Accurate And Efficient Reliability Analysis Of Complex Structural Engineering Problems

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

Evaluation of Alternative Implementation Methods of Failure Sampling Approach for Structural Reliability Analysis

In this paper, several alternative approaches are used to implement the failure sampling method for structural reliability analysis and are evaluated for effectiveness. Although no theoretical limitation exists as to the types of problems that failure sampling can solve, the method is most competitive for problems that cannot be accurately solved with reliability index-based approaches and for which simulation is needed. These problems tend to have non-smooth limit state boundaries or are otherwise highly nonlinear. Results from numerical integration and three extrapolation approaches using the generalized lambda distribution, Johnson\u27s distribution, and generalized extreme value distribution are compared. A variety of benchmark limit state functions were considered for evaluation where the number of random variables, degree of non-linearity, and level of variance were varied. In addition, special limit state functions as well as two complex engineering problems requiring nonlinear finite element analysis for limit state function evaluation were considered. It was found that best results can be obtained when failure sampling is implemented with an extrapolation technique using Johnson\u27s distribution, rather than with numerical integration or the generalized lambda distribution as originally proposed with the method

Failure Sampling with Optimized Ensemble Approach for the Structural Reliability Analysis of Complex Problems

Failure sampling is a structural reliability method based on modified conditional expectation suitable for complex problems for which reliability index-based approaches are inapplicable and simulation is needed. Such problems tend to have non-smooth limit state boundaries or are otherwise highly nonlinear. Previous studies recommended implementation of failure sampling with an extrapolation technique using Johnson\u27s distribution or the generalized lambda distribution. However, what implementation method works best is problem dependent. The uncertainty of which approach provides best results for a particular problem limits the potential effectiveness of the method. In this study, a solution is proposed to this issue that eliminates this uncertainty. The proposed approach is an optimized ensemble that forms a uniquely-weighted solution by utilizing the predictive capability of multiple curves to maximize accuracy for any particular problem. It was found that the proposed approach produces solutions superior to the methods of implementing failure sampling previously presented in the literature

Effect of Moment Gradient and Load Height With Respect to Centroid on the Reliability of Wide Flange Steel Beams Subject to Elastic Lateral Torsional Buckling

The reliability of doubly-symmetric wide flange steel beams designed to the AISC Specification for Structural Steel Buildings subjected to elastic lateral torsional buckling was evaluated when considering variation in moment gradient and load height. The analysis considers continuous loads on spans subjected to various end moments with supports that are torsionally fixed and laterally supported, without additional intermediate restraints. Dead load, occupancy live load, and beam resistance random variables were considered. Beam lateral torsional buckling resistance was evaluated from numerical solution of a fundamental differential equation that accounts for the effect of moment gradient and load height. In some cases, it was found that use of the AISC design procedure results in significant inaccuracies for estimation of elastic lateral torsional buckling resistance, where underestimations occur in regions of reverse curvature bending and when loads are placed below the beam shear center, while large overestimations can occur when loads are placed above the beam shear center. These discrepancies result in significant variation in beam reliability. However, the use of accurate equivalent uniform moment factors can restore uniformity in notional reliability level