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.     

随机结构参数车辆在随机激励下的振动响应

为分析随机结构参数对车辆系统随机振动响应的影响,通过1/4车辆模型,研究了具有随机结构参数的非线性车辆系统在随机过程激励下的振动响应.将簧上质量、簧下质量、悬挂阻尼、悬挂刚度以及轮胎刚度均视为随机变量,考虑轮胎与车身之间弹簧的非线性,将路面不平整引起的对车辆的激励作为平稳白噪声过程建立系统的动力性方程,采用能量差法对非线性车辆系统进行等效线性化处理;通过求解李雅普诺夫方程,获得平稳随机振动响应协方差矩阵,并通过多次迭代求得稳定的等效线性车辆系统参数.算例计算结果表明:能量差法计算位移的相对误差为6.841 5%,而方程差法的相对误差为8.150 5%;用此方法计算随机响应的方差值仅用了0.8 s,而用Monte Carlo法模拟1 000次耗时70 min.      

In-plane Auto-Parametric Vibration of Inclined Cables under Random Transverse Excitation

In-plane auto-parametric stochastic vibration of inclined cables subjected to Gaussian white noise in transverse bridge orientation is investigated. Based on Newton＇s laws of motion and Galerkin＇s modal truncation principle, the influences of geometry nonlinearity induced by sag and large displacement of cables and the initial equilibrium state are taken into account. Meanwhile, the three-dimensional non-linear differential equations of inclined cables for coupling vibration are deduced, equivalent stochastic linearization method is applied to derive the 14-dimensional first-order nonlinear differential equations of state vectors, and the Runge-Kutta integration method is utilized to obtain the root mean square （RMS） response. Results show that when the transverse random excitation imposed on the stayed cable exceeds a critical value, the in-plane transverse vibration of the cable are excited due to tim auto-parametric nonlinear coupling, and the critical value of random excitation increases with the damping ratio. In this motion, the cable response possesses non-stationary characteristics, even though the loading keeps stationary.     

Stability Analysis for Stochastic Optimization Problems

Stochastic optimization offers a means of considering the objectives and constrains with stochastic parameters. However, it is generally difficult to solve the stochastic optimization problem by employing conventional methods for nonlinear programming when the number of random variables involved is very large. Neural network models and algorithms were applied to solve the stochastic optimization problem on the basis of the stability theory. Stability for stochastic programs was discussed. If random vector sequence converges to the random vector in the original problem in distribution, the optimal value of the corresponding approximation problems converges to the optimal value of the original stochastic optimization problem.     

随机齿侧间隙的齿轮系统非线性动力学分析

建立了随机齿侧间隙的单自由度齿轮系统的非线性动力学模型,利用变步长Runge-Kutta法对系统在确定齿侧间隙和随机齿侧间隙两种情况下的运动微分方程分别进行了数值求解,结合系统随量纲-间隙平均值变化的分岔图、相图及Poincaré映射图,分析了系统在确定齿侧间隙和随机齿侧间隙两种情况下的动力学特性,在此基础上研究了随机干扰对齿轮系统的动力学影响,发现随机干扰对系统的周期运动影响较大,对系统的倍化分岔过程影响显著,而对系统的混沌运动影响较小.     

钢管混凝土拱桥的多维平稳随机地震响应

用随机振动理论，对钢管混凝土拱桥的多维地震响应的计算方法和响应特性进行了研究．提出了多维激励作用下的虚拟激励法，采用该方法分析了钢管混凝土拱桥在多维激励作用下的平稳随机响应特性，并探讨了主拱横撑刚度对结构响应特性的影响．结果表明，多维激励作用下的虚拟激励法与传统的随机振动理论具有相同的计算精度，但速度要快得多；横向激励和竖向激励对拱肋内力的影响较大，拱肋内力响应有随横撑剐度增大而增大的趋势。     

多分量多点平稳随机地震响应的快速算法

为了解决多分量多点激励作用下大跨度桥梁平稳随机响应的计算问题,在单分量虚拟激励法的基础上,提出了多分量多点地震激励下计算大跨度桥梁平稳随机响应的虚拟激励法.理论证明,该法具有与经典随机振动理论精确解相同的精度,而计算速度比经典随机振动理论快10倍,且可方便地计入行波效应或部分相干效应.     

