Vehicle time history response calculation method and device, electronic equipment and storage medium

Abstract

The invention discloses a vehicle time history response calculation method and device, electronic equipment and a storage medium. The method comprises the following steps: acquiring a mass matrix, a damping matrix and a stiffness matrix of a to-be-tested vehicle; inputting the mass matrix, the damping matrix and the stiffness matrix into a pre-constructed time history response calculation model; according to the mass matrix, the damping matrix and the stiffness matrix, the time history response of the to-be-tested vehicle is calculated through a time history response calculation model; wherein the time history response comprises a displacement vector, a speed vector and an acceleration vector. According to the embodiment of the invention, the calculation efficiency can be remarkably improved while the calculation precision is ensured, and the method is suitable for time-history response analysis of the key structure of the commercial vehicle under the complex dynamic load.

Description

Technical Field

[0001] This application relates to the field of automotive engineering technology, and in particular to a method, apparatus, electronic device, and storage medium for calculating vehicle time-course response. Background Technology

[0002] In the field of automotive engineering, vehicle dynamics is a core indicator for measuring vehicle safety, comfort, and handling stability. Time-history response, as a key parameter characterizing vehicle dynamics, is crucial for accurate calculation in vehicle research and development, performance optimization, and safety assessment. Time-history response dynamically reflects the changes in a vehicle's motion under different driving conditions (such as rapid acceleration, emergency braking, cornering, and driving on bumpy roads), specifically including key parameters such as displacement vector, velocity vector, and acceleration vector. These parameters are directly related to multiple core aspects, including vehicle chassis tuning, body structure strength design, suspension system optimization, and passenger comfort.

[0003] With the development of commercial vehicle technology, ensuring the safety and reliability of key structures such as the chassis, cab, suspension system, and powertrain under driving, braking, and loading conditions requires precise analysis of their vibration patterns and dynamic characteristics, which is an indispensable crucial aspect of commercial vehicle structural design. Although many numerical methods for commercial vehicle structural dynamics problems have been developed, these methods all have limitations, such as: 1) Finite difference method: highly sensitive to time step and lacking high accuracy. 2) Fine integration method: while accurate and unconditionally stable, it requires calculating Duhamel integrals based on different forms of external dynamic loads, lacking a universal solution format, and often making it very difficult to solve for structural dynamic responses under complex dynamic loads. 3) Time finite element method: its application to variational principles for initial value problems in dynamics is very limited. Therefore, further developing more efficient and universal numerical calculation methods to accurately and efficiently solve large-scale structural dynamics problems in commercial vehicles is of great significance for improving the structural strength, vibration comfort, and driving safety of commercial vehicles. Summary of the Invention

[0004] This application provides a method, apparatus, electronic device, and storage medium for calculating the time history response of a vehicle. While ensuring calculation accuracy, it can significantly improve calculation efficiency and is applicable to the time history response analysis of key structures of commercial vehicles under complex dynamic loads.

[0005] In a first aspect, embodiments of this application provide a method for calculating the time-course response of a vehicle, the method comprising:

[0006] Obtain the mass matrix, damping matrix, and stiffness matrix of the vehicle under test;

[0007] The mass matrix, the damping matrix, and the stiffness matrix are input into a pre-constructed time history response calculation model;

[0008] The time history response of the vehicle under test is calculated using the time history response calculation model based on the mass matrix, the damping matrix, and the stiffness matrix; wherein the time history response includes: displacement vector, velocity vector, and acceleration vector.

[0009] Secondly, embodiments of this application also provide a vehicle time-time response calculation device, the device comprising: an acquisition module, an input module, and a calculation module; wherein,

[0010] The acquisition module is used to acquire the mass matrix, damping matrix, and stiffness matrix of the vehicle under test;

[0011] The input module is used to input the mass matrix, the damping matrix and the stiffness matrix into a pre-constructed time history response calculation model;

[0012] The calculation module is used to calculate the time history response of the vehicle under test based on the mass matrix, the damping matrix, and the stiffness matrix through the time history response calculation model; wherein, the time history response includes: displacement vector, velocity vector, and acceleration vector.

