameters, and vibration reduction parameters into a unified design variable vector and sets the value range for each variable. The NSGA-II optimization engine submodule is connected to the design variable encoding submodule and simultaneously calls the interval coverage calculation module, the body pressure distribution simulation and evaluation module, and the vibration transmission analysis module to evaluate the objective function, performing an iterative optimization process including fast non-dominated sorting, crowding distance calculation, and elite retention strategies, and handling infeasible solutions through constraint dominance principles. The Pareto solution set management submodule is connected to the NSGA-II optimization engine submodule and stores and maintains the Pareto optimal solution set generated by each iteration. The TOPSIS decision submodule is connected to the Pareto solution set management submodule and performs objective value standardization, positiveization, and weight sorting on the Pareto optimal solution set before outputting the final design scheme.

[0015] The beneficial effects achieved by this invention are as follows: This invention establishes a multivariate joint probability distribution model for multiple seated anthropometric parameters, overcoming the shortcomings of traditional methods that independently calculate percentiles for each parameter while ignoring statistical correlations between parameters. Based on this joint probability distribution model, this invention defines the joint probability of multiple parameters simultaneously falling within their respective fit intervals as an interval coverage index, which can accurately reflect the multidimensional fit of the seat design to the target passenger group. This invention performs sensitivity analysis on the fit interval width of each parameter, distributing the interval range of each parameter differently according to the magnitude of the sensitivity coefficient. This allows parameters that contribute significantly to coverage to receive wider fit intervals, while parameters that contribute less to coverage have appropriately narrowed intervals. This sensitivity-based differentiated allocation strategy significantly improves the multidimensional fit rate of the passenger group without increasing the overall seat size, resulting in a more reasonable and compact seat size scheme.

[0016] This invention introduces information entropy theory into the field of comfort evaluation of body pressure distribution, proposing a weighted body pressure distribution entropy index. Unlike traditional seat pressure distribution uniformity indices that only measure the overall dispersion of pressure distribution, the weighted body pressure distribution entropy, while measuring the uniformity of pressure distribution, introduces a pressure perception sensitivity weighting coefficient based on human anatomical locations. This allows the pressure state of highly sensitive areas such as the ischial tuberosities to have a greater impact on the evaluation index. Therefore, when optimization aims to maximize the weighted body pressure distribution entropy, the algorithm not only pursues the uniformity of the overall pressure distribution but also effectively avoids the problem of transferring high pressure to low-sensitivity areas, thus preventing excessive concentrated pressure on highly sensitive areas. Combined with the constraint that the peak pressure in the ischial tuberosity region does not exceed a comfort threshold, this invention can effectively control the peak pressure in key load-bearing areas while achieving a uniform overall pressure distribution, thereby obtaining more accurate and comprehensive seat surface optimization results than traditional indices.

[0017] This invention establishes a four-degree-of-freedom human-seat coupled equivalent linear lumped-parameter vibration model. The seat base, cushion, lower torso, and upper torso are modeled as a series-connected mass-spring-damping subsystem. The power spectral density of the train body vibration under three typical operating conditions—straight-line uniform speed, curve passage, and crossing of switches or bridges—is used as the excitation input. The frequency-weighted vibration transmissibility is calculated using a vertical frequency weighting function specified in international standards. Compared to traditional evaluation methods that treat the seat as a rigid body, this coupled vibration model accurately reflects the vibration transmission characteristics of the seat's elastic structure at different frequencies, especially identifying the resonance amplification effect that may occur when the seat system's natural frequency falls into the human body's vibration-sensitive frequency band. This allows the invention to effectively avoid resonance risks in seat vibration reduction parameter design, ensuring that the seat system attenuates vibrations under all train operating conditions.

[0018] This invention uses three indicators—interval coverage, weighted body pressure distribution entropy, and frequency-weighted vibration transmissibility—as optimization objective functions. It uniformly encodes seat geometric parameters, cushion surface design parameters, and vibration damping parameters as design variables and establishes a coupling constraint relationship between the surface design parameters and vibration damping parameters. A multi-objective genetic algorithm based on non-dominated sorting is employed for collaborative optimization. Compared to traditional methods that optimize parameters independently, this invention's multi-objective collaborative optimization mechanism can automatically assess the impact of surface parameters on vibration transmission performance while optimizing the surface parameters, avoiding the problem of severe degradation of a performance indicator due to neglecting the coupling effect between parameters. By comprehensively sorting the Pareto optimal solution set using the approximation ideal solution sorting method, this invention achieves a reasonable trade-off among the three objectives, outputting a seat parameter design scheme with optimal overall performance. This results in a high level of performance in three dimensions: human body size adaptability, body pressure distribution comfort, and vibration damping performance. Attached Figure Description

[0019] Figure 1 The above are comparison charts of interval coverage between Example 1 and Comparative Example 1, where (a) is a bar chart comparing the 6-dimensional joint coverage C, and (b) is a grouped bar chart comparing the single-dimensional coverage of the 6 human body size parameters.

[0020] Figure 2 The charts show a comparison of body pressure distribution indices between Example 1 and Comparative Example 2. (a) is a horizontal grouped bar chart comparing the weighted body pressure distribution entropy Hw and the SPD index, and (b) is a horizontal grouped bar chart comparing the peak pressure and average contact pressure in the ischial tuberosity region.

[0021] Figure 3 The following is a comparison chart of the vibration transmissibility under various working conditions for Example 1 and Comparative Example 3. (a) is a line graph comparing the frequency-weighted vibration transmissibility Tw under the three working conditions, and (b) is a bar graph comparing the vibration transmissibility under the comprehensive working conditions.

[0022] Figure 4 It is a comprehensive comparative heat map of three core indicators: interval coverage, weighted volume pressure distribution entropy, and vibration transmissibility between Examples 1 to 3 and Comparative Examples 1 to 3.

[0023] Figure 5 This is a flowchart of the parameter design method for business class seats for railway trains according to the present invention. Detailed Implementation

[0024] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. In addition, the forms of the various structures described in the following embodiments are merely illustrative. The present invention is not limited to the structures described in the following embodiments. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] The seat parameter design method provided by this invention includes six main steps, namely: Step S1, joint human body size distribution modeling; Step S2, determination of seat geometric parameters based on interval coverage; Step S3, optimization of seat cushion surface parameters based on body pressure distribution entropy; Step S4, evaluation of seat-human body coupled vibration transmissibility; Step S5, multi-objective parameter collaborative optimization; and Step S6, optimal solution output. (Refer to...) Figure 5 The following sections will describe each step in detail.

[0026] Step S1 involves modeling the joint distribution of human body dimensions. The purpose of this step is to acquire and process the seated human body dimension data of the target passenger group, and to establish a joint probability distribution model that can describe the statistical correlation between multiple size parameters, thus providing a probabilistic analysis basis for the interval coverage calculation in the subsequent step S2.

[0027] Step S1 consists of three sub-steps: sub-step S11 human body size data acquisition, sub-step S12 distribution characteristic verification and preprocessing, and sub-step S13 joint distribution modeling.

[0028] In sub-step S11, sample data of the sitting anthropometric dimensions of the target passenger group are obtained from a standard anthropometric database or actual survey data. The collected sample data includes six sitting posture dimension parameters: seat height, seat depth, hip width, shoulder width, calf plus foot height, and thigh thickness. These six parameters are key anthropometric dimensions directly related to seating comfort in the geometric design of the seat. Among them, seat height determines the backrest height, seat depth determines the seat surface depth, hip width and shoulder width determine the seat surface and backrest width, calf plus foot height determines the seat surface height, and thigh thickness affects the distance between the seat surface and the armrest. The data source can be the percentile standard data given in GB / T10000-2023 "Anthropometric Dimensions of Chinese Adults", or it can be actual measurement data obtained from a special anthropometric survey conducted on a specific passenger group. When using standard data, subsequent modeling can be performed based on the mean, standard deviation, and percentile values ​​provided by the standard. When using actual measurement data, the sample size should meet the basic requirements of statistical analysis.

[0029] In sub-step S12, the distribution characteristics of the six sitting posture dimensional parameters collected in step S11 are tested. The Shapiro-Wilk normality test is used, which is suitable for determining the normality of small to medium-sized samples and is a widely used normality test method in the field of statistics. When the test result of a parameter fails to meet the normality requirement, the parameter is retested after a Box-Cox transformation. The Box-Cox transformation is a power transformation method that transforms non-normal data into approximately normally distributed data by finding the optimal transformation parameters. If the normality requirement is still not met after the Box-Cox transformation, the kernel density estimation method is used to non-parametrically model the marginal distribution of the parameter. The kernel density estimation method does not rely on a preset distribution form but directly estimates the probability density function from the sample data, making it suitable for situations with complex distribution shapes. Through the above processing, a reliable marginal distribution description for each dimensional parameter can be obtained.

