Modelica-based modeling and adaptive parameter optimization method for vehicle single mass system

Abstract

The application relates to the field of automobile dynamics simulation, and particularly discloses a Modelica-based automobile single-mass system modeling and adaptive parameter optimization method, which comprises the following steps: determining a simplified module of an automobile single-mass system and a component connection mode according to demand analysis, and building a basic simulation model based on Modelica; performing initial simulation on the basic simulation model to obtain simulation output results under initial parameters; collecting real vehicle measured data, constructing a comprehensive error function, and iteratively optimizing key physical parameters of the basic simulation model by using a parameter optimization engine until a convergence condition is met to obtain optimized parameters; and feeding back the optimized parameters to the basic simulation model. The application combines the advantages of Modelica multi-field physical modeling and data-driven intelligent optimization algorithms, realizes a leap from manual experience parameter adjustment to automatic intelligent optimization, significantly reduces the dependence on accurate initial parameters, and effectively improves the model simulation precision and engineering application efficiency.

Description

Technical Field

[0001] This invention relates to the field of automotive dynamics simulation technology, and in particular to a method for modeling and adaptive parameter optimization of a single-mass automotive system based on Modelica. Background Technology

[0002] A car is actually a complex, multi-degree-of-freedom vibration system composed of the body, suspension, wheels, and road surface. In the preliminary engineering design or theoretical research phase, a simplified single-mass system model is often used to quickly focus on the fundamental characteristics of the vehicle's vertical vibration. This model ignores secondary factors such as wheel mass and specific suspension guiding mechanisms, treating the body as a concentrated mass block connected to the road surface or wheels via equivalent springs and dampers. This simplification helps researchers quickly grasp core issues such as vibration frequency, damping effect, and ride comfort, extracting the influence laws of key parameters and providing a theoretical foundation for subsequently constructing complex multibody dynamics models.

[0003] Currently, the main methods for modeling and analyzing single-mass systems in automobiles can be categorized as follows:

[0004] 1. Simplified Modeling Method Based on Multibody Dynamics Software: This method typically involves creating a single-mass or quarter-scale vehicle model in commercial software such as ADAMS / CAR, defining sprung mass, suspension stiffness, and damping coefficients parametrically. While this method is simpler than creating a full-body multibody model, its accuracy is highly dependent on accurate input parameters, such as precise center of gravity location and moment of inertia. In practical engineering applications, if the OEM does not provide this data, engineers often need to estimate it using simplified geometry from the CAD model, which introduces a 10%–15% estimation error. Furthermore, despite the model's simplification, a trade-off between model complexity and computational efficiency is still necessary, placing certain demands on computational resources.

[0005] 2. Modeling Method Based on Mathematical Equations: This method directly derives and establishes differential equations describing the system's motion based on classical mechanics theories such as Newton's second law and d'Alembert's principle. Its advantage lies in the clarity of physical concepts. However, to make the equations solvable, this method typically makes many simplifying assumptions about the actual situation, such as ignoring nonlinear characteristics in the suspension system (e.g., dry friction, nonlinear damping force), leading to inherent deviations between the model and the actual system. Simultaneously, parameter uncertainty is also a key factor affecting the accuracy of this method. For example, key parameters such as suspension spring stiffness and shock absorber damping coefficients often need to be estimated, and their accuracy directly affects the reliability of the model's output. For complex road mechanisms or variable working conditions, purely mathematical models often struggle to comprehensively and accurately describe the system's dynamic behavior.

[0006] 3. Modeling methods based on physical experiments: This method directly acquires the system's input and output data by building physical test benches (such as vibration tables) or conducting real-vehicle road tests, thereby identifying system characteristics or establishing empirical models. The disadvantages of this method are high experimental costs, requiring the purchase and maintenance of equipment such as vibration tables and high-precision sensors, and the need for numerous repetitive experiments to cover various operating conditions. Changes in temperature, humidity, and noise interference in the experimental environment can also affect the accuracy of measurement data. Furthermore, models established through specific experiments have poor versatility; when system parameters or the external environment change (such as different vehicle models or different loads), the original model often becomes invalid, requiring re-experimental modeling.

[0007] In summary, existing methods for modeling single-mass automotive systems generally suffer from the following technical bottlenecks:

[0008] Geometric simplification and parameter sensitivity: Existing methods either oversimplify component details or rely on precise data such as the center of mass position and moment of inertia, which often need to be estimated in actual engineering, leading to error accumulation. Inefficient model calibration: Determining model parameters often relies on repeated trial and error based on human experience, a tedious process that is difficult to guarantee accuracy. There is a lack of a means to automatically and efficiently correct model parameters using measured data. Balancing computational resources and accuracy: Traditional multibody simulation methods need to find a balance between model complexity and computational resource consumption, making it difficult to achieve fast computation while ensuring accuracy.

[0009] Therefore, how to provide a modeling and analysis method for a single mass system of a car that can reduce the dependence on precise initial parameters and achieve automatic and accurate correction of model parameters using measured data is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0010] The purpose of this invention is to address the problems in existing technologies that rely on precise data such as the center of mass position and moment of inertia, and that model parameter calibration relies on manual experience and is inefficient. This invention proposes a modeling and adaptive parameter optimization method for a single-mass vehicle system based on Modelica. By leveraging Modelica's multi-domain unified modeling features and combining it with an adaptive optimization algorithm driven by measured data, the invention achieves rapid model construction and high-precision automatic parameter correction.

[0011] To achieve the above objectives, the present invention adopts the following technical solution:

[0012] A Modelica-based method for modeling and adaptive parameter optimization of a single-mass vehicle system includes:

[0013] S1. Based on the requirements analysis, determine the simplified modules and component connection methods of the single mass system of the automobile, and build a basic simulation model based on Modelica;

[0014] S2. Perform initial simulation on the basic simulation model and obtain the simulation output results under the initial parameters;

[0015] S3. Collect and preprocess real vehicle measured data, construct a comprehensive error function to evaluate the difference between the simulation output results and the measured data, and use a parameter optimization engine to iteratively optimize the key physical parameters of the basic simulation model until the convergence condition is met, and obtain the optimized parameters.

[0016] S4. Feed the optimized parameters back to the basic simulation model to obtain a calibrated high-precision vehicle single-mass system model.

[0017] As a further technical solution of the present invention, S1 specifically includes:

[0018] S11. Based on the vehicle ride comfort analysis objective, the vehicle system is simplified according to the frequency decoupling principle. The core simplified modules include at least the sprung mass module representing the vehicle body, the spring damping components representing the suspension system, and the tire model representing the tire stiffness.

[0019] S12. Analyze the physical relationships of each element in the simplified module, determine that the input signal of the system is the vertical displacement of the road surface, and the output signal includes at least the vertical acceleration of the vehicle body. Also determine that the topological connection of each component is as follows: the spring and the damper are connected in parallel, one end is connected to the sprung mass, the other end is connected to the tire model, and the tire model is connected to the road excitation source.

[0020] S13. Select the corresponding component model based on the Modelica standard library, including at least: translational mass block Mass, linear spring Spring, linear damper Damper and displacement source Position;

[0021] S14. When the standard library does not contain the component with the required characteristics, the component model is established through custom modeling, constants are defined in the parameter definition area, and nonlinear physical equations are input in the equation definition area.

[0022] S15. Using Modelica's connect statement, the parameterized component models are physically connected according to the topology connection method to generate a complete basic simulation model of the vehicle single mass system.

[0023] As a further technical solution of the present invention, S14 specifically includes:

[0024] S141. Determine the physical characteristics of the required custom component and analyze its nonlinear behavior, wherein the nonlinear behavior includes at least a piecewise linear relationship between nonlinear spring force and relative displacement, or a nonlinear relationship between nonlinear damping force and relative velocity.

[0025] S142. Create a new component class in the Modelica modeling environment that inherits from some connection interface classes in the standard library. The interface classes include at least Modelica.Mechanics.Translational.Interfaces.PartialCompliant to ensure that the component has standard physical connection ports.

[0026] S143. Declare custom parameters in the parameter definition area of ​​the new component class. The parameters shall include at least the stiffness coefficient, damping coefficient, or input-output data pairs required for table lookup for the piecewise linear interval.

