A method for mapping modeling of semi-trailer whole vehicle structure parameters and driving stability

Abstract

This invention relates to the field of vehicle dynamics modeling and simulation technology, and particularly to a method for mapping the structural parameters of a semi-trailer to its driving stability. The method includes: establishing the viscoelastic constitutive relationship of the suspension and tires using fractional derivative operators to obtain a generalized non-conservative dissipative force vector; constructing a nonholonomic Hamiltonian system by combining road surface stochastic excitations to obtain a set of multidimensional stochastic differential equations describing the system's evolution; subsequently, applying the stochastic averaging method to project the high-dimensional state space onto a one-dimensional energy space and solving for the energy stationary probability density function; further calculating the average first-pass time when the system energy reaches the instability critical threshold as a stability index; and finally constructing a nonlinear mapping function between structural parameters and the average first-pass time. This invention overcomes the shortcomings of traditional models that ignore material memory characteristics, achieving accurate quantitative characterization of physical structural parameters and macroscopic stability margins.

Description

Technical Field

[0001] This invention relates to the field of vehicle dynamics modeling and simulation technology, and in particular to a method for mapping and modeling the structural parameters and driving stability of a semi-trailer. Background Technology

[0002] Semi-trailers, as the main vehicle type for highway freight transport, are characterized by their high center of gravity and articulated coupling between the tractor and trailer. During operation, they are highly susceptible to external random excitations such as road surface unevenness, leading to instability accidents such as rollovers and folding. To improve vehicle active safety, establishing an accurate whole-vehicle dynamics model during the product research and development stage, and using this model as a basis for matching and optimizing key structural parameters such as suspension and tires, is a crucial step in ensuring vehicle stability. Currently, most existing semi-trailer dynamics modeling methods are based on the classical Newton-Euler laws or Lagrange equations, using integer-order calculus to describe the mechanical behavior of the system. This typically simplifies the suspension and tire system to ideal linear stiffness springs and linear viscous dampers, assuming that the damping force is only proportional to the relative velocity at the current moment, and that the stiffness characteristics are mainly constant or exhibit simple nonlinear relationships.

[0003] However, traditional modeling mostly uses integer-order linear models, which ignore the viscoelastic memory characteristics of materials under large deformations, resulting in distorted dynamic response and failure of stability assessment under complex road conditions. Summary of the Invention

[0004] To overcome the above shortcomings, this invention provides a modeling method for mapping semi-trailer vehicle structural parameters to driving stability. It aims to improve the problem that traditional modeling mostly uses integer-order linear models, which ignores the viscoelastic memory characteristics of materials under large deformations, resulting in distorted dynamic response and failure of stability assessment under complex road conditions.

[0005] This invention provides the following technical solution: a method for mapping and modeling the structural parameters of a semi-trailer to its driving stability, comprising the following steps:

[0006] S1. Obtain the structural parameters of the semi-trailer suspension and tires, establish the viscoelastic constitutive relationship using the fractional derivative operator, synthesize the nonlinear restoring force and the fractional damping force, and obtain the generalized nonconservative dissipative force vector.

[0007] S2. Introduce the generalized nonconservative dissipative force vector into the semi-trailer vehicle dynamics system, combine it with the road surface stochastic excitation model, construct a nonholonomic Hamiltonian system under stochastic excitation, and use the total energy of the system as the Hamiltonian function to obtain a set of multidimensional stochastic differential equations describing the evolution of the system state.

[0008] S3. Apply the stochastic averaging method of quasi-Hamiltonian systems to the multidimensional stochastic differential equation system, project the high-dimensional state space to the one-dimensional energy space, derive the one-dimensional stochastic differential equation about the total energy of the system, and establish the corresponding probability density evolution equation based on the one-dimensional stochastic differential equation to obtain the stationary probability density function characterizing the probability of the system energy distribution at different energy levels.

[0009] S4. Set the instability critical energy threshold, construct and solve the differential equation using the probability density function, and calculate the average first crossover time of the system energy from the initial state to the threshold as a stability index.

[0010] S5. Using structural parameters as independent variables and average first crossing time as dependent variable, a nonlinear mapping function is constructed to quantitatively characterize the system stability margin under different structural parameters.

[0011] By adopting the above technical solution, constitutive relations are established using fractional derivative operators and the average first crossing time is calculated based on energy evolution. This improves the problem that traditional modeling mostly uses integer-order linear models, which ignore the viscoelastic memory characteristics of materials under large deformations, resulting in distorted dynamic response and failure of stability assessment under complex road conditions.

[0012] Preferably, in S1, establishing the viscoelastic constitutive relation using fractional derivative operators includes:

[0013] The fractional derivative operator is defined as the power function convolution integral of the deformation rate with respect to time. The kernel function of the convolution integral is used to characterize the decay law of the viscoelastic memory strength of the material.

[0014] A generalized nonconservative dissipative force expression is constructed, consisting of two superimposed parts: the first part is the product of the equivalent viscous damping coefficient and the fractional derivative of the displacement, used to characterize the frequency-varying damping characteristics; the second part is the product of the nonlinear stiffness coefficient and the high power of the displacement, used to characterize the stiffness hardening characteristics under large deformation.

[0015] Preferably, in S2, the use of the total system energy as the Hamiltonian function includes:

[0016] Construct a generalized mass matrix that includes the mass of the tractor, the mass of the semi-trailer, and the rotational inertia of each component about the center of mass. Use the quadratic form of the generalized momentum and the generalized mass matrix to construct the system kinetic energy function.

[0017] Construct a generalized potential energy function consisting of the sum of the elastic potential energy stored when the suspension and tires undergo elastic deformation and the gravitational potential energy caused by changes in the body's attitude such as roll or pitch.

[0018] Adding the system's kinetic energy function to the generalized potential energy function yields the Hamiltonian function, which describes the system's conservative energy.

[0019] Preferably, in S2, the obtained set of multidimensional stochastic differential equations describing the evolution of the system state includes:

[0020] The random excitation of the road surface is modeled as a Gaussian white noise process, and the intensity coefficient matrix of the effect of random excitation on the generalized momentum of the system is determined.

