In this paper, the necessary theoretical analysis for the approximation boundary element method to solve dynamical response of viscoelastic thin plate presented in [1] is.discussed. The theorem of existence and uniq...In this paper, the necessary theoretical analysis for the approximation boundary element method to solve dynamical response of viscoelastic thin plate presented in [1] is.discussed. The theorem of existence and uniqueness of the approximate solution andthe error estimation are also obtained. Based on these conclusions , the principle forchoosing the mesh size and the number of truncated terms in the fundamental solution are given. It isshown that the theoretical ana analysis in this paper are consistent with thenumerical results in [1].展开更多
It has been evident that the theory and methods of dynamic derivatives are playing an increasingly important role in hybrid modeling and computations. Being constructed on various kinds of hybrid grids, that is, tim...It has been evident that the theory and methods of dynamic derivatives are playing an increasingly important role in hybrid modeling and computations. Being constructed on various kinds of hybrid grids, that is, time scales, dynamic derivatives offer superior accuracy and flexibility in approximating mathematically important natural processes with hard-to-predict singularities, such as the epidemic growth with unpredictable jump sizes and option market changes with high uncertainties, as compared with conventional derivatives. In this article, we shall review the novel new concepts, explore delicate relations between the most frequently used second-order dynamic derivatives and conventional derivatives. We shall investigate necessary conditions for guaranteeing the consistency between the two derivatives. We will show that such a consistency may never exist in general. This implies that the dynamic derivatives provide entirely different new tools for sensitive modeling and approximations on hybrid grids. Rigorous error analysis will be given via asymptotic expansions for further modeling and computational applications. Numerical experiments will also be given.展开更多
We investigate numerically the dynamical reactions of a moving wheelset model to real measured track irregularities.The background is to examine whether the dynamics are suitable as the input to the inverse problem:de...We investigate numerically the dynamical reactions of a moving wheelset model to real measured track irregularities.The background is to examine whether the dynamics are suitable as the input to the inverse problem:determine the true track geometry from measured wheelset dynamical reactions.It is known that the method works well for the vertical position of the rails but the computed lateral position is often flawed.We find that the lateral motion of the wheelset often may differ from the track geometry.The cases are investigated closely but the reasons remain unknown.While the wheelset dynamics reflect the larger(>4-6 mm)aperiodic track disturbances and single large disturbances quite well,this does not seem to be the case for general smaller or periodic track irregularities or sections behind single large disturbances.The resulting dynamics of a wheelset to lateral track irregularities are in general not sufficiently accurate to be used as the basis for a description of the track irregularities.展开更多
We prove probabilistic error estimates for high-index saddle dynamics with or without constraints to account for the inaccurate values of the model,which could be encountered in various scenarios such as model uncerta...We prove probabilistic error estimates for high-index saddle dynamics with or without constraints to account for the inaccurate values of the model,which could be encountered in various scenarios such as model uncertainties or surrogate model algorithms via machine learning methods. The main contribution lies in incorporating the probabilistic error bound of the model values with the conventional error estimate methods for high-index saddle dynamics. The derived results generalize the error analysis of deterministic saddle dynamics and characterize the affect of the inaccuracy of the model on the convergence rate.展开更多
为及时发现电能计量装置的潜在隐患,须对计量装置的动态误差水平进行在线动态估计。研究计量装置综合误差的组成,分析不同影响因素引起的计量变差规律,针对无法直接在线测量的电压和电流互感器误差,在匹配动态时间弯曲路径时引入变化率...为及时发现电能计量装置的潜在隐患,须对计量装置的动态误差水平进行在线动态估计。研究计量装置综合误差的组成,分析不同影响因素引起的计量变差规律,针对无法直接在线测量的电压和电流互感器误差,在匹配动态时间弯曲路径时引入变化率有界性约束避免病态弯曲现象,形成改进的动态时间弯曲距离法量化剩磁、环境温度等变差影响因素与计量误差时间序列的相似度;考虑不同因素引起变差的随机性和模糊性,建立用于表征不对称和不规则分布的组合半梯形云模型,针对不同因素采用不同形式的云模型估计电压和电流互感器的运行变差;利用改进动态时间弯曲距离对不同因素引起的变差进行加权获得互感器动态误差,与电能表和二次回路监测误差组合,实现计量装置综合误差的动态估计。根据某110 k V变电站中计量装置的实验监测数据分析,验证所提方法的正确性。展开更多
文摘In this paper, the necessary theoretical analysis for the approximation boundary element method to solve dynamical response of viscoelastic thin plate presented in [1] is.discussed. The theorem of existence and uniqueness of the approximate solution andthe error estimation are also obtained. Based on these conclusions , the principle forchoosing the mesh size and the number of truncated terms in the fundamental solution are given. It isshown that the theoretical ana analysis in this paper are consistent with thenumerical results in [1].