Fault diagnosis for singular stochastic systems

This paper studies the fault diagnosis of singular stochastic systems. The probability distribution of output is measured by probability density functions (PDFs), which are modeled by a square root B-spline expansion. An adaptive nonlinear observer is proposed to estimate the size of the fault occurring in systems. Furthermore, the linear matrix inequality (LMI) approach is applied to establish sufficient conditions for the existence of the observer. Finally, the simulation results are given to indicate the method for diagnosing the fault.     

Stochastic optimal control for first-passage failure of nonlinear oscillators with multi-degrees-of-freedom

To enhance the reliability of the stochastically excited structure,it is significant to study the problem of stochastic optimal control for minimizing first-passage failure.Combining the stochastic averaging method with dynamical programming principle,we study the optimal control for minimizing first-passage failure of multidegrees-of-freedom（MDoF）nonlinear oscillators under Gaussian white noise excitations.The equations of motion of the controlled system are reduced to time homogenous difusion processes by stochastic averaging.The optimal control law is determined by the dynamical programming equations and the control constraint.The backward Kolmogorov（BK）equation and the Pontryagin equation are established to obtain the conditional reliability function and mean first-passage time（MFPT）of the optimally controlled system,respectively.An example has shown that the proposed control strategy can increase the reliability and MFPT of the original system,and the mathematical treatment is also facilitated.     

ATIS影响下的混合随机用户均衡交通分配模型研究

在考虑信息对出行者路径选择行为影响的基础上,基于路网混合随机用户均衡建模理论,建立了ATIS影响下的混合随机用户均衡交通分配模型,证明了该数学规划模型解的等价性,设计了求解算法,并利用算例进行了计算分析.     

随机共振与响应灵敏度相结合的结构损伤检测方法

为了解决强噪声背景环境下的结构损伤识别问题,提出了一种基于非线性降噪和损伤定位相结合的两步法.第一步将结构的激励响应和背景噪声通过非线性随机共振系统进行处理,降低背景噪声的干扰以突出响应;第二步将结构的局部微小损伤模拟为单元弹性模量的减少,求得响应信息对单元弹性模量的灵敏度,据此对结构单元弹性模量进行修正,从而实现结构损伤的定位.数值算例表明,该方法在50%噪声水平环境下,能较好地实现损伤定位,单一损伤识别误差率不超过0.2%,多损伤识别的误差率不超过0.5%.      

变温环境下粘弹性梁的混沌运动

根据Kelvin粘弹性材料本构关系、梁的运动方程及变形几何方程建立了同时具有温度扰动和横向分布力扰动的粘弹性梁非线性动力学模型.用Galerkin方法将系统简化为参数激励和强迫激励耦合的单模态Duffing振子,得到了系统的不动点和同宿轨道.用Melnikov函数法推导出系统混沌运动的临界条件,分析了系统通向混沌的途径.研究表明,非线性粘弹性梁在周期性横向激励及周期性温度联合作用下可能进入混沌运动,并且在发生Smale马蹄意义下的混沌前,将经历多次的次谐分岔.     

采用随机介质理论分析超浅层曲线顶管施工引起的地表沉降

应用随机介质理论对重庆主城排水超浅层曲线顶管顶进过程的地表沉降进行了分析,并推导出简化的沉降计算公式,进行了理论计算沉降与实测沉降对比,对比结果证明该理论在一定条件下也适用于超浅层顶管引起的地表沉降.     

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研究先进出行者信息系统(ATIS)环境下道路网络系统流量的随机动态变化,有利于实现ATIS在网络系统中的进一步优化配置.在出行者经验积累过程基础上,引入ATIS作用下的认知更新过程,将路网系统的路径流量明确视为随机变量,提出了一个基于认知更新的随机动态分配模型.证明了该模型产生的路径流量渐近收敛于一个平稳概率分布.在算例网络中验证了模型的可行性,模拟有ATIS和无ATIS两种情形下路径流量的随机动态变化.结果表明,两种情形路径流量均收敛于平稳概率分布.前者的平均流量近似于随机用户平衡(SUE),而后者的平均流量不是平衡流量,但其网络总费用要低于前者.     