[0021] Based on the Hamiltonian canonical equations, and combining the partial derivatives of the Hamiltonian function with respect to generalized momentum and generalized coordinates, the generalized nonconservative dissipative force vector, and the road surface stochastic excitation term, an Iton-type stochastic differential equation system containing deterministic drift terms and stochastic diffusion terms is constructed.

[0022] Preferably, in S3, the derivation of the one-dimensional stochastic differential equation concerning the total energy of the system includes:

[0023] Within one quasi-period of the system, the dissipation term and the random excitation term are averaged over time to calculate the drift coefficient, which is set as the sum of the statistical average of the work done by the generalized non-conservative dissipation force and the energy correction term caused by the random excitation.

[0024] The diffusion coefficient is calculated by averaging the squares of the random excitation terms over a pseudo-period of the system over a time period. The diffusion coefficient is set as the value that characterizes the intensity of energy fluctuation caused by the power spectral density of the random excitation on the road surface.

[0025] Using the drift coefficient and the diffusion coefficient, a one-dimensional Iton stochastic differential equation describing the evolution of the total energy of the system over time is constructed.

[0026] Preferably, in S3, the solution obtained as a stationary probability density function characterizing the probability distribution of the system's energy at different energy levels includes:

[0027] Based on the one-dimensional Iton stochastic differential equation, the Fokker-Planck-Kolmogorov equation is constructed. The probability density in the Fokker-Planck-Kolmogorov equation changes with time at a rate of zero, and it is transformed into an ordinary differential equation concerning energy.

[0028] The ordinary differential equation is solved by integration to obtain an analytical solution containing an exponential function. The exponential term of the exponential function is set as the integral of the ratio of the drift coefficient to the diffusion coefficient, and the analytical solution is normalized and used as the stationary probability density function.

[0029] Preferably, in S4, setting the instability critical energy threshold includes:

[0030] Obtain the roll angle of the semi-trailer at the moment the wheel leaves the ground during a static rollover test or the folding angle when folding occurs during a folding test, and define it as the physical limit state.

[0031] Substitute the generalized coordinates corresponding to the physical limit state into the generalized potential energy function to calculate the total potential energy value under the physical limit state, and define it as the critical energy threshold of the system.

[0032] Preferably, in S4, the average first-crossing time of the computational system energy from the initial state to the threshold is included as a stability indicator:

[0033] Construct a Pontryagin equation for the mean first crossing time. The Pontryagin equation is set as a second-order ordinary differential equation, where the coefficient of the second derivative term is half of the diffusion coefficient, the coefficient of the first derivative term is the drift coefficient, and the non-homogeneous term of the equation is a constant term.

[0034] Set an absorption boundary condition, namely, the average first crossover time is zero at the critical energy threshold;

[0035] Set the reflection boundary condition, that is, at the energy zero point, the first derivative of the average first crossing time with respect to energy is zero;

[0036] Based on the absorbing boundary conditions and the reflecting boundary conditions, the Pontryagin equation is integrated twice to obtain an analytical expression for the average first crossing time.

[0037] Preferably, in S5, constructing the nonlinear mapping function includes:

[0038] The torsional stiffness of the semi-trailer frame, the suspension damping coefficient, and the fractional order of the suspension are selected as structural parameters as input variables to determine the physical value range of each parameter.

[0039] The Latin hypercube sampling method is used to generate multiple sets of structural parameter samples within the range of the values, and the average first crossing time corresponding to each set of samples is calculated using the aforementioned steps.

[0040] The sample data is trained using a Gaussian process regression algorithm or a radial basis function neural network algorithm to establish a surrogate model between the input and output variables, which serves as the nonlinear mapping function.

[0041] Preferably, in S5, the quantification of the system stability margin under different structural parameters includes:

[0042] Given random excitation conditions on the road surface, an optimization function is established with the objective of maximizing the average first crossing time, and physical feasible region constraints are set for the structural parameters.

[0043] A global optimization algorithm is used to search for structural parameter points within the feasible region that maximize the average first crossing time.

[0044] The combination of structural parameters corresponding to the aforementioned structural parameter points is output as the optimal design parameters that balance lightweighting and driving stability.

[0045] The present invention has the following beneficial effects:

[0046] 1. In this invention, by using fractional derivative operators to establish constitutive relations and calculating the average first crossing time based on energy evolution, the problem of distortion of dynamic response and failure of stability assessment under complex road conditions is improved by using integer linear models for most traditional modeling, which ignore the viscoelastic memory characteristics of materials under large deformation.

[0047] 2. In this invention, the high-dimensional state space is projected to a one-dimensional energy space by applying the stochastic averaging method, thereby deriving a one-dimensional stochastic differential equation for the total energy of the system. This improves the problem that traditional stochastic dynamics analysis mostly uses high-dimensional direct solutions, which are difficult to solve analytically and have low computational efficiency due to severe variable coupling and excessive dimensionality.

[0048] 3. In this invention, by constructing a nonlinear mapping function between structural parameters and the average first crossing time, the physical design parameters and macroscopic stability indicators are directly correlated. This improves the problem that traditional parameter matching mostly relies on repetitive time-domain simulation trial and error, which results in low design efficiency and difficulty in finding the optimal solution due to the huge amount of computation and the lack of obvious patterns. Attached Figure Description

[0049] Figure 1 This is a flowchart of a method for mapping and modeling the structural parameters of a semi-trailer with driving stability, as proposed in this invention.

[0050] Figure 2 The flowchart for establishing a generalized non-conservative dissipative force vector is shown below, illustrating the modeling method for mapping semi-trailer structural parameters and driving stability proposed in this invention.

[0051] Figure 3 The flowchart shows the solution of the stationary probability density function for the modeling method of mapping semi-trailer structural parameters and driving stability proposed in this invention.