[0027] S144. In the equation definition area of ​​the new component class, use the Modelica language to write equations describing the physical behavior of the component. The equations shall include at least the conditional equations for calculating the force output piecewise based on relative displacement or relative velocity, or nonlinear mapping shall be achieved by calling a predefined data table through an interpolation function.

[0028] S145. Save the custom component model to the local model library for use in subsequent model building.

[0029] As a further technical solution of the present invention, S2 specifically includes:

[0030] S21. Set the simulation time parameters, including the simulation start time and end time, and select the numerical integration algorithm and step size control method according to the analysis requirements. The solver is DASSL, which is suitable for rigid systems, or CVODE, which is suitable for high-precision requirements. The step size control adopts fixed step size or adaptive step size.

[0031] S22. Configure the initial parameters of the basic simulation model, including at least: sprung mass parameters, suspension stiffness coefficient, damping coefficient, and road excitation signal type and amplitude. The road excitation uses a sine wave to simulate periodic bumps or band-limited white noise to simulate random road surfaces.

[0032] S23. Run the simulation program to solve the basic simulation model and obtain the dynamic response time-domain data of the system under the initial parameters;

[0033] S24. Extract simulation output results from the dynamic response time-domain data. The simulation output results include at least the vehicle body vertical acceleration and suspension travel, which are used for subsequent ride comfort evaluation and suspension travel verification, respectively.

[0034] As a further technical solution of the present invention, S3 specifically includes:

[0035] S31. Conduct real vehicle road tests under corresponding working conditions, collect vehicle vertical acceleration signals as measured data, and preprocess the measured data, including using statistical criteria to remove outliers, removing high-frequency noise through a low-pass filter, and resampling to obtain a standardized measured dataset.

[0036] S32. Construct a comprehensive error function to quantitatively evaluate the difference between the simulation output results and the standardized measured dataset;

[0037] S33. A two-stage hybrid optimization strategy is adopted to iteratively optimize the key physical parameters. It is determined whether the comprehensive error function value after iterative optimization meets the preset convergence condition. If it does, the optimization is terminated and the optimized parameters are output. If it does not meet the condition, the iteration continues until convergence.

[0038] As a further technical solution of the present invention, S31 specifically includes:

[0039] S311. Select an actual road or test site that is consistent with the simulation conditions, place an acceleration sensor at the center of gravity of the vehicle body, conduct a real vehicle road test, and collect the time domain signal of the vertical acceleration of the vehicle body as the raw measured data.

[0040] S312. Perform outlier detection and removal on the original measured data, and use statistical criteria to identify and remove abnormal data points caused by sensor interference or sudden impact on the road surface. The statistical criteria include at least the 3σ criterion.

[0041] S313. The measured data after removing outliers is subjected to low-pass filtering. A fourth-order Butterworth low-pass filter is used to remove high-frequency noise interference and retain the effective frequency components related to the vertical vibration of the vehicle body. The cutoff frequency of the filter is set to not less than 50Hz according to the characteristics of the suspension system.

[0042] S314. Resample the filtered measured data to reduce the original sampling frequency to the same sampling frequency as the simulation output, and obtain a standardized measured dataset for subsequent comparison and evaluation with the simulation output results.

[0043] As a further technical solution of the present invention, S32 specifically includes:

[0044] S321. Determine the error component types of the comprehensive error function, wherein the error components include at least the root mean square error RMSE used to evaluate the accuracy of amplitude fitting, the frequency error FreqError used to evaluate the degree of matching of the resonance peak positions, the phase error PhaseError used to evaluate the timing alignment of the response, and the peak error PeakError used to evaluate the amplitude of the impulse response.

[0045] S322. Calculate the values ​​of each error component. The root mean square error is obtained by calculating the square root of the mean square of the difference between the simulation output and the measured data. The frequency error is obtained by comparing the difference of the main peak frequency in the spectrum diagrams of the simulation and measured data. The phase error is obtained by calculating the phase difference of the cross-correlation function or transfer function. The peak error is obtained by comparing the difference of the maximum peak value in the time domain response. Assign weight coefficients to each error component. The weight coefficients are determined according to the key requirements of vehicle performance analysis. When the focus is on ride comfort evaluation, increase the weight of the root mean square error. When the focus is on resonance characteristic identification, increase the weight of the frequency error.

[0046] S323. Constructing the comprehensive error function RMSE FreqError PhaseError PeakError, where to The corresponding weight coefficients must satisfy the normalization condition; output the comprehensive error function value. This serves as the objective function value in subsequent parameter optimization iterations.

[0047] As a further technical solution of the present invention, S33 specifically includes:

[0048] S331. Initialize the two-stage hybrid optimization strategy and set the feasible domain range of key physical parameters. The key physical parameters include at least the suspension stiffness coefficient and damping coefficient. The feasible domain range is determined based on the vehicle type and suspension design experience values.

[0049] S332. Perform the first stage of global search, using an improved genetic algorithm to explore the feasible region globally. Set the genetic algorithm parameters to include at least the population size, number of generations, crossover probability, and mutation probability. Iterate and evolve to minimize the comprehensive error function value to obtain the global optimal initial parameter values. Determine whether the genetic algorithm has reached the preset maximum number of generations or whether the comprehensive error function value has stabilized. If so, terminate the global search and output the optimized initial parameter values.

[0050] S333. Perform the second stage of local fine-tuning. Starting from the initial value of the optimization parameters, use the adaptive gradient descent algorithm to perform local fine-tuning search. The adaptive gradient descent algorithm dynamically adjusts the learning rate step size according to the error change rate during the iteration process.

[0051] S334. During the local fine-tuning process, the comprehensive error function value is recalculated after each iteration, and it is determined whether the change in the comprehensive error function value between two adjacent iterations is less than the preset threshold. If the threshold is met, convergence is determined, and the final optimized parameters that meet the convergence condition are output.

[0052] As a further technical solution of the present invention, S4 specifically includes:

[0053] S41. Obtain the optimized key physical parameters from step S3, wherein the key physical parameters include at least the suspension stiffness coefficient and the damping coefficient;

[0054] S42. Write the optimized key physical parameters into the parameter configuration file of the basic simulation model, replace the original initial parameters in the model, and complete the update and calibration of the model parameters;

[0055] S43. Rerun the simulation based on the updated parameters to obtain the dynamic response data of the calibrated high-precision vehicle single-mass system model under the same working conditions, and verify the optimization effect;

[0056] S44. Based on the calibrated high-precision vehicle single-mass system model, predict and analyze vehicle performance.

[0057] As a further technical solution of the present invention, S44 specifically includes:

[0058] S441. Perform frequency domain analysis on the time domain signal of the vehicle vertical acceleration in the dynamic response data, convert it into a frequency domain signal using fast Fourier transform, extract the amplitude-frequency characteristic curve, and identify the main resonance frequency of the system, wherein the main resonance frequency corresponds to the peak point of the amplitude-frequency curve.

[0059] S442. Compare and verify the identified main resonance frequency with the theoretically calculated value or the measured spectrum. When the resonance frequency error is controlled within 2%, the frequency domain characteristics of the model are deemed to meet the requirements.

[0060] S443. Perform time-domain analysis on the vehicle vertical acceleration time-domain signal in the dynamic response data, perform frequency-weighted processing on the acceleration signal according to the ISO2631 standard, and calculate the weighted root mean square value of acceleration as a quantitative evaluation index of vehicle ride comfort.

[0061] S444. Based on the results of frequency domain analysis and time domain analysis, output a vehicle performance analysis report to guide the optimization design of suspension system parameters.

[0062] The beneficial effects of this invention are as follows:

[0063] 1. Based on Modelica's multi-domain unified modeling features, and through object-oriented component design and physical interface connection, it achieves highly reusable and scalable modeling of a single-mass automotive system. Users can focus on physical expression without the need for tedious mathematical derivation. At the same time, it no longer relies on difficult-to-obtain data such as precise center of mass position and moment of inertia, eliminating experimental measurement steps, reducing errors introduced by geometric simplification and parameter sensitivity, and saving experimental economic costs.

