离散变量框架结构的可靠性优化

以框架结构系统的可靠性分析为基础,给出离散变量框架结构可靠性优化的相对差商方法及迭代格式,并用算例证明了该法的有效性及实用性。     

Fuzzy reliability analysis of aseismic structures

The structural reliability analysis taking account of the fuzziness in both earthquake loads and structural resistances is put forward in this paper. For this purpose, the concepts such as fuzzy earthquake intensity, fuzzy response spectrum, fuzzy structural response and satisfaction degree to fuzzy-random constraint are defined. This procedure may be taken as a basis for establishing a more rational optimum design of structures.     

非完整信息条件下的结构可靠性鲁棒设计

在非完整信息条件下,建立区间变量、模糊变量、随机变量同时存在的可靠性设计模型,并给出相应的序列优化设计方法;同时考虑设计变量的实现值与设计值之间的差别以及约束条件的鲁棒性,提出基于info-gap决策理论的鲁棒优化模型,研究可靠性鲁棒设计的序列求解策略。算例1表明:模糊可靠性设计比随机可靠性设计结果保守,当模糊设计指标α=0时(对应区间可靠度)结果最为保守。算例2表明:不同的鲁棒性指标αt对应不同的鲁棒优化解,当αt大于0.20时,不存在相应的鲁棒优化解。利用本文提出的鲁棒序列优化求解方法对目标函数计算1291次即可,而常规优化算法需8107次,表明本文算法大大提高了计算效率。     

桁架结构概率-非概率混合可靠性拓扑优化

研究了桁架结构概率-非概率混合可靠性拓扑优化问题。建立了以结构重量为目标函数、混合可靠性指标为约束条件的拓扑优化数学模型,针对强度为随机变量和应力为区间变量、强度为区间变量和应力为随机变量两种情况推导了可靠性指标对设计变量的灵敏度计算公式。实例结果表明：混合可靠性拓扑优化的截面尺寸和结构重量相对于非概率可靠性优化都更大,使得结构除了能够容许载荷存在一定变异程度外,也允许位移和强度存在一定变异程度。     

论不确定性结构力学的发展

结构力学是直接为工程结构设计服务的,而工程设计中包含大量不确定性因素和信息,包括随机性、模糊性和未确知性信息.由于引用统计数学方法处理随机性问题,在结构力学中产生了可靠性理论和随机振动理论.随着模糊性和未确知性问题的提出和研究,近年来在结构力学中又逐渐形成了一些新的分支,包括结构的不确定性优化设计,广义(模糊随机)可靠性理论,模糊随机振动理论和模糊地震工程学等.本文简要地介绍这四个新的分支的发展情况,主要介绍作者及其学生们的工作,并着重介绍基本概念.      

RELIABILITY-BASED DESIGN OF COMPOSITES UNDER THE MIXED UNCERTAINTIES AND THE OPTIMIZATION ALGORITHM

This paper proposed a reliability design model for composite materials under the mixture of random and interval variables. Together with the inverse reliability analysis technique, the sequential single-loop optimization method is applied to the reliability-based design of composites. In the sequential single-loop optimization, the optimization and the reliability analysis are decoupled to improve the computational efficiency. As shown in examples, the minimum weight problems under the constraint of structural reliability are solved for laminated composites. The Particle Swarm Optimization （PSO） algorithm is utilized to search for the optimal solutions. The design results indicate that, under the mixture of random and interval variables, the method that combines the sequential single-loop optimization and the PSO algorithm can deal effectively with the reliability-based design of composites.     

基于非概率可靠性的结构优化设计研究

基于不确定参量的凸集合描述,研究了考虑非概率可靠性约束时,结构优化设计模型的求解问题。由于非概率可靠性指标是用一个极小极大模型来定义的,故以该指标作为设计约束,将得到一个嵌套的二级优化模型。为了求解该模型,提出了一种序列线性化的计算方法。利用非概率可靠性分析的拉格朗日乘子,逐步构造可靠性指标的一阶近似,通过序列线性规划法求解二级优化问题。该算法可用于区间变量和超椭球凸集模型并存的情形,具有较好的适用性。论文给出了主要的敏度计算公式,并通过简单算例对所提算法进行了验证。     

Multiobjective fuzzy optimum design of antenna structures

On the basis of the recently proposed general fuzzy optimization [1–2], this paper investigates the multiobjective fuzzy optimum design of antenna structures, in which the weight objective, precision objective, lowest frequency objective and safety degree objective are included. This is a successful application of fuzzy optimization to large engineering structures.     