[0030] In substep S13, the correlation coefficients between each pair of the six sitting posture dimension parameters are calculated. When all parameters meet the normality requirement, the Pearson correlation coefficient is used to measure the degree of linear correlation, and a 6-dimensional mean vector is constructed. The covariance matrix is ​​used as a parameter to establish a multivariate normal joint probability distribution model. The probability density function of the multivariate normal distribution model is uniquely determined by the mean vector and the covariance matrix. The off-diagonal elements in the covariance matrix reflect the linear correlation between the various size parameters. When there are parameters that do not meet the normality requirement, the Copula function is used to combine the marginal distributions of each parameter to establish a joint probability distribution model. The Copula function is a mathematical tool that connects multiple univariate marginal distributions into a multivariate joint distribution, with the theoretical basis provided by Sklar's theorem. The Copula function can separate the marginal distributions and the correlation structure, so even if the marginal distributions of each parameter are different, a joint distribution can be flexibly established. Commonly used Copula function types include GaussianCopula and t-Copula. After establishing the joint probability distribution model, this model will serve as the probability basis for calculating the interval coverage in step S2.

[0031] Unlike traditional methods that take the percentiles of each size parameter independently, the joint probability distribution model established in step S1 can retain the statistical correlation structure between each size parameter, so that the subsequent interval coverage calculation can reflect the true probability that multiple parameters simultaneously meet the adaptation requirements.

[0032] Step S2 determines the seat geometry parameters based on interval coverage. This step utilizes the joint probability distribution model established in step S1 to calculate the multidimensional joint coverage probability using the Monte Carlo method, replacing the traditional single percentile extreme value method, thus optimizing seat size allocation while ensuring the target coverage rate.

[0033] Step S2 includes four sub-steps: sub-step S21 setting the adaptation range, sub-step S22 calculating the range coverage, sub-step S23 adjusting the range based on sensitivity, and sub-step S24 mapping and outputting geometric dimension parameters.

[0034] In sub-step S21, a design adaptation range is set for each of the six sitting posture dimension parameters. Each adaptation range is determined by the lower design limit of that parameter. and design limit Composition, in which For parameter sequence number, The values ​​1 to 6 correspond to seat height, seat depth, hip width, shoulder width, calf plus foot height, and thigh thickness, respectively. The initial values ​​for the fit range are taken from the 5th percentile to the 95th percentile of the corresponding parameter. The fit range means that when a passenger's body dimension falls within this range, the seat can provide suitable support and space for that passenger in that dimension.

[0035] In sub-step S22, the Monte Carlo method is used to calculate the interval coverage. Specifically, this involves randomly selecting intervals from the joint probability distribution model established in step S13. 1 sample point. The value of is no less than 10000 to ensure the statistical accuracy of the calculation results. For each sample point, it is determined whether all six parameter values ​​simultaneously fall within their respective fit intervals. The number of sample points that simultaneously satisfy all six interval constraints is counted. Calculate the interval coverage using the following formula. . ; in, For interval coverage, dimensionless, its physical meaning is the joint probability that all dimensional parameters are simultaneously adapted by the seat design scheme; The number of sample points that simultaneously satisfy all 6 adaptation interval constraints; This represents the total number of sample points drawn from the joint distribution model. The Monte Carlo method is a numerical computation method based on large-scale random sampling. Its basic principle is to approximate theoretical probability using the statistical frequency of random samples. When the sample size is sufficiently large, The estimated value will converge to the theoretical coverage probability. Interval Coverage This differs fundamentally from traditional one-dimensional percentile coverage. Traditional methods, when taking the P5 to P95 range for a single parameter, achieve 90% coverage for each parameter. However, the joint probability of all six parameters being covered simultaneously is far below 90% due to correlations and dimensionality effects among the parameters. Interval Coverage The multidimensional joint probability is calculated directly under the joint distribution, thus more accurately reflecting the true suitability of the seat design to the target group.

[0036] In sub-step S23, the coverage target value is set. In order to satisfy Not less than Under the constraints, the adaptation range of each parameter is optimized and adjusted. The adjustment strategy is based on sensitivity analysis. Specifically, a unit perturbation is applied to the adaptation range width of each size parameter, and the range coverage is recalculated according to the method in sub-step S22. This yields the sensitivity coefficients of interval coverage to the interval width of each parameter. The sensitivity coefficients reflect the marginal contribution of a unit change in interval width to coverage. Following the order of sensitivity coefficients from largest to smallest, the parameter intervals with high sensitivity (those contributing significantly to coverage) are expanded first, while the intervals with low sensitivity (those contributing little to coverage) are contracted. This ensures that, while satisfying… Not less than Under the constraint of minimizing the overall size increment of the seat. Compared with the traditional method of uniformly taking the same percentile range for each parameter, the sensitivity-based interval adjustment method can differentiate the allocation according to the actual contribution of each parameter to the coverage, reducing unnecessary size redundancy under the condition of achieving the same coverage.

[0037] In sub-step S24, based on the correspondence between human sitting posture dimensions and seat structural dimensions, the optimized adaptation ranges are converted into seat structural design parameters. The seat depth design value is taken as the upper limit of the seat depth adaptation range. This design ensures that passengers with greater seat depth will not lack thigh support due to an excessively short seat surface. The seat width design value is taken as the upper limit of the hip width adaptation range. Upper limit of the shoulder width matching range The seat height is determined by taking the larger of the two values, plus lateral allowance, to ensure ample space for wider passengers. The seat height design value is the seat surface height corresponding to the midpoint of the lower leg plus foot height adaptation range. The backrest height is the upper limit of the seat height adaptation range. Subtract the seat height to ensure the backrest provides support for the upper back and head and neck of passengers with higher sitting heights. The initial backrest angle is taken as the midpoint between 100° and 110°, which is the ergonomically recognized comfortable angle range for a semi-reclining sitting posture. This yields the initial geometric parameters of the seat, which are used for multi-objective collaborative optimization in subsequent step S5.

[0038] Step S3 involves optimizing the cushion surface parameters based on body pressure distribution entropy. This step introduces information entropy theory to quantitatively evaluate the uniformity and orderliness of body pressure distribution, and constructs a weighted body pressure distribution entropy index by combining the differential sensitivity of different parts of the human body to pressure, thereby guiding the optimized design of the cushion surface shape parameters.

[0039] Step S3 includes four sub-steps: sub-step S31 parametric cushion surface modeling, sub-step S32 body pressure distribution simulation and normalization, sub-step S33 weighted body pressure distribution entropy calculation, and sub-step S34 surface parameter optimization.

[0040] In sub-step S31, a coordinate system is established with the seat reference point, H, as the origin. H is the baseline reference point in seat design. Five shaping parameters of the seat cushion surface are defined within this coordinate system: the height of the front edge of the cushion, the depth of the ischial tuberosity region's indentation, the height of the side wing protrusions, the longitudinal radius of curvature, and the lateral radius of curvature. Using these five shaping parameters as control variables, a parametric geometric model of the seat cushion surface is generated through B-spline interpolation. B-spline surfaces offer local control, meaning that modifying a control point only affects a local area of ​​the surface, making them suitable for independently adjusting the shape of different areas of the seat cushion. The height of the front edge of the cushion controls the support height at the front of the thigh; the depth of the ischial tuberosity region's indentation controls the degree of indentation in the main weight-bearing area of ​​the buttocks; the height of the side wing protrusions controls the lateral wrapping of the buttocks and thighs; and the longitudinal and lateral radii of curvature control the surface curvature of the seat cushion in the front-to-back and left-to-right directions, respectively.

[0041] In sub-step S32, the seat cushion surface geometry model generated in step S31 is imported into finite element analysis software to establish a contact analysis model including the seat cushion foam material layer and the contact area between the human buttocks and thighs. The seat cushion material is typically polyurethane foam, whose mechanical behavior can be described by a hyperelastic constitutive model. The human buttocks and thigh model can be a simplified rigid or elastic contact body. The seat cushion contact area is discretized into... OK A rectangular mesh is used. Contact simulation is performed after applying a seated human body gravity load, and the normal contact pressure value at each mesh node is extracted. Then, the pressure value at each node is divided by the sum of the pressure values ​​at all nodes to obtain the normalized pressure value. This makes all nodes after normalization... The sum is 1. The purpose of normalization is to transform the stress value into a quantity with probability distribution characteristics so that information entropy theory can be applied for evaluation later.

[0042] In substep S33, based on the corresponding anatomical location of each grid node on the cushion and experimental data on human pressure perception sensitivity or published human factors engineering literature, a pressure sensitivity weight coefficient is assigned to each node. Different parts of the human body have varying degrees of sensitivity to contact pressure. The ischial tuberosity region, due to its thinner subcutaneous fat and muscle tissue, is the most sensitive to pressure, and its weighting coefficient is set to the highest. The mid-thigh region, with its thicker muscle tissue, is the next most sensitive. The anterior thigh region is the least sensitive. Based on this, the weighted entropy of body pressure distribution is calculated using the following formula. .