[0052] Figure 4 This invention presents a flowchart of the construction of a nonlinear mapping function and parameter optimization process for a semi-trailer vehicle structural parameters and driving stability mapping modeling method. Detailed Implementation

[0053] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] Example 1:

[0055] In the first embodiment of the present invention, a method for mapping and modeling the structural parameters of a semi-trailer to its driving stability is provided, such as... Figures 1-4 As shown, it includes the following steps:

[0056] S1. Obtain the structural parameters of the semi-trailer suspension and tires, establish the viscoelastic constitutive relationship using the fractional derivative operator, synthesize the nonlinear restoring force and the fractional damping force, and obtain the generalized nonconservative dissipative force vector.

[0057] Furthermore, in S1, establishing the viscoelastic constitutive relation using fractional derivative operators includes:

[0058] The fractional derivative operator is defined as the convolution integral of the deformation velocity as a power function of time. The kernel function of the convolution integral is used to characterize the decay law of the viscoelastic memory strength of the material.

[0059] A generalized nonconservative dissipative force expression is constructed, consisting of two superimposed parts: the first part is the product of the equivalent viscous damping coefficient and the fractional derivative of the displacement, used to characterize the frequency-varying damping characteristics; the second part is the product of the nonlinear stiffness coefficient and the high power of the displacement, used to characterize the stiffness hardening characteristics under large deformation.

[0060] Specifically, the core of this step lies in addressing the problem that traditional integer-order models cannot accurately describe the distortion of the mechanical response of semi-trailer air suspension airbags and tire rubber materials under large deformations and wide-frequency excitation. The implementation process begins with obtaining physical parameters, constructing a mathematical model that includes memory terms, and ultimately outputting a generalized force vector for the dynamic equations.

[0061] Data input and parameter definition begin with obtaining the basic physical parameters of the semi-trailer's suspension and tire systems. Input data includes: the initial stiffness of the suspension airbags, the lateral stiffness of the tires, the equivalent viscous damping coefficient of the material, and the fractional order characterizing the material's memory properties. These parameters are obtained through materials mechanics experiments or from technical manuals provided by the manufacturer.

[0062] To construct a fractional derivative operator for viscoelastic rubber-like materials, this scheme abandons the simple linear damping assumption and introduces a Caputo-type fractional derivative operator. This operator correlates the current stress state with the deformation history over a past period through convolution integrals. The definition of the Caputo fractional derivative is shown below:

[0063] ;

[0064] in Represents displacement variable of The fractional derivative, which is the core variable of the fractional damping force term; The order is a fraction, and its range is [value range missing]. This parameter directly determines the decay rate of the material's viscoelastic memory strength. When it approaches 0, it exhibits pure elasticity; when it approaches 1, it exhibits pure viscosity. This is the gamma function, used to normalize fractional calculus. This is the current calculation time; Let be the integral variable, representing a past historical moment, and be the integration interval. It covers the entire deformation history from the initial moment to the current moment; To be at a historical moment Deformation rate; It is the kernel function of the convolution integral, i.e., the power function kernel.

[0065] The synthesis of the generalized nonconservative dissipative force vector, based on the above operator, constructs a generalized nonconservative dissipative force containing nonlinear stiffness and fractional damping terms. The mathematical expression for this force consists of two nonlinear superpositions, as shown in the following equation:

[0066] ;

[0067] in This is a generalized nonconservative dissipative force, which serves as the input for the nonconservative force term in the subsequent Hamiltonian system equations. It is the equivalent viscous damping coefficient, which is related to the physical properties of the material; For suspension or tires Vertical or lateral deformation displacement at any given moment; It is a nonlinear stiffness coefficient used to characterize the hardening properties of materials under large deformations; The term is a cubic power of the displacement, representing the physical phenomenon that stiffness increases nonlinearly and rapidly with increasing displacement.

[0068] By constructing the above formula, the power function kernel This process plays a role in weighting the data. Historical states closer to the current moment have a greater weight, and vice versa. This mathematical approach accurately simulates the stress relaxation and creep characteristics of rubber materials, meaning that the current stress on the material depends not only on the current deformation rate but also on the cumulative effect of past deformation history.

[0069] The second part of the formula The introduction of the cubic term solves the problem of underestimating the stiffness of the linear model when the semi-trailer encounters large impacts and large rolls. The cubic term makes the model approximately linear during small deformations, while the stiffness hardens rapidly during large deformations, thus limiting excessive rolls under extreme conditions.

[0070] The data output process, after the above calculations, generates a corresponding [database name] for each independent suspension and tire of the semi-trailer. Expression. These scalar forces are assembled into a generalized force vector according to the vehicle's topology. This vector As the direct input data for step S2, it is substituted into the non-conservative force terms of the Hamiltonian dynamics equations and participates in the subsequent solution of the vehicle state evolution.

[0071] S2. Introduce the generalized nonconservative dissipative force vector into the semi-trailer dynamics system, combine it with the road surface stochastic excitation model, construct a nonholonomic Hamiltonian system under stochastic excitation, and use the total energy of the system as the Hamiltonian function to obtain a set of multidimensional stochastic differential equations describing the evolution of the system state.

[0072] Furthermore, in S2, the Hamiltonian function with the total system energy includes:

[0073] Construct a generalized mass matrix that includes the mass of the tractor, the mass of the semi-trailer, and the rotational inertia of each component about the center of mass. Use the quadratic form of the generalized momentum and the generalized mass matrix to construct the system kinetic energy function.

[0074] Construct a generalized potential energy function consisting of the sum of the elastic potential energy stored when the suspension and tires undergo elastic deformation and the gravitational potential energy caused by changes in the body's attitude such as roll or pitch.

[0075] Adding the system's kinetic energy function to the generalized potential energy function yields the Hamiltonian function, which describes the system's conservative energy.

[0076] In S2, the system of multidimensional stochastic differential equations describing the evolution of the system state is obtained, including:

[0077] The random excitation of the road surface is modeled as a Gaussian white noise process, and the intensity coefficient matrix of the effect of random excitation on the generalized momentum of the system is determined.

