Research In Efficient Algorithms Of Reliability

For all sorts of uncertainties are unavoidable in practical engineering, we do more and more researches in these uncertainties in order to gain a deeper understanding of engineering performance, to understand the requirement of the use function and optimize the structure. Based on the reliability analysis principle.this paper expands the theory of reliability analysis and application of engineering structure.as well deepens the cognition of the reliability, so that these can provide theory support to the design of the real structure using reliability analysis.1. The first part overviews the basic knowledge and professional terms, and details the iterative format and iterative process of six methods of reliability calculation:HL-RF method, improved HL-RF method, adjusting steps method, general computing method,Gauss-Hermite integral method and Monte Carlo method.Through a lot of examples, we draw the following conclusions:improved HL-RF method has a high efficiency, because its total number of function evaluations is smaller. This property can greatly reduce the computing time and computer storage space for the complex structures which need finite element analysis. The adjusting steps method can adjust the iteration step length to achieve convergence in the iterative process. General computing method does not need to calculate partial differentials of the performance function, which is the greatest characteristic of this algorithm. Gauss-Hermite integral method is higher in computational accuracy, lower in computation efficiency and the total number of function evaluations is larger. This algorithm can be applied to those engineering structures which need high accuracy of reliability analysis.2. Performance measure approach (PMA) and Reliability index approach (RIA) are completely equivalent in evaluation of probability constraints. Compared with RIA, PMA is considered to be more efficient, stable and less dependent on the probability distribution of random variable type. And as random variables'distribution types gradually deviate from the normal distribution, the number of function evaluations in PMA is relatively stable. However RIA can not gain the result when the random variables obey uniform distribution. It is more stable and less dependent on the probability distribution of random variable type, which appears particularly important in reliability-based optimization design.3. Under the circumstances of mastering few original data, interval non-probabilistic reliability provides a possible choice for structural reliability analysis. The interval uncertainty analysis includes three kinds of models:non-probabilistic reliability based on interval variables, non-probabilistic reliability based on convex models and probabilistic reliability analysis to tackle the interval uncertainties. The results of non-probabilistic measure of reliability based on convex models is less conservative than non-probabilistic measure of reliability based on interval variables, and most closely to the using the probabilistic reliability analysis to tackle the interval uncertainties.Therefore the non-probabilistic measure of reliability based on convex model analysis is a more economical and reasonable index.