[0064] 2. An adaptive parameter optimization algorithm based on measured data is introduced, and a two-stage hybrid optimization strategy (combining improved genetic algorithm global search with adaptive gradient descent local fine-tuning) is adopted to achieve a leap from manual experience-based parameter tuning to automatic intelligent optimization. The algorithm automatically corrects model parameters to improve simulation accuracy, reduce resonance frequency error, reduce computation time, and significantly shorten the model calibration cycle.

[0065] 3. A high-precision single-mass vehicle system model is formed through standardized interface encapsulation, supporting frequency domain and time domain analysis. It can accurately identify the main resonance frequency of the system, quantitatively evaluate vehicle ride comfort according to ISO2631 standard, and the analysis results can be directly used to guide the optimization design of suspension parameters or the introduction of active control strategies, significantly reducing the number of real vehicle tests, reducing development costs, and shortening the R&D cycle. Attached Figure Description

[0066] Figure 1 This is a flowchart illustrating the Modelica-based modeling and adaptive parameter optimization method for a single-mass vehicle system proposed in this invention.

[0067] Figure 2 This is a schematic diagram of the structure of the automobile single-mass system simulation model proposed in this invention;

[0068] Figure 3 This is a schematic diagram of the test results of the simulation of the single-mass system of a car according to the present invention. Figure 1 ;

[0069] Figure 4 This is a schematic diagram of the test results of the simulation of the single-mass system of a car according to the present invention. Figure 2 . Detailed Implementation

[0070] To make the technical means, creative features, objectives and effects of this invention easier to understand, the invention will be further described below in conjunction with specific embodiments.

[0071] Please see the appendix Figure 1 - Appendix Figure 4 A modeling and adaptive parameter optimization method for a single-mass vehicle system based on Modelica, including:

[0072] S1. Based on the requirements analysis, determine the simplified modules and component connection methods for the single-mass vehicle system, and build a basic simulation model based on Modelica; specifically including:

[0073] S11. Based on the vehicle ride comfort analysis objectives, the vehicle system is simplified according to the frequency decoupling principle, and the core simplified module is determined as follows:

[0074] S111. Based on the vehicle ride comfort analysis objectives, the vehicle system is reasonably simplified. A car is an extremely complex multibody dynamics system. To focus on specific performance characteristics (such as ride comfort and tire dynamic load), reasonable simplification is necessary. The single-mass system is the most basic and classic model for studying the vertical vibration of the vehicle body. It ignores wheel mass, suspension nonlinearity, and vehicle pitch / roll motion, focusing on the inherent characteristics of the vehicle body in the vertical direction.

[0075] The main performance requirements for automobiles include:

[0076] Ride comfort requirements: Primarily concerned with the vibration acceleration experienced by passengers (or cargo);

[0077] Handling stability requirements: The main concern is the contact state between the tires and the ground (tire pressure changes, dynamic loads), which is crucial for steering and braking safety and is directly related to the movement of unsprung mass and the force transmission of the suspension.

[0078] Suspension travel limit requirements: To prevent the suspension from impacting the limit block, it is necessary to examine the relative displacement of the sprung and unsprung masses, which is directly related to the vertical motion of the sprung mass.

[0079] S112. For single-mass system models, the main analysis objective is usually locked onto the vertical vibration ride comfort of the vehicle, especially the preliminary assessment of the motion of the vehicle body (sprung mass).

[0080] Simplified according to the principle of frequency decoupling. Automotive suspension systems typically have two main vertical resonant frequencies:

[0081] The body (sprout) resonance frequency is usually in Within the range, mainly composed of sprung mass and suspension stiffness Decide: ,in: The vertical resonant frequency of the vehicle body, in Hz; Suspension spring stiffness, in N / m; The mass is the sprung mass, expressed in kg.

[0082] The resonant frequency of a wheel (unsprung) is usually in Within the range, it is mainly composed of unsprung mass. and tire stiffness Decide: ,in: The vertical resonant frequency of the wheel, in Hz; The vertical stiffness of the tire, in units of: ; The unsprung mass is expressed in kg.

[0083] S113. When the core objective is research When considering vehicle ride comfort, wheel hop modes above 10Hz can be temporarily ignored. Therefore, the unsprung mass is considered infinitesimal (i.e., zero mass), thus simplifying the system to a single-mass model; the role of the tire is simplified to a motion constraint on the lower support of the suspension (i.e., directly transmitting road surface displacement).

[0084] Based on the above simplification, the core simplification module must include at least the following:

[0085] Sprout mass module : Represents the equivalent mass of the vehicle body, frame, occupants, and most of the load, and is the direct experience of ride comfort;

[0086] Spring damping assembly: Connecting the vehicle body and wheels, it is the core component for isolating road impacts, simplified as a linear spring. and linear dampers Parallel components;

[0087] Tire Model: Tires possess elasticity and damping. In the initial analysis of low-frequency vehicle body vibration, the stiffness of the tire is much greater than that of the suspension. Its deformation and damping have a relatively small impact on the low-frequency dominant frequency of the vehicle body motion. The tire can be further simplified as a massless rigid contact point or an equivalent spring. .

[0088] This leads to the classic 1 / 4 vehicle single-mass vibration model, which is a simplified model of sprung mass + spring + shock absorber + tire.

[0089] S12. Analyze the physical relationships of each element in the simplified module, and determine the system's input and output signals and component topology connections, specifically as follows:

[0090] S121. Analyze the physical relationships between the elements in the system, establish the system dynamic equations, and assume: The load is the sprung mass, expressed in kg. Suspension spring stiffness, unit ; This is the suspension damping coefficient, in units of... ; For tire vertical stiffness, in units ; The vertical displacement of the sprung mass is given, with downward displacement being positive, and the unit is meters (m). The vertical displacement of the upper end of the tire, in meters (m). The vertical displacement of the road surface is expressed in meters (m).

[0091] In a single-mass model that neglects unsprung mass, the force balance equations are:

[0092] Tire force equation: ,in: This represents the dynamic force of the tire, measured in N.

[0093] Suspension force equation: ,in: This refers to the suspension spring damping force, expressed in Newton-meters (N). Vertical velocity of the sprung mass, in units ; The vertical velocity of the upper end of the tire, in units .

[0094] Assuming the unsprung mass is zero, in Equilibrium of forces: ,Right now: ;

[0095] Equation of motion for the sprung mass: ,in: The vertical acceleration of the sprung mass, in units .

[0096] S122. Determine the system's input and output signals:

[0097] Input signal (1): Vertical displacement of road surface The type is Real displacement signal, and the unit is meters.

[0098] Output signals (including at least the following four): Sprung mass displacement Unit: m; sprung mass velocity ,unit Spring-loaded mass acceleration ,unit Used for ride comfort assessment; suspension dynamic deflection Unit: meters (m), used for travel verification; tire dynamic load. , unit N.

[0099] S123. Determine the topology connection method for each component:

[0100] Spring and damper in parallel: spring's flange a With the flap of the damper a Connected together, connected to the span of the sprung mass. b ; spring's flange b With the flap of the damper bThey are connected together, forming a single connection to the upper end of the tire model;

[0101] One end is connected to the sprung mass: the connection is made through a physical interface to ensure coordination between force transmission and displacement;

[0102] The other end is connected to the tire model: the upper end of the tire model is connected to the spring-damping parallel assembly, and the lower end is connected to the road excitation source;

[0103] The tire model is connected to the road surface excitation source: road surface displacement. As a system input, it is applied to the lower end of the tire model through the displacement source component.

[0104] S13. Select the corresponding component model based on the Modelica standard library, specifically as follows:

[0105] Select the basic components from the Modelica standard library Modelica.Mechanics.Translational, as shown in Table 1 below, including:

[0106] Table 1. Basic Components Table

[0107]

[0108] Each component communicates through Modelica's physical interface (flange). a ,flange b Connect the components to ensure energy conservation and consistency of signal transmission. Example connection statement:

[0109] Sprung mass connected to the spring: connect(spring.flange) a ,sprungMass.flange b )

[0110] Spring and damper connected in parallel: connect(spring.flange) b ,damper.flange b )

[0111] Road surface stimulus input: connect(positionSource.flange, tireSpring.flange) b） .

