Lateral stability control method of straddle-type monorail vehicle based on multi-objective optimization

Abstract

The present invention discloses a method for controlling the lateral stability of a straddle-type monorail vehicle based on multi-objective optimization. The method comprises the following steps: determining target parameters that affect the vehicle's lateral stability; constructing a vehicle lateral stability optimization control model using the root mean square (RMS) yaw acceleration, the root mean square (RMS) lateral acceleration, and the rollover coefficient as optimization targets and the target parameters as design parameters; adjusting the values ​​of the parameters in the vehicle lateral stability optimization control model so that the vehicle lateral stability optimization control model achieves a minimum value; using the design parameters set when the vehicle lateral stability optimization control model achieves the minimum value as optimization control parameters; and controlling the vehicle's lateral stability using the optimization control parameters. The present invention can measure different optimization targets on the same dimension, thereby improving the vehicle's lateral stability under variable operating conditions.

Description

Technical Field

[0001] The present invention relates to the field of monorail vehicle operation control, and in particular to a lateral stability control method of a straddle-type monorail vehicle based on multi-objective optimization. Background Art

[0002] As a new urban rail transit system with a unique running mechanism, the new single-axle bogie straddle-type monorail vehicle has become an important transportation option for urban residents due to its strong gradeability, compact footprint, low noise, and low cost. However, due to its single wheelset, the single-axle bogie's structural instability reduces the vehicle's lateral stability during operation. Therefore, improving the vehicle's lateral stability is particularly important.

[0003] Currently, vehicle stability control and ride comfort are primarily achieved through the use of external energy and control methods, such as magnetorheological control, predictive performance control, and decoupled vibration control. Intelligent algorithms are currently being widely used to optimize vehicle design parameters to improve lateral stability and ride quality. For example, the use of genetic algorithms to optimize vehicle suspension parameters has improved ride comfort and reduced rollover coefficient. Improved genetic algorithms are being used to optimize vehicle structural and dynamic parameters, enhancing ride comfort. Multi-objective particle swarm optimization has been used to optimize single-axle bogies, effectively improving vehicle lateral stability.

[0004] However, these techniques primarily optimize suspension parameters for a single operating condition, ignoring the impact of operating conditions such as speed and passenger load on lateral stability. This results in parameter optimization results that are not optimal under varying operating conditions. Furthermore, the various sub-objectives in the optimization are conflicting; improving one sub-objective may lead to performance degradation in one or more sub-objectives. Therefore, a multi-objective optimization-based lateral stability control method for straddle-type monorail vehicles is needed to address these issues. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to overcome the defects in the prior art and provide a lateral stability control method for a straddle-type monorail vehicle based on multi-objective optimization, which can measure different optimization objectives in the same dimension and improve the lateral stability of the vehicle under variable operating conditions.

[0006] The lateral stability control method of a straddle-type monorail vehicle based on multi-objective optimization of the present invention comprises:

[0007] Determine target parameters that affect vehicle lateral stability;

[0008] Taking the root mean square of yaw acceleration, the root mean square of lateral acceleration and rollover coefficient as optimization targets and the target parameters as design parameters, a vehicle lateral stability optimization control model is constructed.

[0009] Adjust the parameter values ​​in the vehicle lateral stability optimization control model so that the vehicle lateral stability optimization control model reaches the minimum value, use the design parameters set when the vehicle lateral stability optimization control model reaches the minimum value as the optimization control parameters, and use the optimization control parameters to control the vehicle lateral stability.

[0010] Furthermore, the target parameters include controllable parameters and noise parameters;

[0011] The controllable parameters include longitudinal drawbar length, half vehicle span, running wheel vertical stiffness, running wheel lateral stiffness, guide wheel stiffness, stabilizing wheel stiffness, and lateral shock absorber damping;

[0012] The noise parameters include load and vehicle speed.

[0013] Furthermore, the controllable parameters are determined according to the following method:

[0014] Through the sensitivity analysis method based on orthogonal experiments and the constructed dynamic simulation model, the vehicle's lateral stability evaluation index is simulated and calculated to obtain the degree of influence of each parameter on the evaluation index. The parameters whose influence degree meets the set requirements are regarded as controllable parameters.