[0013] Thirdly, embodiments of this application provide an electronic device, including:

[0014] One or more processors;

[0015] Memory, used to store one or more programs.

[0016] When the one or more programs are executed by the one or more processors, the one or more processors implement the vehicle time-course response calculation method described in any embodiment of this application.

[0017] Fourthly, embodiments of this application provide a storage medium storing a computer program thereon, which, when executed by a processor, implements the vehicle time-course response calculation method described in any embodiment of this application.

[0018] This application proposes a method, apparatus, electronic device, and storage medium for calculating time-history response. First, the mass matrix, damping matrix, and stiffness matrix of the vehicle under test are obtained. Then, these matrices are input into a pre-constructed time-history response calculation model. Finally, the time-history response of the vehicle under test is calculated using the model based on these matrices. The time-history response includes displacement vector, velocity vector, and acceleration vector. In other words, this technical solution directly obtains the actual mass matrix, damping matrix, and stiffness matrix of the vehicle under test. These three matrices are core parameters describing the vehicle's dynamic characteristics, fully preserving the actual structural features and dynamic coupling relationships of the vehicle, providing a reliable data foundation for subsequent accurate calculations. Model-based calculations allow for rapid output of results, significantly shortening the time for obtaining the time-history response compared to experimental testing. Furthermore, it enables comprehensive and accurate output of time-history response parameters, meeting multi-dimensional R&D needs. This application overcomes the limitations of traditional finite difference methods, which are sensitive to time steps, and the difficulty of calculating Duhamel integrals in the fine integration method for complex dynamic external loads on commercial vehicles (such as road excitation, braking impact, cargo dynamic loads, engine vibration, etc.). It significantly improves computational efficiency while maintaining computational accuracy, making it suitable for time-history response analysis of key structures in commercial vehicles under complex dynamic loads. In existing technologies, while the fine integration method is accurate and unconditionally stable, it requires calculating Duhamel integrals based on different forms of dynamic external loads, lacking a universal solution format, making it very difficult to solve for structural dynamic responses under complex dynamic loads. Furthermore, the variational principles applicable to initial value problems in the time-based finite element method are very limited. Therefore, compared to existing technologies, the vehicle time-history response calculation method, device, electronic equipment, and storage medium proposed in this application significantly improve computational efficiency while maintaining computational accuracy, making it suitable for time-history response analysis of key structures in commercial vehicles under complex dynamic loads. Moreover, the technical solution of this application is simple and convenient to implement, easy to popularize, and has a wider range of applications. Attached Figure Description

[0019] Figure 1 A flowchart illustrating a method for calculating vehicle time-time response according to an embodiment of this application;

[0020] Figure 2 A flowchart illustrating a method for calculating vehicle time-time response according to another embodiment of this application;

[0021] Figure 3 This is a schematic diagram of the structure of a spring-mass system provided in an embodiment of this application;

[0022] Figure 4 A schematic diagram of the structure of a vehicle time-time response computing device provided in an embodiment of this application;

[0023] Figure 5 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0024] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the application and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present application, not the entire structure.

[0025] Figure 1 This is a flowchart illustrating a method for calculating vehicle time-time response according to an embodiment of this application. This method can be executed by a time-time response computing device or electronic device, which can be implemented in software and / or hardware, and can be integrated into any smart device with network communication capabilities. Figure 1 As shown, the method for calculating the vehicle's time-time response may include the following steps:

[0026] S101. Obtain the mass matrix, damping matrix, and stiffness matrix of the vehicle under test.