结构系统可靠性优化设计的神经网络方法

针对具有非正态随机参数的可靠性(优化)设计,提出了随机摄动-Edgeworth级数方法,采用该方法将可靠性概率约束转化为等价的确定型约束,可以迅速准确地获得优化设计信息。针对具有多失效模式的结构系统可靠性优化设计,提出了随机模拟一神经网络方法(MCS—NN),将随机模拟方法与神经网络技术有机结合,为结构系统可靠性优化设计提供了一种新方法。     

天线结构多目标模糊优化设计

本文在结构模糊优化设计理论的最新成果——普遍型模糊优化的基础上研究解决了包括重量、精度、动力基频和安全度等目标在内的天线结构多目标模糊优化设计问题,使得天线结构优化更令面、更合理、更实际。这是在计算机上对多变量、多工况、多约束、多目标大型结构进行模糊优化设计的成功应用的实践。     

大型结构可靠性优化设计的大系统方法

首先回顾了基于可靠性的结构设计方法并对其进行了简要的评述;其次介绍了目前正处于热点的大系统设计方法,并提出了应用大系统方法进行大型结构可靠性设计的策略．该策略的主要思路是从结构方案阶段即考虑结构可靠度指标及重量指标的最优分配．一个大型结构可以分解成一系列子系统,而该系统中的每一个又可以分解成一系列二级子系统,直至最基本的子系统．建议对于大型复杂结构,最基本的子系统并非结构元件,而应是能用有限元模型进行基于可靠性优化设计的子结构．      

多层非线性抗震钢结构的损失估计与优化设计

本文通过结构的动力可靠性分析和损失估计建立了以动力可靠性为约束的非线性抗震结构双目标(造价与损失期望)优化设计模型,提出了具体实现这种优化设计思想的实际可行的方法。文中将地震地面运动模拟为平稳过滤有色噪声,建立了以破坏指数刻划的结构体系的模糊震害等级,提出了结构模糊动力可靠性分析和损失估计的具体方法,从而使优化设计模型中各有关量的分析和计算得以具体地实现。     

任意分布参数的梁结构刚度可靠性灵敏度分析

在刚度可靠性设计理论与灵敏度分析方法的基础上,研究了任意分布参数的梁结构刚度可靠性灵敏度分析问题,提出了刚度可靠性灵敏度分析的计算方法,给出了可靠性灵敏度的变化规律,研究了设计参数的改变对梁结构刚度可靠性的影响,为任意分布参数的梁结构刚度可靠性设计提供了理论依据。     

Reliability-based design for soil tillage machines

Using classical design methods for tillage machines does not completely guarantee a safety and satisfactory performance, due in part to the randomness of tillage forces. This randomness is derived from the variability in soil engineering properties and the variations in tool design parameters and operational conditions. In this paper, a reliability-based design approach was developed, for the first time, by integrating the randomness of tillage forces into the design analysis of tillage machines, aiming at achieving reliable machines. The proposed approach was based on the uncertainty analysis of basic random variables and the failure probability of tillage machines. The failure probability was estimated according to two performance criteria related to the structural design requirement and the quality of tillage operation. Two reliability methods, namely the Monte Carlo simulation technique and the first-order reliability methods were used for this purpose. This approach was implemented for the design of a chisel plough shank.The results showed that there were many values of the shank dimensions that guaranteed the required reliability level. However, in order to achieve the best design solution from an economic point of view, minimizing the volume of the shank structure was integrated into the reliability-based design approach. This led to the reduction of the initial volume of the shank structure by 6.86%. It was concluded that integrating the economical constraint into the reliability-based design approach can lead to optimal designs of tillage tools that ensures the required reliability level at low cost.     