[0112] S14. When linear components in the standard library cannot meet the requirements for describing actual physical characteristics (such as nonlinear spring characteristics and nonlinear damping characteristics), component models are created through custom modeling methods; specifically:

[0113] S141. Determine the physical characteristics of the required custom component and analyze its nonlinear behavior, specifically:

[0114] The physical properties required for the custom component must include at least:

[0115] (1) Piecewise linear relationship between nonlinear spring force and relative displacement:

[0116] The spring force and relative displacement have a piecewise linear relationship, and the equivalent stiffness Determined based on the relative displacement range: ,in: Spring force, in N; The relative displacement of the spring is expressed in meters (m). For the equivalent stiffness, is a piecewise function: = ,in: This is the stiffness coefficient for the first interval, in N / m, with a typical value of 18000. This is the stiffness coefficient for the second interval, in N / m, with a typical value of 32000. This is the stiffness coefficient for the third interval, in N / m, with a typical value of 50,000. This represents the displacement threshold for the first interval, in meters (m), with a typical value of 0.1. This is the displacement threshold for the second interval, in meters (m), with a typical value of 0.2.

[0117] Alternatively, nonlinear mapping can be achieved through table lookup: ,in: The data is obtained by linear interpolation through a predefined data table. The data table format is: table=[0,0;0.1,1800;0.2,5000], which means: stiffness is 0 N / m when displacement is 0 m, 1800 N / m when displacement is 0.1 m, and 5000 N / m when displacement is 0.2 m.

[0118] (2) Nonlinear relationship between nonlinear damping force and relative velocity:

[0119] The nonlinear relationship between damping force and relative velocity is investigated using a piecewise viscous damping model: ,in: Damping force, in N; The relative velocity across the two ends of the damper, in units ; Here is the equivalent damping coefficient, and here is a piecewise function: = ,in: Damping coefficient for the low-speed range, unit: Typical value 300; This is the damping coefficient for the high-speed range, in units of... Typical value 1500; For speed threshold, in units The typical value is 0.2; the negative sign indicates that the direction of the damping force is always opposite to the direction of the relative velocity, which plays a role in dissipating energy and suppressing vibration.

[0120] S142. Create a new component class in the Modelica modeling environment that inherits from some connection interface classes in the standard library to ensure that the component has standard physical connection ports.

[0121] For the translational mechanics component, it inherits from the interface class: Modelica.Mechanics.Translational.Interfaces.PartialCompliant. This interface class predefines the following standard physical ports and internal variables: flag a The left-side translational flange port is used for force transmission and displacement coordination between adjacent components; b This is the right-side translational flange port, used for connecting adjacent components and coordinating force transmission and displacement; rel For relative displacement internal variables, defined as ,in and respectively flag a and flag b The absolute displacement at v; rel As an internal variable of relative velocity, it is defined as follows: f is an internal variable of the force, representing the force transmitted by the component through the flange, satisfying... (Equilibrium of action and reaction forces). By inheriting this interface class, custom components automatically obtain the above standard physical ports and conservation quantity definitions, ensuring interoperability with Modelica standard library components. The class declaration structure is as follows: the new component class name is "NonlinearSpring" or "NonlinearDamper", and the extension declaration is inherited from the above interface class.

[0122] S143. Declare custom parameters in the parameter definition area (parameter section) of the new component class, including physical constants, interval thresholds, and lookup table data:

[0123] For nonlinear spring assemblies, declare the following parameters: first interval stiffness coefficient The physical meaning is the linear stiffness within a small displacement range; the stiffness coefficient of the second interval. Physically, it refers to the stiffness within a moderate displacement range; the stiffness coefficient for the third interval. Physically, it refers to the stiffness within a large displacement range; the first interval displacement threshold. Physically, it refers to the displacement boundary that distinguishes the first and second stiffness intervals; the displacement threshold of the second interval. The physical meaning is the displacement boundary that distinguishes the second and third stiffness intervals; the nonlinear enable flag useNonlinear is a Boolean parameter with a default value of true, used to control whether nonlinear characteristics are enabled (when false, it degenerates into a linear spring).

[0124] For nonlinear damping components, declare the following parameters: damping coefficient in the low-speed range. Physically, it refers to the damping coefficient during low-speed motion; the damping coefficient in the high-speed range. Physically, it refers to the damping coefficient during high-speed motion; velocity threshold. In physical terms, it refers to the speed boundary that distinguishes between low-speed and high-speed ranges.

[0125] For lookup table-type nonlinear springs, declare the following parameter: the stiffness lookup table data, which is a two-dimensional real number array, with a default value of: The first column represents the displacement value in meters (m); the second column represents the corresponding stiffness coefficient in meters (m). This indicates that the stiffness is 0 when the displacement is 0m. The stiffness is when the displacement is 0.1m. The stiffness is when the displacement is 0.2m. The interpolation smoothness parameter is an enumeration type, which defaults to linear piecewise interpolation.

[0126] S144. In the equation definition area (equation section) of the new component class, use the Modelica language to write equations describing the physical behavior of the component:

[0127] (1) Nonlinear spring force calculation equation:

[0128] When the nonlinear enable flag is true, the spring force Based on the absolute value of relative displacement Calculate the size in segments: f = When the nonlinear enable flag is false, it degenerates into linear spring mode. Relative velocity is defined as the derivative of relative displacement with respect to time. .

[0129] (2) Look up the nonlinear spring force calculation equation from the table:

[0130] equivalent stiffness coefficient Obtained through table lookup interpolation function, in terms of relative displacement As input, perform linear interpolation on a predefined table of data: The spring force is calculated as follows: Relative velocity is also defined as: .

[0131] (3) Equation for calculating nonlinear damping force:

[0132] Equivalent damping coefficient Based on the absolute value of relative velocity Size segmentation determination: = The damping force is calculated as follows (the negative sign indicates that the direction of the damping force is always opposite to the direction of the relative velocity): Relative displacement is defined as the difference in displacement between the two flanges. ;

[0133] Relative velocity is defined as: ;in respectively flag a and flag b The absolute displacement at that point This corresponds to the speed.

[0134] S145. Save the custom component model to the local model library. After saving, it can be called during subsequent model building using the import statement or graphical drag-and-drop method; forming a reusable custom component library that supports rapid modeling and parameter configuration for different vehicle models and suspension characteristics.

[0135] S15. Using Modelica's connect statement, the parameterized component models are physically connected according to the topological connection method to generate a complete basic simulation model of the vehicle's single mass system, specifically:

[0136] S151. In the Modelica modeling environment, each component is instantiated and assigned actual parameter values ​​to form an executable simulation model structure. Based on the standard library components selected in S13 and the custom component model in S14, the following instance is declared: the sprung mass module is instantiated as a translational mass block, with mass parameters... The linear suspension spring assembly is instantiated as a linear spring with stiffness parameters... The linear suspension damper assembly is instantiated as a linear damper with a damping coefficient. The tire equivalent spring assembly is instantiated as a linear spring with stiffness parameters... The road surface displacement excitation source component is instantiated as a displacement source, and the input signal is... The vehicle body acceleration sensor assembly is instantiated as an acceleration sensor; the suspension relative displacement sensor assembly is instantiated as a relative position sensor.

[0137] Simultaneously declare model variables: input signal Vertical displacement of the road surface; intermediate variable The vertical displacement of the upper end of the tire; the output signal includes the vehicle body displacement. Vehicle speed Vehicle acceleration Suspension dynamic deflection and tire dynamic load .

[0138] S152. Establish the topological connections determined in S12 using Modelica's connect statement to achieve physical coupling between components:

[0139] Mechanical topology connection: the spring's flange a and the flap of the damper a Commonly connected to the span of the sprung mass b ; spring's flange b and the flap of the damper b The flange is connected to the tire's equivalent spring. a ;flange of the tire's equivalent spring b Connect to the road surface displacement excitation source.

[0140] Sensor connection: The accelerometer is connected to the spandrel of the sprung mass. b To measure vehicle body acceleration; the two ends of the relative displacement sensor are respectively connected to the flange of the sprung mass. b Flange equivalent to a tire spring a To measure the dynamic deflection of the suspension.