[0015] The lateral stability evaluation index includes the root mean square of yaw angular acceleration, the root mean square of lateral acceleration and the rollover coefficient;

[0016] The yaw angular acceleration root mean square F1 mentioned in the evaluation index is:

[0017] The lateral acceleration root mean square F2 mentioned in the evaluation index is:

[0018] The overturning coefficient F3 mentioned in the evaluation index is:

[0019] Where N represents the number of sample points; represents the yaw angular acceleration value of the i-th sample point; represents the lateral acceleration value of the i-th sample point; P d is the difference in vertical load between the left and right running wheels; P st It is the sum of the vertical loads on the left and right running wheels; P2 and P1 are the vertical loads on the running wheels on the load-increasing and load-reducing sides respectively.

[0020] Furthermore, the vehicle lateral stability optimization control model is determined according to the following formula:

[0021]

[0022] Where P1(x) is the membership function of the root mean square of the yaw acceleration; P2(x) is the membership function of the root mean square of the lateral acceleration; P3(x) is the membership function of the rollover coefficient; w k is the weight coefficient; m is the maximum value of parameter k; D(x) is the objective function of the lateral stability optimization control model;

[0023]

[0024] In the formula, the objective functions F of robust optimization are k (x)=λμ k 2 (x)+(1-λ)σ k 2 (x), k = 1, 2, 3, λ is the weighting factor, μ k (x) is the mean of the objective function, σ k (x) is the mean square error of the objective function; F 1a and F 1b They represent the maximum and minimum values ​​of the yaw angular acceleration root mean square function F1(x); F 2a and F 2b They represent the maximum and minimum values ​​of the lateral acceleration root mean square function F2(x); F 3a and F 3b They represent the maximum and minimum values ​​of the overturning coefficient function F3(x) respectively;

[0025] G1(x), G2(x), G3(x) and G4(x) are wheel load reduction rate, vehicle body roll angle, steering torque and total weighted acceleration root mean square value respectively; G 1-th , G 2-th , G 3-th and G 4-th They are wheel load reduction rate threshold, vehicle body roll angle threshold, steering torque threshold and total weighted acceleration root mean square value threshold;

[0026] and are the mean and mean square error of the j-th design parameter; x jL and x jU are the lower and upper limits of the j-th design parameter respectively.

[0027] Furthermore, the wheel load reduction rate G1(x) is determined according to the following formula:

[0028]

[0029] Among them, P1 is the vertical load of the wheel on the unloaded side; P2 is the vertical load of the wheel on the loaded side.

[0030] Furthermore, the total weighted acceleration root mean square value is determined according to the following method:

[0031] Calculate the weighted root mean square values ​​of the lateral x, vertical y, and longitudinal z accelerations according to the following formula:

[0032]

[0033] Where i = x, y, z; ω(f) is the frequency weighting function; G a (f) is the power spectral density function; f is the vehicle acceleration frequency;

[0034] The total weighted acceleration root mean square value G4(x) is determined according to the following formula:

[0035]

[0036] Among them, a ωx is the root mean square value of the weighted acceleration in the lateral direction x, a ωy is the root mean square value of the weighted acceleration in the vertical y direction, a ωz is the root mean square value of the weighted acceleration in the longitudinal direction z.

[0037] The beneficial effects of the present invention are as follows: the present invention discloses a lateral stability control method for a straddle-type monorail vehicle based on multi-objective optimization, which takes the root mean square of yaw angular acceleration, the root mean square of lateral acceleration, and the rollover coefficient as optimization objective functions, obtains optimization parameters based on a sensitivity analysis method of an orthogonal test, considers dynamic operating conditions with changes in load and vehicle speed, introduces fuzzy sets and robustness optimization theory, and obtains suspension parameter optimization results through iterative optimization, thereby obtaining a suspension parameter combination and an optimal solution with high reliability and high robustness, improving the lateral stability of the vehicle under dynamic operating conditions, and providing technical support for the stability optimization design of monorail vehicles under the influence of uncertain factors such as variable operating conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0039] Figure 1 (a) is a left side view of the single-axle bogie straddle-type monorail vehicle model structure of the present invention;

[0040] Figure 1 (b) is a front view of the structure of a single-axle bogie straddle-type monorail vehicle model according to the present invention;

[0041] Figure 1 (c) is a top view of the single-axle bogie straddle-type monorail vehicle model structure of the present invention;

