Parameters optimum of multiple underframe suspended equipment on high-speed railway vehicle carbody vibration control by using an improved genetic algorithm

Abstract

Carbody vibration control and ride comfort improvement are important research parts of high-speed railway vehicle dynamic. The effectiveness of utilizing carbody underframe suspended equipment as dynamic vibration absorbers for carbody vibration suppression has been validated. While previous research has focused mainly on a single suspended equipment without considering its vibration tolerance, a balance must be struck between reducing carbody vibration and maintaining equipment performance. To address the challenging, a multi-objective and multi-parameter optimization method is employed, integrating an improved niche genetic algorithm (INGA) into the numerical simulation process. Considering carbody flexible and multi-suspended equipment, a rigid-flexible dynamics model of a high-speed railway vehicle is established and validated on a vehicle dynamics test rig. Based on the numerical analysis, the optimal parameter combination of the stiffness and the longitudinal installation position is obtained from an evaluation function that comprehensively assesses the vibration performance of both the vehicle carbody and the equipment. Comparative analysis between the results obtained from the optimal and primitive parameters demonstrates that the optimization process not only achieves significant improvements in carbody vibration reduction but also effectively controls equipment vibration within reasonable limits. The multi-objective and multi-parameter optimization method applied on carbody underframe suspended system proves to be valuable in improving the dynamic performance of high-speed railway vehicles.

Keywords

high-speed railway vehicle carbody vibration control suspended equipment multi-objective and multi-parameter optimization improved niche genetic algorithm

1. Introduction

Improving passenger ride comfort has always been a significant area of research for high-speed railway trains. With a growing number of high-speed trains in operation and a substantial increase in mileage, the contradiction between various operating environments and vehicle suspension parameters is becoming increasingly prominent. The issue of vehicle abnormal vibration has become more common, exerting a substantial adverse impact on passenger ride comfort.

A typical approach involves the combination of passive and active control suspension systems on the vehicle bogie. Researchers have conducted numerous parameter optimization studies focusing on carbody and bogie vibration performance, referencing prior works (Savoskin et al., 2018; Pandey and Bhattacharya, 2020; Wang et al., 2023). The principal subjects of optimization include components within the primary and secondary suspension of the bogie, encompassing the primary spring, secondary air spring, anti-yaw damper, traction rod, among others (Bokaeian et al., 2021; Wu et al., 2018). In addition, some multi-objective optimization methods have been employed to optimize the key suspension parameters, balancing multiple complex and conflicting performance indexes. Yao et al. (2020) used a multi-objective optimization method to optimize key parameters simultaneously to balance the multiple complicated and conflicting performance indexes. Ripamonti and Chiarabaglio (2019) modified an oil damper to achieve high performances at low frequencies and transmit low force at high frequencies.

Once the conventional passive suspension have been optimized, the dynamic performance of the vehicle system attains its pinnacle, thereby constraining its adaptability in the face of wheel/rail wear, suspension parameter degradation, and dissimilarities in track excitation in diverse railway lines. Research on active control has emerged as a prominent research domain over the past few decades. Common suspension components include the primary vertical damper, anti-yaw damper, and secondary lateral damper. Braghin et al. (2006) developed an electro-mechanical actuator applied between the carbody and the bogie to improve the vehicle operational performance, both in straight and curve track. Pearson et al. (2004) compared the effect of control algorithms for actively stabilized wheelsets on high-speed railway vehicles to provide stability across a range of operating conditions. Metin and Guclu (2011) placed an active damper on the secondary suspension to compare the performance of fuzzy logic and PID control methods. Fu et al. (2022) conducted an analysis of semi-active primary suspensions to improve vehicle ride comfort, showing that the proposed scheme is effective in reducing carbody vibration from 1 Hz to 20 Hz. Wu et al. (2023) proposed active control algorithms for a secondary lateral damper to enable the vehicle operate in different track conditions and at various speeds. Various control strategies are analyzed based on performance indicators such as vehicle ride comfort, carbody vibration acceleration, and time delay. The impact of different control strategies on reducing performance indicators is assessed and an optimal control strategy is proposed.

