机会约束的影子价格

为了进一步对随机规划进行研究，通过定义机会约束规划的可靠规划的对偶规划，得到了随机规划的对偶规划的一些性质．从对偶规划的最优解出发，得到了机会约束的影子价格的概念，它反映了随机约束条件对于目标函数最优值的影响．通过实例来说明它在经济决策中的应用．     

开挖边坡岩土体位移及变形分析中的随机介质理论

提出了用岩土体的变形表示岩土体强度的随机介质理论方法,分析了边坡工程应用随机介质理论的原理及基本方程,获得了由开挖边坡工程引起地表及岩土体内部移动及变形的分析公式,探讨了计算参数的选择,并通过工程实例,验证了其可靠性。从而对莫尔-库仑准则作为滑坡判据的极限平衡分析法和应力-应变数值分析法有所突破。     

First passage probability of structures under non-Gaussian stochastic behavior

An analytical moment-based method was proposed for calculating first passage probability of structures under non-Ganssian stochastic behaviour. In the method, the third-moment standardization that constants can be obtained from first three-order response moments was used to map a non-Ganssian structural response into a standard Gaussian process; then the mean up-crossing rates, the mean clump size and the initial passage probability of some critical barrier level by the original structural response were estimated. Finally, the formula for calculating first passage probability was established on the assumption that the corrected up-crossing rates are independent. By a nonlinear single-degree-of-freedom system excited by a stationary Gaussian load,it is demonstrated how the procedure can be used for the type of structures considered. Further, comparisons between the results from the present procedure and those from Monte-Carlo simulation are performed.     

轮对系统随机动态分叉研究

运用随机平均法对轮对系统的随机分叉行为进行研究,对比亚临界和超临界分叉2种典型轮对系统随机动态分叉的差异,分析动态分叉与Hopf分叉的区别,定义全局随机临界速度,提出新的失稳判定方法。结果表明,随机激扰对轮对系统的稳定性影响很大,在随机激扰的作用下,轮对系统的临界速度会随着随机激扰的强度增大而显著降低,当轮对仅受轨道随机激励时随机激扰对稳定性的影响不大,但遇到大风等强激扰环境时,随机激扰的影响将不可忽视。随机动态分叉点对应的速度可作为全局随机临界速度,且最大Lyapunov指数法可作为新的失稳判定方法。     

停车许可证的动态最优供给策略

考虑可预约和不可预约公共停车设施共存情况，制定停车许可证动态最优供给策略.构建随机最优控制模型以实现系统总时间损失期望值最小化，利用动态规划原理推导出最优性条件，即哈密尔顿-雅克比-贝尔曼方程，采用一种预设最优值函数方法得到动态最优供给策略的解析解.结果表明：动态最优供给策略为一个反馈控制，即车辆排队时间的函数；依据排队时间是否存在，动态最优供给策略分为两种情况.以北京市国贸地区为例进行蒙特卡洛实验可知：相较停车许可证完全供给策略，动态最优供给策略可节约时间0.45~1.94 min/veh；随着停车许可证用户行为不确定性增加，动态最优供给策略节约时间的平均值上升，变异系数下降.     

轨道不平顺激励下车辆-桥梁垂向随机振动方差解法

提出时滞多维非白噪声轨道不平顺激励下车辆-桥梁垂向随机振动的时域分析方法。采用白噪声滤波法模拟单轮对下的不平顺,在宽频带内识别滤波器参数以实现波长选择功能。基于Pade近似构造累次时滞滤波器以反映各轮对下不平顺之间的时滞关系。结合成型和时滞滤波器,构造以一致白噪声为输入、时滞多维非白噪声不平顺为输出的合成滤波器。建立车辆-桥梁垂向振动模型,并与合成滤波器联立得到一致白噪声激励下的车-桥-滤波器扩阶状态方程。继而提出求解此扩阶时变系统随机振动方差响应的递推算法。算例结果与MonteCarlo模拟法符合良好,表明该方法具有足够的精度,且对时间步长不敏感。     

A polynomial chaos approach to the analysis of vehicle dynamics under uncertainty

The ability of ground vehicles to quickly and accurately analyse their dynamic response to a given input is critical to their safety and efficient autonomous operation. In field conditions, significant uncertainty is associated with terrain and/or vehicle parameter estimates, and this uncertainty must be considered in the analysis of vehicle motion dynamics. Here, polynomial chaos approaches that explicitly consider parametric uncertainty during modelling of vehicle dynamics are presented. They are shown to be computationally more efficient than the standard Monte Carlo scheme, and experimental results compared with the simulation results performed on ANVEL (a vehicle simulator) indicate that the method can be utilised for efficient and accurate prediction of vehicle motion in realistic scenarios.     

An enhanced SPSA algorithm for the calibration of Dynamic Traffic Assignment models

Simultaneous perturbation stochastic approximation (SPSA) is an efficient and well established optimization method that approximates gradients from successive objective function evaluations. It is especially attractive for high-dimensional problems and has been successfully applied to the calibration of Dynamic Traffic Assignment (DTA) models. This paper presents an enhanced SPSA algorithm, called Weighted SPSA (W-SPSA), which incorporates the information of spatial and temporal correlation in a traffic network to limit the impact of noise and improve convergence and robustness. W-SPSA appears to outperform the original SPSA algorithm by reducing the noise generated by uncorrelated measurements in the gradient approximation, especially for DTA models of sparsely correlated large-scale networks and a large number of time intervals. Comparisons between SPSA and W-SPSA have been performed through rigorous synthetic tests and the application of W-SPSA for the calibration of real world DTA networks is demonstrated with a case study of the entire expressway network in Singapore.