【作者】 田明俊；

【导师】 周晶；

【作者基本信息】 大连理工大学 ， 水工结构工程， 2006， 博士

【摘要】 本文在分析现有反演问题求解方法的基础上,针对智能反演中存在的搜索早熟及计算量大等困难,将一些新颖智能算法引入工程反问题求解领域,开展了智能反演方法的研究。本文的主要研究工作如下: 阐述了本文的选题背景及意义,对岩土工程中反问题研究的发展现状进行简单回顾,对反问题求解方法进行了较详细的分类,指出智能反演方法研究是反演方法研究的一个重要内容,改善算法早熟收敛现象、减少计算量及提高结果可信度是智能反演方法研究所要解决的问题,确定了本文的研究内容。 介绍了新近为求解复杂组合优化问题而提出的蚁群算法及其研究现状,尝试将其运用于结构参数的反演计算。为此,先对待反演参数的搜索空间进行离散,将参数反演问题转化成一个组合优化问题,并对参数组合优化问题与一般优化问题的计算量进行了比较,指出前者的计算量远远小于后者,然后针对结构参数反演问题的特点,改进蚁群算法,重新定义了算法参数的内涵,建立了蚁群算法反演结构参数的计算格式。计算表明,改进蚁群算法可有效地求解结构参数反演问题,有较强的抗噪能力,并能较好地改善搜索的早熟现象。 对粒子群算法理论及应用研究发展现状进行了阐述,总结了该算法的优点及不足,在此基础上,通过数学分析,给出了保证算法收敛的参数取值范围。为了使粒子群算法能更有效地进行结构参数的反演计算,构建了一种以时间和目标函数标准差为自变量的动态惯性权重计算式,并充分利用粒子群算法的特点,提出了一种约束自适应方法。算例表明,粒子群算法一般只需较小的种群规模和较少的迭代次数就可以得到问题较好的解,计算量小,收敛较快,在减少反问题计算量方面有一定的优势。 发展基于智能算法的混合反演方法的研究,是提高反演解的精度和提高计算效率的有效途径。在对各种混合结构形式进行比较分析的基础上,选择镶嵌结构形式将粒子群算法与单纯形法混合,构成参数识别的粒子单纯形法,并提出了一种以时间和目标函数值标准差为变量的混合概率函数计算式,使得混合算法能适时地进行混合,提高了算法求解精度而不至于过大地提高计算量。在指出算子与算法的混合能进一步减少反演计算量的基础上,将基于浓度和适应度的双重选择机制—免疫选择机制引入到粒子群算法中,构成了一种参数识别的免疫粒子群算法。用算例验证了两种混合方法的有效性。 为了提高反演结果的可信度,分析了参数反演结果失真的原因,并定义了参数反演的局部模型和全局模型,讨论了提高反演结果可信度的方法。从有限元平衡方程出发,分多种情况讨论了保证反演计算结果唯一的条件,在此基础上提出了补偿观测信息的虚拟位移法,并提出了结构参数识别的子域法,以减少反演计算量。计算表明,虚拟位移法能充分地利用先验信息,提高了反演结果的可信度。 最后,总结了本文的主要研究内容及成果,并对有待进一步研究的问题进行了展望。更多还原

【Abstract】 In order to improve premature convergence and reduce calculation cost of inversion, this dissertation is devoted to studying intelligent inversion algorithms based on some novel intelligent algorithms considering some inverse problems existing in civil engineering.Based on the extensive investigation of the literature, research situation of inverse problems in geotechnical engineering is summarized. Inversion algorithms existing in different subjects are classified in detail. Among these algorithms, intelligent inversion algorithms are one of main research directions in the study of inverse problems. Premature convergence, enormous calculation cost and reliability of solution are realized the main existing problems in intelligent inversion algorithms. The significance of this dissertation is expounded and the research methods are determined.In order to improve premature convergence existing in current intelligent inversion algorithms, Ant Colony Algorithm, a new simulating evolutionary algorithm proposed recently for solving hard combinatorial optimization problems, is introduced and modified for parameter inversion in civil engineering. For the purpose applying Ant Colony Algorithm to parameter inversion, the search space of parameters to be inversed is discretized firstly so that inverse problem is transformed into a combinatorial optimization problem. And then Ant Colony Algorithm is modified by replacing tour length and visibility in it with objective function value and standard deviation of objective function value respectively. The results of a numerical simulation show that the modified Ant Colony Algorithm can improve premature efficiently.Particle Swarm Optimization, a new simulating evolutionary algorithm proposed recently, is suggested to reduce the calculation cost of solving inverse problems. The principle and the main characteristics of Particle Swarm Optimization are introduced, and the advantages and weaknesses of this novel optimizer are summarized. A theoretical analysis on the convergence behavior of it is carried out and the value ranges of parameters guarantee the convergence of the algorithm is given. Particle Swarm Optimization is modified so that it can solve inverse problems more efficiently. The auto-adaptive ability of origin algorithm to the constraint conditions is increased and an expression of dynamic inertia weight is proposed. Numerical results show that Particle Swarm Optimization can quickly locate the optimum with a small population size and it can reduce calculation cost of solving inverse problems efficiently.For hybrid algorithms can take advantages of sub-algorithms in it, hybrid optimization strategies are suggested to solve inverse problems. Two types of hybrid algorithms based on intelligent algorithms are proposed. Firstly, simplex method is chosen and combined with Particle Swarm Optimization to improve local searching ability of Particle Swarm Optimization. Based on the compare of different types of hybrid frameworks for hybrid algorithms, the inlaid framework is chosen to combine these two algorithms. And a hybrid probability function depended on time and standard deviation of objective function value ispresented to improve the efficiency of solutions. Secondly, immune selection mechanism is chosen and combined with Particle Swarm Optimization to reduce calculation cost. Both of these two hybrid algorithms were applied to parameter inversion in civil engineering. Numerical results show that hybrid algorithms are of strong ability to obtain global minima, and its performances are superior to those of single methods.In order to improve the reliability of inverse result, the numerical approximation method is adopted to analysis reasons for the distortion of inverse result. And local model and global model for parameter inversion are defined. According to the balance equation of finite element method, the conditions that must be satisfied to avoid the nonuniqueness of inverse result are discussed. According to these conditions, two kinds of method are proposed and applied to parameters inversion. One is virtual displacement method. It can compensate the deficiency of observed data to improve the reliability of inverse result. Another is sub-region method. For only part of analysis object is calculated in this method, it can reduce calculation cost. The results of an example show that the virtual displacement method is of strong ability to obtain global minima, and it can improve the reliability of inverse result efficiently.The main contributions are summarized and further works are suggested at the end of this dissertation,更多还原