[0027] In specific embodiments of this application, the mass matrix is ​​a square matrix describing the mass distribution and inertial characteristics of each mass point (or component) of the vehicle under test. Its elements reflect the mass coupling relationship in different degrees of freedom of the vehicle. The main diagonal elements correspond to the concentrated mass or moment of inertia in each degree of freedom direction, and the off-diagonal elements correspond to the inertial coupling effect between different degrees of freedom. It is a core parameter characterizing the inertial characteristics of the vehicle and directly affects the ease with which the vehicle's motion state changes. The damping matrix is ​​a square matrix characterizing the damping effect (energy dissipation characteristics) between the moving components of the vehicle under test. Damping originates from the dampers of the vehicle's suspension system, tire friction, and friction between components. The matrix elements reflect the damping force transmission relationship in different degrees of freedom directions. The main diagonal elements are the damping coefficients of each degree of freedom, and the off-diagonal elements are the coupling damping coefficients between different degrees of freedom. Its function is to describe the law of energy dissipation during vehicle motion and affect the attenuation characteristics of vehicle vibration. The stiffness matrix is ​​a square matrix describing the structural resistance to deformation of the vehicle under test. It is related to the elastic characteristics of vehicle body structure and suspension system elastic elements (such as springs). The matrix elements reflect the correspondence between load and deformation in different degrees of freedom. The main diagonal elements are the stiffness coefficients of each degree of freedom (force or torque required per unit deformation), and the off-diagonal elements are the coupling stiffness coefficients between different degrees of freedom. Its core function is to characterize the elastic deformation law of vehicle structure under stress.

[0028] S102. Input the mass matrix, damping matrix, and stiffness matrix into the pre-built time history response calculation model.

[0029] In a specific embodiment of this application, the pre-constructed time-history response calculation model is essentially a numerical calculation framework built upon the fundamental equations of vehicle dynamics. The model has a pre-defined algorithm for solving these equations, and the mass matrix, damping matrix, and stiffness matrix are the core coefficient matrices of these dynamic equations. These are prerequisites for the model to complete the calculation, and the model's solution logic relies on the numerical information of these three matrices to be activated. Only after these three are input collaboratively can the model fully capture the coupling effect of inertia, damping, and elasticity during vehicle motion, laying the foundation for subsequent accurate calculation of displacement, velocity, and acceleration vectors.

[0030] Based on three major matrices and a dedicated calculation model, this application can simultaneously and accurately calculate core time-history response parameters such as displacement vector, velocity vector, and acceleration vector. These parameters comprehensively cover the key representation dimensions of vehicle motion state and can provide comprehensive and reliable data support for multiple core R&D stages such as vehicle chassis tuning, body structure strength design, suspension system optimization, and passenger comfort assessment. This effectively solves the problem that existing technologies cannot simultaneously meet the multi-dimensional R&D data requirements.

[0031] S103. Based on the mass matrix, damping matrix, and stiffness matrix, calculate the time history response of the vehicle under test using the time history response calculation model; wherein, the time history response includes: displacement vector, velocity vector, and acceleration vector.

[0032] The method for calculating the vehicle time-history response proposed in this application first obtains the mass matrix, damping matrix, and stiffness matrix of the vehicle under test; then, the mass matrix, damping matrix, and stiffness matrix are input into a pre-constructed time-history response calculation model; finally, based on the mass matrix, damping matrix, and stiffness matrix, the time-history response of the vehicle under test is calculated through the time-history response calculation model. The time-history response includes displacement vector, velocity vector, and acceleration vector. In other words, the technical solution of this application directly obtains the actual mass matrix, damping matrix, and stiffness matrix of the vehicle under test. These three matrices are the core basic parameters describing the vehicle's dynamic characteristics, fully preserving the actual structural features and dynamic coupling relationships of the vehicle. This avoids information loss caused by simplified models from the data source, providing a reliable data foundation for subsequent accurate calculations. Model-based calculations can quickly output results, significantly shortening the time-history response acquisition time compared to experimental testing. Furthermore, it can achieve comprehensive and accurate output of time-history response parameters, meeting multi-dimensional R&D needs. This application overcomes the limitations of traditional finite difference methods, which are sensitive to time steps, and the difficulty of calculating Duhamel integrals in the fine integration method for complex dynamic external loads on commercial vehicles (such as road excitation, braking impact, cargo dynamic loads, engine vibration, etc.). It significantly improves computational efficiency while maintaining accuracy, making it suitable for time-history response analysis of key structures in commercial vehicles under complex dynamic loads. In existing technologies, while the fine integration method is accurate and unconditionally stable, it requires calculating Duhamel integrals based on different forms of dynamic external loads, lacking a universal solution format, making it very difficult to solve for structural dynamic responses under complex dynamic loads. Furthermore, the variational principles applicable to initial value problems in the time-based finite element method are very limited. Therefore, compared to existing technologies, the time-history response calculation method proposed in this application can fully utilize the vehicle mass matrix, damping matrix, and stiffness matrix to accurately calculate the vehicle displacement vector, velocity vector, and acceleration vector, avoiding deviations caused by neglecting component coupling effects and nonlinear elastic characteristics in traditional simplified models, thus better reflecting the actual operating state of the vehicle. Moreover, the technical solution of this application is simple and convenient to implement, easy to popularize, and has a wider range of applications.