[0078] Based on the Hamiltonian canonical equations, and combining the partial derivatives of the Hamiltonian function with respect to generalized momentum and generalized coordinates, the generalized nonconservative dissipative force vector, and the road surface stochastic excitation term, an Iton-type stochastic differential equation system containing deterministic drift terms and stochastic diffusion terms is constructed.

[0079] Specifically, this step, based on the generalized non-conservative dissipative force vector obtained in S1, introduces the principle of energy conservation and transformation, transforming the dynamics problem of the semi-trailer multibody system into a state evolution problem under a Hamiltonian system. The implementation process includes the construction of the system energy function, the matrix processing of stochastic excitations, and the derivation of the Iton-type stochastic differential equation system.

[0080] The construction of the system's energy function and Hamiltonian function first involves determining the system's generalized coordinates based on the principles of Lagrange mechanics. With generalized momentum Generalized coordinates It includes the degrees of freedom of the tractor and semi-trailer, such as the tilt angle, pitch angle, and vertical displacement.

[0081] Construct the total kinetic energy function of the system This function is expressed in quadratic form using the generalized momentum and generalized mass matrices, as shown in the following equation:

[0082] ;

[0083] in The total kinetic energy of the system is a scalar quantity. Let be the generalized momentum vector of the system, whose dimension is consistent with the system's degrees of freedom; It is the transpose of the generalized momentum vector; The generalized mass matrix includes the mass of the tractor, the mass of the semi-trailer, and the moment of inertia of each component about its center of mass, reflecting the inertial coupling relationship between the components of the system. It is the inverse of the generalized mass matrix.

[0084] Construct the total potential energy function of the system This function consists of two parts: elastic potential energy and gravitational potential energy, as shown in the following equation:

[0085] ;

[0086] in The total potential energy of the system is a scalar. For the first The linear stiffness component of a suspension or tire; For the first The deformation of an elastic element is a function of generalized coordinates; For the first The mass of a rigid body; It is the acceleration due to gravity; For the first The vertical height change of the center of mass of a rigid body is used to characterize the change in gravitational potential energy caused by body roll or pitch.

[0087] Based on the above kinetic and potential energy, the Hamiltonian function of the system is obtained. :

[0088] ;

[0089] The construction of stochastic excitation and nonholonomic dynamic equations treats road surface roughness as an external random disturbance, modeled using a Gaussian white noise process. This is combined with the generalized nonconservative dissipative force vector containing fractional-order memory terms obtained in step S1. We establish the equations for a nonholonomic Hamiltonian system subject to random excitation.

[0090] ;

[0091] in For the differential increment of the generalized coordinates; The differential increment of generalized momentum; is the partial derivative of the Hamiltonian function with respect to the generalized momentum, and its physical meaning is the generalized velocity; The partial derivative of the Hamiltonian function with respect to the generalized coordinates is physically represented by the conservative force term. The generalized nonconservative dissipative force vector output by step S1 contains fractional-order viscoelastic damping force and nonlinear restoring force, characterizing the energy dissipation mechanism of the system. The intensity coefficient matrix of random excitation is determined by the road surface grade and vehicle speed. The differential increment of the Wiener process corresponds to Gaussian white noise excitation; For time step.

[0092] The construction of the Hamiltonian function unifies the complex dynamic coupling relationships of a vehicle into an energy form. Through... Describing inertial forces, The text describes the elastic restoring force and the gravitational restoring torque. In particular, the introduction of the gravitational potential energy term clarifies the role of the potential energy release caused by tilting in promoting instability in heavy semi-trailers under high center of gravity conditions.

[0093] The construction of Itō-type stochastic differential equations combines deterministic mechanics with stochastic dynamics. The drift term in the equations... It includes the system's conservative and dissipative forces, reflecting the vehicle's motion trend and energy decay law under the condition of no external interference; diffusion term This quantifies the intensity of the disturbance to the system's momentum caused by random road surface irregularities. This equation structure directly fits the subsequent stochastic averaging method, providing a standard mathematical model foundation for solving the probability density function.

[0094] Data input / output flow: Inputs include: mass parameters of the tractor and semi-trailer, moment of inertia parameters, suspension geometric parameters, and the generalized nonconservative dissipative force vector calculated in step S1. .

[0095] Output: A set of multidimensional Iton stochastic differential equations describing the state evolution of the system. This set of equations is used as the computational object in step S3 to derive the one-dimensional energy diffusion equation.

[0096] S3. Apply the stochastic averaging method of quasi-Hamiltonian systems to the multidimensional stochastic differential equation system, project the high-dimensional state space to the one-dimensional energy space, derive the one-dimensional stochastic differential equation about the total energy of the system, and establish the corresponding probability density evolution equation based on the one-dimensional stochastic differential equation to obtain the stationary probability density function characterizing the probability of the system energy distribution at different energy levels.

[0097] Furthermore, in S3, the one-dimensional stochastic differential equations concerning the total energy of the system are derived as follows:

[0098] Within one quasi-period of the system, the dissipation term and the random excitation term are averaged over time to calculate the drift coefficient. The drift coefficient is set as the sum of the statistical average of the work done by the generalized non-conservative dissipation force and the energy correction term caused by the random excitation.

[0099] The diffusion coefficient is calculated by averaging the squares of the random excitation terms over a pseudo-period of the system. The diffusion coefficient is set as the value that characterizes the intensity of energy fluctuation caused by the power spectral density of the random excitation on the road surface.

[0100] By utilizing the drift coefficient and diffusion coefficient, a one-dimensional Iton stochastic differential equation is constructed to describe the evolution of the total energy of the system over time.

[0101] In S3, the stationary probability density functions characterizing the distribution probability of the system's energy at different energy levels are obtained by solving for:

[0102] The Fokker-Planck-Kolmogorov equation is constructed based on the one-dimensional Iton stochastic differential equation. The probability density in the Fokker-Planck-Kolmogorov equation changes with time at a rate of zero, and it is transformed into an ordinary differential equation concerning energy.

[0103] The ordinary differential equation is solved by integration to obtain an analytical solution containing an exponential function. The exponential term of the exponential function is set as the integral of the ratio of the drift coefficient to the diffusion coefficient, and the analytical solution is normalized and used as the stationary probability density function.