[0042] Figure 2 (a) is a schematic diagram of the yaw acceleration sensitivity percentage of the present invention;

[0043] Figure 2 (b) is a schematic diagram of the lateral acceleration sensitivity percentage of the present invention;

[0044] Figure 2 (c) is a schematic diagram of the sensitivity percentage of the capsizing coefficient of the present invention;

[0045] Figure 3 The figure is a schematic diagram of the multi-objective robust optimization process of vehicle lateral stability based on fuzzy sets of the present invention. DETAILED DESCRIPTION

[0046] The present invention is further described below with reference to the accompanying drawings, as shown in the drawings:

[0047] The lateral stability control method of a straddle-type monorail vehicle based on multi-objective optimization of the present invention comprises:

[0048] Determine target parameters that affect vehicle lateral stability;

[0049] Taking the root mean square of yaw acceleration, the root mean square of lateral acceleration and rollover coefficient as optimization targets and the target parameters as design parameters, a vehicle lateral stability optimization control model is constructed.

[0050] Adjust the parameter values ​​in the vehicle lateral stability optimization control model so that the vehicle lateral stability optimization control model reaches the minimum value, use the design parameters set when the vehicle lateral stability optimization control model reaches the minimum value as the optimization control parameters, and use the optimization control parameters to control the vehicle lateral stability.

[0051] The present invention obtains the suspension parameters of a single-axle bogie that affect lateral stability through sensitivity analysis, introduces fuzzy set and robustness optimization theory, considers the influence of fluctuations of uncertain factors, and proposes a multi-objective robustness optimization method based on fuzzy sets. The method optimizes vehicle design parameters and improves vehicle lateral stability. The method is applied to the multi-objective optimization design of the lateral stability of a single-axle bogie straddle-type monorail vehicle, providing technical support for the optimization design of monorail vehicles.

[0052] In this embodiment, the target parameters include controllable parameters and noise parameters;

[0053] The controllable parameters include longitudinal drawbar length, half vehicle span, running wheel vertical stiffness, running wheel lateral stiffness, guide wheel stiffness, stabilizing wheel stiffness, and lateral shock absorber damping;

[0054] The noise parameters include load and vehicle speed.

[0055] In order to improve the lateral stability of single-axle bogie straddle-type monorail vehicles, it is necessary to establish a dynamic model of single-axle bogie straddle-type monorail vehicles, such as Figure 1 As shown. Figure 1 Three views of a single-axle bogie straddle-type monorail vehicle show that it consists of a carbody and bogies, each of which has running wheels, guide wheels, and stabilizer wheels. The carbody and bogies are connected by a suspension system consisting of air springs, lateral dampers, vertical dampers, and lateral stops.

[0056] Considering the lateral, vertical, roll, pitch, and yaw motions of the vehicle and bogie, the following equations are derived from the Lagrange equations:

[0057]

[0058] Where: T is kinetic energy; U is potential energy; W is damping energy; Q j is the generalized force and moment; q j is the generalized coordinate. Among them, kinetic energy, potential energy, and damping energy can be expressed as:

[0059]

[0060] Where: m 11 ,m 2i are the masses of the car body and bogie respectively;

[0061] are the longitudinal, lateral, vertical speed and angular velocity respectively; I is the moment of inertia; K 1ijn ,C 1ijn is the vertical stiffness and damping of the air spring; K 2ijn ,C 2ijn is the stiffness and damping of the running wheel; K 3ijn ,C 3ijn is the stiffness and damping of the guide wheel; K 4ijn ,C 4ijn is the stiffness and damping of the stabilizing wheel; K 5ijn ,C 5ijn is the lateral stiffness and damping of the air spring; R rijn (r = 1, 2, 3, 4, 5) is the relative displacement of the spring and shock absorber; i is the bogie position (i = 1, 2 represents the front and rear bogies respectively); j is the longitudinal position of the tire in the bogie (j = 1, 2 represents the front and rear tires respectively); n is the lateral position of the tire in the bogie (n = 1, 2 represents the left and right tires respectively); δ rj is the Kronecker function (r=1,2,3,4,5).

