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System reliability analysis of structures subjected to fatigue induced sequential failures using evolutionary algorithms

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Title: System reliability analysis of structures subjected to fatigue induced sequential failures using evolutionary algorithms
Author(s): Kurtz, Nolan S.
Advisor(s): Song, Junho
Department / Program: Civil & Environmental Eng
Discipline: Civil Engineering
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: M.S.
Genre: Thesis
Subject(s): system reliability analysis genetic algorithms Non-dominated based Sorting Genetic Algorithm II (NSGA-II) Monte Carlo Simulation (MCS) sequential failures structural reliability fatigue multi-objective optimization dominant failure mode search inspection cycle progressive collapse
Abstract: In the past, many catastrophic failures have occurred due to lack of redundancy and managerial oversight. For example, it was found that local failures due to improper welds that connected the suspended truss to the anchor trusses caused the collapse of the Grand Sung-Soo Bridge in Seoul, South Korea on October 21, 1994. Due to a lack of structural redundancy, the initial bridge rib failure was followed by other bridge failures leading to system collapse. With proper system reliability analysis, such cascading failures could be foreseen by stakeholders. To help make better risk-informed decisions, system reliability methods have been developed to analyze general structures subjected to the risk of cascading system-level failures caused by local fatigue-induced failures. For efficient reliability analysis of such complex system problems, many research efforts have been made to identify critical failure sequences with significant likelihoods by an event-tree search coupled with system reliability analyses: however, this approach is time-consuming or intractable due to repeated calculations of the probabilities of innumerable failure modes, which often necessitates using heuristic assumptions or simplifications. Recently, a decoupled approach was proposed: critical failure modes are first identified in the space of random variables without system reliability analyses or an event-tree search, then an efficient system reliability analysis was performed to compute the system failure probability based on the identified modes. In order to identify critical failure modes in the decreasing order of their relative contributions to the system failure probability, a simulation-based selective searching technique was developed by use of a genetic algorithm. The system failure probability was then computed by a multi-scale system reliability method that can account for the statistical dependence among the component events as well as among the identified failure modes. Part of this work presents this decoupled approach in detail and demonstrates its applicability to complex bridge structural systems that are subjected to the risk of cascading failures induced by fatigue. Using a recursive formulation for describing limit-states of local fatigue cracking, the system failure event is described as a disjoint cut-set event. Critical cut-sets, i.e. failure sequences with significant likelihood are identified by the selective searching technique using a genetic algorithm. Then, the probabilities of the cut-sets are computed by use of crude Monte Carlo simulations. Owing to the mutual exclusiveness of the cut-sets, the lower-bound on the system cascading failure probability is obtained by a simple addition of the cut-set probabilities. A numerical example of a bridge structure demonstrates that the proposed search method skillfully identifies the dominant failure modes contributing most to the system failure probability, and the system reliability analysis method accurately evaluates the system failure probability with statistical dependence fully considered. An example bridge with approximately 100 truss elements is considered to investigate the applicability of the method to realistic large-size structures. The efficiency and accuracy of the method are demonstrated through comparison with Monte Carlo simulations. The aforementioned system reliability analysis is based off of an a priori inspection cycle time and computes the probability that the time until the system failure is smaller than the given inspection cycle. Since most field practitioners do not know this value beforehand, a new method has been developed to perform simplified reliability analysis for many performance levels simultaneously. The First-Order Reliability Method (FORM) is often used for structural reliability analysis. The proposed method uses a multi-objective genetic algorithm, called Non-dominated based Sorting Genetic Algorithm II (NSGA II) to perform many FORM analyses simultaneously to generate a Pareto Surface of design points. From this Pareto surface, data on cases of “critical but unlikely failures” for short inspection cycle times and cases of “less-critical but highly likely failures” for long inspection cycle times can be found at once. From the nature of this method, this approach is termed as “Multi-Objective” FORM. Part of this work presents this Multi-objective FORM in detail. The applicability of this approach is shown through two numerical examples. The first example is a general situation with few random variables. The second example analyzes a statically indeterminate truss subjected to cyclic loading. Both numerical examples are validated with crude-MCS results and show that the method can find a full Pareto Surface, which provides reliability analysis results at a range of performance levels along with the probability distribution of the performance quantity.
Issue Date: 2011-01-21
URI: http://hdl.handle.net/2142/18514
Rights Information: Copyright 2010 Nolan Kurtz
Date Available in IDEALS: 2011-01-21
2013-01-22
Date Deposited: 2010-12
 

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