[0104] Specifically, this step aims to solve the analytical problem of solving high-dimensional nonlinear systems under stochastic excitation. The high-dimensional state-space dynamic equations obtained in S2 are reduced in dimensionality using the stochastic averaging method, transforming them into a one-dimensional stochastic process concerning the total energy of the system, and then the energy probability density function is solved.

[0105] The drift coefficient and diffusion coefficient are calculated using the stochastic averaging method for quasi-Hamiltonian systems, applied to the multidimensional stochastic differential equations of the S2 output. Since the damping force and stochastic excitation terms are small relative to the Hamiltonian conservative force terms, the total energy of the system... Change is a slow process. Within a quasi-period of the system... The internal time-averaged calculation is performed on the dissipation term and the random excitation term.

[0106] Define drift coefficient This coefficient reflects the average rate of change of the system's energy, that is, the difference between the average energy input and dissipation. Its calculation formula is as follows:

[0107] ;

[0108] in Let be the system's drift coefficient, and be the total energy. The function; For the system at energy The pseudo-period of time; For the iso-energy orbits along the Hamiltonian system The integral; It is a generalized nonconservative dissipative force vector containing fractional damping terms; It is a generalized velocity vector; This is a random excitation intensity coefficient matrix; For the trace operation of a matrix, The term represents the Iton correction term caused by random excitation, which is used to correct the effect of white noise on the average energy of the system.

[0109] Define diffusion coefficient This coefficient reflects the intensity of energy fluctuations caused by random excitation. Its calculation formula is as follows:

[0110] ;

[0111] in The square value of the system's diffusion coefficient characterizes the degree of energy dispersion. This is the transpose of the random excitation intensity coefficient matrix.

[0112] The construction of the one-dimensional Iton stochastic differential equation is based on the calculated drift coefficient. With diffusion coefficient , to the system from dimensional state space Projected into one-dimensional energy space Construct a one-dimensional Iton stochastic differential equation describing the evolution of the system's total energy over time:

[0113] ;

[0114] in It represents the stochastic differential increment of the system's total energy; This represents the differential increment of standard Brownian motion. The physical meaning of this equation is that the change in the system's energy is determined by both the deterministic average dissipation / input and the random fluctuations.

[0115] To solve for the stationary probability density function and obtain the statistical distribution of the system's energy, the corresponding Fokker-Planck-Kolmogorov (FPK) equation is established based on the aforementioned one-dimensional Iton equation. This equation describes the energy probability density function. Evolution over time:

[0116] ;

[0117] For a stationary stochastic process of semi-trailer travel, let the rate of change of probability density over time be... 0, transforming the partial differential equation into a function of energy. Ordinary differential equations:

[0118] ;

[0119] Integrate the above equation and solve for the solution, taking into account the normalization condition. The stationary probability density function of the system energy is obtained. Analytical solution:

[0120] ;

[0121] in Let be the probability density function of the system energy when it is in a steady state; This is the normalization constant; For integration dummy variables; For an exponential function, the exponential term... It reflects the energy distribution pattern under the confrontation of drift force and diffusion force.

[0122] The application of the stochastic averaging method effectively reduces the system's dimensionality, simplifying the originally complex and difficult-to-solve high-dimensional nonlinear multibody dynamics equations of a semi-trailer into a single-variable energy evolution equation, thus making it possible to analytically solve the stationary probability density. This method avoids the numerical difficulties of solving high-dimensional FPK equations and significantly improves computational efficiency. Through the stationary probability density function... It can intuitively quantify the stability characteristics of the system: if A single-peaked distribution with the peak value close to zero energy indicates that the vehicle's motion is likely within a stable region; a bimodal distribution or a peak value drifting towards higher energy levels suggests a risk of significant system oscillations or random bifurcation. This probability distribution provides the direct mathematical basis for subsequent calculations of the first travel time.

[0123] Data input / output process: Input: Multidimensional stochastic differential equation system and Hamiltonian function expression output from step S2.

[0124] Output: The stationary probability density function of the system's total energy. This function serves as input to step S4, used to construct the Pontryagin equation.

[0125] S4. Set the critical energy threshold for instability, construct and solve the differential equation using the probability density function, and calculate the average first crossover time of the system energy from the initial state to the threshold as a stability index.

[0126] Furthermore, in S4, setting the instability critical energy threshold includes:

[0127] Obtain the roll angle of the semi-trailer at the moment the wheel leaves the ground during a static rollover test or the folding angle when folding occurs during a folding test, and define it as the physical limit state.

[0128] Substitute the generalized coordinates corresponding to the physical limit state into the generalized potential energy function to calculate the total potential energy value under the physical limit state, and define it as the critical energy threshold of the system.

[0129] In S4, the average first-crossing time for the system energy to reach the threshold from the initial state is used as a stability metric, including:

[0130] Construct a Pontryagin equation for the mean first crossing time. The Pontryagin equation is set as a second-order ordinary differential equation, where the coefficient of the second derivative term is half of the diffusion coefficient, the coefficient of the first derivative term is the drift coefficient, and the non-homogeneous term of the equation is a constant term.

[0131] Set an absorption boundary condition, namely, the average first crossover time is zero at the critical energy threshold;

[0132] Set the reflection boundary condition, that is, at the energy zero point, the first derivative of the average first crossing time with respect to energy is zero;

[0133] Based on the absorbing boundary conditions and the reflecting boundary conditions, the Pontryagin equation is integrated twice to obtain an analytical expression for the average first crossing time.

[0134] Specifically, this step aims to establish a quantitative evaluation standard for stability within the energy domain, transforming abstract probability distributions into intuitive time-dimensional indicators. The implementation process encompasses determining the critical energy threshold, constructing the Pontryagin equation, and analytically solving for the mean first crossover time.