[0062] The constructed dynamic model of a single-axle bogie straddle-type monorail vehicle shows that the vehicle has numerous dynamic parameters, and each parameter has a different effect on the vehicle's lateral stability. As shown in Table 1, which lists the main dynamic parameters of a single-axle bogie straddle-type monorail vehicle, it is necessary to study the effect of each parameter on the vehicle's lateral stability and determine the optimal parameters for the vehicle's lateral stability.

[0063] Table 1

[0064]

[0065] The present invention uses the root mean square of yaw acceleration, the root mean square of lateral acceleration, and the rollover coefficient as evaluation indicators of vehicle lateral stability, i.e., optimization targets, as shown in formulas (5)-(7):

[0066]

[0067] Where F1(x), F2(x), and F3(x) represent the root mean square of yaw acceleration, the root mean square of lateral acceleration, and the rollover coefficient, respectively; N represents the number of sampling points; represents the yaw angular acceleration value of the i-th sample point; represents the lateral acceleration value of the i-th sample point; P d is the difference in vertical load between the left and right running wheels; P st It is the sum of the vertical loads on the left and right running wheels; P2 and P1 are the vertical loads on the running wheels on the load-increasing and load-reducing sides.

[0068] Since there are many design parameters involved, this paper uses the sensitivity analysis method of orthogonal experiment to analyze each parameter. Orthogonal experiment design is a mathematical analysis method for multi-factor experiments. The specific steps are: (1) determining the orthogonal experiment factors and factor levels; (2) constructing the orthogonal experiment table; (3) conducting the orthogonal experiment and analyzing the results. The core of this is the construction of the orthogonal experiment table. The orthogonal experiment table is an n×m matrix generated according to a certain rule and is usually presented in the form of a table:

[0069] L n (r1×r2×...×r m ) (8)

[0070] In the formula, L is the symbol for the orthogonal test table; n is the number of experiments; m is the number of factors; r is the number of factor levels. The orthogonal test table L can usually be simplified to n (r1×r2×...×r m ) is recorded as L n (r m ).

[0071] The orthogonal test design of the present invention is a test of 50 horizontal combinations, and the running wheel lateral stiffness (K 2yijn ) is 2 levels, and the other design parameters are 5 levels, that is, the orthogonal test table is L 50 (2 1 ×5 11 ).

[0072] Through the sensitivity analysis method based on orthogonal test, the lateral stability optimization target of the single-axle bogie straddle-type monorail vehicle is simulated and calculated with the help of the constructed dynamic simulation model, and the influence of each parameter on the optimization target is obtained, such as Figure 2 shown.

[0073] The sensitivity is less than 5%, which can be regarded as having little effect on the output index. Figure 2 It can be seen that the parameters that have a greater impact on the yaw angular acceleration are arranged as follows: K 2ijn >K 3ijn >K 4ijn >L1>L2>C y >K 2yijn , the parameters that have a significant impact on lateral acceleration are arranged from large to small as follows: K 2ijn >K 4ijn The parameters that have the greatest impact on the overturning coefficient are: K 2ijn >K 3ijn >K 4ijn The most significant parameters affecting the lateral stability of a single-axle bogie straddle-type monorail vehicle are the longitudinal traction rod length (L1), half vehicle span (L2), and the vertical stiffness of the running wheels (K 2ijn ), running wheel lateral stiffness (K 2yijn ), guide wheel stiffness (K 3ijn ), Stability wheel stiffness (K 4ijn ), lateral shock absorber damping (C y ).

[0074] In robustness optimization, design parameters can be divided into controllable factors and noise factors. According to the analysis of the lateral stability design parameters of the single-axle bogie straddle-type monorail vehicle in the previous chapter, the longitudinal traction rod length (L1), half vehicle span (L2), running wheel vertical stiffness (K 2ijn ), running wheel lateral stiffness (K 2yijn ), guide wheel stiffness (K 3ijn ), Stability wheel stiffness (K 4ijn ), lateral shock absorber damping (C y ) can be regarded as a controllable factor, which is a factor that can be determined by the designer.

[0075] During the operation of the vehicle, the load and speed are constantly changing dynamically, which will also affect the lateral stability of the vehicle, causing the lateral stability of the vehicle to change accordingly. Therefore, the load M and speed v are selected as noise factors, which are factors that are not controlled by the designer. That is, the optimized design parameters are: L1, L2, K 2ijn , K 2yijn , K 3ijn , K 4ijn 、C y , M and v. The range of design parameters is shown in Table 2.