[0141] Output signal assignment: The absolute displacement of the sprung mass. The absolute velocity of the sprung mass. The values ​​are measured by the accelerometer. These are measurements from a relative displacement sensor. Calculated by superimposing the relative displacement of the tire springs and the road surface displacement. It is calculated by multiplying the tire stiffness by the tire deformation.

[0142] S153. The mathematical constraints corresponding to the above physical interface connections are as follows:

[0143] The displacement of the left end of the spring is equal to that of the mass on the spring: The displacement of the left end of the damper is equal to that of the mass on the spring. The right end of the spring has the same displacement as the left end of the tire spring. The right end of the damper is connected to the tire spring.

[0144] The displacements at the left end are equal: The right end of the tire spring is displaced equal to the road surface displacement. The acceleration sensor reading is equal to the acceleration of the sprung mass. The displacement of the first end of the relative displacement sensor is equal to the displacement of the spring-loaded mass. The displacement sensor's second end is equal to the displacement of the tire's upper end. .

[0145] S154. Based on the above connections, the system automatically generates the complete state-space equations. Define the state vector:

[0146] The state equation is:

[0147] External incentive The displacement of the road surface is transmitted through the tire stiffness.

[0148] S155. After completing the connection, encapsulate the basic simulation model and define standardized input / output interfaces.

[0149] Input interface: Road surface displacement input interface It receives external road surface excitation signals.

[0150] Output interface: Vehicle acceleration output interface Output key indicators for ride comfort analysis; suspension dynamic deflection output interface. Output suspension travel verification indicators.

[0151] Interface connection: .

[0152] S156. After generating the basic simulation model, perform the following integrity checks: Degrees of freedom check to confirm that the system has the correct number of degrees of freedom (one vertical degree of freedom for a single-mass system); Constraint consistency check to confirm that the constraint equations formed by all connection statements are linearly independent; Algebraic loop check to confirm that there are no algebraic loops or that the algebraic loops have been correctly solved; Initial condition setting to set the initial displacements. initial velocity .

[0153] The final generated complete basic simulation model of a single-mass automotive system has standardized input and output interfaces and can be directly used for subsequent simulation settings, parameter optimization, and performance analysis.

[0154] S2. Perform initial simulation on the basic simulation model and obtain the simulation output results under the initial parameters; specifically including:

[0155] S21. Set the simulation time parameters, numerical integration algorithm, and step size control method, specifically as follows:

[0156] S211. Set simulation time parameters, including simulation start time. and simulation end time Based on the dynamic characteristics of a single-mass automotive system, the simulation time range is typically set as follows: ,in This is the start time of the simulation. The simulation ends at [time], and the total simulation duration is [duration]. .

[0157] S212. Select a numerical integration algorithm based on the analysis requirements. The single-mass automotive system is a stiff system, and its stiffness ratio is determined by the differences in the system's characteristic time scales: stiffness ratio ,in For system characteristic values, This represents the real part. For a single-mass system, the eigenvalues ​​are determined by the eigenvalues ​​of the system matrix. Typically, the system is quite stiff, requiring a solver suitable for rigid systems.

[0158] S213. Solver Selection:

[0159] The DASSL solver (Differential-Algebraic System Solver) employs a multi-step integration method using the backward difference formula (BDF), which is suitable for rigid differential-algebraic equation systems. It has good numerical stability and efficiency and is the default recommended solver.

[0160] CVODE solver (CVariable-coefficient ODEsolver): An adaptive multi-step integration method using the Adams-Moulton method (non-rigid) or the BDF method (rigid), suitable for high-precision scenarios. The solution performance of rigid systems can be optimized by setting the linear solver type.

[0161] S214. Step size control mode selection:

[0162] Fixed step size mode: Sets a constant integration step size. Typical values ​​are: Fixed step size is suitable for real-time simulation or hardware-in-the-loop testing, but may sacrifice computational efficiency or accuracy.

[0163] Adaptive step size mode: Sets the relative tolerance and absolute tolerance Typical values ​​are: The adaptive step size automatically adjusts the step size based on the local truncation error. This meets the error control requirements. ,in For local truncation error estimation, This is the state vector.

[0164] S22. Configure the initial parameters of the basic simulation model and the road excitation signal, specifically as follows:

[0165] S221. Configure the initial physical parameters of the basic simulation model, including: sprung mass parameters Suspension stiffness coefficient Suspension damping coefficient Tire stiffness coefficient .

[0166] S222. Configure the type and amplitude of the road surface excitation signal. The road surface excitation is an external input to the system. Different types are selected according to the analysis objectives.

[0167] Sine wave excitation (simulating periodic turbulence): ,in: This represents the amplitude of a sine wave, in meters (m), and is a typical value. (Indicates an amplitude of 5cm); Excitation frequency, in Hz, typical value (Indicates a 1Hz frequency); This is a time variable, with the unit being seconds (s).

[0168] Band-limited white noise excitation (simulating random road surface): Where BLWN is a band-limited white noise function; This is the lower cutoff frequency, in Hz, typical value. ;

[0169] This is the upper cutoff frequency, in Hz, typical value. ; Power spectral density level, in units of The power spectral density is determined based on the road surface grade. (This is related to the road surface roughness coefficient.) Relationship ,in: Reference spatial frequency cycles The road surface roughness coefficient; This refers to spatial frequency, measured in cycles per minute (m). The frequency exponent is usually taken as... ; Vehicle speed, in units of .

[0170] Step excitation (simulating sudden road surface changes): = ,in: This represents the step amplitude, in meters (m), and is a typical value. ; This represents the step start time, in seconds, and is a typical value. .

[0171] S23. Run the simulation program and obtain the dynamic response time-domain data, specifically:

[0172] Run the simulation program to perform numerical calculations on the basic simulation model; the solution process uses the solver and step size control strategy set in S21 to perform integral solutions on the system parameters and excitation signals configured in S22.

[0173] The core of numerical solution is the iterative calculation of the state equation. For the nth time step, the state update formula is: ,in: For the first The state vector of the step, For the first The integral step size of the step. It is an increment function, determined by the selected solver.

[0174] For the DASSL solver, backward difference formula : ,in and For BDF coefficients, This is the function on the right-hand side of the system's differential equation.

[0175] Newton's iterative solution of nonlinear equations: ,in: For Jacobian matrices, This is the residual function.

[0176] Obtain the time-domain data of the system's dynamic response under initial parameters, including the time series of state variables and output variables: ,in The total number of sampling points is determined by the simulation duration and the output step size.

[0177] S24. Extract simulation output results for subsequent evaluation and verification: Extract key simulation output results from the dynamic response time-domain data for subsequent ride comfort evaluation and suspension travel verification; specifically:

[0178] Vehicle body vertical acceleration time domain data: Vertical acceleration of the vehicle body is a core indicator for evaluating vehicle ride comfort, and it is evaluated according to the ISO 2631-1 standard.

[0179] Calculate the root mean square value of acceleration: ,in Frequency-weighted acceleration is achieved through a filter: , For vertical vibrations, the frequency weighting function specified in ISO 2631-1 is: = .

[0180] Suspension dynamic travel time domain data: The suspension travel is used to check whether the suspension exceeds the design limits.

[0181] Calculate the maximum dynamic stroke: The verification criteria are as follows: ,in The suspension design travel limit is typically set to a certain value. .

[0182] Additional extracted data (for subsequent parameter optimization): Vehicle displacement time domain data Vehicle speed time domain data Tire dynamic load time domain data .

[0183] The simulation output results are stored in the form of a data file, as... The baseline data for parameter optimization in the steps are compared and analyzed with the measured data.

[0184] S3. Collect and preprocess real-vehicle measured data, construct a comprehensive error function to evaluate the difference between the simulation output and the measured data, and use a parameter optimization engine to iteratively optimize the key physical parameters of the basic simulation model until the convergence condition is met, obtaining the optimized parameters; specifically including:

[0185] S31. Real-vehicle road testing and measured data preprocessing: Real-vehicle road testing is conducted under corresponding operating conditions, and the vertical acceleration signal of the vehicle body is collected as measured data. The measured data is then preprocessed to obtain a standardized measured dataset; specifically:

[0186] S311. Real-vehicle road testing and raw data collection:

[0187] Select an actual road or test site consistent with the S22 simulation conditions to ensure comparability of road excitation conditions. Place an acceleration sensor at the vehicle's center of gravity, and set the sensor sampling frequency to [value missing]. Typical values ​​are: Collection time Based on the analysis requirements, the typical value is: ;

[0188] The time-domain signal of the vehicle's vertical acceleration was collected as the raw measured data, denoted as: ,in This represents the number of sampling points for the original data.