[0043] ; in, is the weighted volume pressure distribution entropy, which is dimensionless and ranges from 0 to 1; For the first Line number The pressure sensitivity weighting coefficients of the human body parts corresponding to the grid nodes are dimensionless. For the first Line number The normalized pressure value of the column grid node, dimensionless; The natural logarithm operator; The number of grid rows; Number of grid columns; Indicates all Sum of the nodes.

[0044] The theoretical basis of the above formula stems from Shannon information entropy. Shannon information entropy is a fundamental quantity in information theory used to measure the uncertainty of probability distributions. In the application of body pressure distribution, when the normalized pressure value... When the pressure is uniformly distributed across all nodes, the entropy reaches its maximum value of 1; when the pressure is concentrated at a few nodes, the entropy approaches 0. (Weighted volume pressure distribution entropy) A human body part sensitivity weight was introduced based on Shannon entropy. This makes the pressure distribution in highly sensitive areas have a greater impact on the entropy value. When all nodes are assigned the same value, the weighted volume pressure distribution entropy degenerates into the standard normalized Shannon entropy. In the denominator... As a normalization factor, make The value ranges from 0 to 1. Compared with the traditional SPD (seat pressure distribution uniformity index), the weighted body pressure distribution entropy considers both the uniformity of pressure distribution and the differential sensitivity of different parts of the body, thus having a stronger evaluation ability to distinguish the comfort differences of different pressure distribution patterns.

[0045] In sub-step S34, the weighted volume pressure distribution entropy is used. Maximizing the desired effect, the five cushion surface shaping parameters defined in step S31 are used as optimization variables. It should be noted that... Maximizing the pressure distribution does not aim for absolute uniformity, as the optimization process simultaneously imposes the constraint that the maximum contact pressure in the ischial tuberosity region must not exceed the human body's pressure comfort threshold. This constraint ensures that the pressure level in the ischial tuberosity region, as the main weight-bearing area of ​​the human body in a sitting posture, remains within an acceptable range. Furthermore, the total contact area of ​​the seat cushion must not be less than a preset minimum value to ensure sufficient bearing area between the human body and the cushion. The solution is obtained within the manufacturing process limits of each shape parameter to achieve... The optimal combination of surface parameters that yields the maximum value. The solution method can be sequential quadratic programming or other numerical methods suitable for constrained nonlinear optimization problems.

[0046] Step S4 is the evaluation of the seat-human body coupled vibration transmissibility. This step establishes a human body-seat coupled vibration dynamics model, and calculates the frequency-weighted vibration transmissibility by combining the vehicle body vibration excitation signal under the actual operating conditions of railway trains, so as to quantitatively evaluate the vibration reduction performance of the seat under actual use conditions.

[0047] Step S4 includes four sub-steps: sub-step S41 establishing a four-degree-of-freedom equivalent linear vibration model, sub-step S42 solving in the frequency domain, sub-step S43 obtaining the excitation under the working condition, and sub-step S44 calculating the frequency-weighted vibration transmissibility.

[0048] In substep S41, the human-seat system is simplified into an equivalent linear lumped parameter model of four mass-spring-damping subsystems connected in series vertically. This model is widely used internationally for seat vibration comfort analysis, and its basic structure is as follows. The first mass block represents the seat base, including the seat frame and adjustment mechanism, with a mass of [mass value missing]. Through stiffness and damping Connected to the vehicle floor. The second mass block represents the seat cushion, including the foam layer and the cover, with a mass of [mass value missing]. Through stiffness and damping Connected to the seat base. The third mass block represents the lower torso, namely the pelvis and thighs, with a mass of... Through stiffness and damping Connected to the seat cushion. The fourth mass block represents the upper torso, i.e., the part above the lumbar spine, with a mass of... Through stiffness and damping It connects to the lower torso of the human body. The mass values ​​of each mass block are determined based on the seat structural design parameters and the parameters of the standard human biomechanical model. The mass, stiffness, and damping parameters of each part of the human body can be referenced from the human mechanical impedance model data provided in the ISO 5982 standard. Although the actual human-seat system has nonlinear characteristics, under small-amplitude vibration conditions, the equivalent linear model can well approximate its dynamic behavior, and the model parameters have clear physical meanings, making it easy to establish a correspondence with the seat structural design parameters.

[0049] In sub-step S42, based on the 4-DOF equivalent linear model established in step S41, a system of differential equations of motion for the four mass blocks in the vertical direction is written. The vertical vibration displacement of the vehicle floor is used as the excitation input of the system. A Fourier transform is performed on the system of equations of motion, transforming the time-domain differential equations into a system of frequency-domain algebraic equations. Solving this system of frequency-domain equations yields the transfer function between the displacement response of the upper torso at each frequency and the excitation from the vehicle floor. The physical meaning of the transfer function is the input-output amplitude and phase relationship of the system at various frequencies, and its magnitude is... Indicates at angular frequency The ratio of the vibration amplitude of the upper torso of the human body to the vibration amplitude of the vehicle floor.

[0050] In sub-step S43, typical train operating conditions are divided into three categories. Condition I is the straight-line uniform speed operation condition, where vibration energy is concentrated in the lower frequency band. Condition II is the curve-passing condition, where lateral vibration components are superimposed on vertical vibration. Condition III is the turnout or bridge-passing condition, which includes broadband impact vibration components. The power spectral density of the vertical vibration of the car body floor is obtained for each type of condition. Power spectral density describes the distribution of vibration energy at various frequencies and is a fundamental input for random vibration analysis. It is obtained through fitting measured data from the railway line or through vehicle dynamics simulation.

[0051] In sub-step S44, combining the transfer function obtained in step S42 and the power spectral density of each operating condition obtained in step S43, the frequency-weighted vibration transmissibility is calculated using the following formula. .

[0052] ; in, The frequency-weighted transmissivity is dimensionless. The magnitude of the transfer function; The vertical frequency weighting function specified in ISO 2631-1 standard; The power spectral density of the vertical vibration of the vehicle body floor is expressed in m³ / s. 2 / s 3 ; Angular frequency, in rad / s; This is for integration operations within the frequency range of 0.5Hz to 80Hz.

[0053] The physical meaning of the above formula is as follows: The numerator is the root mean square value of the frequency-weighted acceleration reaching the upper torso after being transmitted through the seat system, and the denominator is the root mean square value of the frequency-weighted acceleration excited by the vehicle floor. The ratio of the two is the vibration transmissibility. The frequency weighting function... This is a weighted curve defined for the vertical vibration of the human body in a seated position. The curve has the highest weight in the 4Hz to 8Hz range, reflecting the physiological characteristics of the human body being most sensitive to vibration in this frequency band. When the value is less than 1, it indicates that the seat system dampens vibrations; when... A value greater than 1 indicates that the seat system amplifies vibrations in certain frequency bands. For the three operating conditions defined in step S43, the corresponding power spectral density is substituted into the calculation to obtain the frequency-weighted vibration transmissibility for each operating condition. The constraints on the seat vibration reduction parameters include that the static sinking of the seat cushion is within a reasonable range and that the peak value of the transfer function amplitude of the seat system within the human body's vertical vibration sensitive frequency range of 4Hz to 8Hz is lower than a preset threshold. The former ensures that the seat cushion will not be excessively compressed or too hard under static load, while the latter ensures that the seat will not generate resonance amplification within the most sensitive frequency range for the human body.

[0054] Step S5 is multi-objective parameter collaborative optimization. This step integrates the seat geometry parameters, cushion surface shape parameters, and vibration reduction parameters involved in the preceding steps S2 to S4 into a unified multi-objective optimization framework, and performs collaborative optimization using the NSGA-II algorithm.

[0055] Step S5 consists of three sub-steps: sub-step S51, design variable unified encoding; sub-step S52, coupling relationship establishment and objective function construction; and sub-step S53, NSGA-II solution and constraint handling.

[0056] In sub-step S51, the geometric dimensions, seat cushion surface design parameters, and vibration damping parameters of the seat are uniformly encoded into a single design variable vector. The geometric dimensions include four variables: seat width, seat depth, seat height, and backrest angle. The surface design parameters include five variables: seat cushion front edge upturn height, ischial tuberosity region indentation depth, seat cushion side wing upturn height, seat cushion longitudinal radius of curvature, and seat cushion lateral radius of curvature. The vibration damping parameters include four variables: base connection stiffness, base connection damping, seat cushion equivalent stiffness, and seat cushion equivalent damping. The design variable vector contains a total of 13 variables. The value range of each variable is determined according to relevant standard specifications, material properties, and manufacturing process constraints.

[0057] In sub-step S52, the coupling constraint relationship between the surface shaping parameters and the vibration reduction parameters is first established. In actual seat structures, the surface shape of the seat cushion affects the contact area between the human body and the cushion, and the change in the contact area alters the equivalent stiffness of the cushion. The equivalent stiffness of the cushion is then... Expressed as the elastic modulus of the seat cushion foam material The actual contact area between the human body and the seat cushion and effective thickness of the seat cushion function .in The value is determined by the surface modeling parameters and the human body model, and increases with the increase of the depth of the ischial tuberosity region depression and the height of the lateral bulge. Provided by the cushion material supplier, it is considered a known constant during the optimization process; After the seat cushion is formed, the surface parameters can be indirectly determined. Through the above coupling relationship, the influence of changes in surface parameters on vibration transmission performance is incorporated into a unified optimization framework.