文摘It has been evident that the theory and methods of dynamic derivatives are playing an increasingly important role in hybrid modeling and computations. Being constructed on various kinds of hybrid grids, that is, time scales, dynamic derivatives offer superior accuracy and flexibility in approximating mathematically important natural processes with hard-to-predict singularities, such as the epidemic growth with unpredictable jump sizes and option market changes with high uncertainties, as compared with conventional derivatives. In this article, we shall review the novel new concepts, explore delicate relations between the most frequently used second-order dynamic derivatives and conventional derivatives. We shall investigate necessary conditions for guaranteeing the consistency between the two derivatives. We will show that such a consistency may never exist in general. This implies that the dynamic derivatives provide entirely different new tools for sensitive modeling and approximations on hybrid grids. Rigorous error analysis will be given via asymptotic expansions for further modeling and computational applications. Numerical experiments will also be given.
文摘We investigate numerically the dynamical reactions of a moving wheelset model to real measured track irregularities.The background is to examine whether the dynamics are suitable as the input to the inverse problem:determine the true track geometry from measured wheelset dynamical reactions.It is known that the method works well for the vertical position of the rails but the computed lateral position is often flawed.We find that the lateral motion of the wheelset often may differ from the track geometry.The cases are investigated closely but the reasons remain unknown.While the wheelset dynamics reflect the larger(>4-6 mm)aperiodic track disturbances and single large disturbances quite well,this does not seem to be the case for general smaller or periodic track irregularities or sections behind single large disturbances.The resulting dynamics of a wheelset to lateral track irregularities are in general not sufficiently accurate to be used as the basis for a description of the track irregularities.
基金supported by the National Natural Science Foundation of China(Nos.12225102,T2321001,12288101 and 12301555)the National Key R&D Program of China(Nos.2021YFF1200500 and 2023YFA1008903)the Taishan Scholars Program of Shandong Province(No.tsqn202306083).
文摘We prove probabilistic error estimates for high-index saddle dynamics with or without constraints to account for the inaccurate values of the model,which could be encountered in various scenarios such as model uncertainties or surrogate model algorithms via machine learning methods. The main contribution lies in incorporating the probabilistic error bound of the model values with the conventional error estimate methods for high-index saddle dynamics. The derived results generalize the error analysis of deterministic saddle dynamics and characterize the affect of the inaccuracy of the model on the convergence rate.
文摘为及时发现电能计量装置的潜在隐患,须对计量装置的动态误差水平进行在线动态估计。研究计量装置综合误差的组成,分析不同影响因素引起的计量变差规律,针对无法直接在线测量的电压和电流互感器误差,在匹配动态时间弯曲路径时引入变化率有界性约束避免病态弯曲现象,形成改进的动态时间弯曲距离法量化剩磁、环境温度等变差影响因素与计量误差时间序列的相似度;考虑不同因素引起变差的随机性和模糊性,建立用于表征不对称和不规则分布的组合半梯形云模型,针对不同因素采用不同形式的云模型估计电压和电流互感器的运行变差;利用改进动态时间弯曲距离对不同因素引起的变差进行加权获得互感器动态误差,与电能表和二次回路监测误差组合,实现计量装置综合误差的动态估计。根据某110 k V变电站中计量装置的实验监测数据分析,验证所提方法的正确性。
