结构可靠度优化设计的高效稳健算法研究

发布时间：2018-09-08 18:09

【摘要】：实际工程中存在着大量的不确定性因素,例如载荷环境、材料属性、几何形状、初始条件、制造公差、边界条件等。可靠度理论从概率的角度对结构的安全程度进行评估。而可靠度优化是在可靠度概念的基础上,借助优化技术对产品在保障安全性能的前提下实现结构造价或某些性能方面的最优设计。可靠度优化本质上是一个双层嵌套的迭代求解过程,需要同时处理可靠度分析和外层优化的整体性能。计算精度、求解效率以及算法的稳健性是可靠度优化方法最重要的三个因素,目前学者们围绕这三个方面做了大量研究,形成了包含双循环方法、解耦法以及单循环算法在内的三大类优化算法。然而这些方法在处理强非线性功能函数、非正态随机变量、大变异系数等问题的时候容易出现收敛速度过慢甚至不收敛现象。因此,提出一种效率高、稳健性好以及适用范围广的方法具有重要的理论和实际意义。本文将从内层可靠度／逆可靠度分析出发,提出高效、稳健的可靠度/逆可靠度计算方法,并在此基础上由内而外逐步深入探索计算性能更好的结构可靠度优化方法。1.提出了基于修正混沌控制的HL-RF可靠度指标计算方法。深入研究了HL-RF迭代格式在处理非正态随机变量或强非线性功能函数时不收敛的机理,通过调整迭代点在不同方向上的步长控制,极大改善了可靠度分析的稳健性的同时提高了计算效率。此外,引入了功能函数类型的判定准则,实现了对迭代点振荡现象判定。通过对不同算法的比较,验证了修正的混沌控制方法具有更好的效率和稳健性。2.针对包含凹功能函数可靠度优化计算的不收敛问题进行研究,提出了基于混合混沌控制的序列优化与可靠性评定方法。首先研究了凹功能函数迭代的失效机理,指出了逆可靠度分析迭代点振荡具有方向性,进一步建立了修正的混沌控制方法,使得凹函数逆可靠度问题的计算效率大幅提高。然后引入共轭均值法的函数判定准则,提出了混合混沌控制方法,完成了对于凸函数和凹函数问题的高效计算。最后,将混合混沌控制方法与序列优化与可靠性评定方法结合,实现了包含凹功能函数可靠度优化问题高效、稳定的求解。3.针对包含多个不同功能函数类型的可靠度优化问题,提出了自适应混合循环算法。首先在修正混沌控制方法的基础上,通过结构响应的非线性程度与迭代向量夹角之间的关系构造了自适应混沌控制的方法,克服了修正混沌控制方法对于控制因子的依赖性。然后构建了设计变量振荡的判定准则,将单层循环方法的高效性和双层优化方法的稳健性结合起来,避免了设计者对于黑箱函数的算法选择困难,直接实现对包含不同类型功能函数优化模型高效、稳定的计算。4.针对含有多个局部最优点和高非线性约束的加筋柱壳结构,构造了基于自适应混沌算法、代理模型和演化算法的全局可靠度优化方法,实现了含几何缺陷加筋柱壳结构的可靠度优化设计。首先利用自适应混沌控制进行快速逆可靠度分析,然后采用粒子群算法良好的全局搜索能力和代理模型计算量较小的特点,建立了快速的全局寻优方法。继而采用最优点更新准则对代理模型局部精度逐步更新,形成了包括可靠度分析、全局优化搜索和代理模型更新策略在内三层嵌套的优化设计流程,并用标准数值算例验证其有效性。最后对含缺陷的加筋柱壳结构进行建模和求解,同时与确定性优化设计和初始设计的对比,发现可靠度优化设计比两者具有更好的经济效益和安全性能。
[Abstract]:There are many uncertainties in practical engineering, such as load environment, material property, geometry shape, initial condition, manufacturing tolerance, boundary condition and so on. Reliability theory evaluates the safety degree of structure from the perspective of probability. Reliability optimization is based on the concept of reliability, with the help of optimization technology to guarantee the product. Reliability optimization is essentially a two-layer nested iterative solution process that deals with both reliability analysis and the overall performance of the outer optimization. Computational accuracy, solution efficiency and algorithm robustness are the three most important aspects of reliability optimization methods. At present, scholars have done a lot of research on these three aspects, forming three kinds of optimization algorithms including double-cycle method, decoupling method and single-cycle algorithm. However, these methods tend to converge very slowly when dealing with strong nonlinear function, non-normal random variables, large coefficient of variation and other problems. Therefore, it is of great theoretical and practical significance to propose a method with high efficiency, good robustness and wide application. In this paper, an efficient and robust reliability/inverse reliability calculation method is proposed based on the analysis of internal reliability/inverse reliability, and the calculation performance is explored step by step from inside to outside. An improved method for structural reliability optimization is proposed. 1. A method for calculating HL-RF reliability index based on modified chaotic control is proposed. The mechanism of non-convergence of HL-RF iteration scheme in dealing with non-normal random variables or strongly nonlinear function functions is studied. The reliability is greatly improved by adjusting the step-size control of iteration points in different directions. In addition, the criterion of function type is introduced to judge the oscillation phenomena of iteration points. The comparison of different algorithms shows that the modified chaos control method has better efficiency and robustness. The convergence problem is studied and a method of sequence optimization and reliability evaluation based on hybrid chaos control is proposed. Firstly, the failure mechanism of concave function iteration is studied, and the directionality of oscillation of iteration point in inverse reliability analysis is pointed out. By introducing the function criterion of the conjugate mean method, a hybrid chaotic control method is proposed, which completes the efficient computation of convex and concave function problems. Finally, the hybrid chaotic control method is combined with sequence optimization and reliability evaluation method to realize the reliability optimization problem with concave function. 3. An adaptive hybrid cycle algorithm is proposed for reliability optimization problems involving multiple different function types. Firstly, based on the modified chaotic control method, an adaptive chaotic control method is constructed by the relationship between the nonlinear degree of structural response and the angle between iterative vectors, which overcomes the modified chaotic control method. Secondly, a criterion for determining the oscillation of design variables is constructed, which combines the efficiency of the single-layer cyclic method with the robustness of the double-layer optimization method, avoiding the difficulty for the designer to select the black-box function algorithm and directly realizing the high efficiency and stability of the optimization model with different types of function. 4. For stiffened cylindrical shells with multiple local optimum points and high nonlinear constraints, a global reliability optimization method based on adaptive chaos algorithm, proxy model and evolutionary algorithm is constructed. Reliability optimization design of stiffened cylindrical shells with geometric imperfections is realized. Firstly, adaptive chaos control is used for fast invertibility. Reliability analysis is carried out, and then a fast global optimization method is established based on the good global search ability of particle swarm optimization and the small amount of computation of agent model. Finally, a three-layer nested optimization design process is presented to verify the effectiveness of the proposed method, and a numerical example is given to demonstrate the effectiveness of the proposed method.
【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TB472

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