The research on suppressing carbody vibration primarily focuses on vibration isolation. Passive or active control suspensions are installed on the bogie to isolate vibrations transmitted from the bogie to the carbody. The secondary suspension with active control has proven effective in reducing carbody vibrations, but it can also amplify bogie frame vibrations. As the main load-bearing structure of the bogie, the vibration of the frame are crucial for the overall performance of the bogie. Additionally, any failure within the active suspension system can lead to a substantial deterioration in the dynamic performance, thereby exacerbating carbody vibrations and posing a considerable safety risk. Consequently, due to limitations in control strategies, the practical application of active suspension systems is less common.

To achieve higher train speeds, two important measures are considered: lightweight design of the vehicle carbody and power-decentralized traction mode. Lightweight design reduces the stiffness of the carbody, leading to increased elastic vibrations. In the power-decentralized traction mode, different functional equipment such as traction transformers and auxiliary converters are suspended on the carbody underframe, as shown in Figure 1. The collective mass of these components spans a wide spectrum, ranging from a few tens of kilograms to several tons, thereby approaching that of carbody’s aluminum alloy structure. The coupling relationship between the carbody and suspended equipment significantly can affect carbody vibration. Therefore, based on this concept, the equipment provides a good research route for carbody vibration control.

To reduce carbody elastic vibration, particularly the first-order vertical bending frequency, the equipment suspended on the carbody underframe is treated as a dynamic vibration absorber (DVA) and the optimal parameters are analyzed (Shi et al., 2014; Wang et al., 2018; Gong et al., 2013). The effectiveness of this approach has been substantiated through a combination of theoretical analyses, numerical simulations, and rig tests. Moreover, active control systems have been applied to the equipment and different control strategies have been compared in terms of carbody vibration reduction (Wang et al., 2020a, 2020b). The equipment not only provides damping effects on carbody vertical vibration but also has the capability to suppress lateral vibration (Wang et al., 2016). With the progressive accrual of operational mileage, the wheel/rail contact relationship deteriorates due to wear, thereby exacerbating carbody lateral vibrations. It is pertinent to note that different parameters demonstrate varying degrees of efficacy in ameliorating carbody lateral vibrations.

To achieve optimal control on carbody vibration, it is essential to comprehensively consider the matching of equipment suspension stiffness, damping ratio, and longitudinal location. However, current research does not adequately consider the equipment vibration tolerance. The equipment vibration is an important factor in its effectiveness and maintaining its vibration within a reasonable range is crucial in carbody vibration reduction. Furthermore, existing research predominantly concentrates on a single equipment, neglecting the complexity of the coupling vibration mechanism between the carbody and multiple-suspended equipment. When dealing with multiple-suspended equipment, there are interactions between each equipment and the design of parameters involves multiple parameter combinations and multiple indicators. Genetic algorithms (GA) are commonly used for multi-objective and multi-parameter optimization analysis, comprehensively considering the vibration performance of the carbody and equipment (Holland, 1992). However, standard GA has limitations in terms of global convergence, leading to the emergence of derived algorithms. Among these, Niche genetic algorithms (NGA) have emerged as a distinctive choice, heralding substantial advantages in the pursuit of local and global optima in optimization quandaries (Glibovets and Gulayeva, 2013; Bingül and Yıldız, 2023). As NGA proves to be an effective method for optimizing parameters, it requires the presetting of certain basic parameters based on experience, such as crossover probability, mutation probability, and niche distance. An erroneous choice of these parameters could impede the attainment of an optimal solution and underutilize NGA's inherent capability to sustain population diversity. Therefore, an improved niche genetic algorithm (INGA) is proposed to conduct research on carbody vibration control, providing technical support for the improvement of high-speed railway vibration performance.

The overall structure of the research is organized as follows. In Section 2, considering flexible carbody and multi-suspended equipment, a rigid-flexible dynamics model of a high-speed railway vehicle is firstly established and then model validation through a rig test is introduced in detail. In Section 3, INGA is proposed to conduct multi-objective and multi-parameter optimization and an evaluation function is obtained that comprehensively assesses the vibration performance of the carbody and equipment. In Section 4, a comparative analysis between the results obtained from the optimal and primitive parameters is conducted and some conclusions are drawn in Section 5.

