Research On Algorithms Of Non-probabilistic Convex Reliability And Its Theories

The reliability of engineering structures is a long-term focus in the engineering industry. The traditional probabilistic or fuzzy reliability analysis has some limitation, which the probability density function or the membership function require adequate amounts of samples in the probability theory or the fuzzy mathematics. However, in practice engineering, only limited data can be obtained or efficient samples need highly expensive studies. Moreover, the structures are under construction or still on the drawing board, probability distribution of parameters of the structures are not yet available, or not agree with the actual situation. So, for a finite number of samples, probability distribution or membership function of parameters are difficult to ascertain, but the bound can easily be determined. This is a reasonable method that the convex model describes this parameters. The non-probabilistic convex reliability is based on the convex model.Since the1990s, with the concept of non-probabilistic convex reliability proposed by Ben-Haim and Elishakoff, scholars have done a lot of research in this field and theory is tend to further perfect but there are still many insufficient, such as some thoughts are mistaken, there is a lack of proper and effective algorithms to solve the reliability index.The fundamental goal of this research work is to present some algorithms for non-probabilistic reliability based on convex model. And there has some research on the correlation of non-probabilistic convex reliability. The main works have completed as follows:(1) A comparative research between traditional reliability and non-probabilistic convex reliability, and the impact on the reliability from the different convex model, have been studied.(2)The gradient projection method is one of the feasible direction method based on constrained optimization. The gradient projection is adopted to solve non-probabilistic reliability index. When the convergence point is not the most possible failure one. the spatial dimensional reduction is proposed.(3) Monte-Carlo Simulation (MCS) is a direct numerical simulation technique, which the amount of computation is huge, and the results are high credibility. For different reliability index, MCS for non-probabilistic reliability is proposed, which provide an exact and reliable test method for other algorithms.(4) Response Surface Method (RSM) is an universal approach for reliability analysis with complex and implicit limit state equation. Combining the gradient projection method, the linear response surface method、the linear weighted response surface method and the second response surface method is orderly presented for non-probabilistic convex reliability.(5) Support Vector Machine (SVM) is a new machine learning method based on Statistic Learning Theory (SLT), it is especially pertinent for small samples. On the basis of Support Vector Classification (SVC) and Support Vector Regression (SVR), the non-probabilistic convex reliability analysis method are proposed and compared, in which the curse of dimensionality is avoided and larger amount of computation and lower efficiency in MCS and RSM are resolved.(6) The independence and correlation among uncertain parameters are there all the time, which is irrelevant to their sample size. This paper preliminarily discusses the independence and correlation about the convex model. The different convex model describes the independence among uncertain parameters, the correlation can only be considered on a convex.