[0135] The determination of the instability critical energy threshold is first based on obtaining the extreme attitude parameters of the semi-trailer through physical experiments or multibody dynamics simulations. For rollover stability, the roll angle at the moment the wheels leave the ground is selected; for folding stability, the folding angle when the angle between the tractor and the semi-trailer reaches the mechanical limit is selected. The generalized coordinate vectors corresponding to these extreme angles are then... Substitute into the generalized potential energy function constructed in step S2 In this context, the calculated potential energy value is defined as the critical energy threshold of the system. .

[0136] This approach maps the instability boundary in geometric space to the potential energy barrier height in energy space. When the total energy of the system exceeds this threshold, it means that the system has crossed the saddle point of the potential energy well and irreversible instability has occurred.

[0137] The Pontryagin equations are constructed based on the first-pass theory, where the system's energy changes from the initial state. First time reaching the critical energy threshold The required time is a random variable. The statistical mean of this random variable, i.e., the mean time to first crossing. This satisfies the Pontryagin equation. This equation is a second-order non-homogeneous ordinary differential equation, and its mathematical expression is as follows:

[0138] ;

[0139] in Let be the mean first travel time to be solved, and be the current system energy. The function; For system energy variables; Let be the second derivative of the average first crossing time with respect to energy; This is the first derivative of the average first-pass time with respect to energy; The diffusion coefficient, calculated in step S3, characterizes the intensity of random disturbance. The drift coefficients calculated in step S3 characterize the deterministic energy flow; The constant nonhomogeneous term on the right-hand side of the equation originates from the probability flow conservation condition defined in the average time term.

[0140] Boundary condition setting and analytical solution: To solve the above second-order differential equation, two boundary conditions need to be set: First, the absorbing boundary condition. When the system energy reaches the critical threshold... When this occurs, the instability event is considered to have occurred immediately, and the remaining survival time is zero. 0. Second, reflection boundary conditions. The system energy cannot be negative, and there is no probability flow to the negative energy region at the zero energy point, i.e., at... The first derivative of the average first crossing time at point 0 is zero, expressed as: .

[0141] Based on the above boundary conditions, the Pontryagin equation is solved by quadratic integration to obtain an analytical expression for the mean first crossing time:

[0142] ;

[0143] in For the system from initial energy The average time from evolution to instability; This represents the initial energy state of the system. The critical energy threshold; , These are intermediate dummy variables in the integration process; The system energy stationary probability density function obtained by solving step S3.

[0144] By constructing and solving the Pontryagin equation, the fuzzy concept of stability is transformed into a concrete mean time to failure (MTBF) metric. Unlike traditional methods that judge stability solely based on whether the load transfer rate exceeds a certain threshold at a specific moment, the MTBF comprehensively considers the statistical characteristics of random road surface excitation, the vehicle's nonlinear damping characteristics, and the system's energy reserves. This metric reflects the vehicle's ability to resist random disturbances and maintain stable driving under current operating conditions; a higher value indicates a lower probability of rollover or folding on random road surfaces, and a higher safety margin.

[0145] Data input / output flow: Input: the stationary probability density function output from step S3. Drift coefficient diffusion coefficient and the critical energy threshold calculated in this step. .

[0146] Output: Average first crossing time This scalar index serves as the dependent variable data in step S5, used to construct the mapping function.

[0147] S5. Using structural parameters as independent variables and average first crossing time as dependent variable, construct a nonlinear mapping function to quantitatively characterize the system stability margin under different structural parameters.

[0148] Furthermore, in S5, constructing the nonlinear mapping function includes:

[0149] The torsional stiffness of the semi-trailer frame, the suspension damping coefficient, and the fractional order of the suspension are selected as structural parameters as input variables to determine the physical value range of each parameter.

[0150] The Latin hypercube sampling method is used to generate multiple sets of structural parameter samples within the range of values, and the average first crossing time corresponding to each set of samples is calculated using the aforementioned steps.

[0151] The Gaussian process regression algorithm or the radial basis function neural network algorithm is used to train the sample data to establish a surrogate model between the input and output variables, which serves as a nonlinear mapping function.

[0152] In S5, the quantitative characterization of system stability margins under different structural parameters includes:

[0153] Given random excitation conditions on the road surface, an optimization function is established with the objective of maximizing the average first crossing time, and physical feasible region constraints are set for the structural parameters.

[0154] A global optimization algorithm is used to search for structural parameter points within the feasible region that maximize the average first crossing time.

[0155] The combination of structural parameters corresponding to the structural parameter points is output as the optimal design parameters that balance lightweighting and driving stability.

[0156] Specifically, this step aims to establish a rapid response model between the physical structural parameters of the semi-trailer and its macroscopic stability indicators, addressing the problem that steps S1 to S4 involve complex stochastic differential equations, resulting in excessively long computation times and making them unsuitable for direct application in engineering iterative design. The implementation process encompasses three stages: experimental design, surrogate model training, and global optimization.

[0157] Variable definition and experimental design first determine the input and output of the mapping model. The input variables are the set of structural parameters. This vector contains the torsional stiffness of the semi-trailer frame. Suspension damping coefficient And the fractional order that characterizes the memory of materials The output variable is the average first crossing time calculated in step S4. .

[0158] Define the physical value range for the input variables, i.e., the design space. :

[0159] ;

[0160] in This is the lower bound vector of structural parameters, determined by the manufacturing process and material physical properties; This is the upper bound vector of the structural parameters.

[0161] The Latin hypercube sampling method (LHS) was used in the above design space. Perform space-filling sampling within to generate A statistically representative sample set of structural parameters Substitute this sample set sequentially into the calculation processes S1 to S4 to obtain the corresponding set of response values. .

[0162] The construction of nonlinear mapping functions is based on the sample set. A nonlinear mapping function is established using a radial basis function neural network (RBFNN). The mathematical expression of this mapping function is as follows:

[0163] ;

[0164] in This is the predicted average first crossing time, i.e., the output of the nonlinear mapping function; The structure parameter vector is any input. This represents the number of neurons in the hidden layer. For the first The connection weights from each hidden layer node to the output layer; For the first The center vector of each radial basis function; Here, is the Euclidean norm, representing the distance between the input vector and the center; The radial basis function is usually chosen as the Gaussian kernel function to measure the intensity of the local response at a point in space.