2. Model establishment and verification

2.1. Model establishment

To investigate the coupling vibration behavior between the flexible carbody and the suspended equipment, a rigid-flexible dynamics model of a high-speed railway vehicle is constructed using the SIMPACK platform. In the multibody dynamics simulation model, only the carbody is considered to be flexible, while all other components are modeled as rigid bodies. The vehicle carbody, bogie frame, and three suspended equipment have six degrees of freedom (DOFs), allowing translational and rotational motions with respect to the longitudinal, lateral, and vertical directions. The rotary arm axle-box exhibits one DOF of pitching motion and the wheelset has four DOFs. The three equipment represent the traction converter, traction transformer, and braking unit, which are named Equipment 1, Equipment 2, and Equipment 3 in the simulation model. As a result, the dynamics model of a high-speed railway vehicle with a total of 60 DOFs is established and some key parameters of the vehicle system are presented in Table 1. These parameters are all input parameters for the dynamic model, which can have a significant impact on the research result.

Table 1.

Some key parameters of the high-speed railway vehicle.

Description	Sign	Value	Unit
Mass of carbody	m _c	26	t
Inertia of carbody pitching motion	Ic	1274	t·m²
Carbody Mass per unit length	ρA	1.06	t·m⁻²
Carbody bending stiffness	EI	4.28e9	N·m²
Mass of bogie frame	m _b	2.53	t
Vertical damping of primary suspension	c _1z	40	kN·s·m⁻¹
Vertical damping of secondary suspension	c _2z	30	kN·s·m⁻¹
Vertical stiffness of primary suspension	k _1z	2.40	MN·m⁻¹
Vertical stiffness of secondary suspension	k _2z	0.38	MN·m⁻¹
Half-length between bogie center	L _s	8.75	m
Half-length of wheel base	L _w	1.25	m
Mass of equipment 1	m _e1	1.04	t
Mass of equipment 2	m _e2	1.29	t
Mass of equipment 3	m _e3	2.85	t

The complete finite element (FE) model of vehicle carbody has a large number of nodes and DOFs, which is not suitable for the dynamic analysis. Therefore, Guyan method (Koutsovasilis and Beitelschmidt, 2008) is used to reduce DOFs of carbody FE model and obtain the substructure FE model of the vehicle carbody. The substructure FE model includes mass matrix, stiffness matrix, and geometric information. By using the interface programs of FEMBS, the substructure FE carbody model is imported into the dynamics model. A rigid-flexible coupling dynamics model of a high-speed railway vehicle is obtained in Figure 2.

2.2. Model validation

The suspension self-vibration characteristic of the vehicle system is an inherent property that depends on the suspension parameters, mass, and inertia. The difference of the suspension modal frequency between the simulation model and the test is a key indicator to evaluate whether the model is accurate. Suspension frequency tests can be conducted using a test rig or through a vehicle drop test on a wedge. In this paper, the suspension frequency test is performed using the Full-scale Roller and Vibration Rig of Rolling Stock (FRVR) (Liang et al., 2023), as shown in Figure 3.

FRVR is a comprehensive testing platform designed to dynamically simulate the vehicle vibration performance at different running speeds. The vehicle wheelset on the rig is driven by a driving wheel to simulate the running speed, while hydraulic actuators apply excitations such as track irregularities and harmonic excitation. The sweep-frequency excitation method is used to analyze the vehicle vibration response by applying displacement excitation that varies with frequency over time. When the vehicle has a natural frequency within the swept frequency range, the vibration response at that frequency can significantly increase, leading to the phenomenon of vibration resonance. It is manifested as a clear dominant vibration frequency in the frequency domain. The displacement excitation can be expressed as follows:

s = A \sin (c_{2} t^{2} + c_{1} t + c_{0})

(1)

where A is the excitation amplitude. c₀, c₁, and c₂ are the functions of the time and excitation frequency. In the verification test conducted on FRVR to validate the model, the amplitude is 0.5 mm and the variation range of excitation frequency is from 0.5 Hz to 20 Hz.