[0033] Figure 2 This is a flowchart illustrating a method for calculating vehicle time-time response according to another embodiment of this application. Further optimizations and extensions are possible based on the above technical solution, and it can be combined with the various optional implementation methods described above. For example... Figure 2 As shown, the method for calculating the vehicle's time-time response may include the following steps:

[0034] S201. Obtain the mass matrix, damping matrix, and stiffness matrix of the vehicle under test.

[0035] S202. Input the mass matrix, damping matrix, and stiffness matrix into the pre-built time history response calculation model.

[0036] S203. Construct the general form of structural dynamics equations based on the mass matrix, damping matrix, and stiffness matrix using the time history response calculation model.

[0037] In a specific embodiment of this application, the general form of the structural dynamics equation is:

[0038]

[0039] in, , , These are the mass matrix, damping matrix, and stiffness matrix of the vehicle under test; The external stimulus for the vehicle under test is... , , These represent the displacement, velocity, and acceleration of the vehicle under test under external excitation; and These represent the initial displacement and initial velocity of the vehicle under test.

[0040] S204. By introducing state-space vectors, the general form of structural dynamics equations is transformed from second-order differential equations into first-order state-space equations.

[0041] In this step, a state space vector is introduced. By treating displacement and velocity as independent variables, the original second-order differential equation is transformed into a first-order state-space equation:

[0042]

[0043] in, ;

[0044] In the above formula, It is a state space vector The first derivative; It is the coefficient matrix of the state-space equation, which is composed of the physical parameters of the vehicle under test; It is a zero matrix, whose dimensions and displacements are... The dimensions are consistent; It is an identity matrix, and its dimensions are the same as those of the identity matrix. The dimensions are consistent; , , These are the mass matrix, damping matrix, and stiffness matrix of the vehicle under test; yes The inverse matrix; and yes The submatrix of the lower block of the matrix. Furthermore, Yes The vector obtained after adaptability processing.

[0045] S205. Calculate the time history response of the vehicle under test using the first-order state-space equation.

[0046] Furthermore, calculating the time history response of the vehicle under test using the first-order state-space equation can include the following steps: applying a homogeneous expansion method, by introducing a constant 1, to add a dimension to the state-space vector, resulting in an expanded state-space vector; using the expanded state-space vector, transforming the first-order state-space equation into a homogeneous differential equation; and calculating the time history response of the vehicle under test using the homogeneous differential equation.

[0047] Furthermore, calculating the time history response of the vehicle under test using the homogeneous differential equation may include the following steps: representing the solution of the homogeneous differential equation using a Magnus series; truncating the first term of the Magnus series and taking a step size of h; applying the point numerical integration formula to the integral in the truncated Magnus series based on the step size h to obtain the second-order approximate solution formula for the Magnus series; and calculating the time history response of the vehicle under test using the second-order approximate solution formula for the Magnus series. Further, calculating the time history response of the vehicle under test using the second-order approximate solution formula for the Magnus series may include the following steps: substituting the truncated Magnus series into the exponent matrix corresponding to the second-order approximate solution formula for the Magnus series and performing a Taylor expansion to obtain the solution of the homogeneous differential equation at each time step; and calculating the time history response of the vehicle under test based on the solution of the homogeneous differential equation at each time step.

