β分布在岩土工程模糊可靠性分析中的应用

Application of β distribution in fuzzy reliability analysis of geotechnical engineering

基于概率论,给出了一种模糊可靠性指标的计算模型.选用分布区域有限的β分布作为随机变量的概率分布类型,由功能函数中随机变量的相关数据确定模糊事件的"模糊临界区间".将β分布函数引入到模糊失效事件的隶属函数中,使隶属函数具有在整个定义域上光滑、曲线中心对称的特点.针对岩土工程问题中功能函数较简单的情况,推导出计算模糊事件失效概率的具体表达式.通过实例得出了竖向承载桩承载力的模糊失效概率与相应的可靠性指标.计算实例表明,本方法在进行可靠性分析中具有精度高、计算简便等优点.

Based on the probability theory, a model to calculate the fuzzy reliability index was presented. β distribution of which boundary is finite is chosen to fit the random variables. The ＂fuzzy critical section＂ is determined on the basis of the data of random variables in performance function. β distribution function is introduced to determine the membership function of a fuzzy failure event. Therefore, the membership function is smooth within its domain, and has the characteristic of center symmetry. By utilizing the character of performance functions which are relatively simple in geoteehnieal problems, an explicit formula to estimate the fuzzy failure probability is derived. The fuzzy failure probability of the bearing capacity of axially loaded piles and the corresponding reliability index are given as an instance. It is demonstrated through the example that the method presented in this paper is proved to have the advantages of high accuracy and simple computation.