In the model validation experiment, carbody vertical vibration performance with the suspended equipment is analyzed and compared with the simulation results, as shown in Figure 4. The elastic connection and rigid connection of the equipment are included. The measuring point is located in the middle of the carbody.

When the equipment is rigidly suspended, there are two main frequencies in the carbody vertical vibration. The simulation and rig test results both have a dominant frequency at 1.2 Hz, belonging to a rigid mode, namely, carbody floating motion. And the other is the carbody elastic mode. The simulation result is 12.6 Hz and the test result is 12.4 Hz. Under rigid suspension, the simulation and test results are similar in the vibration main frequency, but there are certain differences in amplitude. When the equipment is elastically suspended, the carbody vertical vibration shows three main frequencies. The carbody floating frequency of the simulation and test result are the same with slight differences in amplitude. According to the DVA theory, the suspended equipment with elastic suspension acts as a DVA, splitting the carbody vertical bending frequency into two main vibration frequencies and reducing the vibration amplitude. In the simulation results, carbody elastic vibration is 8.2 Hz and 15.6 Hz, while in the bench test, it is 7.4 Hz and 15.5 Hz, respectively. Lower frequency refers to the movement of the vehicle carbody and equipment in the same direction, while higher frequency refers to reverse movement. The difference between simulation and experiment is mainly in the low frequency, with a frequency difference of about 10%, but the amplitude difference between the two is relatively small.

Considering the main frequencies and vibration trends, whether the equipment is rigidly or elastically suspended, the simulation and experimental results of carbody vibration characteristics have a good agreement, verifying the accuracy of the established dynamic model.

3. Multi-objective and multi-parameter optimization

When the carbody vibration performance is studied with a single suspended equipment, the suspension stiffness, damping, and longitudinal installation position of the equipment can have good effects on carbody vibration control. However, when it comes to the multiple-suspended equipment, the parameter design involves the optimal combination of multiple parameters and also needs to comprehensively consider both the carbody and equipment vibration. Therefore, traditional parameter optimization methods are no longer suitable for addressing this multi-objective and multi-parameter problem.

To enhance the parameter optimization performance, INGA is proposed with four improvements (Long et al., 2022). Firstly, the niche distance parameter is dynamically set as a function related to the evolution progress, allowing it to adapt to the changing population structure. Secondly, Gray Code is used for individual coding, which improves the encoding efficiency. Thirdly, the crossover probability and mutation probability are automatically adjusted based on individual fitness, enabling a more adaptive and effective search. Lastly, an elite retention strategy is adopted to preserve the best individuals in each generation, preventing the loss of valuable information during the evolutionary process. By incorporating these enhancements, INGA aims to improve the overall performance and efficiency of parameter optimization.

3.1. Variable parameter

The parameters for optimizing mainly include the horizontal stiffness k_y, vertical stiffness k_z, and longitude installation position L_x of the suspended equipment. The stiffness of each equipment is defined as k_yi and k_zi, respectively, i = 1, 2, 3. The distance between the longitudinal installation position and the carbody center is L_xi. When the value of L_xi is positive, the installation position of the equipment is close to the front bogie. And the equipment is close to the rear bogie when the value is negative. The initial values of parameters are named k_yi0, k_zi0, and L_xi0, calculated on the simulation model with a single suspended equipment, and will be discussed later.

The range of variable parameters are shown as follows:

\begin{array}{l} 0.5 k_{y 10} \leq k_{y 1} \leq 2 k_{y 10}, 0.5 k_{z 10} \leq k_{z 1} \leq 2 k_{z 10} \\ 0.5 k_{y 20} \leq k_{y 2} \leq 2 k_{y 20}, 0.5 k_{z 20} \leq k_{z 2} \leq 2 k_{z 20} \\ 0.5 k_{y 30} \leq k_{y 3} \leq 2 k_{y 30}, 0.5 k_{z 30} \leq k_{z 3} \leq 2 k_{z 30} \\ - 2.5 \leq L_{x 1} \leq 2.5, - 2.5 \leq L_{x 2} \leq 2.5, - 2.5 \leq L_{x 3} \leq 2.5 \end{array}