[0048] Optionally, calculating the time history response of the vehicle under test using a homogeneous differential equation may include the following steps: representing the solution of the homogeneous differential equation using a Magnus series; truncating the first and second terms of the Magnus series and taking a step size of h; applying the Gauss-Legendre numerical quadrature formula to the integral in the truncated Magnus series based on the step size h to obtain a fourth-order approximate solution formula for the Magnus series; and calculating the time history response of the vehicle under test using the fourth-order approximate solution formula for the Magnus series. Further, calculating the time history response of the vehicle under test using the fourth-order approximate solution formula for the Magnus series may include the following steps: substituting the truncated Magnus series into the exponent matrix corresponding to the fourth-order approximate solution formula for the Magnus series and performing a Taylor expansion to obtain the solution of the homogeneous differential equation at each time step; and calculating the time history response of the vehicle under test based on the solution of the homogeneous differential equation at each time step.

[0049] Specifically, calculating the time history response of the vehicle under test using the first-order state-space equation can include the following steps: applying a homogeneous expansion method, by introducing a constant 1, to expand the state-space vector... Adding a dimension yields the increased-dimensional state space vector. By using the increased-dimensional state-space vector, the first-order state-space equation is transformed into a homogeneous differential equation:

[0050]

[0051] The above formula can be written as: ;in,

[0052] Due to the addition of one dimension in the processing, the generalized load The coefficient matrix appearing in the homogeneous differential equation (5) In the middle, leading to It is a time-varying matrix that changes with time, and and They cannot be exchanged, that is:

[0053] According to Magnus's theory, if a matrix series is found:

[0054] The matrix series must satisfy the following conditions:

[0055] Then the general solution of the homogeneous differential equation (5) can be expressed as:

[0056] In the above formula (9), it is called For Magnus series. In the above formula (8),

[0057]

[0058] In the above formula (10), For linear operators; Let be the Bernoulli number; the definitions of linear operators and Bernoulli numbers are shown in formulas (11) and (12):

[0059]

[0060]

[0061] According to the above formula (12), the first four Bernoulli numbers are as follows: Furthermore, The expansion can be written as:

[0062]

[0063] Applying Picard's fixed-point iteration theorem to the above formula (13), we can obtain:

[0064]

[0065] Since the Magnus series expansion has infinitely many terms, it is necessary to truncate the Magnus series appropriately as needed.

[0066] Furthermore, by using multivariate numerical integration methods, an approximate matrix of the Magnus series is calculated, thereby obtaining the matrix exponent of the Magnus series. Regarding the truncation order of the Magnus series, the following conclusions are drawn:

[0067]

[0068] Discretize the differential equation (5) in the time domain as follows: Nodes ,common Each time step It is a natural number greater than or equal to 1; the time step is . At each time step In the equation (9), the solution is:

[0069]

[0070] in, It is the first Each time point It is the first An approximation of the Magnus series at each time step. The first term is truncated, resulting in:

[0071]

[0072] Take step size as ,right By applying the point numerical integration formula in the integral, we can obtain... The approximation is:

[0073]

[0074] For ease of representation, it is noted as:

[0075]

[0076] The second-order approximate solution formula based on Magnus expansion can be expressed as:

[0077]

[0078] Furthermore, By truncating the first two terms, we can obtain:

[0079]

[0080] Take step size as By applying the Gauss-Legendre numerical quadrature formula for two points in two variables, we can obtain... The approximation is:

[0081]

[0082] in,

[0083]

[0084] remember:

[0085] The fourth-order approximate solution formula based on Magnus expansion can be expressed as:

[0086]

[0087] The two approximations described above can be represented as similar block matrix forms:

[0088]

[0089] Furthermore, Substitute into And perform a Taylor expansion:

[0090]

[0091] in, Is and Identity matrices with the same dimensions Is and An identity matrix with the same dimensions. Clearly, the top-left part of the above matrix is... The Taylor expansion of the above matrix. Further simplification of the upper right corner of the matrix is ​​as follows:

[0092]

[0093] and then,

[0094] Furthermore, the original differential equation at each time step The solution can be expressed as:

[0095]

[0096] in, This is the vector obtained by adding one dimension to the original state vector, which can be expanded as follows:

[0097]

[0098] Furthermore, through simple matrix operations, we can obtain:

[0099]

[0100] in, In the original state-space differential equation The state vector at time t, In the original state-space differential equation The state vector at time t, It is the coefficient matrix in the state-space equation.

