Hybrid Reliability Analysis For Structure With Fluctuant Distribution Parameters And Its Application

Reliability is an important performance index of the mechanical equipments, engineering facilities, etc. Most of the traditional reliability analysis methods are used in a certain condition to get the structural reliability index. But there is a lot of uncertainty in the real world, such as the actual conditions of the machine do not meet the requirements of the guidebook, or those variables which should be constants in theory fluctuate in the actual present. These all require reliability analysis algorithm of the ability to cope with complex situation as to solve practical problems better.Based on the above ideas, we try to solve the probability-Interval hybrid reliability problems with volatility distribution parameters, the main contents are as follows:1. We analysed the model for hybrid reliability problems. This model is a double-nested optimization problem, the outer circle searches in the space of interval parameters, the inner circle searches in the design variable space, which made reference to the traditional reliability analysis techniques, such as: reliability index method, performance measure approach.2. During the process of constructing the hybrid model, we found that the monotonicity of cumulative probability function to it's distribution parameters will lead to some kind of law which affect the mapping of limit state curve from the original space to the standard normal space. This paper analyzes monotony of the cumulative probability function to the distribution parameters, which covers a variety type of probability distribution commonly used in the projects. This lead to two properties, which proved that the extreme value of reliability index will only occur on the border of parameter interval, when the distributed parameter is volatility.3. According to the proposed properties, we make some improvements to the original hybrid model algorithm, which including: with first-order Taylor expansion to simulate the limit state equation, we simplified the optimization problem in the distribution parameter space; we decoupled the original double-nested optimization problem, from double-nested iteration to parallel search. The improved method has been used in several numerical and engineering examples to verify the validity of the algorithm. 4. Sensitivity analysis could help designer to distinguish the parameter which have a major impact on the target performance from those who are not very useful for the design objectives. Traditional sensitivity analysis method gets the sensitivity index often at the cost of a large number of reliability calculation. For the question of this paper, we try to get the analytical expression of the reliability-sensitive index directly, avoid the traditional strategy. This paper lists the analytical expression for six categories of sensitive index. Based on this result, we can get the sensitivity index from only one time of reliability analysis. Practical examples demonstrate the efficiency and accuracy of the algorithm.