[0076] Design parameters x=[x1,x2,x3,x4,x5,x6,x7,x8,x9]=[L1,L2,K 2ijn ,K 2yijn ,K 3ijn ,K 4ijn ,C y ,M,v]

[0077] Table 2

[0078]

[0079] In this embodiment, due to the special structural characteristics of the single-axle bogie straddle-type monorail vehicle, its running mechanism is unique, and the vehicle dynamics performance will affect the vehicle stability, comfort and safety. The present invention uses three indicators, namely, operating stability, smoothness, and curve negotiating ability, as optimization constraints.

[0080] 1. The wheel load reduction rate refers to the difference in load between the inner and outer tires, and can be used to evaluate running stability and curve passing performance. It can be expressed as:

[0081]

[0082] Where P1 is the vertical force on the wheel on the unloaded side, and P2 is the vertical force on the wheel on the loaded side. According to the test and appraisal specifications specified in vehicle standards, the wheel load reduction ratio is: ΔP / P ≤ 0.6.

[0083] 2. The size of the vehicle's roll angle not only affects the vehicle's ability to navigate curves, but also affects the vehicle's stability and passenger comfort. The vehicle's roll angle (θ) should not be too large and should be kept below 10°, that is:

[0084] θ<10° (10).

[0085] 3. When the vehicle passes through a curve, the radial force of the guide wheel will change, and the steering torque of the bogie will also change accordingly. Therefore, during the optimization process, in order to prevent the curve passability from being affected, the optimized steering torque should not be too large:

[0086] M d≤1.4M0 (11)

[0087] Where M d is the steering torque when the vehicle is running; M0 is the initial steering torque.

[0088] 4. The evaluation of human body vibration is used as an evaluation index for vehicle running stability. Considering the three directions of lateral, vertical and longitudinal, the acceleration time domain curve is measured, the spectrum curve is transformed, and the power spectrum density function G is obtained by spectrum analysis. a (f). Calculate the weighted acceleration root mean square value a by formula (12) ωi (i=x,y,z):

[0089]

[0090] Where ω(f) is the frequency weighting function; G a (f) is the power spectrum density function. The root mean square value of the acceleration in the lateral, vertical and longitudinal directions is calculated by formula (13) to obtain the total weighted root mean square value of acceleration:

[0091]

[0092] According to a ω Relationship with human riding comfort, limit a ω <0.315m / s 2 .

[0093] The robust optimization method is to find the optimal solution of the optimization objective function while considering the impact of design parameter fluctuations on the optimization objective, reducing the sensitivity of the target response to the design parameters, and obtaining design parameters and optimal solutions with high reliability and high robustness. The mathematical model for constructing multi-objective robust optimization is:

[0094]

[0095] Among them, F k (x) is the kth sub-objective function; m is the number of sub-objective functions; μ k (x) and σ k (x) are the mean and mean square error of the optimization function respectively; G i (x) is the i-th constraint; and are the mean and mean square error of the i-th constraint condition respectively; C is the constraint value; q is the number of constraints; and are the mean and mean square error of the j-th design variable; x jL and x jUare the lower and upper limits of the j-th design variable respectively; p is the number of design variables; n is the quality level of the σ constraint, and changes in the value of n can change the optimization quality.

[0096] Equation (14) describes a multi-objective optimization problem (MOP), in which the sub-objectives constrain each other, and the optimization objectives vary in different dimensions and ranges. In order to simplify the multi-objective optimization problem, fuzzy sets are introduced, and each optimization objective is expressed through a membership function, so that the optimization objectives can be evaluated on the same dimension. This paper adopts a parabolic membership function, and its corresponding membership function form is as follows:

[0097]

[0098] Where s is the exponent of the membership function; s = 1 or 2 represents a linear or quadratic membership function, respectively. Since the multi-objective optimization problem is highly nonlinear, we use a quadratic membership function here, F kb and F ka They are the function F in the kth sub-goal optimization process k The maximum and minimum values ​​of (x).