[0101] Thus, the general numerical solution scheme (32) for solving the structural dynamic response is obtained. When in formula (32)... As shown in formula (18), the format is a second-order format; when in formula (32) When the formula (24) is shown, the format is a fourth-order format.

[0102] Furthermore, this application can utilize the precise integration method to process matrix exponents. .

[0103] To verify the computational accuracy and efficiency of this application, a simple spring-mass block example is designed. Figure 3 This is a schematic diagram of a spring-mass system provided in one embodiment of this application. Figure 3 As shown, the spring-mass system has ten degrees of freedom. The springs at both ends of the system are fixed, and the mass of each mass block is... The stiffness of each spring is A simple sinusoidal load is applied to each mass block. When a spring-mass system is excited by a sinusoidal load, the precise integration method can obtain the exact solution of the response at each time step, regardless of the step size. The dynamic response of the system is calculated in Matlab using both the Newmark method and the method provided in this application. The calculation accuracy under the same step size and the calculation efficiency under the same step size and number of calculation steps are compared. Rayleigh damping is used in the example. The dynamic control equation of the spring-mass system is given by equation (1), where,

[0104]

[0105] Substituting formula (41) into formula (3), we can obtain the system state matrix and the non-homogeneous terms.

[0106] To compare the computational accuracy of different methods, the relative errors of the system displacement vectors were compared. Here, the displacement vector refers to the displacement vector that includes the entire system's degrees of freedom at each time point in the time domain. The relative error can be expressed as:

[0107]

[0108] in This represents the numerical solution calculated using the Newmark method or the method presented in this paper. The reference solution is shown in Table 1. Table 1 shows the errors between the numerical and exact solutions of the displacement calculated by each method under different step sizes. This example demonstrates that, under the same step size, the computational accuracy of the proposed method is significantly better than that of the Newmark method; furthermore, the fourth-order method in this paper has better computational accuracy than the second-order method. The Newmark method requires small step sizes to obtain relatively accurate results, while the proposed method can approximate the exact solution well even with large step sizes.

[0109]

[0110] Table 1

[0111] To compare the computational efficiency of the proposed method, each method performed the same number of steps with the same time length. The CPU computation time for both the Newmark method and the proposed method was recorded in Table 2. This example shows that, with the same time length and number of computation steps, the computational efficiency of the proposed second-order method is 4.2 to 4.7 times that of the Newmark method, and the computational efficiency of the proposed fourth-order method is 5.3 to 5.4 times that of the Newmark method, significantly better than the Newmark method. The computational efficiency of the proposed fourth-order method is comparable to that of the proposed second-order method.

[0112]

[0113] Table 2

[0114] Figure 4 This is a schematic diagram of the structure of a vehicle time-time response computing device provided in an embodiment of this application. Figure 4 As shown, the vehicle time-course response calculation device includes: an acquisition module 401, an input module 402, and a calculation module 403; wherein,

[0115] The acquisition module 401 is used to acquire the mass matrix, damping matrix and stiffness matrix of the vehicle under test;

[0116] The input module 402 is used to input the mass matrix, the damping matrix and the stiffness matrix into a pre-constructed time history response calculation model;

[0117] The calculation module 403 is used to calculate the time history response of the vehicle under test based on the mass matrix, the damping matrix and the stiffness matrix through the time history response calculation model; wherein, the time history response includes: displacement vector, velocity vector and acceleration vector.

[0118] The vehicle time-time response calculation device described above can execute the method provided in any embodiment of this application, and has the corresponding functional modules and beneficial effects for executing the method. Technical details not described in detail in this embodiment can be found in the vehicle time-time response calculation method provided in any embodiment of this application.

[0119] Figure 5 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Figure 5 A block diagram of an exemplary electronic device suitable for implementing embodiments of the present application is shown. Figure 5 The electronic device 12 shown is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of this application.