[0189] S312. Outlier Detection and Removal:

[0190] Outlier detection and removal are performed on the original measured data. Statistical criteria are used to identify and remove abnormal data points caused by sensor interference or sudden road impacts. The sample mean and sample standard deviation of the data sequence are calculated, and data points deviating from the mean by more than three times the standard deviation are identified as outliers. Specifically, if the absolute difference between a data point and the sample mean is greater than three times the sample standard deviation, the data point is marked as an outlier and corrected using linear interpolation of adjacent data points or mean replacement methods, thereby obtaining a clean dataset after outlier removal.

[0191] S313. Low-pass filtering:

[0192] The measured data after outlier removal were low-pass filtered using a fourth-order Butterworth low-pass filter to remove high-frequency noise interference while retaining effective frequency components related to the vertical vibration of the vehicle body. This filter exhibits a maximally flat amplitude response, with no ripple in the passband and monotonically attenuating in the stopband. The filter's cutoff frequency is set according to the suspension system characteristics, ensuring coverage of the main frequency components of the vehicle body's vertical vibration while effectively filtering out high-frequency electromagnetic interference and sensor noise; a typical cutoff frequency is set to no less than 50 Hz.

[0193] S314. Resampling Processing:

[0194] The filtered measured data is resampled to reduce the original high sampling frequency to the same sampling frequency as the simulation output, thus obtaining a standardized measured dataset. The resampling process employs an anti-aliasing filtering combined with interpolation. First, a low-pass filter is used to prevent spectral aliasing, and then an interpolation algorithm is used to calculate the data values ​​at the new sampling time. This ensures the spectral characteristics and time-domain waveform accuracy of the data sequence, meeting the needs of subsequent comparison and evaluation with the simulation output results.

[0195] S32. Construct a comprehensive error function to quantitatively evaluate the difference between the simulation output results and the standardized measured dataset; specifically:

[0196] S321. Determine the types of error components in the comprehensive error function:

[0197] Root mean square error (RMSE) is used to assess the accuracy of amplitude fitting. ,in The simulated vertical acceleration of the vehicle body is output. This is to measure the vertical acceleration of the vehicle body.

[0198] Frequency error (FreqError) assesses the degree of formant position matching. Fast Fourier Transform (FFT) is performed on both simulated and measured data to obtain the spectrum. Identify the main peak frequency: Frequency error: .

[0199] Phase error assesses the timing alignment of the response and calculates the cross-correlation function between simulation and measured data. Optimal latency: ;

[0200] Phase error: Or, it can be calculated using the phase difference of the transfer function: ,in The phase angle in the frequency domain. This represents the number of frequency points.

[0201] Peak error assesses the magnitude of the impulse response and identifies the maximum peak value in the time-domain response. Peak error: .

[0202] S322. Calculate the error components and assign weighting coefficients:

[0203] Calculate the values ​​of each of the above error components and assign weighting coefficients to each error component. The weighting coefficients are determined based on the key requirements of vehicle performance analysis:

[0204] When focusing on the overall smoothness assessment, increase the weight of the root mean square error: ;

[0205] When focusing on resonance characteristic identification, increase the weight of frequency error: ;

[0206] When focusing on transient impact response, increase the weight of peak error: ;

[0207] The weighting coefficients satisfy the normalization condition: .

[0208] S323. Construct the comprehensive error function:

[0209] Comprehensive error function Defined as the sum of all weighted error components: RMSE FreqError PhaseError PeakError, where This is the vector of key physical parameters to be optimized.

[0210] Output the comprehensive error function value As the objective function value in the S33 parameter optimization iteration process, the optimization objective is to minimize .

[0211] S33. A two-stage hybrid optimization strategy is adopted to iteratively optimize the key physical parameters; specifically:

[0212] S331. Initialize optimization strategy and feasible region settings:

[0213] Initialize the two-stage hybrid optimization strategy and set the feasible region range of key physical parameters. Vector of parameters to be optimized: The feasible range of each parameter is determined based on the vehicle type and suspension design experience values: Feasible range of suspension stiffness coefficient: Feasible region for suspension damping coefficient: Feasible range for tire stiffness coefficient: Feasible region constraints: .

[0214] S332. Perform the first phase of global search, using an improved genetic algorithm to explore the feasible region globally:

[0215] Genetic algorithm parameter settings: population size Maximum number of generations Crossover probability Probability of mutation .

[0216] Chromosome coding: Each individual is represented as ,in For evolutionary generations, For individual indexes.

[0217] Fitness function: .

[0218] Selection method: Use tournament selection or roulette selection to retain elite individuals.

[0219] Crossover operation: using real number encoded arithmetic crossover ,in For random crossover coefficients.

[0220] Mutation operation: Gaussian mutation is used. ,in For the first The standard deviation of each parameter It follows a standard normal distribution.

[0221] Termination judgment: If the maximum number of generations has been reached. Or the change in optimal fitness over five consecutive generations is less than a threshold. If the global search is terminated, the initial values ​​of the optimization parameters will be output. .

[0222] S333. Perform the second stage of local fine-tuning to obtain global search results. Starting from this point, an adaptive gradient descent algorithm is used for a local fine-grained search:

[0223] Gradient calculation (numerical difference): ,in For the first A unit vector in each parameter direction. It represents a small perturbation.

[0224] Adaptive learning rate adjustment: = ,in For the first The learning rate for the next iteration. This is the learning rate increase factor. The coefficient for reducing the learning rate.

[0225] Parameter update: .

[0226] Boundary handling: If the updated parameters exceed the feasible region, project to the boundary: .

[0227] S334. Convergence determination, optimization termination, and parameter output:

[0228] During local fine-tuning, the comprehensive error function value is recalculated after each iteration. Convergence is determined when the following conditions are met simultaneously: the change in the comprehensive error function value between two consecutive iterations is less than a preset function value change threshold, and the gradient norm of the comprehensive error function is less than a preset gradient norm threshold.

[0229] If the above convergence conditions are met, or the preset maximum number of iterations is reached, the optimization process terminates, and the final optimized parameters are output. The comprehensive error function value after optimization termination needs further evaluation to determine whether it meets the preset comprehensive convergence conditions, including that the comprehensive error function value is not greater than the preset target error value, each individual error does not exceed its corresponding maximum permissible error, and the total number of iterations does not exceed the maximum permissible number of iterations.

[0230] If all the above comprehensive convergence conditions are met, the optimization is confirmed to be successful, the final optimized parameters and the corresponding comprehensive error function value are output, and the subsequent steps feed the optimized parameters back to the basic simulation model. If the comprehensive convergence conditions are not met but the maximum number of iterations has been reached, the current optimal parameters are output and a convergence warning is issued; if the convergence conditions are not met and the maximum number of iterations has not been reached, the process returns to continue iterative optimization.

[0231] S4. Feed the optimized parameters back to the basic simulation model to obtain a calibrated high-precision vehicle single-mass system model; specifically including:

[0232] S41. Obtain the optimized key physical parameters from step S3 to form a calibrated parameter set:

[0233] The optimized key physical parameters include at least: optimized values ​​for suspension stiffness coefficient. Optimized value of suspension damping coefficient Optimized value of tire stiffness coefficient Optimize parameter vector .

[0234] Simultaneously, obtain the comprehensive performance indicators of the optimization process, including the final comprehensive error function value. The values ​​of each error component (root mean square error, frequency error, phase error, peak error) and the total number of iterations are used for subsequent optimization effect evaluation.

[0235] S42. Write the optimized key physical parameters into the parameter configuration file of the basic simulation model, replacing the original initial parameters in the model, and complete the update and calibration of the model parameters:

[0236] Parameter substitution mapping relationship: Suspension stiffness parameters in the basic model Replace with optimized value Suspension damping parameters in the basic model Replace with optimized value Tire stiffness parameters in the basic model Replace with optimized value .