[0099] The value of each optimization objective represented by each membership function is in the range of 0 to 1, and each optimization objective is measured on the same dimension. In addition, the weight coefficient is introduced and combined with the membership function to transform it into a single objective problem:

[0100]

[0101] Among them, w k is the kth sub-objective function F k The weight coefficient of (x) is assumed to be the same as that of the objective function. Therefore:

[0102] w1+w2+...+w m =1 (17)

[0103] w1=w2=...=w m (18)

[0104] In this way, a multi-objective robust optimization mathematical model based on fuzzy sets can be established:

[0105]

[0106] This invention performs multi-objective optimization for lateral stability, targeting the root mean square (RMS) yaw acceleration, the root mean square (RMS) lateral acceleration, and the rollover coefficient, all of which are target components with desired characteristics. Using controllable factors and noise factors as design parameters, a multi-objective robust optimization method based on fuzzy sets is employed to construct the vehicle lateral stability optimization control model as follows:

[0107]

[0108] Where G1(x), G2(x), G3(x), and G4(x) are the constraints of wheel load reduction rate, vehicle roll angle, steering torque, and total weighted acceleration root mean square value, respectively; the weight coefficient w1 = w2 = w3 = 1 / 3; P1(x) is the membership function of the yaw angular acceleration root mean square; P2(x) is the membership function of the lateral acceleration root mean square; and P3(x) is the membership function of the rollover coefficient. It can be expressed as:

[0109]

[0110] Where, the objective functions of robust optimization are:

[0111] F k (x) = F[μ k (x),σ k (x)]=λμ k 2 (x)+(1-λ)σ k 2 (x)k=1,2,3,λ is the weighting factor, takeλ=0.5. 1a and F 1b They represent the maximum and minimum values ​​of the yaw angular acceleration root mean square function F1(x) during the optimization process; F 2a and F 2b They represent the maximum and minimum values ​​of the lateral acceleration root mean square function F2(x) during the optimization process; F 3a and F 3b They represent the maximum and minimum values ​​of the overturning coefficient function F3(x) during the optimization process respectively.

[0112] In this embodiment, modeFRONTIER and ADAMS joint simulation is used to perform multi-objective robustness optimization of vehicle single-axle bogie suspension parameters based on fuzzy sets. The specific process is as follows: Figure 3 As shown, the steps of the optimization process are as follows:

[0113] (1) In modeFRONTIER, input the ADAMDS vehicle dynamics simulation model file, analyze the dynamics model file through modeFRONTIER parsing function, and extract the design parameter variables that need to be optimized x=[x1,x2,x3,x4,x5,x6,x7,x8,x9]=[L1,L2,K 2ijn ,K 2yijn ,K 3ijn ,K 4ijn ,C y ,M,v],

[0114] So that it can be adjusted dynamically.

[0115] (2) Perform dynamic calculations through modeFRONTIER, automatically update the vehicle dynamics simulation model, complete the calculation of the vehicle optimization objective function, and output the calculation result file.

[0116] (3) The optimization parameters are optimized within the range of values ​​using the NSGA-II optimization algorithm. Iterative optimization is performed according to the optimization convergence criterion to obtain a parameter combination for multi-objective robust optimization based on fuzzy sets. The optimization algorithm parameters are configured as a population of 30, 20 generations of evolution, a crossover probability of 0.8, and 600 iterative optimization calculations.

[0117] (4) The Monte Carlo analysis principle is used to analyze the objective function before and after optimization, and the average value and mean square error of the objective function are obtained to analyze the reliability and robustness before and after optimization.

[0118] (5) The vehicle dynamics model is used to simulate and analyze the optimization results, and the changes in each sub-target of lateral stability before and after optimization are compared.

[0119] A multi-objective robustness optimization based on fuzzy sets was performed on the vehicle's lateral stability. Iterative optimization calculations were performed until convergence or the maximum number of generations was reached, achieving optimization of both the vehicle design parameters and the objective function. After 600 iterations, the vehicle design parameters achieved numerical convergence. Based on the optimization results of the objective function, the mean value of the optimization objective converged to approximately 0.00001. Table 3 compares the design parameters and objective function results for the single-axle bogie straddle-type monorail vehicle before and after optimization.

[0120] Table 3

[0121]

[0122] As shown by the optimization results of the single-axle bogie straddle-type monorail vehicle, according to the optimization results, the robust optimization based on fuzzy sets reduced the yaw angular acceleration root mean square, lateral acceleration root mean square, and rollover coefficient by 8.3%, 5.4%, and 26.8%, respectively, compared with before optimization, achieving the purpose of minimizing the objective function and improving the lateral stability.