[0120] like Figure 5 As shown, the electronic device 12 is represented in the form of a general-purpose computing device. The components of the electronic device 12 may include, but are not limited to: one or more processors or processing units 16, system memory 28, and bus 18 connecting different system components (including system memory 28 and processing unit 16).

[0121] Bus 18 represents one or more of several bus architectures, including a memory bus or memory controller, a peripheral bus, a graphics acceleration port, a processor, or a local bus using any of the various bus architectures. For example, these architectures include, but are not limited to, the Industry Standard Architecture (ISA) bus, the Micro Channel Architecture (MAC) bus, the Enhanced ISA bus, the Video Electronics Standards Association (VESA) local bus, and the Peripheral Component Interconnect (PCI) bus.

[0122] Electronic device 12 typically includes a variety of computer system readable media. These media can be any available media that can be accessed by electronic device 12, including volatile and non-volatile media, removable and non-removable media.

[0123] System memory 28 may include computer system readable media in the form of volatile memory, such as random access memory (RAM) 30 and / or cache memory 32. Electronic device 12 may further include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, storage system 34 may be used to read and write non-removable, non-volatile magnetic media (… Figure 5 Not shown; usually referred to as a "hard drive"). Although Figure 5 As not shown, a disk drive for reading and writing to a removable non-volatile disk (e.g., a "floppy disk") and an optical disk drive for reading and writing to a removable non-volatile optical disk (e.g., a CD-ROM, DVD-ROM, or other optical media) may be provided. In these cases, each drive may be connected to bus 18 via one or more data media interfaces. Memory 28 may include at least one program product having a set (e.g., at least one) of program modules configured to perform the functions of the embodiments of this application.

[0124] A program / utility 40 having a set (at least one) of program modules 42 may be stored, for example, in memory 28. Such program modules 42 include, but are not limited to, an operating system, one or more application programs, other program modules, and program data. Each or some combination of these examples may include an implementation of a network environment. Program modules 42 typically perform the functions and / or methods described in the embodiments of this application.

[0125] Electronic device 12 can also communicate with one or more external devices 14 (e.g., keyboard, pointing device, display 24, etc.), and with one or more devices that enable a user to interact with electronic device 12, and / or with any device that enables electronic device 12 to communicate with one or more other computing devices (e.g., network card, modem, etc.). This communication can be performed via input / output (I / O) interface 22. Furthermore, electronic device 12 can also communicate with one or more networks (e.g., local area network (LAN), wide area network (WAN), and / or public networks, such as the Internet) via network adapter 20. As shown, network adapter 20 communicates with other modules of electronic device 12 via bus 18. It should be understood that, although... Figure 5 As not shown, other hardware and / or software modules may be used in conjunction with electronic device 12, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0126] The processing unit 16 executes various functional applications and data processing by running programs stored in the system memory 28, such as implementing the vehicle time-course response calculation method provided in the embodiments of this application.

[0127] This application also provides a computer storage medium.

[0128] The computer-readable storage medium of this application embodiment can be any combination of one or more computer-readable media. The computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. For example, a computer-readable storage medium can be—but is not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this document, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0129] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media may also be any computer-readable medium other than computer-readable storage media, capable of sending, propagating, or transmitting programs for use by or in connection with an instruction execution system, apparatus, or device.

[0130] The program code contained on a computer-readable medium may be transmitted using any suitable medium, including—but not limited to—wireless, wire, optical fiber, RF, etc., or any suitable combination thereof.

[0131] Computer program code for performing the operations of this application can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0132] This application also provides a computer program product.

[0133] Various embodiments of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard products (ASSPs), systems-on-a-chip (SoCs), payload-programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments may include implementations in one or more computer program products, which may include one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be an application-specific or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0134] Note that the above are merely preferred embodiments and the technical principles employed in this application. Those skilled in the art will understand that this application is not limited to the specific embodiments described herein, and various obvious changes, readjustments, and substitutions can be made without departing from the scope of protection of this application. Therefore, although this application has been described in detail through the above embodiments, this application is not limited to the above embodiments, and may include many other equivalent embodiments without departing from the concept of this application, the scope of which is determined by the scope of the appended claims.