随机交通网络约束最可靠路径问题

为了模拟仿真交通网络中,约束条件下考虑风险性车辆路径选择行为,建立随机交通网络环境下约束最可靠路径问题数学规划模型,并讨论了其对偶问题.采用梯度下降算法求解对偶问题,获得原问题最优值的上界和下界,通过迭代获得原问题的近似解.针对Sioux Falls network展开数值试验并对数值结果进行了对比分析.计算结果表明：在随机交通网络环境下,无约束和有约束条件下求解的最可靠路径是不同的;不同的资源约束条件下求解的最可靠路径也是不同的,资源约束条件对交通网络中最可靠路径的选择有很大的影响.     

考虑出行者损失厌恶的后悔随机用户均衡模型

在经典随机后悔最小化模型的基础上,通过引入出行者获益损失的不对称偏好,建立了考虑出行者损失厌恶的属性水平的后悔函数及基于Logit形式的随机用户均衡模型.在提出的属性水平的后悔函数中,等尺度的获益和损失所产生的欣喜和后悔的差异,受后悔欣喜偏好参数和出行者损失厌恶共同影响.此外,与上述随机用户均衡模型等价的变分不等式问题被给出,并用相继平均法求解.最后,用1个算例网络来验证所提出模型的合理性和算法的可行性.结果表明,出行者的损失厌恶对其路径选择行为具有较大的影响,并且随着损失厌恶程度的增大,出行者更倾向于选择最短路径.     

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城市道路交通系统是一个同时具有离散和连续动态,并包含大量随机不确定因素的动态系统,具有动态、并发及同步等特征.在目前交通状况日益复杂的情况下,其动态及随机不确定特性愈加明显.对城市道路交通系统进行建模分析,是深入了解交通状况、进行交通诱导及控制的关键.本文在基本Petri网的基础上,将广义随机Petri网(GSPN)与交通流概念相结合,建立了符合交通流概念的动态流随机Petri网(FSPN)模型.该模型可以很好地描述城市道路交通流的动态及随机特性,并能对城市道路交通系统中的某些随机现象作出很好的解析描述.文中针对四相位十字交叉口给出了动态流随机Petri网建模实例;活性分析表明,该模型能有效避免系统并发性带来的死锁现象.最后仿真运行分析和性能分析进一步证明了动态流随机Petri网的有效性.     

基于随机服务过程的物流集货运作机理

为提高物流网络节点(物流中心)的集货运作管理效率,应用随机服务系统理论与方法描述了物流网络节点的集货过程及其特征,与分散运作管理模式进行了对比,研究了物流网络节点集货的运作机理,建立了集货运作机理模型(马尔可夫排队模型)。算例分析结果表明:在同等条件下,与分散运作模式相比,集货运作模式系统各项运行指标具有明显的优势,服务设施利用率提高了23.4%,货物在系统中的平均滞留时间缩短了56.12%;当繁忙程度为90%时,分散运作模式系统运行指标发生急剧变化,而集货运作模式的各项运行指标变化不明显,货物在系统中的平均滞留时间不到分散运作模式下的1/5。     

Technique of Probability Density Function Shape Control for Nonlinear Stochastic Systems

The shape control of probability density function(PDF) of the system state is an important topic in stochastic systems. In this paper, we propose a control technique for PDF shape of the state variable in nonlinear stochastic systems. Firstly, we derive and prove the form of the controller by investigating the Fokker-PlanckKolmogorov(FPK) equation arising from the stochastic system. Secondly, an approach for getting approximate solution of the FPK equation is provided. A special function including some parameters is taken as the approximate stationary solution of the FPK equation. We use nonlinear least square method to solve the parameters in the function, and capture the approximate solution of the FPK equation. Substituting the approximate solution into the form of the controller, we can acquire the PDF shape controller. Lastly, some example simulations are conducted to verify the algorithm.     

MODELING OF NONLINEAR SYSTEMS BY MULTIPLE LINEARIZED MODELS

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