[0058] Then, three optimization objective functions are constructed. The first objective is to maximize the interval coverage, that is, to maximize the probability of the seat size scheme adapting to the target passenger group under the joint distribution. The second objective is to maximize the weighted body pressure distribution entropy, that is, to make the body pressure distribution as uniform as possible while satisfying the pressure constraints of the key load-bearing areas. The third objective is to minimize the comprehensive operating condition frequency-weighted vibration transmissibility, that is, to maximize the seat's vibration attenuation effect on the vehicle body. The comprehensive operating condition frequency-weighted vibration transmissibility is the value of the vibration transmissibility of each of the three operating conditions defined in step S43, weighted by the proportion of running time. There is a certain competition among the above three objectives, and it is impossible to reach their respective extreme values ​​simultaneously. Therefore, a multi-objective optimization method is needed to find the optimal trade-off between these objectives.

[0059] In sub-step S53, the NSGA-II algorithm is used for multi-objective optimization. NSGA-II, or Non-Dominated Sort Genetic Algorithm II with Elite Strategy, is one of the most widely used multi-objective evolutionary optimization algorithms. The core mechanisms of the algorithm include fast non-dominated sorting, crowding distance calculation, and an elite retention strategy. Fast non-dominated sorting divides individuals in the population into multiple levels based on dominance relationships; individuals in level 1 are not dominated by any other individuals. Crowding distance measures the dispersion of individuals within the same level in the objective space, used for selection among individuals of the same level to maintain the diversity of the solution set. The elite retention strategy merges parent and offspring generations and reorders the selection, ensuring that superior individuals are not lost. The population size, number of iterations, crossover probability, and mutation probability are set. The crossover operator uses the simulated binary crossover (SBX) operator, and the mutation operator uses the polynomial mutation operator.

[0060] In each generation of fitness evaluation, the constraints need to be checked. Infeasible solutions are handled using the constraint dominance principle. This principle, proposed by Deb in the aforementioned literature, states that feasible solutions dominate infeasible solutions, and infeasible solutions are ranked according to the degree of constraint violation, with individuals exhibiting lower constraint violations given priority. Constraints include: all geometric dimensions within the standard range specified for railway passenger car seats; all surface modeling parameters within the manufacturing process allowable range; the maximum contact pressure in the ischial tuberosity region not exceeding the human body pressure comfort threshold; the static sinking of the seat cushion within a reasonable range; and the peak amplitude of the transfer function of the seat system within the sensitive frequency range being lower than a preset threshold. After a set number of iterations, a Pareto optimal solution set is output. Each solution in the Pareto optimal solution set represents a seat parameter scheme that achieves different trade-offs among the three objectives; no single solution can improve other objectives without worsening at least one objective.

[0061] Step S6 is the optimal solution output. This step selects the solution with the best overall performance from the Pareto optimal solution set as the final design result.

[0062] Step S6 includes two sub-steps: sub-step S61, which is the standardization and positive transformation of the target value, and sub-step S62, which is the determination of weights and the comprehensive ranking.

[0063] In substep S61, the three objective function values ​​of each candidate scheme in the Pareto optimal solution set are standardized. The standardization method involves subtracting the minimum value of the objective function from the solution set and then dividing by the difference between the maximum and minimum values, ensuring that the standardized objective values ​​fall within the range of 0 to 1. Since the interval coverage and weighted volume pressure distribution entropy are maximized, while the comprehensive operating condition vibration transmissibility is minimized, their directions are inconsistent. Therefore, the minimized objective, i.e., the comprehensive operating condition vibration transmissibility, undergoes a forward transformation. This forward transformation is achieved by subtracting the standardized value of the objective from 1, ensuring that the standardized objective is in a direction where larger values ​​are preferred.

[0064] In sub-step S62, based on the design priority of the business chairs, the weights of three objectives—interval coverage, weighted body pressure distribution entropy, and comprehensive operating condition vibration transmissibility—are determined using the Analytic Hierarchy Process (AHP) or the entropy weight method. The AHP determines the weights of each indicator by constructing pairwise comparison judgment matrices and finding the eigenvector corresponding to their largest eigenvalue, making it suitable for situations where decision-maker preferences need to be incorporated. The entropy weight method determines weights entirely based on the dispersion of the data itself, making it suitable for situations where objective weighting is desired. After determining the weights, positive and negative ideal solutions are constructed. The positive ideal solution is a virtual solution where the positive standard value of each objective is the optimal value in the solution set, and the negative ideal solution is a virtual solution where the positive standard value of each objective is the worst value in the solution set. The weighted Euclidean distance from each candidate solution to the positive and negative ideal solutions is calculated. The comprehensive proximity is calculated, which is equal to the distance to the negative ideal solution divided by the sum of the distances to the positive and negative ideal solutions. A larger comprehensive proximity indicates that the solution is closer to the positive ideal solution and further away from the negative ideal solution. Sort the solutions by overall similarity from highest to lowest, and output the values ​​of all 13 design variables corresponding to the best-ranked solution. This is the final seat parameter design scheme. The TOPSIS (Topology for Ideal Solution Ranking) method is a classic multi-attribute decision-making method proposed by Hwang and Yoon in 1981.

[0065] The following describes the parameter design system for commercial seats in railway trains provided by this invention. The seat parameter design system of this invention includes a processor, a memory, and a computer program stored in the memory and executable by the processor. When the processor executes the computer program, it implements the following functional modules. The system consists of a human body size data management module, a section coverage calculation module, a body pressure distribution simulation and evaluation module, a vibration transmission analysis module, a multi-objective collaborative optimization module, and a result output and reporting module.

[0066] The human body size data management module is connected to the interval coverage calculation module. This module receives and stores multiple seated human body size sample data of the target passenger group, performs distribution characteristic tests and correlation analysis on the sample data, and establishes a multivariate joint probability distribution model. This module outputs the established model to the interval coverage calculation module. This module includes a data import submodule, a data preprocessing submodule, and a joint distribution modeling submodule. The data import submodule reads human body size sample data from external data sources and stores it in a unified format. The data preprocessing submodule is connected to the data import submodule and is used to remove outliers and test distribution characteristics on the imported sample data. The joint distribution modeling submodule is connected to the data preprocessing submodule and is used to establish a multivariate normal joint probability distribution model or a joint probability distribution model based on the valid sample data. This module undertakes the complete data processing flow from raw data to probability model, providing a standardized model interface for subsequent coverage calculation.

[0067] The interval coverage calculation module is connected to both the human body size data management module and the multi-objective collaborative optimization module. This module receives the joint probability distribution model and the fit intervals for each size parameter, and calculates the interval coverage using Monte Carlo sampling statistics and sensitivity analysis. This module then outputs the coverage value to the multi-objective collaborative optimization module. During the multi-objective optimization iteration process, this module is invoked whenever the geometric size parameters in the design variables change to re-evaluate the coverage of the corresponding scheme.

[0068] The body pressure distribution simulation and evaluation module is data-connected to the multi-objective collaborative optimization module. This module generates a parametric surface geometry model based on the received cushion surface design parameters, calls the finite element simulation engine to calculate body pressure distribution data, normalizes the data, assigns pressure sensitivity weights to different body parts, and then calculates the weighted body pressure distribution entropy. This module outputs the entropy value to the multi-objective collaborative optimization module. This module includes a parametric modeling submodule, a finite element simulation submodule, and an entropy calculation submodule. The parametric modeling submodule receives the cushion surface design parameters and generates a 3D surface geometry model using B-spline interpolation. The finite element simulation submodule, connected to the parametric modeling submodule, performs cushion-human contact simulation calculations on the 3D surface geometry model and outputs contact pressure data for each node. The entropy calculation submodule, also connected to the finite element simulation submodule, normalizes the contact pressure data, assigns pressure sensitivity weights based on experimental data or literature to different body parts, and then calculates the weighted body pressure distribution entropy.

[0069] The vibration transmission analysis module is data-connected to the multi-objective collaborative optimization module. This module is used to establish a 4-DOF human-seat coupled equivalent linear vibration model based on received vibration reduction parameters, receive vibration excitation data from train operating conditions, and calculate the frequency-weighted vibration transmissibility under each condition. This module outputs the transmissibility results to the multi-objective collaborative optimization module. This module includes a dynamic modeling submodule, a vibration excitation input submodule, and a transmissibility calculation submodule. The dynamic modeling submodule is used to establish the mass matrix, stiffness matrix, and damping matrix of the 4-DOF equivalent linear coupled vibration model based on seat structural parameters and human biomechanical parameters. The vibration excitation input submodule is used to store and manage the power spectral density data of the car body floor vibration under various train operating conditions. The transmissibility calculation submodule is connected to both the dynamic modeling submodule and the vibration excitation input submodule, and is used to solve the vibration model in the frequency domain and calculate the frequency-weighted vibration transmissibility by combining the power spectral density of each condition and the ISO2631-1 standard frequency weighting function.