[0123] To further analyze the lateral stability of the vehicle before and after optimization, a robustness analysis of the optimization results is required. Monte Carlo analysis is used to determine whether the optimized results are more robust than those before optimization. Monte Carlo analysis was performed 1000 times to obtain the mean and mean square error of the vehicle's yaw acceleration, lateral acceleration, and rollover coefficient before and after optimization, as shown in Table 4.

[0124] Table 4

[0125]

[0126] Table 4 shows that compared to the pre-optimization period, the mean and mean square deviation of the yaw acceleration root mean square, lateral acceleration root mean square, and rollover coefficient have significantly decreased, with the mean square deviation decreasing by 8.9%, 14.3%, and 51.3%, respectively. This indicates that robust optimization based on fuzzy sets reduces the fluctuation of the objective function. Furthermore, the optimization results are more robust and reliable, reducing the objective function's sensitivity to external factors (dynamic operating conditions such as speed and load), and enhancing its anti-interference capability.

[0127] To validate the effectiveness of multi-objective robust optimization of vehicle lateral stability based on fuzzy sets, the vehicle design parameters before and after optimization were input into a rail vehicle multibody dynamics simulation model for dynamic performance simulation. The simulation time was set to 30 seconds, and the vehicle's yaw acceleration, lateral acceleration, and rollover coefficient were compared before and after optimization. After the multi-objective robust optimization of the design parameters based on fuzzy sets, the waveforms of the yaw acceleration, lateral acceleration, and rollover coefficient remained essentially consistent in the time domain. However, the fluctuation amplitudes in the entire time domain plot were reduced by 10.3%, 10.4%, and 25.6% compared to before optimization, reducing the peak values ​​of the yaw acceleration, lateral acceleration, and rollover coefficient. Furthermore, the fluctuation amplitudes in the frequency domain plots of the yaw acceleration and lateral acceleration were also reduced by 6.4% and 4.5% compared to before optimization. This indicates that the optimized design parameters reduced the fluctuation of dynamic performance, improving the vehicle's lateral stability and operational performance under multiple operating conditions.

[0128] The changes in the RMS yaw acceleration, RMS lateral acceleration, and maximum rollover coefficient under different vehicle speeds and loads were considered and analyzed. Based on the original and optimized design parameters shown in Table 3, the vehicle's lateral stability optimization objective was simulated using a vehicle dynamics simulation model at speeds of 20 km / h, 25 km / h, 30 km / h, 35 km / h, and 40 km / h. The optimized objective results at different speeds were obtained before and after optimization. After the multi-objective robust optimization of the vehicle design parameters based on fuzzy sets, the RMS yaw acceleration, RMS lateral acceleration, and maximum rollover coefficient at the same speed were all smaller than before optimization, and the fluctuations across the entire speed range were reduced by 11.35%, 3.44%, and 23.05%, respectively. These analyses demonstrate that the optimized vehicle design parameter combination effectively improves the vehicle's lateral stability and reduces its fluctuations.

[0129] Similarly, based on the original and optimized design parameters in Table 3, the vehicle's lateral stability optimization objective was simulated using a vehicle dynamics simulation model under unloaded, half-loaded, and fully loaded conditions. The optimized objective results under different loads before and after optimization were obtained. After the fuzzy set-based multi-objective robust optimization, the vehicle's yaw acceleration root mean square (RMS), lateral acceleration root mean square (RMS), and maximum rollover coefficient under the same load were all lower than before optimization. Furthermore, the fluctuations within the entire load range were reduced by 4.03%, 10.34%, and 30.3%, respectively. This analysis demonstrates that the optimized vehicle design parameter combination effectively improves the vehicle's lateral stability and reduces the fluctuations in dynamic performance.

[0130] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A lateral stability control method for a straddle-type monorail vehicle based on multi-objective optimization, characterized by: include: Determine target parameters that affect vehicle lateral stability; Taking the root mean square of yaw acceleration, the root mean square of lateral acceleration and rollover coefficient as optimization targets and the target parameters as design parameters, a vehicle lateral stability optimization control model is constructed. Adjust the parameter values ​​in the vehicle lateral stability optimization control model so that the vehicle lateral stability optimization control model reaches the minimum value, use the design parameters set when the vehicle lateral stability optimization control model reaches the minimum value as the optimization control parameters, and use the optimization control parameters to control the vehicle lateral stability.

