时变可靠性的区间PHI2分析方法

The interval PHI2 analysis method for time-dependent reliability

时变可靠性问题中存在大量不确定性参数,对其进行不确定建模及时变可靠性分析具有重要的工程意义.传统方法评估承受随机载荷作用的结构可靠性时,通常假定强度、刚度、阻尼等随机变量的分布参数是确定的,但是实际工程中很多情况难以给出分布参数的精确值.本文针对分布参数为区间的一类随机不确定性问题,提出了一种求解时变可靠性的区间PHI2方法(简称I-PHI2),可获得结构在设计周期内的时变可靠性区间.首先,针对分布参数为区间的不确定性问题建立时变可靠性分析模型;其次,采用区间分析方法确定随机变量和随机过程的区间分布参数,同时对其进行标准化处理;再次,推导了含区间参数的跨越率解析表达式,获得了跨越率的上下边界;最后,采用传统的时不变可靠性工具一次二阶矩方法进行求解,获得了结构时变可靠度指标和失效概率的区间.通过两个数值算例验证了I-PHI2方法的有效性.

The uncertainty modeling and time-dependent reliability of inherently uncertain parameters is very important in under stochastic loadings through traditional methods, analysis for time-dependent structures with a large number engineering. When evaluating the reliability of structures the distribution parameters of random variables, such as strength, stiffness and damping, are usually determined, but the accurate value of distribution parameters can hardly be known in practical engineering. In this paper an interval PHI2 （I-PHI2） method is proposed to solve the time-dependent reliability for random problems with the {nterval distribution parameters. I-PHI2 method can provide the reliability interval for assessing design reliability over the whole lifecycle of uncertain structures. Firstly, the time-dependent reliability analysis model is built for uncertain problem of interval distribution parameters. Secondly, the interval distribution parameters of random variables and stochastic processes are determined by use of the interval analysis method and then transferred into the standard coordinate space. Thirdly, the analytical expression of out-crossing rate in which there are many interval parameters are derived and the corresponding upper and lower bounds of out-crossing rate can be obtained. Finally, based on the traditional time-independent reliability tools such as FORM, an efficient algorithm for time-dependent structure is developed to obtain the upper and lower bounds of time-dependent reliability index and failure probability. Two numerical examples are presented for verification of the validity of I-PHI2 method.