[0070] The multi-objective collaborative optimization module is connected to the interval coverage calculation module, the body pressure distribution simulation and evaluation module, and the vibration transmission analysis module. This module is at the core of the system, responsible for coordinating the calls to these three evaluation modules for objective function evaluation and executing a multi-objective genetic algorithm based on non-dominated sorting for collaborative optimization. This module includes a design variable encoding submodule, an NSGA-II optimization engine submodule, a Pareto solution set management submodule, and a TOPSIS decision submodule. The design variable encoding submodule encodes geometric parameters, surface modeling parameters, and vibration reduction parameters into a unified design variable vector and sets the value range for each variable. The NSGA-II optimization engine submodule is connected to the design variable encoding submodule and simultaneously calls the interval coverage calculation module, the body pressure distribution simulation and evaluation module, and the vibration transmission analysis module to evaluate the objective function, executing an iterative optimization process including fast non-dominated sorting, crowding distance calculation, and an elite retention strategy, and handling infeasible solutions through constraint dominance principles. The Pareto solution set management submodule is connected to the NSGA-II optimization engine submodule and stores and maintains the Pareto optimal solution set generated by each iteration. The TOPSIS decision submodule is connected to the Pareto solution set management submodule. It is used to standardize, normalize, and sort the Pareto optimal solution set by objective value and output the final design scheme.

[0071] The results output and reporting module is connected to the multi-objective collaborative optimization module. This module receives the parameter values ​​of the final design scheme and the evaluation results of each objective function, generating a design report that includes seat parameters and performance evaluation. This module presents the system's design results to designers in an intuitive and readable format.

[0072] The various functional modules interact with each other through standardized data interfaces. During the optimization iteration process, the multi-objective collaborative optimization module iteratively calls the interval coverage calculation module, the body pressure distribution simulation and evaluation module, and the vibration transmission analysis module to evaluate each candidate scheme. The calculation results from these three modules are then aggregated into the multi-objective collaborative optimization module for non-dominated sorting and population updating. This modular architecture allows each evaluation module to be developed and tested independently, and also facilitates the replacement or upgrading of the calculation methods of a particular module as needed.

[0073] Example 1: Example 1 uses the railway train business seat parameter design method described in steps S1 to S6 of the present invention to perform full-process parameter design for a certain type of EMU business seat.

[0074] In step S1, following sub-step S11, seated anthropometric data of Chinese adult males aged 18-60 years are obtained from the GB / T10000-2023 standard, selecting six parameters: seat height, seat depth, hip width, shoulder width, calf plus foot height, and thigh thickness. In sub-step S12, the Shapiro-Wilk normality test is performed on each of the six parameters. All values ​​are greater than 0.05, indicating that all parameters follow a normal distribution. In sub-step S13, the Pearson correlation coefficient matrix of the six parameters is calculated. The correlation coefficient between sitting height and sitting depth is 0.72, the correlation coefficient between sitting depth and hip width is 0.45, and the correlation coefficients of the remaining parameter pairs are between 0.31 and 0.58. A six-dimensional normal joint probability distribution model is established based on the mean vector and covariance matrix.

[0075] In step S2, following sub-step S21, the initial values ​​of the adaptation intervals for each parameter are set to the range of P5 to P95. In sub-step S22, 50,000 sample points are extracted from the joint distribution model, and the initial interval coverage is calculated. The value is 0.689. In sub-step S23, the coverage target value is set. The sensitivity coefficient was 0.90. Sensitivity analysis revealed that sitting depth and sitting height had the highest sensitivity coefficients, while hip width had the lowest. Based on sensitivity ranking, the range of sitting depth and sitting height was expanded first, while the range of hip width was appropriately narrowed. After multiple iterations, the coverage was improved. The sensitivity was 0.903. After sensitivity analysis, the unidimensional coverage of each parameter was 0.92 for seat height, 0.94 for seat depth, 0.88 for hip width, 0.90 for shoulder width, 0.91 for calf and foot height, and 0.90 for thigh thickness. In sub-step S24, the optimized adaptation range was mapped to seat geometric parameters, resulting in a seat depth of 520mm, a seat width of 500mm, a seat height of 430mm, a backrest height of 580mm, and a backrest angle of 105°.

[0076] In step S3, following sub-step S31, a parametric seat cushion surface model is established. In sub-step S32, the seat cushion contact area is discretized into a 20x15 rectangular mesh, and the contact pressure values ​​of each node are obtained through finite element simulation and normalized. In sub-step S33, a weight coefficient of 1.5 is assigned to nodes in the ischial tuberosity region, 1.0 to the mid-thigh region, and 0.8 to the anterior thigh region, and the weighted body pressure distribution entropy is calculated. In sub-step S34, optimization is performed with the goal of maximizing the weighted body pressure distribution entropy, constraining the maximum contact pressure in the ischial tuberosity region to not exceed 60 mmHg. The optimized weighted body pressure distribution entropy is shown below. The value was 0.841, the SPD was 0.248, the peak pressure in the ischial tuberosity region was 42.3 mmHg, and the average contact pressure was 18.6 mmHg.

[0077] In step S4, following sub-steps S41 to S44, a 4-DOF equivalent linear vibration model is established, and the frequency-weighted vibration transmissibility for each working condition is calculated. Working condition I is linear uniform motion. The value is 0.71, which corresponds to condition II, i.e., the curve passing through. The value is 0.76, and the operating condition is III, which involves the passage of turnouts or bridges. The value is 0.79, and the vibration transmissibility under comprehensive operating conditions is 0.742.

[0078] In step S5, the 13 design variables are uniformly coded, and the NSGA-II population size is set to 200, with 500 iterations, a crossover probability of 0.9, and a mutation probability of 1 / 13. Through co-optimization, a Pareto optimal solution set of 47 schemes is obtained. In step S6, the Analytic Hierarchy Process (AHP) is used, with weights set to coverage 0.3, volume pressure entropy 0.4, and vibration transmissibility 0.3. The final schemes are then sorted and output using the TOPSIS method. The three objective values ​​of the final schemes are as follows: , , .

[0079] Example 2 differs from Example 1 in that the distribution characteristics of the human body size data in step S1 are different. In sub-step S12, the thigh thickness parameter failed the Shapiro-Wilk test, even after the Box-Cox transformation. Therefore, kernel density estimation is used to non-parametrically model the marginal distribution of this parameter. In sub-step S13, since there are parameters that do not meet the normality requirement, a joint probability distribution model is established using the Gaussian Copula function combined with the marginal distributions of each parameter. The remaining steps are the same as in Example 1. The three target values ​​of the final scheme are as follows: , , .

[0080] Example 3 differs from Example 1 in that the TOPSIS weight settings in step S6 are different. In sub-step S62, the weights are set to coverage 0.2, body pressure entropy 0.5, and vibration transmissibility 0.3 using the analytic hierarchy process, placing greater emphasis on body pressure comfort. The remaining steps are the same as in Example 1. The three target values ​​of the final scheme are as follows: , , Compared with Example 1, the body pressure distribution entropy increased by 0.011, the coverage decreased by 0.008, and the vibration transmissibility increased by 0.019, reflecting the trade-off between the targets under different weight settings.

[0081] Comparative Example 1 uses the traditional independent percentile method to determine the seat's geometric dimensions. Each of the six sitting posture dimension parameters is independently assigned a range from P5 to P95 as the design interval. No joint distribution model is established, and no sensitivity-based interval adjustment is performed. The single-dimensional coverage of each parameter is 0.90. The seat's geometric dimensions are directly determined based on the P95 value of each parameter. Steps S3 to S6 are the same as in Example 1. The joint distribution model established in Example 1 is used to back-calculate the 6-dimensional joint interval coverage of Comparative Example 1. The value is 0.683. The three target values ​​of the final scheme are as follows: , , .

[0082] Comparative Example 2 uses the traditional SPD index instead of the weighted body pressure distribution entropy index for cushion surface parameter optimization. The objective function in step S3 is replaced with SPD minimization, without introducing human body part sensitivity weights or imposing peak pressure constraints on the ischial tuberosity region. Steps S1, S2, and S4 to S6 are the same as in Example 1. The three target values ​​of the final solution are as follows: , , The SPD was 0.231, the peak pressure in the ischial tuberosity region was 51.7 mmHg, and the average contact pressure was 17.9 mmHg.

[0083] Comparative Example 3 uses an independent optimization method to replace the NSGA-II multi-objective collaborative optimization. Steps S2, S3, and S4 are performed independently for their respective single-objective optimizations, without uniformly encoding the 13 design variables or establishing coupling constraints between surface parameters and vibration reduction parameters. In step S6, the parameters after independent optimization are directly combined and output. The three objective values ​​of the final scheme are as follows: , , The vibration transmissibility for each working condition is 0.82 for working condition I, 0.93 for working condition II, and 1.05 for working condition III.

