چكيده به لاتين
Uncertainty is an integral part of an engineering system and any design and analysis without considering these uncertainties is deficient. Reliability analysis based on probability theory is one of the existing tools to analyze the effect of uncertainties on the engineering systems. Commonly because of high computational burden or low accuracy, these methods have not yet been widely used in practical engineering issues; but by continual increase of computers’ computational power on one hand and improvement of reliability methods on the other hand, reliability-based analysis and design are becoming indispensable in an engineering process.
Methods based on random populations that are also known as simulation methods form one group of reliability analysis methods. One of the challenges that these methods deal with is the high computational cost. Numerous advanced simulation methods with better performance and lower computational expenses than the primary methods have so far been put forward. With this regard, the main objective of the present dissertation is to improve the existing simulation methods. In the following, four improved simulation methods are proposed and their performance is examined and compared with existing methods through well-known benchmark problems. In one of the proposed approaches, directional sampling in combination with the importance sampling forms an adaptive simulation technique. In another effort, using the Markov chain in conjunction with a newly proposed adaptive importance sampling technique, a method with far better performance than the original importance sampling method is created. As another case, a new line sampling with adaptability is proposed which shows acceptable performance and finally, employing the Monte Carlo simulation, the accuracy of the first order reliability method is improved and on the other hand, the computational burden of Monte Carlo method is decreased. Performance and efficiency of each of these methods is examined via mathematical and structural limit states and compared to existing methods. At the end of each chapter corresponding to each method, the method is employed to solve a reliability based design optimization of planar truss with deterministic and probabilistic constraints. At the conclusion section, all of the four methods are compared and their strength and weaknesses are counted.
