The vehicle-road coupling dynamics problem is a prominent issue in transportation,drawing significant attention in recent years.These dynamic equations are characterized by high-dimensionality,coupling,and time-varyin...The vehicle-road coupling dynamics problem is a prominent issue in transportation,drawing significant attention in recent years.These dynamic equations are characterized by high-dimensionality,coupling,and time-varying dynamics,making the exact solutions challenging to obtain.As a result,numerical integration methods are typically employed.However,conventional methods often suffer from low computational efficiency.To address this,this paper explores the application of the parameter freezing precise exponential integrator to vehicle-road coupling models.The model accounts for road roughness irregularities,incorporating all terms unrelated to the linear part into the algorithm's inhomogeneous vector.The general construction process of the algorithm is detailed.The validity of numerical results is verified through approximate analytical solutions(AASs),and the advantages of this method over traditional numerical integration methods are demonstrated.Multiple parameter freezing precise exponential integrator schemes are constructed based on the Runge-Kutta framework,with the fourth-order four-stage scheme identified as the optimal one.The study indicates that this method can quickly and accurately capture the dynamic system's vibration response,offering a new,efficient approach for numerical studies of high-dimensional vehicle-road coupling systems.展开更多
An improved precise integration method （IPIM） for solving the differential Riccati equation （DRE） is presented. The solution to the DRE is connected with the exponential of a Hamiltonian matrix, and the precise in...An improved precise integration method （IPIM） for solving the differential Riccati equation （DRE） is presented. The solution to the DRE is connected with the exponential of a Hamiltonian matrix, and the precise integration method （PIM） for solving the DRE is connected with the scaling and squaring method for computing the exponential of a matrix. The error analysis of the scaling and squaring method for the exponential of a matrix is applied to the PIM of the DRE. Based ,on the error analysis, the criterion for choosing two parameters of the PIM is given. Three kinds of IPIMs for solving the DRE are proposed. The numerical examples machine accuracy solutions. show that the IPIM is stable and gives the展开更多
基金Supported by the National Natural Science Foundation of China(No.U22A20246)the Key Project of Natural Science Foundation of Hebei Province of China(Basic Research Base Project)(No.A2023210064)the Science and Technology Program of Hebei Province of China(Nos.246Z1904G and 225676162GH)。
文摘The vehicle-road coupling dynamics problem is a prominent issue in transportation,drawing significant attention in recent years.These dynamic equations are characterized by high-dimensionality,coupling,and time-varying dynamics,making the exact solutions challenging to obtain.As a result,numerical integration methods are typically employed.However,conventional methods often suffer from low computational efficiency.To address this,this paper explores the application of the parameter freezing precise exponential integrator to vehicle-road coupling models.The model accounts for road roughness irregularities,incorporating all terms unrelated to the linear part into the algorithm's inhomogeneous vector.The general construction process of the algorithm is detailed.The validity of numerical results is verified through approximate analytical solutions(AASs),and the advantages of this method over traditional numerical integration methods are demonstrated.Multiple parameter freezing precise exponential integrator schemes are constructed based on the Runge-Kutta framework,with the fourth-order four-stage scheme identified as the optimal one.The study indicates that this method can quickly and accurately capture the dynamic system's vibration response,offering a new,efficient approach for numerical studies of high-dimensional vehicle-road coupling systems.
基金Project supported by the National Natural Science Foundation of China(Nos.10902020 and 10721062)
文摘An improved precise integration method （IPIM） for solving the differential Riccati equation （DRE） is presented. The solution to the DRE is connected with the exponential of a Hamiltonian matrix, and the precise integration method （PIM） for solving the DRE is connected with the scaling and squaring method for computing the exponential of a matrix. The error analysis of the scaling and squaring method for the exponential of a matrix is applied to the PIM of the DRE. Based ,on the error analysis, the criterion for choosing two parameters of the PIM is given. Three kinds of IPIMs for solving the DRE are proposed. The numerical examples machine accuracy solutions. show that the IPIM is stable and gives the