[0084] Experiment 1 compares and verifies the interval coverage of Example 1 and Comparative Example 1. The interval coverage of Example 1 and Comparative Example 1 under a 6-dimensional joint distribution is calculated respectively. The model also includes the individual one-dimensional coverage of each parameter. A Monte Carlo method was used to extract 50,000 sample points from the joint distribution model for evaluation.

[0085] Experimental results are as follows Figure 1 As shown. Figure 1 This is a comparison chart of the interval coverage of Example 1 and Comparative Example 1. Figure 1 China's a-value display shows 6-dimensional joint coverage. In the columnar comparison, the combined coverage of Example 1 was 0.903, while that of Comparative Example 1 was 0.683. Figure 1 Example b shows a grouped comparison of the single-dimensional coverage rates of six parameters: sitting height, sitting depth, hip width, shoulder width, calf plus foot height, and thigh thickness. In Example 1, the single-dimensional coverage rate of sitting depth is 0.94 and sitting height is 0.92, both higher than that of Comparative Example 1 (0.90), while the single-dimensional coverage rate of hip width is 0.88, slightly lower than that of Comparative Example 1 (0.90).

[0086] from Figure 1 As can be seen, in Comparative Example 1, although the individual coverage of each parameter was 90% when using the traditional independent percentile method, the 6-dimensional joint coverage was only 0.683, far below the design expectation of 90%. In Example 1, after adopting the sensitivity-based interval adjustment method in step S2 of this invention, the joint coverage increased to 0.903, a 32.1% improvement compared to Comparative Example 1. Figure 1 Further observation in step b reveals that Example 1 increased the single-dimensional coverage of the two parameters with the highest sensitivity coefficients, seat depth and seat height, to 0.94 and 0.92, respectively, while reducing the single-dimensional coverage of the parameter with the lowest sensitivity coefficient, hip width, to 0.88. This differentiated allocation strategy directly reflects the sensitivity analysis method in step S23 of this invention. This result indicates that the traditional method of uniformly allocating coverage to each parameter ignores the statistical correlation between multidimensional parameters and the differences in the contribution of each parameter to the joint coverage. This invention preserves the correlation structure between parameters by establishing a joint probability distribution model in step S1, and then achieves optimized resource allocation through sensitivity analysis in step S23, thereby increasing the multidimensional fit rate of the passenger group from 68.3% to 90.3% without increasing the overall seat size.

[0087] Experimental Example 2 compares and verifies the evaluation indicators of body pressure distribution between Example 1 and Comparative Example 2. Weighted body pressure distribution entropy is used respectively. The seat pressure distribution of the two schemes was evaluated using the traditional SPD index, and the peak pressure and average contact pressure in the ischial tuberosity region were recorded.

[0088] Experimental results are as follows Figure 2 As shown. Figure 2 This is a comparison chart of body pressure distribution indices between Example 1 and Comparative Example 2. Figure 2 In the middle, 'a' is a horizontally grouped bar chart, showing the weighted volume pressure distribution entropy. A comparison of the two indicators, SPD and Example 1 The value is 0.841, and the SPD is 0.248, compared to Comparative Example 2. The value is 0.743, and the SPD value is 0.231. Figure 2In Figure b, a horizontally grouped bar chart is presented, showing the comparison between the peak pressure and the average contact pressure in the ischial tuberosity region. In Example 1, the peak pressure in the ischial tuberosity region was 42.3 mmHg and the average contact pressure was 18.6 mmHg. In Comparative Example 2, the peak pressure in the ischial tuberosity region was 51.7 mmHg and the average contact pressure was 17.9 mmHg.

[0089] from Figure 2 As can be seen, the SPD value of Comparative Example 2 is 0.231, slightly better than that of Example 1 (0.248), indicating that its overall pressure distribution has a slightly smaller statistical dispersion. However, the peak pressure in the ischial tuberosity region of Comparative Example 2 is as high as 51.7 mmHg, which is 22.2% higher than that of Example 1 (42.3 mmHg), approaching the upper limit of the comfort threshold of 60 mmHg. Meanwhile, the weighted body pressure distribution entropy of Comparative Example 2... The value is only 0.743, far lower than 0.841 in Example 1. This seemingly contradictory phenomenon reveals the inherent limitations of the SPD index. SPD only measures the overall dispersion of pressure distribution and does not distinguish the differentiated sensitivity of different parts of the human body to pressure. When optimization aims to minimize SPD, the algorithm tends to shift the high pressure in the ischial tuberosity region to less sensitive areas such as the anterior thigh. Although the overall statistical dispersion is reduced, the ischial tuberosity region, the most pressure-sensitive area, actually bears higher concentrated pressure. The weighted body pressure distribution entropy proposed in step S33 of this invention introduces a human body part sensitivity weight coefficient, so that the pressure state in the ischial tuberosity region has 1.5 times the influence on the evaluation index as much as the mid-thigh region. Combined with the constraint in step S34 that the peak pressure in the ischial tuberosity region does not exceed the comfort threshold, the peak pressure in the key load-bearing area is effectively controlled while achieving a uniform distribution of overall pressure.

[0090] Experimental Example 3 compares and verifies the vibration transmissibility of Example 1 and Comparative Example 3. The frequency-weighted vibration transmissibility of Example 1 and Comparative Example 3 under three types of train operating conditions is calculated respectively.

[0091] Experimental results are as follows Figure 3 As shown. Figure 3 This is a comparison chart of the vibration transmissibility under various operating conditions for Example 1 and Comparative Example 3. Figure 3 The graph in section 'a' is a line graph showing the frequency-weighted vibration transmissibility of Example 1 and Comparative Example 3 under operating conditions I, II, and III. Trend of change. Example 1 under three types of working conditions. The values ​​were 0.71, 0.76, and 0.79 respectively, all below 1.0, indicating that the seat system damped vibration under all operating conditions. Comparative Example 3 under three operating conditions... The values ​​are 0.82, 0.93, and 1.05 respectively, with condition III exceeding 1.0. The figure also indicates... The reference line, i.e. the baseline without attenuation. Figure 3 The bar chart in section b shows the comparison of vibration transmissibility under comprehensive working conditions. Example 1 has a transmissibility of 0.742, while Comparative Example 3 has a transmissibility of 0.891.

[0092] from Figure 3 As can be seen from the data, the vibration transmissibility of Comparative Example 3 under Condition III reached 1.05, exceeding the baseline of 1.0 for no attenuation. This indicates that the seat system not only failed to attenuate vibrations under conditions of turnout or bridge passage, but also amplified the vibrations transmitted from the vehicle body. Looking at the trend line, Comparative Example 3... The value shows a steep upward trend from operating condition I to operating condition III, while the value of Example 1... The increase in value is significantly gradual. The fundamental reason for this difference is that when using the independent optimization method in Comparative Example 3, the seat cushion indentation depth was increased in step S3 to improve the entropy of body pressure distribution. However, this geometric change simultaneously reduced the effective bearing area and thickness of the seat cushion, resulting in a decrease in the equivalent stiffness of the seat cushion. Since steps S2 to S4 are executed independently, the changes in surface parameters are not fed back into the vibration model of step S4, causing the first natural frequency of the seat system to shift from around 3Hz to around 5Hz, falling into the human body's vertical vibration sensitive frequency range of 4~8Hz. This results in resonance amplification under broadband excitation conditions such as turnouts or bridge passages. In step S5 of this invention, the coupling constraint relationship between the surface shaping parameters and the vibration reduction parameters is established through sub-step S52. The equivalent stiffness of the seat cushion is expressed as a function of the contact area and the seat cushion thickness, enabling the NSGA-II algorithm to automatically evaluate the impact of the surface parameters on vibration transmission performance while optimizing the surface parameters. This multi-parameter collaborative optimization mechanism enabled Example 1 to effectively avoid the risk of resonance while increasing the entropy of body pressure distribution, and the overall vibration transmission rate under working conditions was reduced by 16.7% compared with Comparative Example 3.

[0093] Experiment 4 compares all three implementation examples and three comparative examples across three core metrics. The evaluation metrics include interval coverage. Weighted volume pressure distribution entropy Frequency-weighted vibration transmissibility under combined operating conditions .

[0094] Experimental results are as follows Figure 4 As shown. Figure 4 A heatmap comparing all embodiments and comparative examples based on three core indicators is provided. The horizontal axis of the heatmap represents six schemes, and the vertical axis represents the three core indicators. The intensity of the color blocks indicates the degree of superiority or inferiority of each indicator value. Higher interval coverage and weighted volume pressure distribution entropy are considered better, while lower comprehensive operating condition vibration transmission rate is also considered better. The indicator data for each scheme are summarized below. Example 1... 0.903 0.841 It is 0.742. Example 2 0.911 It is 0.837. It is 0.748. Example 3 0.895 0.852, It is 0.761. (Comparative Example 1) 0.683 It is 0.839. It is 0.745. (Comparative Example 2) 0.901 0.743 It is 0.746. (Comparative Example 3) It is 0.897. 0.814 It is 0.891.