2. The lateral stability control method for a straddle-type monorail vehicle based on multi-objective optimization according to claim 1, characterized in that: The target parameters include controllable parameters and noise parameters; The controllable parameters include longitudinal drawbar length, half vehicle span, running wheel vertical stiffness, running wheel lateral stiffness, guide wheel stiffness, stabilizing wheel stiffness, and lateral shock absorber damping; The noise parameters include load and vehicle speed.

3. The lateral stability control method for a straddle-type monorail vehicle based on multi-objective optimization according to claim 2, characterized in that: Determine the controllable parameters as follows: Through the sensitivity analysis method based on orthogonal experiments and the constructed dynamic simulation model, the vehicle's lateral stability evaluation index is simulated and calculated to obtain the degree of influence of each parameter on the evaluation index. The parameters whose influence degree meets the set requirements are regarded as controllable parameters. The lateral stability evaluation index includes the root mean square of yaw angular acceleration, the root mean square of lateral acceleration and the rollover coefficient; The yaw angular acceleration root mean square F1 mentioned in the evaluation index is: The lateral acceleration root mean square F2 mentioned in the evaluation index is: The overturning coefficient F3 mentioned in the evaluation index is: Where N represents the number of sample points; represents the yaw angular acceleration value of the i-th sample point; represents the lateral acceleration value of the i-th sample point; P d is the difference in vertical load between the left and right running wheels; P st It is the sum of the vertical loads on the left and right running wheels; P2 and P1 are the vertical loads on the running wheels on the load-increasing and load-reducing sides respectively.

4. The method for controlling lateral stability of a straddle-type monorail vehicle based on multi-objective optimization according to claim 1, characterized in that: The vehicle lateral stability optimization control model is determined according to the following formula: Where P1(x) is the membership function of the root mean square of the yaw acceleration; P2(x) is the membership function of the root mean square of the lateral acceleration; P3(x) is the membership function of the rollover coefficient; w k is the weight coefficient; m is the maximum value of parameter k; D(x) is the objective function of the lateral stability optimization control model; In the formula, the objective functions F of robust optimization are k (x)=λμ k 2 (x)+(1-λ)σ k 2 (x), k = 1, 2, 3, λ is the weighting factor, μ k (x) is the mean of the objective function, σ k (x) is the mean square error of the objective function; F 1a and F 1b They represent the maximum and minimum values ​​of the yaw angular acceleration root mean square function F1(x); F 2a and F 2b They represent the maximum and minimum values ​​of the lateral acceleration root mean square function F2(x); F 3a and F 3b They represent the maximum and minimum values ​​of the overturning coefficient function F3(x) respectively; G1(x), G2(x), G3(x) and G4(x) are wheel load reduction rate, vehicle body roll angle, steering torque and total weighted acceleration root mean square value respectively; G 1-th , G 2-th , G 3-th and G 4-th They are wheel load reduction rate threshold, vehicle body roll angle threshold, steering torque threshold and total weighted acceleration root mean square value threshold; and are the mean and mean square error of the j-th design parameter; x jL and x jU are the lower and upper limits of the j-th design parameter respectively.

5. The method for controlling lateral stability of a straddle-type monorail vehicle based on multi-objective optimization according to claim 4, characterized in that: The wheel load reduction rate G1(x) is determined according to the following formula: Among them, P1 is the vertical load of the wheel on the unloaded side; P2 is the vertical load of the wheel on the loaded side.

6. The method for controlling lateral stability of a straddle-type monorail vehicle based on multi-objective optimization according to claim 4, characterized in that: Determine the total weighted rms acceleration as follows: Calculate the weighted root mean square values ​​of the lateral x, vertical y, and longitudinal z accelerations according to the following formula: Where i = x, y, z; ω(f) is the frequency weighting function; G a (f) is the power spectral density function; f is the vehicle acceleration frequency; The total weighted acceleration root mean square value G4(x) is determined according to the following formula: Among them, a ωx is the root mean square value of the weighted acceleration in the lateral direction x, a ωy is the root mean square value of the weighted acceleration in the vertical y direction, a ωz is the root mean square value of the weighted acceleration in the longitudinal direction z.

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