Access Type

Open Access Dissertation

Date of Award

January 2015

Degree Type

Dissertation

Degree Name

Ph.D.

Department

Civil and Environmental Engineering

First Advisor

Christopher D. Eamon

Abstract

ABSTRACT

ACCURATE AND EFFIFICIENT RELIABILITY ANALYSIS OF COMPLEX STRUCTURAL ENGINEERING PROBLEMS

by

KAPIL DILIP PATKI

December 2015

Advisor: Dr. Christopher Douglas Eamon

Major: Civil Engineering

Degree: Doctor of Philosophy

Accurate probabilistic analysis of complex engineering problems with reasonable computational effort is a popular area of research in structural reliability analysis. For probabilistically complex problems such as those involving nonlinear FE analysis; traditional simulation methods often require unfeasibly great computational effort, while low-cost reliability index approaches may lack sufficient accuracy. This dissertation report addresses this issue by developing a simulation-based method referred to as Advanced Failure Sampling (FS).

In this research, the Advanced FS Method is developed with an objective to solve complex structural reliability problems with reasonable computational effort. In order to achieve this, a thorough evaluation of this method is conducted. This research report suggests and explores various techniques needed to implement to transform the existing FS method into a complete, robust algorithm for reliability analysis; the Enhanced FS approach. These enhancements include: developing an optimal algorithm for construction of probability density function (PDF) of resistance samples; determining a more efficient way to simulate the resistance samples; and determining the optimal interval size for a typical resistance sample size of 1000. The process of developing an optimal algorithm for constructing a PDF estimate of the resistance samples included exploring the use of various curve-fit methods and developing an optimized ensemble technique to maximize accuracy of the failure probability calculation. The Markov Chain Monte Carlo method was investigated with an aim to further reduce the computational effort of FS. Moreover, to evaluate the effectiveness of these suggestions, a database of test problems is described and presented in this report. These problems are solved with the FS method using the different techniques suggested above to guide and validate formulation of the Enhanced FS approach. The test problems include a wide variety of limit states that were designed to consider different parameters of interest such as: number of random variables (RVs); degree of nonlinearity; level of variance; and type of RV probability distribution. The method was also validated further for complex realistic engineering problems requiring finite element analysis. The results obtained from the research indicate that significantly better results for a wide variety of problems can be obtained when FS is implemented with a curve fit technique using the JSD distribution; in the Enhanced FS approach, rather than the NI and GLD methods as originally implemented in FS. It was observed that the optimized ensemble further reduced the lowest effective error (obtained from finding the minimum of errors due to JSD, GLD & GEV) in most cases, and was found to be more effective than the use of a single curve alone. It was found that the Advanced FS Method has the capabilities of producing accurate and efficient results for complex, computationally demanding reliability problems for which traditional methods may provide unacceptably inaccurate or unfeasibly computationally costly solutions.

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