[0095] from Figure 4 As can be seen, the color blocks in the heatmaps of the three embodiments exhibit a uniform dark distribution, indicating that they have achieved a good overall level in all three core indicators, with no significant weakness in any one indicator. In contrast, each of the three comparative examples shows a distinct light-colored area, corresponding to a weakness in their respective design methods. Comparative Example 1 shows weakness in coverage. The lightest color is most noticeable on the rows because of its The value is only 0.683, far lower than the other five schemes, which intuitively reflects the shortcomings of the traditional independent percentile method in multidimensional size adaptation. Comparative Example 2 shows the weighted volume pressure distribution entropy. The rows are light-colored, and their The value is 0.743, the lowest among all schemes, indicating that the SPD method without incorporating location sensitivity weights has a systematic bias in the accuracy of comfort evaluation. Comparative Example 3 shows the vibration transmissibility... The rows are light-colored, and their The value of 0.891 is the highest and worst among all schemes, indicating that the independent optimization method without considering the coupling effect between parameters cannot guarantee global performance. The color difference between the three embodiments is small, and the difference mainly reflects the reasonable trade-off between the objectives under different TOPSIS weight settings in step S6. All are located on the Pareto optimal front, indicating that the method of the present invention is superior to the corresponding traditional methods in three dimensions: interval coverage, body pressure distribution comfort, and vibration attenuation performance.

[0096] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. 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 designing parameters of business class seats for railway trains, characterized in that, Includes the following steps: S1. Joint distribution modeling of human body dimensions: Collect multiple seated human body dimension data of the target passenger group, conduct distribution characteristic tests and correlation analysis on each dimension data, and establish a multivariate joint probability distribution model of multiple dimension parameters. S2. Determination of seat geometric dimension parameters based on interval coverage: Based on the multivariate joint probability distribution model, the joint probability of multiple dimension parameters falling into their respective design adaptation intervals is used as the interval coverage. Under the constraint that the interval coverage is not lower than the preset target value, the interval allocation is adjusted by sensitivity analysis of the adaptation intervals of each parameter to determine the seat geometric dimension parameters. S3. Optimization of seat cushion surface parameters based on body pressure distribution entropy: Establish a parameterized seat cushion surface model, obtain body pressure distribution data of the seat cushion contact area through finite element simulation, introduce part sensitivity weights based on human body pressure perception characteristics to calculate weighted body pressure distribution entropy, and optimize the seat cushion surface shape parameters with the goal of maximizing the weighted body pressure distribution entropy and satisfying the pressure constraints of key load-bearing areas. S4. Evaluation of seat-human body coupled vibration transmissibility: Establish a multi-degree-of-freedom human body-seat coupled equivalent linear lumped parameter vibration model, use the car body vibration signal under typical train operating conditions as excitation input, calculate the frequency-weighted vibration transmissibility, evaluate and optimize the seat's vibration reduction performance. S5. Multi-objective parameter collaborative optimization: The interval coverage, the weighted body pressure distribution entropy and the frequency-weighted vibration transmissibility are used as the optimization objective functions. The seat geometric parameters, surface shape parameters and vibration reduction parameters are uniformly encoded as design variables. The coupling constraint relationship between surface parameters and vibration reduction parameters is established. A multi-objective genetic algorithm based on non-dominated sorting is used for collaborative optimization. Infeasible solutions are handled through the constraint dominance principle to obtain the Pareto optimal solution set. S6. Optimal Solution Output: The candidate solutions in the Pareto optimal solution set are standardized by objective function value, the minimization objective is transformed into a positive transformation, and the final seat parameter design scheme is output by comprehensively sorting the candidate solutions according to the design priority weight using the approximation ideal solution sorting method.

2. The method for designing parameters of business class seats for railway trains according to claim 1, characterized in that, Step S1 includes the following sub-steps: S11. Human body size data collection: Obtain sample data of the sitting human body size of the target passenger group from the human body size standard database or actual survey data. The sample data includes six sitting posture size parameters: sitting height, sitting depth, hip width, shoulder width, calf plus foot height and thigh thickness. S12. Distribution characteristic test and preprocessing: The six sitting posture size parameters are subjected to Shapiro-Wilk normality test respectively; when a parameter fails the test, it is subjected to Box-Cox transformation and then retested; if the normality requirement is still not met after transformation, the kernel density estimation method is used to nonparametrically model the marginal distribution of the parameter. S13. Joint distribution modeling: Calculate the correlation coefficients between each pair of the six sitting posture size parameters; when all parameters meet the normality requirement, construct the mean vector and covariance matrix to establish a multivariate normal joint probability distribution model; when there are parameters that do not meet the normality requirement, use the Copula function to combine the marginal distributions of each parameter to establish a joint probability distribution model; the established joint probability distribution model is used for interval coverage calculation in the subsequent step S2.

3. The method for designing parameters of business class seats for railway trains according to claim 2, characterized in that, Step S2 includes the following sub-steps: S21. Fit Range Setting: Set a design fit range for each of the six sitting posture size parameters. Each fit range is determined by the lower limit of the design range for that parameter. and design limit Composition, in which This is the parameter number; the initial value is taken from the 5th percentile to the 95th percentile of the corresponding parameter. S22. Interval Coverage Calculation: Randomly sample from the joint probability distribution model established in step S13. One sample point, No less than 10,000; determine whether the six parameter values ​​of each sample point simultaneously fall within their respective fit intervals; count the number of sample points that simultaneously satisfy all six interval constraints. Calculate the interval coverage using the following formula. : ; in, For interval coverage, dimensionless, it represents the joint probability that all dimensional parameters are simultaneously adapted by the seat design scheme; The number of sample points that simultaneously satisfy all six adaptation interval constraints; This represents the total number of sample points drawn from the joint distribution model; S23. Sensitivity-based range adjustment: Set the target coverage value. Apply a unit perturbation to the adaptation interval width for each size parameter and recalculate the interval coverage. The sensitivity coefficients of interval coverage to the interval width of each parameter are obtained; in descending order of sensitivity coefficients, the parameter intervals with high sensitivity are expanded first, while the parameter intervals with low sensitivity are contracted, while satisfying the condition... Not less than To minimize the overall size increment of the seat under constraints; S24. Geometric Dimension Parameter Mapping and Output: Based on the correspondence between human sitting posture dimensions and seat structural dimensions, the optimized adaptation ranges are converted into seat structural parameters: the seat depth design value is taken as the upper limit of the seat depth adaptation range. The seat width design value is taken as the upper limit of the hip width adaptation range. Upper limit of the shoulder width matching range The larger of the values ​​is taken, plus a lateral margin; the seat height design value is the seat surface height corresponding to the median value of the lower leg plus foot height adaptation range; the backrest height is the upper limit value of the seat height adaptation range. Subtract the seat height; take the initial backrest angle as the midpoint between 100° and 110°; thus obtain the initial geometric dimensions of the seat.

4. The method for designing parameters of business class seats for railway trains according to claim 1, characterized in that, Step S3 includes the following sub-steps: S31. Parametric seat cushion surface modeling: Using the seat reference point as the origin of the coordinate system, define the shape parameters of the seat cushion surface, including the height of the front edge of the seat cushion, the depth of the ischial tuberosity region, the height of the side wing of the seat cushion, the longitudinal radius of curvature of the seat cushion, and the lateral radius of curvature of the seat cushion; using the above shape parameters as control quantities, generate a parametric seat cushion surface geometric model through B-spline interpolation. S32. Body Pressure Distribution Simulation and Normalization: Import the geometric model of the seat cushion surface into finite element software to establish a contact analysis model including the seat cushion material layer and the human buttock-thigh contact area; discretize the seat cushion contact area into... OK A rectangular grid of columns; Contact simulation was performed after applying a seated human body gravity load, and the normal contact pressure values ​​at each mesh node were extracted. ; Divide the pressure value of each node by the sum of the pressure values ​​of all nodes to obtain the normalized pressure value. This makes the sum of the normalized pressure values ​​of all nodes equal to 1; S33. Weighted Body Pressure Distribution Entropy Calculation: Based on the corresponding anatomical location of each grid node on the cushion, and drawing on experimental data on human pressure perception sensitivity or published human factors engineering literature, assign a pressure sensitivity weight coefficient to each node. The weighting coefficient of the ischial tuberosity region is higher than that of the mid-thigh region, and the weighting coefficient of the mid-thigh region is higher than that of the anterior thigh region. Calculate the weighted volume pressure distribution entropy using the following formula. : ； in, is the weighted volume pressure distribution entropy, which is dimensionless and ranges from 0 to 1; For the first Line number The pressure sensitivity weighting coefficients of the human body parts corresponding to the grid nodes are dimensionless. For the first Line number The normalized pressure value of the column grid node, dimensionless; The natural logarithm operator; The number of grid rows; Number of grid columns; Indicates all Sum of the nodes; The closer the value is to 1, the more uniform the body pressure distribution is after considering site sensitivity; S34. Surface parameter optimization: using the weighted volume pressure distribution entropy... The optimization objective is to maximize the surface shape parameters of each seat cushion defined in step S31. The constraints include that the maximum contact pressure in the ischial tuberosity area does not exceed the human body pressure comfort threshold and the total contact area of ​​the seat cushion is not less than the preset minimum value. Solving for each shape parameter within the manufacturing process allowable range yields the desired result. The optimal combination of surface parameters that yields the maximum value.