(2)

3.2. Performance index

The suspended equipment plays a dynamic vibration absorption role by increasing equipment vibration to reduce carbody vibration. The equipment itself has a functional role and its vibration tolerance is very important to play the role. For example, traction converters need to function as converters to convert electrical energy between DC and AC systems. Therefore, while considering the suppression on vehicle carbody vibration, it is necessary to monitor equipment vibration, and comprehensively consider the vibration performance of the carbody and equipment. The carbody vibration performance is evaluated by the ride comfort index and the equipment is evaluated by the maximum value of lateral and vertical acceleration.

The ride comfort index is a comprehensive evaluation index that takes into account of carbody longitudinal, lateral, and vertical vibration acceleration. Its calculation method is based on the standard of EN 12299:2009 (2009), as follows:

N = 6 \sqrt{{(a_{XP 95}^{W_{d}})}^{2} + {(a_{YP 95}^{W_{d}})}^{2} + {(a_{ZP 95}^{W_{b}})}^{2}}

(3)

where a_XP95, a_YP95, and a_ZP95 are the carbody longitudinal, lateral, and vertical vibration acceleration with a confidence level of 95%. W_d and W_b are weighting coefficients. The measurement points are located on the vehicle carbody floor above the equipment and the carbody center, named as N_i, i = 1,2,3,4.

The maximum value of the equipment lateral and vertical vibration acceleration based on the standard of UIC 518 (2009) can be expressed as:

a_{y i} = \max (a_{Y i}), a_{z i} = \max (a_{Z i})

(4)

where a_Yi and a_Zi are the lateral and vertical accelerations of the ith equipment, i = 1,2,3.

3.3. Evaluation function

As there are no clear limits in relevant standards and specifications for the equipment lateral and vertical vibration accelerations, the maximum vibration acceleration of the equipment is limited within 2.5 m/s², referring to the vibration limits of the vehicle carbody. Then, taking into account the vibration characteristics of the vehicle carbody and equipment, an evaluation function is established as follows:

\begin{array}{l} N = \sum_{i = 1}^{4} N_{i} / 4, a_{y} = \sum_{i = 1}^{3} a_{y i} / 3, a_{z} = \sum_{i = 1}^{3} a_{z i} / 3 \\ Ω = w_{1} \frac{N}{N_{\lim}} + w_{2} \frac{a_{y}}{a_{y \lim}} + w_{3} \frac{a_{z}}{a_{z \lim}} \end{array}

(5)

where the ride comfort index N is the average value of the four measuring points. a_y and a_z are the average value of three equipment. a_ylim and a_zlim are the acceleration limit values. w₁, w₂, and w₃ are weighting coefficients for carbody and equipment vibration. The larger the weighting coefficient, the greater the impact of the vibration on the evaluation function. As the research objective is mainly to reduce the carbody vibration and ensure the equipment vibration within a reasonable range, the weighted coefficients w₁, w₂, and w₃ are 0.7, 0.15, and 0.15, respectively.

3.4. Calculation flow

Data interaction between the dynamic model and INGA is conducted based on MATLAB. The parameter combination obtained by INGA is the input of the dynamic model and the evaluation function calculated by the dynamic model is used as input to INGA. Iterative calculation is carried out and calculation flowchart of dynamics simulation based on INGA is shown in Figure 5. The initial population is randomly selected as 20 individuals, with a total of 50 iterations.

4. Numerical analysis of vehicle dynamic performance

4.1. Optimal parameter

A multi-objective and multi-parameter optimization analysis is carried out for carbody vibration suppression method based on multi-suspended equipment. The interaction between INGA and the dynamics model enables data exchange and iterative calculations to find the optimal parameter combination. In each generation, 20 parameter combinations are evaluated and an optimal parameter combination is identified through the minimization of the evaluation function. The variation trend of optimal parameters under 50 generations are achieved and some are listed in Figure 6. During the initial iterations of the genetic algorithm, the suspension parameters of the equipment undergo significant changes as the algorithm explores different combinations. Nevertheless, as the iterations progress, the parameters tend to stabilize and converge towards their optimal values.

