Digital Representation of Structural Response for the Reliability Assessment of Complex Systems

用于复杂系统可靠性评估的结构响应的数字表示目前结构工程的研究方向是基于性能的设计和安全评估标准的发展，这些标准考虑了在估计系统行为和未来载荷条件时的各种不确定性。系统可靠性方法提供了解决这些重要问题的方法。然而，大多数现有的分析可靠性技术在以下方面有一个或多个限制：a)准确地模拟高载荷下的结构行为，b)考虑不同的性能标准，c)识别多个同等重要的失效模式，d)考虑载荷组合。模拟技术与通用有限元程序包相结合的应用为解决许多这些悬而未决的问题提供了强大的潜力。这项研究的目的是开发一种基于模拟的结构系统可靠性评估方法，该方法将真实地模拟结构系统在高载荷下的行为，可在实际情况下实施，并使用高效的算法为复杂结构提供准确的解决方案。对结构系统进行基于模拟的可靠性分析所需的第一个工具是一个准确而高效的非线性分析程序，该程序能够在特定(确定性)条件下对结构的行为进行建模。第二个工具是一个系统的搜索算法，它可以识别考虑载荷和材料特性的随机性的概率主导失效模式。复杂非线性结构响应的闭合解很难获得，只有通过应用有限元方法才能对其行为进行数字表示。在不同载荷强度和材料特性下的响应的点估计通常是通过对牛顿-拉夫森算法的变分来获得的。由于数值误差的累积和这些范围内刚度矩阵的特性，这些点估计可能经常错误地识别极限承载力，并且可能不能准确地模拟荷载曲线的软化部分。在这项研究中，奇异值分解(SVD)方法将与Lanczos算法相结合，用于精确跟踪结构在高荷载下的响应。验证了该方法的有效性、稳健性和稳定性。由于问题的随机性，只能使用可靠性技术来建立结构的安全评估。由于具有多种失效模式的结构的行为最好地以数字形式表示，现代启发式技术可能提供最合适的工具来评估其可靠性。特别是，遗传算法(GA)已被证明为具有多种失效模式的结构的可靠性分析提供了稳健的技术，但由于它们所基于的猎枪搜索策略，可能效率低下。为了提高遗传算法的效率，引入了一种基于遗传精英原理的过滤算子。改进后的遗传算法为复杂结构的可靠性评估、失效模式识别和随机变量控制提供了一种有效的方法。该项目将把先进的计算数学工具引入结构力学领域。这项研究将强调所提出的方法在基于模拟的土木工程结构设计中的应用，尽管它们将适用于各种领域，如电子电路设计和微电子机械系统。对学生进行矩阵计算方法、人工智能和统计计算等学科的培训将是主要目标。这种培训将为未来几代结构工程师提供所需的全面教育，以便在不确定的情况下做出决策并提供现实生活中复杂问题的解决方案。

DIGITAL REPRESENTATION OF STRUCTURAL RESPONSE FOR THE RELIABILITY ASSESSMENT OF COMPLEX SYSTEMSABSTRACTCurrent research efforts in structural engineering are geared toward the development of performance based design and safety evaluation criteria that take into consideration the various uncertainties in estimating system behavior and future loading conditions. System reliability methods provide the means to address these important points. However, most existing analytical reliability techniques have one or more limitations in their ablity to: a) accurately model structural behavior at high loads, b) consider different performance criteria, c) identify multiple equally important failure modes, and d) account for load combinations. The application of simulation techniques in conjunction with general purpose finite element packages provides methods with a strong potential for resolving many of these outstanding issues. The purpose of this research is then to develop a simulation-based method for the reliability assessment of structural systems, which would realistically model their behavior at high loads, be implementable in practical situations, and provide accurate solutions for complex structures using efficient algorithms. The first tool required to perform a simulation-based reliability analysis of a structural system consists of an accurate and efficient nonlinear analysis program capable of modeling the behavior of the structure for a specific (deterministic) set of conditions. The second tool is a systematic search algorithm that can identify probabilistically dominant failure modes accounting for the randomness of loads and material properties. Closed-form solutions for the response of complex nonlinear structures are difficult to obtain and only a digital representation of their behavior is possible through the application of the finite element method. Point estimates of the response under different load intensities and material properties are usually obtained from variations on the Newton-Raphson algorithm. These point estimates may often misidentify the ultimate capacity and may not accurately model the softening part of the loading curve due to the accumulation of numerical errors and because of the properties of the stiffness matrix in these ranges. In this study, the Singular Value Decomposition, SVD, method in combination with the Lanczos algorithm will be used to accurately trace the response of a structure at high loads. The efficiency, robustness, and stability of the proposed method will be demonstrated. Due to the random nature of the problem, the safety assessment of a structure can only be established using reliability techniques. Since the behavior of a structure with several failure modes is best represented in digital form, modern heuristic techniques may provide the most appropriate tools to assess its reliability. In particular, Genetic Algorithms, GA, have been shown to provide robust techniques for the reliability analysis of structures with multiple failure modes but may be inefficient due to the shotgun search strategy that they are based upon. To improve the efficiency of GA, a filtration operator will be introduced based on the principle of genetic elitism. The modified GA will provide an efficient method to estimate the reliability of complex structures, as well as identify its dominant failure modes and controlling random variables. This project will introduce advanced tools of computational mathematics into the field of structural mechanics. The study will stress the application of the proposed methods for the simulation based design of civil engineering structures although they will be applicable to fields as varied as electronic circuit design and Micro-Electro-Mechanical-Systems. Training of students in the subjects of matrix computational methods, artificial intelligence, and statistical computing will be a primary goal. Such training will provide future generations of structural engineers with the well-rounded education needed to make decisions and provide solutions to real life complex problems under uncertainty.