5. The method for designing parameters of business class seats for railway trains according to claim 1, characterized in that, Step S4 includes the following sub-steps: S41. Establishment of a four-degree-of-freedom equivalent linear vibration model: The human-seat system is simplified into an equivalent linear lumped parameter model of four mass-spring-damping subsystems connected in series vertically; the first mass block represents the seat base, with a mass of... Through stiffness and damping Connected to the vehicle floor; The second mass block represents the seat cushion, and its mass is... Through stiffness and damping Connected to the seat base; the third mass block represents the lower torso of the human body, with a mass of Through stiffness and damping Connect to the seat cushion; The fourth mass block represents the upper torso of the human body, with a mass of [missing information]. Through stiffness and damping It is connected to the lower torso of the human body; the mass value of each mass block is determined according to the structural design parameters of the seat and the biomechanical parameters of the human body. S42. Frequency Domain Solution: Based on the four-degree-of-freedom equivalent linear model, write a set of differential equations of motion for the four mass blocks in the vertical direction, using the vertical vibration displacement of the vehicle floor as the system excitation input; perform a Fourier transform on the set of equations of motion to obtain the transfer function between the human torso displacement response and the vehicle floor excitation. ; S43. Operational Excitation Acquisition: Typical train operating conditions are divided into three categories: straight-line uniform speed operation, curve passing operation, and turnout or bridge passing operation; the power spectral density of the vertical vibration of the car body floor is acquired for each type of operating condition. The data is obtained through fitting actual measured data of the line or vehicle dynamics simulation. S44. Calculation of frequency-weighted vibration transmissibility: Combining the transfer function obtained in step S42 and the power spectral density of each operating condition obtained in step S43, the frequency-weighted vibration transmissibility is calculated using the following formula. : ； in, The frequency-weighted transmissivity is dimensionless. The magnitude of the transfer function; It is a vertical frequency weighting function; The power spectral density of the vertical vibration of the vehicle body floor; Angular frequency; A value less than 1 indicates that the seat system has a vibration damping effect; the frequency-weighted vibration transmissibility corresponding to each of the three working conditions is obtained by substituting the corresponding power spectral density into the calculation.

6. The method for designing parameters of business class seats for railway trains according to claim 1, characterized in that, Step S5 includes the following sub-steps: S51. Unified Coding of Design Variables: The geometric dimensions, seat surface shape parameters, and vibration damping parameters of the seat are uniformly coded into a single design variable vector. The geometric dimensions include seat width, seat depth, seat height, and backrest angle. The surface shape parameters include the height of the seat cushion front edge, the depth of the ischial tuberosity region indentation, the height of the seat cushion side wing bulge, the longitudinal radius of curvature of the seat cushion, and the lateral radius of curvature of the seat cushion. The vibration damping parameters include the base connection stiffness, the base connection damping, the equivalent stiffness of the seat cushion, and the equivalent damping of the seat cushion. S52. Establishing Coupling Relationships and Constructing Objective Functions: Establishing the coupling constraint relationship between surface shaping parameters and vibration reduction parameters, and setting the equivalent stiffness of the seat cushion. Expressed as the elastic modulus of the seat cushion foam material The actual contact area between the human body and the seat cushion and effective thickness of the seat cushion function ,in Determined jointly by surface modeling parameters and human body model. The cushion material is provided by the supplier, thus incorporating the impact of surface parameter variations on vibration transmission performance into the optimization framework; the three optimization objectives are constructed as follows: maximizing interval coverage, maximizing weighted body pressure distribution entropy, and minimizing the comprehensive operating condition frequency-weighted vibration transmission rate; the comprehensive operating condition frequency-weighted vibration transmission rate is the value of the vibration transmission rate of each of the three operating conditions weighted by the proportion of running time. S53, NSGA-II Solution and Constraint Handling: Set the population size, number of iterations, crossover probability, and mutation probability. The crossover operator uses simulated binary crossover, and the mutation operator uses polynomial mutation. In the fitness evaluation of each generation, infeasible individuals are handled by the constraint domination principle, that is, feasible solutions dominate infeasible solutions, and infeasible solutions are sorted according to the degree of constraint violation. Population diversity and convergence are maintained by fast non-dominated sorting and crowding distance calculation, and the Pareto optimal solution set is output.

7. The method for designing parameters of business class seats for railway trains according to claim 6, characterized in that, Step S6 includes the following sub-steps: S61. Target value standardization and forward transformation: The three objective function values ​​of each candidate scheme in the Pareto optimal solution set are standardized. The standardization method is to subtract the minimum value of the objective in the solution set from each objective function value and then divide by the difference between the maximum and minimum values ​​of the objective in the solution set. The minimum objective, namely the vibration transmissibility under the comprehensive working condition, is forward transformed by subtracting the standardized value of the objective from 1, so that after standardization, each objective is in the direction of being larger and better. S62. Weight Determination and Comprehensive Ranking: Based on the design priority of the business seats, the weights of the three objectives—interval coverage, weighted body pressure distribution entropy, and comprehensive working condition vibration transmissibility—are determined using the analytic hierarchy process or the entropy weight method. Construct positive ideal solutions and negative ideal solutions respectively. The positive ideal solution is a virtual solution in which the positive standard value of each objective takes the optimal value in the solution set, and the negative ideal solution is a virtual solution in which the positive standard value of each objective takes the worst value in the solution set. Calculate the weighted Euclidean distance from each candidate solution to the positive ideal solution and the negative ideal solution. Calculate the overall proximity score, which is equal to the distance to the negative ideal solution divided by the sum of the distances to the positive ideal solution and the distances to the negative ideal solution. Sort the overall proximity scores from largest to smallest and output the values ​​of all design variables corresponding to the best-ranked scheme as the final seat parameter design scheme.

8. A parameter design system for business class seats on railway trains, used to implement the method according to any one of claims 1 to 7, characterized in that, It includes a processor, a memory, and a computer program stored in the memory and executable by the processor. When the processor executes the computer program, it implements the following functional modules: The human body size data management module is connected to the interval coverage calculation module. It is used to receive and store multiple sitting human body size sample data of the target passenger group, perform distribution characteristic tests and correlation analysis on the sample data, establish a multivariate joint probability distribution model, and output the established model to the interval coverage calculation module. The interval coverage calculation module is connected to the human body size data management module and the multi-objective collaborative optimization module respectively. It is used to receive the multivariate joint probability distribution model and the adaptation interval of each size parameter, calculate the interval coverage through Monte Carlo sampling statistics and sensitivity analysis, and output the coverage value to the multi-objective collaborative optimization module. The body pressure distribution simulation and evaluation module is connected to the multi-objective collaborative optimization module. It is used to generate a parameterized surface geometric model based on the received cushion surface shape parameters, call the finite element simulation engine to calculate body pressure distribution data, normalize the body pressure distribution data and assign pressure sensitivity weights according to human body parts, calculate the weighted body pressure distribution entropy, and output the entropy value to the multi-objective collaborative optimization module. The vibration transmission analysis module is connected to the multi-objective collaborative optimization module. It is used to establish a four-degree-of-freedom human-seat coupling equivalent linear vibration model based on the received vibration reduction parameters, receive vibration excitation data of train operation conditions, calculate the frequency-weighted vibration transmission rate under each operation condition, and output the transmission rate results to the multi-objective collaborative optimization module. The multi-objective collaborative optimization module is connected to the interval coverage calculation module, the body pressure distribution simulation and evaluation module, and the vibration transmission analysis module, respectively. It is used to take interval coverage, weighted body pressure distribution entropy, and frequency-weighted vibration transmissibility as objective functions, and geometric dimension parameters, surface modeling parameters, and vibration reduction parameters as design variables. It establishes the coupling constraint relationship between surface parameters and vibration reduction parameters, executes a multi-objective genetic algorithm based on non-dominated sorting for collaborative optimization, handles infeasible solutions through constraint dominance principles, generates a Pareto optimal solution set, and outputs the final design scheme through the approximation ideal solution sorting method. The results output and reporting module is connected to the multi-objective collaborative optimization module to receive the parameter values ​​of the final design scheme and the evaluation results of each objective function, and to generate a design report containing seat parameters and performance evaluation.

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