This phenomenon is also reflected in the evaluation function, as presented in Figure 7. Initially, the evaluation function values change significantly, signifying the exploration of different parameter combinations. As the iterations continue, the fluctuations in the evaluation function become less pronounced and eventually reache a plateau. It indicates that the algorithm has found the optimal parameter combination that minimizes the evaluation function. It is worth noting that even though the numerical decrease in the evaluation function value may seem small (from 0.544 to 0.477), it still represents a significant improvement in the performance of the carbody vibration control. The reduction in the evaluation function amplitude is substantial and indicates the effectiveness of the optimized parameter combination.

Furthermore, in the analysis of multiple-suspended equipment, the optimal parameters are obtained based on the optimal parameters of a single suspended equipment (referred to as the primitive parameters, PP). Through the iterative calculations of INGA, the optimal parameters (OP) that minimize the evaluation function are determined. The suspension stiffness of three suspended equipment does not affect each other, but there is an interference problem in the installation position of the equipment, which is not limited in the optimization analysis and needs to be selected reasonably. By considering these factors and conducting the multi-objective and multi-parameter optimization analysis, the optimal parameter combination for the suspended equipment can be determined, leading to effective carbody vibration suppression.

Three optimal parameter combinations are selected based on the evaluation function values, as shown in Table 2. From the perspective of parameters, OP_ 1 and OP_ 3 are relatively similar, with relatively high stiffness, while OP_2 is relatively small. If the suspension stiffness is high, the equipment vibration will intensify and correspondingly the carbody vibration will decrease. On the contrary, the equipment vibration can be decreased when the stiffness is reduced. Besides, there is no interference in the equipment installation position of OP_1 and OP_2, while it happens with OP_3. Considering a comprehensive analysis of the parameters and their effects, OP_1 is selected as the optimal parameter combination for further performance comparison analysis with PP.

Table 2.

The parameter combination of PP and OP.

Parameters (Unit)	k _y1	k _z1	k _y2	k _z2	k _y3	k _z3	L _x1	L _x2	L _x3
Parameters (Unit)	MN/m						m
PP	0.6	1.2	0.7	1.3	1.4	2.8	0	0	0
OP_1	1.3	2.3	0.7	1.9	1.5	3.8	−0.1	−0.2	0.7
OP_2	1.1	1.6	0.6	1.5	1.3	3.5	−0.1	−0.1	0.5
OP_3	1.3	2.6	0.8	2.3	1.8	3.8	0.2	0.2	−0.5

4.2. Comparison of vehicle dynamic performance

Under the operating speed of 350 km/h, the vibration performance of the high-speed railway vehicle is analyzed using the parameter combinations of PP and OP obtained from the multi-objective and multi-parameter optimization analysis, shown in Figure 8. The results of the analysis show varying degrees of changes in both carbody and equipment vibration performance. There is a significant decrease in vehicle ride comfort at different measuring points. For example, the ride comfort at the middle of the vehicle carbody N₄ decreases from 2.16 to 1.87 and N₁ on the carbody floor above equipment 1 shows the largest decrease from 2.34 to 2.09. Regarding the lateral vibration of the equipment, a_y1 and a_y3 exhibit a reduction of 0.23 m/s² and 0.20 m/s², respectively, while a_y2 remains relatively unchanged. The vertical vibration of the equipment changes relatively significantly, with the largest increase in a_z1, reaching 0.70 m/s². Besides, the maximum value is 2.18 m/s², which is still less than the limit value of 2.5 m/s². The vibration of a_z3 also increases, but the vertical vibration of a_z2 decreases by 0.17 m/s².

Comprehensive consideration of the carbody and equipment vibration performance, the evaluation indicator N for carbody vibration characteristics is significantly decreased. The average value of ride comfort index on four measuring points is reduced from 2.18 to 1.91. The evaluation index a_y of equipment lateral vibration has decreased from 0.82 m/s² to 0.68 m/s² and the vertical vibration evaluation index a_z shows an increasing trend, from 1.43 m/s² to 1.67 m/s².