Claims

1. A method for calculating the time-history response of a vehicle, characterized in that, The method includes: Obtain the mass matrix, damping matrix, and stiffness matrix of the vehicle under test; The mass matrix, the damping matrix, and the stiffness matrix are input into a pre-constructed time history response calculation model; The time history response of the vehicle under test is calculated using the time history response calculation model based on the mass matrix, the damping matrix, and the stiffness matrix; wherein the time history response includes: displacement vector, velocity vector, and acceleration vector.

2. The method according to claim 1, characterized in that, Based on the mass matrix, the damping matrix, and the stiffness matrix, the time-history response of the vehicle under test is calculated using the time-history response calculation model, including: The general form of the structural dynamics equations is constructed using the time-history response calculation model based on the mass matrix, the damping matrix, and the stiffness matrix. By introducing a state-space vector, the general form of the structural dynamics equations is transformed from second-order differential equations into first-order state-space equations. The time history response of the vehicle under test is calculated using the first-order state-space equation.

3. The method according to claim 2, characterized in that, The time history response of the vehicle under test is calculated using the first-order state-space equation, including: By applying the homogeneous expansion method, a constant 1 is introduced to add a dimension to the state space vector, resulting in an expanded state space vector. The first-order state-space equation is transformed into a homogeneous differential equation using the increased-dimensional state-space vector. The time history response of the vehicle under test is calculated using the homogeneous differential equation.

4. The method according to claim 3, characterized in that, The time history response of the vehicle under test is calculated using the homogeneous differential equation, including: The solution to the homogeneous differential equation is expressed using Magnus series; The first term of the Magnus series is truncated and a step size of h is taken; based on the step size h, the point numerical integration formula is applied to the integral in the truncated Magnus series to obtain the second-order approximate solution formula of the Magnus series. The time history response of the vehicle under test is calculated using the second-order approximate solution formula of the Magnus series.

5. The method according to claim 3, characterized in that, The time history response of the vehicle under test is calculated using the homogeneous differential equation, including: The solution to the homogeneous differential equation is expressed using Magnus series; The first and second terms of the Magnus series are truncated and the step size is h. Based on the step size h, the Gauss-Legendre numerical quadrature formula for two points in two variables is applied to the integral in the truncated Magnus series to obtain the fourth-order approximate solution formula for the Magnus series. The time history response of the vehicle under test was calculated using the fourth-order approximate solution formula of the Magnus series.

6. The method according to claim 4, characterized in that, The time history response of the vehicle under test is calculated by solving the formula using the second-order approximation of the Magnus series, including: Substitute the truncated Magnus series into the exponent matrix corresponding to the second-order approximate solution formula of the Magnus series and perform Taylor expansion to obtain the solution of the homogeneous differential equation at each time step. The time history response of the vehicle under test is calculated based on the solution of the homogeneous differential equation at each time step.

7. The method according to claim 5, characterized in that, The time history response of the vehicle under test is calculated using the fourth-order approximate solution formula of the Magnus series, including: Substitute the truncated Magnus series into the exponent matrix corresponding to the fourth-order approximate solution formula of the Magnus series and perform Taylor expansion to obtain the solution of the homogeneous differential equation at each time step. The time history response of the vehicle under test is calculated based on the solution of the homogeneous differential equation at each time step.

8. A calculation device for vehicle time-time response, characterized in that, The device includes: an acquisition module, an input module, and a calculation module; wherein... The acquisition module is used to acquire the mass matrix, damping matrix, and stiffness matrix of the vehicle under test; The input module is used to input the mass matrix, the damping matrix and the stiffness matrix into a pre-constructed time history response calculation model; The calculation module is used to calculate the time history response of the vehicle under test based on the mass matrix, the damping matrix, and the stiffness matrix through the time history response calculation model; wherein, the time history response includes: displacement vector, velocity vector, and acceleration vector.

9. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs. When the one or more programs are executed by the one or more processors, the one or more processors implement the method for calculating the vehicle time-course response as described in any one of claims 1 to 7.

10. A storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements the method for calculating the vehicle time-course response as described in any one of claims 1 to 7.

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