[0165] The weights are determined by minimizing the prediction error through a training algorithm. and center This allows us to obtain an explicit surrogate model that can replace the complex dynamic solution process.

[0166] Stability margin quantification and parameter optimization are performed by constructing an optimization model that aims to maximize the average first-crossing time, thus quantifying the stability margin. The optimization model is expressed as follows:

[0167] ;

[0168] in The optimal combination of structural parameters is the result of the optimization search. The set of independent variables that maximizes the objective function; This is used to identify constraints.

[0169] The above model is solved using global optimization algorithms such as genetic algorithms or particle swarm optimization. The algorithm searches the surface defined by the surrogate model to find a solution. The point that reaches the global maximum.

[0170] The core function of constructing the nonlinear mapping function is to decouple computational efficiency from model accuracy. While S1 to S4 offer high accuracy, their individual computations are time-consuming, failing to meet the demands of thousands of iterative optimizations. This step transforms complex calculus operations into simple algebraic operations using a surrogate model, achieving millisecond-level stability prediction.

[0171] By optimizing to maximize the average first-pass time, a shift from passive verification to proactive design is achieved. The system directly outputs the optimal stiffness and damping matching scheme that balances fractional-order memory characteristics and adaptability to random road surfaces, ensuring that the vehicle still has the maximum safety time margin, i.e., the longest average normal driving time before instability, while maintaining a lightweight design.

[0172] Data input / output flow: Input: Average first crossing time calculated in step S4. The set range of structural parameters , .

[0173] Output: Optimal combination of structural parameters and the corresponding maximum average first crossing time This output directly guides the selection of shock absorbers, frame cross-section design, and rubber compound selection for semi-trailers.

[0174] Example 2:

[0175] In the development of high-end precision instrument transport semi-trailers for long-haul logistics, vehicles generally employ ultra-lightweight frames combined with long-stroke air suspension and high-performance tires to adapt to complex road conditions. However, this presents significant challenges in dynamic matching design: Firstly, the suspension airbags and tire rubber materials exhibit strong viscoelastic memory characteristics. Traditional dynamic models based on integer derivatives neglect the material's memory decay, failing to accurately describe the frequency-varying damping characteristics and nonlinear stiffness hardening effect under large deformation conditions, leading to simulation model distortion. Secondly, existing technologies often use deterministic indices for steady-state verification, making it difficult to reveal the energy accumulation or random bifurcation behavior induced by the coupling of random road excitation and nonlinear systems. Furthermore, they lack quantitative indicators to characterize the average first crossing time of the system from its initial state to the instability boundary, preventing designers from establishing accurate parameter mapping and optimization models between lightweighting and driving stability, thus hindering the elimination of hidden instability risks. To address these issues, this invention provides a method for mapping and modeling the structural parameters and driving stability of a semi-trailer, the structure of which is as follows... Figure 1 As shown. The specific implementation process of this method is as follows:

[0176] By establishing a viscoelastic constitutive relation using fractional derivative operators and characterizing the material's memory properties and history dependence, this study accurately describes the frequency-varying damping and large-deformation nonlinear stiffness hardening of the suspension and tires under broadband excitation. This solves the distortion problem of traditional linear models describing polymer materials and ensures the accuracy of dissipative force input. Based on this, a nonholonomic Hamiltonian system under random excitation is constructed. Using energy as the core, the complex mechanical equilibrium equations are transformed into energy evolution equations, uniformly describing the coupling mechanism between the drift effect caused by internal damping dissipation and the diffusion effect caused by external random disturbances. Subsequently, the stochastic averaging method is applied to project the high-dimensional state space onto a one-dimensional energy space, overcoming the difficulty of analytically solving high-dimensional nonlinear systems. The statistical distribution law of the system's energy is intuitively revealed by obtaining the stationary probability density function. Furthermore, this function is used to calculate the average first-pass time, establishing a time-dimensional stability quantification index. This overcomes the limitations of traditional transient simulations and quantitatively evaluates the reliability of the vehicle maintaining stable driving. Finally, by constructing a nonlinear mapping function between structural parameters and stability indices, the decoupling relationship between physical design parameters and macroscopic stability indices was realized. This provides a direct quantitative evaluation basis and a rigorous mathematical theoretical foundation for parameter matching and reverse design of semi-trailers without the need for repeated time-domain simulations.

[0177] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for modeling the mapping between the overall structural parameters of a semi-trailer and its driving stability, characterized in that, Includes the following steps: S1. Obtain the structural parameters of the semi-trailer suspension and tires, establish the viscoelastic constitutive relationship using the fractional derivative operator, synthesize the nonlinear restoring force and the fractional damping force, and obtain the generalized nonconservative dissipative force vector. S2. Introduce the generalized nonconservative dissipative force vector into the semi-trailer dynamics system, combine it with the road surface stochastic excitation model, construct a nonholonomic Hamiltonian system under stochastic excitation, and use the total energy of the system as the Hamiltonian function to obtain a set of multidimensional stochastic differential equations describing the evolution of the system state. S3. Apply the stochastic averaging method of quasi-Hamiltonian systems to the multidimensional stochastic differential equation system, project the high-dimensional state space to the one-dimensional energy space, derive the one-dimensional stochastic differential equation about the total energy of the system, and establish the corresponding probability density evolution equation based on the one-dimensional stochastic differential equation to obtain the stationary probability density function characterizing the probability of the system energy distribution at different energy levels. S4. Set the instability critical energy threshold, construct and solve the differential equation using the probability density function, and calculate the average first crossover time of the system energy from the initial state to the threshold as a stability index. S5. Using structural parameters as independent variables and average first crossing time as dependent variable, a nonlinear mapping function is constructed to quantitatively characterize the system stability margin under different structural parameters.