结构可靠性优化的三阶段解耦方法

为提高基于可靠性的结构优化效率,提出一种三阶段解耦分析方法。第一阶段利用可靠性安全因子进行确定性优化,并将确定性优化结果作为初始样本点;第二阶段利用可靠性灵敏度和重量因子对样本点进行调整,获取目标函数与失效概率的数据集合;第三阶段利用目标函数与失效概率的关系,曲线获取可接受失效概率对应的目标函数,并求解最终优化设计变量。本文方法只需一次确定性优化,且现有结构可靠性求解算法均可使用,适应性强。算例分析结果表明,本文方法可以明显减少失效概率评估次数,且计算结果对可靠性安全因子与重量因子不敏感。     

结构能度可靠性方法研究

结构系统可靠性研究分随机模型、模糊模型和非概率模型.本文分析了传统随机模型的局限性,利用蒙特卡诺的基本思想.提出了一种新的基于区间分析的模糊可靠性度量体系及分析方法.从物理、几何等方面解释了文中理论的合理性.该方法确定的失效可能度综合了更多的结构有用信息,能够反映结构的实际可靠状态.最后还提出了基于本文可靠性度量方法的结构优化设计模型,通过实例介绍了该方法的具体应用.     

Theory and solution of general fuzzy optimization for structures

In order to consider the overall fuzzy factors and fuzzy information in optimum design of engineering structures, the theory and solution of general fuzzy programming with wide generality are proposed in this paper. On the basis of this programming, an example of structural optimum design with multi-objective is given.     

Non-probabilistic reliability method and reliability-based optimal LQR design for vibration control of structures with uncertain-but-bounded parameters

Uncertainty is inherent and unavoidable in almost all engineering systems. It is of essential significance to deal with uncertainties by means of reliability approach and to achieve a reasonable balance between reliability against uncertainties and system performance in the control design of uncertain systems. Nevertheless, reliability methods which can be used directly for analysis and synthesis of active control of structures in the presence of uncertainties remain to be developed, especially in non-probabilistic uncertainty situations. In the present paper, the issue of vibration con- trol of uncertain structures using linear quadratic regulator （LQR） approach is studied from the viewpoint of reliabil- ity. An efficient non-probabilistic robust reliability method for LQR-based static output feedback robust control of un- certain structures is presented by treating bounded uncertain parameters as interval variables. The optimal vibration con- troller design for uncertain structures is carried out by solv- ing a robust reliability-based optimization problem with the objective to minimize the quadratic performance index. The controller obtained may possess optimum performance un- der the condition that the controlled structure is robustly re- liable with respect to admissible uncertainties. The proposed method provides an essential basis for achieving a balance between robustness and performance in controller design ot uncertain structures. The presented formulations are in the framework of linear matrix inequality and can be carried out conveniently. Two numerical examples are provided to illustrate the effectiveness and feasibility of the present method.     

含模糊变量和区间变量的结构可靠性优化设计方法

提出了基于能度可靠性理论的含模糊变量和区间变量的结构优化设计方法.运用能度可靠性理论建立了含模糊变量和区间变量的结构混合可靠性模型,采用结构的最大失效可能度作为混合模型的可靠性度量,给出最大失效可能度的计算方法,并以混合可靠性模型的最大失效可能度为约束条件建立了混合结构优化设计模型.实例计算表明了本文方法的有效性.     

论不确定性结构力学的发展

结构力学是直接为工程结构设计服务的,而工程设计中包含大量不确定性因素和信息,包括随机性、模糊性和未确知性信息．由于引用统计数学方法处理随机性问题,在结构力学中产生了可靠性理论和随机振动理论．随着模糊性和未确知性问题的提出和研究,近年来在结构力学中又逐渐形成了一些新的分支,包括结构的不确定性优化设计,广义(模糊随机)可靠性理论,模糊随机振动理论和模糊地震工程学等．本文简要地介绍这四个新的分支的发展情况,主要介绍作者及其学生们的工作,并着重介绍基本概念．