To further study the coupling vibration performance of the vehicle carbody and equipment, the frequency domain analysis result of carbody vertical vibration on the middle position is analyzed under PP and OP, shown in Figure 9. The frequency response range considered by the dynamic model is limited, and the influence of parameters on vehicle vibration is also within 40 Hz. Therefore, only the vibration characteristics within 40 Hz are considered here. From the results, the parameter combinations of the suspended equipment can be categorized into three regions in terms of their influence on carbody vibration. Within the frequency range of 3 Hz, namely, Region 1, the carbody vibration frequency and amplitude do not change for both sets of parameters. The main frequency belongs to the carbody floating motion, indicating that the equipment suspension parameters have no effect on the carbody rigid motion. In the range of 7 Hz ∼ 20 Hz, that is, Region 2, there is a significant difference in vehicle vibration between the two sets of parameters. There are fewer dominant frequency under PP, but the amplitude is relatively larger, while the vertical vibration dominant frequency increases under OP with significantly reduced amplitude. The main reason is that multiple-suspended equipment play a multiple DVA role, transforming one peak into multiple peaks and significantly reducing the amplitude of the peaks. In the range of 20 Hz ∼ 30 Hz, namely, Region 3, there are still some dominant frequencies in the carbody vertical vibration. However, the vibration frequencies and amplitudes under PP and OP are similar, indicating that parameters have no effect on carbody vibration within this range.

Comparing the performance indicators under the two sets of parameters, it is evident that the vehicle vibration performance of the high-speed railway vehicle has been further improved through the multi-objective and multi-parameter optimization. The optimization process not only achieves significant improvements in carbody vibration but also effectively controls equipment vibration within reasonable limits, achieving the expected optimization purpose. The multi-objective and multi-parameter optimization method proves to be valuable in improving the dynamic performance of high-speed railway vehicles.

5. Conclusion

To balance the contradiction between carbody vibration suppression and vibration tolerance of multiple-suspended equipment, a multi-objective and multi-parameter optimization method is applied and an improved niche genetic algorithm is integrated into the numerical simulation process to determine the optimal parameters. Comparative analysis between the results obtained from the optimal and primitive parameters is conducted and some conclusions can be draw as follows:

(1) Considering flexible carbody and multi-suspended equipment, a rigid-flexible dynamics model of a high-speed railway vehicle is established and validated through a rig test. INGA is integrated into the numerical simulation process to determine the optimal parameters.

(2) An evaluation function that comprehensively assesses the vibration performance of the vehicle carbody and equipment is proposed and its value reaches a plateau after 40 generations, indicating that the optimal parameter combination is obtained.

(3) A comparative analysis between PP and OP demonstrates that the optimization process not only achieves improvements in carbody vibration reduction but also controls equipment vibration within reasonable limits. The carbody vibration N is reduced from 2.18 to 1.91. The equipment lateral vibration a_y decreases by 0.14 m/s² and the vertical a_z increases by 0.24 m/s².

(4) The multi-objective and multi-parameter optimization method applied on carbody underframe suspended system proves to be valuable in improving the dynamic performance of high-speed railway vehicles, which can also be applied to other types of railway vehicles.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China [grant numbers 52102441 and U2034210], Independent Research and Development Project of the State Key Laboratory of Traction Power [grant number 2022TPL-T10], and Natural Science Foundation of Sichuan Province [grant number 2022NSFSC1886].

ORCID iDs

Qunsheng Wang

Jing Zeng

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, et al. (2018) Methodology to optimize wedge suspensions of three-piece bogies of railway vehicles. Journal of Vibration and Control 24(3): 565–581.

25.

Gan

Shi

, et al. (2023) Experimental investigations on the semi-active control of a valve-driven secondary lateral damper for a high-speed rail vehicle. Journal of Vibration and Control 29(13-14): 3025–3037.

26.

Yao

, et al. (2020) Suspension parameters optimum of high-speed train bogie for hunting stability robustness. International Journal of Reality Therapy 8(3): 195–214.