2. The method for mapping and modeling the structural parameters and driving stability of a semi-trailer according to claim 1, characterized in that, In S1, establishing the viscoelastic constitutive relation using fractional derivative operators includes: The fractional derivative operator is defined as the power function convolution integral of the deformation rate with respect to time. The kernel function of the convolution integral is used to characterize the decay law of the viscoelastic memory strength of the material. A generalized nonconservative dissipative force expression is constructed, consisting of two superimposed parts: the first part is the product of the equivalent viscous damping coefficient and the fractional derivative of the displacement, used to characterize the frequency-varying damping characteristics; the second part is the product of the nonlinear stiffness coefficient and the high power of the displacement, used to characterize the stiffness hardening characteristics under large deformation.

3. The method for mapping and modeling the structural parameters and driving stability of a semi-trailer according to claim 1, characterized in that, In S2, the Hamiltonian function based on the total system energy includes: Construct a generalized mass matrix that includes the mass of the tractor, the mass of the semi-trailer, and the rotational inertia of each component about the center of mass. Use the quadratic form of the generalized momentum and the generalized mass matrix to construct the system kinetic energy function. Construct a generalized potential energy function consisting of the sum of the elastic potential energy stored when the suspension and tires undergo elastic deformation and the gravitational potential energy caused by changes in the vehicle's attitude such as roll or pitch. Adding the system's kinetic energy function to the generalized potential energy function yields the Hamiltonian function, which describes the system's conservative energy.

4. The method for mapping and modeling the structural parameters and driving stability of a semi-trailer according to claim 1, characterized in that, In S2, the resulting set of multidimensional stochastic differential equations describing the evolution of the system state includes: The random excitation of the road surface is modeled as a Gaussian white noise process, and the intensity coefficient matrix of the effect of random excitation on the generalized momentum of the system is determined. Based on the Hamiltonian canonical equations, and combining the partial derivatives of the Hamiltonian function with respect to generalized momentum and generalized coordinates, the generalized nonconservative dissipative force vector, and the road surface stochastic excitation term, an Iton-type stochastic differential equation system containing deterministic drift terms and stochastic diffusion terms is constructed.

5. The method for mapping and modeling the structural parameters and driving stability of a semi-trailer according to claim 1, characterized in that, In S3, the derivation of the one-dimensional stochastic differential equation concerning the total energy of the system includes: Within one quasi-period of the system, the dissipation term and the random excitation term are averaged over time to calculate the drift coefficient, which is set as the sum of the statistical average of the work done by the generalized non-conservative dissipation force and the energy correction term caused by the random excitation. The diffusion coefficient is calculated by averaging the squares of the random excitation terms over a pseudo-period of the system over a time period. The diffusion coefficient is set as the value that characterizes the intensity of energy fluctuation caused by the power spectral density of the random excitation on the road surface. Using the drift coefficient and the diffusion coefficient, a one-dimensional Iton stochastic differential equation describing the evolution of the total energy of the system over time is constructed.

6. The method for mapping and modeling the structural parameters and driving stability of a semi-trailer according to claim 1, characterized in that, In S3, the stationary probability density function that characterizes the probability distribution of the system's energy at different energy levels obtained by solving includes: Based on the one-dimensional Iton stochastic differential equation, the Fokker-Planck-Kolmogorov equation is constructed. The probability density in the Fokker-Planck-Kolmogorov equation changes with time at a rate of zero, and it is transformed into an ordinary differential equation concerning energy. The ordinary differential equation is solved by integration to obtain an analytical solution containing an exponential function. The exponential term of the exponential function is set as the integral of the ratio of the drift coefficient to the diffusion coefficient, and the analytical solution is normalized and used as the stationary probability density function.

7. The method for mapping and modeling the structural parameters and driving stability of a semi-trailer according to claim 1, characterized in that, In S4, setting the instability critical energy threshold includes: Obtain the roll angle of the semi-trailer at the moment the wheel leaves the ground during a static rollover test or the folding angle when folding occurs during a folding test, and define it as the physical limit state. Substitute the generalized coordinates corresponding to the physical limit state into the generalized potential energy function to calculate the total potential energy value under the physical limit state, and define it as the critical energy threshold of the system.

8. The method for mapping and modeling the structural parameters and driving stability of a semi-trailer according to claim 1, characterized in that, In S4, the average first-crossing time of the computational system energy from the initial state to the threshold is included as a stability metric: Construct a Pontryagin equation for the mean first crossing time. The Pontryagin equation is set as a second-order ordinary differential equation, where the coefficient of the second derivative term is half of the diffusion coefficient, the coefficient of the first derivative term is the drift coefficient, and the non-homogeneous term of the equation is a constant term. Set an absorption boundary condition, namely, the average first crossover time is zero at the critical energy threshold; Set the reflection boundary condition, that is, at the energy zero point, the first derivative of the average first crossing time with respect to energy is zero; Based on the absorbing boundary conditions and the reflecting boundary conditions, the Pontryagin equation is integrated twice to obtain an analytical expression for the average first crossing time.

9. The method for mapping and modeling the structural parameters and driving stability of a semi-trailer according to claim 1, characterized in that, In S5, the construction of the nonlinear mapping function includes: The torsional stiffness of the semi-trailer frame, the suspension damping coefficient, and the fractional order of the suspension are selected as structural parameters as input variables to determine the physical value range of each parameter. The Latin hypercube sampling method is used to generate multiple sets of structural parameter samples within the range of the values, and the average first crossing time corresponding to each set of samples is calculated using the aforementioned steps. The sample data is trained using a Gaussian process regression algorithm or a radial basis function neural network algorithm to establish a surrogate model between the input and output variables, which serves as the nonlinear mapping function.

10. The method for mapping and modeling the structural parameters and driving stability of a semi-trailer according to claim 1, characterized in that, In S5, the quantification characterization of the system stability margin under different structural parameters includes: Given random excitation conditions on the road surface, an optimization function is established with the objective of maximizing the average first crossing time, and physical feasible region constraints are set for the structural parameters. A global optimization algorithm is used to search for structural parameter points within the feasible region that maximize the average first crossing time. The combination of structural parameters corresponding to the aforementioned structural parameter points is output as the optimal design parameters that balance lightweighting and driving stability.

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