[0237] The system's natural frequency after parameter updates: Updated damping ratio: Updated damped natural frequency: .

[0238] Through parameter updates, the basic simulation model changes from its initial parameter state. Evolves into a high-precision state after calibration. The model accuracy is significantly improved, and the simulation error is controlled within the preset range.

[0239] S43. Rerun the simulation based on the updated parameters to obtain the dynamic response data of the calibrated high-precision vehicle single-mass system model under the same working conditions, and verify the optimization effect.

[0240] Keep the simulation time parameters set in S21 and the road excitation signal type and amplitude set in S22 unchanged, only update the physical parameters to the optimized values, and re-execute the numerical integration solution.

[0241] Obtain the time-domain data of the calibrated dynamic response: .

[0242] Optimization effect verification index: Simulation accuracy improvement rate In typical cases, the optimized simulation accuracy improvement rate reaches [percentage missing]. The above is the degree of agreement with the measured data. ,in The coefficient of determination, the closer to 1, the higher the degree of agreement; typical value after optimization. .

[0243] S44. Prediction and analysis of vehicle performance based on a calibrated high-precision single-mass vehicle system model; specifically:

[0244] S441. Perform frequency domain analysis on the time domain signal of the vehicle body vertical acceleration in the calibrated dynamic response data, and use Fast Fourier Transform to convert it into a frequency domain signal.

[0245] Discrete Fourier Transform: ;

[0246] Amplitude-frequency characteristics: ;

[0247] Frequency resolution: ;

[0248] Frequency sequence: .

[0249] Extract the amplitude-frequency response curve and identify the system's principal resonant frequency. The principal resonant frequency corresponds to the peak point of the amplitude-frequency curve. .

[0250] S442. Compare and verify the identified main resonance frequency with the theoretically calculated value or the measured spectrum:

[0251] Theoretically calculated natural frequency: ;

[0252] Resonance frequency error: ;

[0253] Or compare with the measured principal resonance frequency: ;

[0254] When the resonance frequency error is controlled within Within: The frequency domain characteristics of the model are deemed to meet the requirements, and the calibrated high-precision model can be used for subsequent performance prediction.

[0255] S443. Perform time-domain analysis on the vehicle body vertical acceleration time-domain signal in the calibrated dynamic response data, and quantitatively evaluate ride comfort according to ISO2631-1 standard:

[0256] Frequency-weighted acceleration calculation: ,in For vertical vibration (z-axis), the frequency weighting function specified in ISO 2631-1 is as follows:

[0257] = ;

[0258] Weighted root mean square acceleration value: .

[0259] Smoothness rating: Comfortable; I feel a little uncomfortable; It's quite uncomfortable; Discomfort; Extremely uncomfortable.

[0260] S444. Based on the results of frequency domain and time domain analysis, output a vehicle performance analysis report to guide the optimization design of suspension system parameters. The report includes:

[0261] Model calibration information: optimized key physical parameter values, comprehensive error function values, various error components, number of optimization iterations, and simulation accuracy improvement rate.

[0262] Frequency domain characteristic analysis: amplitude-frequency characteristic curve, main resonance frequency identification results, comparison with theoretical and measured values, resonance frequency error.

[0263] Time-domain characteristic analysis: acceleration time-domain response curves under typical working conditions, weighted root mean square acceleration values, and ride comfort level assessment.

[0264] Suspension travel verification: maximum suspension travel value, comparison with design limit, and travel utilization rate.

[0265] Design guidance suggestions: Based on the analysis results, propose suggestions for optimizing and adjusting suspension stiffness and damping parameters, or suggestions for introducing active control strategies, to provide a theoretical basis for actual engineering design.

[0266] The calibrated high-precision single-mass vehicle system model can be used for rapid prediction of vehicle performance under different operating conditions, supports virtual simulation optimization of suspension systems, significantly reduces the number of real vehicle tests, lowers development costs, and shortens the R&D cycle.

[0267] As can be seen from the above description, the embodiments of the present invention achieve the following technical effects:

[0268] Leveraging Modelica's multi-domain unified modeling capabilities, object-oriented component-based design enables highly reusable and scalable models. The modeling approach, combining standard library components with custom components, ensures both model versatility and accurate description of nonlinear characteristics. Component models can be rapidly reused in simulation analyses of different vehicle models and suspension structures.

[0269] Modelica, as a modeling language for engineers, features object-oriented declarative modeling, continuous-discrete hybrid modeling, and unified modeling across multiple domains. Users can focus more on the physical representation of the objects themselves, achieving consistency in energy conservation and signal transmission through physical interface connections, without the need for tedious mathematical derivations and equation solver programming, significantly lowering the technical barrier to modeling.

[0270] No longer relying on precise centroid location, moment of inertia, or other difficult-to-obtain data, and eliminating experimental measurement steps, this significantly reduces errors introduced by geometric simplification and parameter sensitivity, saving experimental costs. Through an adaptive parameter optimization algorithm driven by measured data, model parameters are automatically corrected, improving simulation accuracy by over 80%, controlling resonance frequency error to within 2%, and reducing computation time by 40%.

[0271] An adaptive parameter optimization algorithm based on measured data is introduced, achieving a leap from manual experience-based parameter tuning to automatic intelligent optimization. A two-stage hybrid optimization strategy is employed: the first stage uses an improved genetic algorithm for global exploration to avoid getting trapped in local optima; the second stage uses an adaptive gradient descent algorithm for fine-tuning local parameters to ensure convergence accuracy. This automatically finds the optimal parameter combination without manual intervention, significantly shortening the model calibration cycle.

[0272] A complete basic simulation model of a single-mass automotive system is formed through standardized interface encapsulation. It has standardized input and output interfaces and can be directly integrated with external signal sources, data acquisition modules or other subsystem models. It supports rapid prediction of vehicle performance under different operating conditions and provides a reliable platform for virtual simulation optimization of suspension systems.

[0273] Frequency and time domain analyses based on a calibrated high-precision model can accurately identify the system's main resonance frequency, assess vehicle ride comfort levels, and provide quantitative evaluation according to the ISO 2631 standard. The analysis results can be directly used to guide the optimization design of suspension stiffness and damping parameters, or provide a theoretical basis for the introduction of active suspension control strategies, significantly reducing the number of real-vehicle tests, lowering development costs, and shortening the R&D cycle.

[0274] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of the invention is limited to these examples; within the framework of the invention, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of the different aspects of the invention as described above, which are not provided in detail for the sake of brevity.

[0275] This invention is intended to cover all such substitutions, modifications, and variations that fall within the broad scope of this specification. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for modeling and adaptive parameter optimization of a single-mass vehicle system based on Modelica, characterized in that, include: Based on the requirements analysis, the simplified modules and component connection methods of the single mass system of the vehicle are determined, and a basic simulation model is built based on Modelica. Perform an initial simulation on the basic simulation model and obtain the simulation output results under the initial parameters; Real vehicle measured data is collected and preprocessed. A comprehensive error function is constructed to evaluate the difference between the simulation output and the measured data. A parameter optimization engine is used to iteratively optimize the key physical parameters of the basic simulation model until the convergence condition is met, and the optimized parameters are obtained. Specifically, it includes: Real-vehicle road tests were conducted under corresponding working conditions, and the vertical acceleration signal of the vehicle body was collected as measured data. The measured data was preprocessed to obtain a standardized measured dataset. A comprehensive error function was constructed to quantitatively evaluate the difference between the simulation output results and the standardized measured dataset. A two-stage hybrid optimization strategy was adopted to iteratively optimize the key physical parameters. It was determined whether the value of the comprehensive error function after iterative optimization met the preset convergence condition. If it met the condition, the optimization was terminated and the optimized parameters were output. If it did not meet the condition, the iteration continued until convergence. The optimization employs a two-stage hybrid optimization strategy to iteratively optimize key physical parameters. Specifically, this includes: initializing the two-stage hybrid optimization strategy and setting the feasible region range for the key physical parameters, which at least include the suspension stiffness coefficient and damping coefficient. The feasible region range is determined based on vehicle type and suspension design experience. The first stage involves a global search, using an improved genetic algorithm to explore the feasible region and iteratively evolve to minimize the comprehensive error function value, obtaining the initial global optimal parameter values. The algorithm is then judged whether it has reached the preset maximum number of generations or whether the comprehensive error function value has stabilized. If both conditions are met, the global search is terminated and the initial optimized parameter values ​​are output. The second stage involves local fine-tuning, starting with the initial optimized parameter values ​​and using an adaptive gradient descent algorithm for local fine-tuning. The adaptive gradient descent algorithm dynamically adjusts the learning rate step size based on the error change rate during iteration. During local fine-tuning, the comprehensive error function value is recalculated after each iteration, and the change in the comprehensive error function value between two adjacent iterations is judged to be less than a preset threshold. If this is met, convergence is determined, and the final optimized parameters that meet the convergence condition are output. The optimized parameters are fed back to the basic simulation model to obtain a calibrated high-precision vehicle single-mass system model.

2. The method for modeling and adaptive parameter optimization of a single-mass vehicle system based on Modelica according to claim 1, characterized in that, The process of determining simplified modules and component connection methods for the vehicle single-mass system based on requirements analysis, and building a basic simulation model based on Modelica, specifically includes: Based on the vehicle ride comfort analysis objectives, the vehicle system is simplified according to the frequency decoupling principle. The core simplified modules are determined to include at least the sprung mass module representing the vehicle body, the spring damping components representing the suspension system, and the tire model representing the tire stiffness. Analyze the physical relationships of each element in the simplified module, determine that the input signal of the system is the vertical displacement of the road surface, and the output signal includes at least the vertical acceleration of the vehicle body. Also determine that the topological connection of each component is as follows: the spring and the damper are connected in parallel, one end is connected to the sprung mass, the other end is connected to the tire model, and the tire model is connected to the road excitation source. Based on the Modelica standard library, select the corresponding component models, including at least: translational mass block Mass, linear spring Spring, linear damper Damper and displacement source Position; When the standard library does not contain the components with the required characteristics, a component model is created through a custom modeling method, constants are defined in the parameter definition area, and nonlinear physical equations are input in the equation definition area. The Modelica connect statement is used to physically connect the parameterized component models according to the topology connection method, generating a complete basic simulation model of a single-mass automotive system.

3. The method for modeling and adaptive parameter optimization of a single-mass vehicle system based on Modelica according to claim 2, characterized in that, When the standard library does not contain components with the required characteristics, a component model is created through a custom modeling approach. Constants are defined in the parameter definition region, and nonlinear physical equations are input in the equation definition region. Specifically, this includes: Determine the physical characteristics of the required custom components and analyze their nonlinear behavior, which includes at least a piecewise linear relationship between nonlinear spring force and relative displacement, or a nonlinear relationship between nonlinear damping force and relative velocity. Create new component classes in the Modelica modeling environment that inherit from some of the connection interface classes in the standard library; Declare custom parameters in the parameter definition area of ​​the new component class. The parameters shall include at least the stiffness coefficient, damping coefficient, or input-output data pairs required for table lookup for the piecewise linear interval. In the equation definition area of ​​the new component class, equations describing the physical behavior of the component are written using the Modelica language. The equations include at least the conditional equations for calculating the force output piecewise based on relative displacement or relative velocity, or nonlinear mapping is achieved by calling a predefined data table through an interpolation function. Save the custom component model to the local model library for use when building subsequent models.

4. The method for modeling and adaptive parameter optimization of a single-mass vehicle system based on Modelica according to claim 3, characterized in that, The basic simulation model is subjected to initial simulation to obtain simulation output results under initial parameters, specifically including: Set simulation time parameters, including simulation start time and end time, and select numerical integration algorithm and step size control method according to analysis requirements. The solver is DASSL suitable for rigid systems or CVODE suitable for high precision requirements. The step size control adopts fixed step size or adaptive step size. Configure the initial parameters of the basic simulation model, including at least: sprung mass parameters, suspension stiffness coefficient, damping coefficient, and road excitation signal type and amplitude. The road excitation uses a sine wave to simulate periodic bumps or band-limited white noise to simulate random road surfaces. Run the simulation program to solve the basic simulation model and obtain the dynamic response time-domain data of the system under the initial parameters; The simulation output results are extracted from the dynamic response time-domain data. The simulation output results include at least the vehicle vertical acceleration and suspension travel, which are used for subsequent ride comfort evaluation and suspension travel verification, respectively.

5. The method for modeling and adaptive parameter optimization of a single-mass vehicle system based on Modelica according to claim 4, characterized in that, The process involves conducting real-vehicle road tests under corresponding operating conditions, collecting vertical acceleration signals of the vehicle body as measured data, and preprocessing the measured data to obtain a standardized measured dataset. Specifically, this includes: Select an actual road or test site that matches the simulation conditions, place an acceleration sensor at the center of gravity of the vehicle body, conduct a real vehicle road test, and collect the time-domain signal of the vertical acceleration of the vehicle body as the raw measured data; Outlier detection and removal are performed on the original measured data. Statistical criteria are used to identify and remove abnormal data points caused by sensor interference or sudden impacts on the road surface. The measured data after removing outliers were subjected to low-pass filtering. A fourth-order Butterworth low-pass filter was used to remove high-frequency noise interference and retain the effective frequency components related to the vertical vibration of the vehicle body. The filtered measured data is resampled to reduce the original sampling frequency to the same sampling frequency as the simulation output, thus obtaining a standardized measured dataset for subsequent comparison and evaluation with the simulation output results.

6. The method for modeling and adaptive parameter optimization of a single-mass vehicle system based on Modelica according to claim 5, characterized in that, The construction of the comprehensive error function, used to quantitatively evaluate the difference between the simulation output results and the standardized measured dataset, specifically includes: Determine the error component types of the comprehensive error function, wherein the error components include at least the root mean square error (RMSE), frequency error (FreqError), phase error (PhaseError), and peak error (PeakError); Calculate the values ​​of each error component separately, and assign weight coefficients to each error component. The weight coefficients are determined based on the key requirements of vehicle performance analysis. Construct the comprehensive error function J(θ) = w1·RMSE + w2·FreqError + w3·PhaseError + w4· PeakError, where w1 to w4 are the corresponding weight coefficients, outputs the comprehensive error function value J(θ), which serves as the objective function value in the subsequent parameter optimization iteration process.

7. The method for modeling and adaptive parameter optimization of a single-mass vehicle system based on Modelica according to claim 6, characterized in that, The optimized parameters are fed back to the basic simulation model to obtain a calibrated high-precision vehicle single-mass system model, which specifically includes: Obtain optimized key physical parameters, which include at least the suspension stiffness coefficient and damping coefficient; The optimized key physical parameters are written into the parameter configuration file of the basic simulation model, replacing the original initial parameters in the model, thus completing the update and calibration of the model parameters. The simulation was rerun based on the updated parameters to obtain the dynamic response data of the calibrated high-precision vehicle single-mass system model under the same working conditions, and to verify the optimization effect. Vehicle performance is predicted and analyzed based on the calibrated high-precision single-mass vehicle system model.

8. The method for modeling and adaptive parameter optimization of a single-mass vehicle system based on Modelica according to claim 7, characterized in that, Based on the calibrated high-precision vehicle single-mass system model, vehicle performance is predicted and analyzed, specifically including: Frequency domain analysis is performed on the time domain signal of the vehicle vertical acceleration in the dynamic response data. The fast Fourier transform is used to convert it into a frequency domain signal, the amplitude-frequency characteristic curve is extracted, and the main resonance frequency of the system is identified. The identified main resonance frequency is compared and verified with the theoretical calculation value or the measured spectrum. When the resonance frequency error is controlled within 2%, the frequency domain characteristics of the model are deemed to meet the requirements. Time-domain analysis is performed on the vehicle vertical acceleration time-domain signal in the dynamic response data, frequency-weighted processing is performed on the acceleration signal, and the weighted root mean square value of acceleration is calculated as a quantitative evaluation index of vehicle ride comfort. Based on the results of frequency domain analysis and time domain analysis, a vehicle performance analysis report is output to guide the optimal design of suspension system parameters.

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