Research On Non-probabilistic Algorithms For Reliability Of Structures And Systems

The fuzzy random reliability, profust reliability and non-probabilistic reliability are studied in this paper. Firstly, equivalence between three fuzzy random reliability formulas available, an objective membership function which could impersonally characterizes the ambiguity of a structure's performance and non-probabilistic reliability index of a convex model are put forward or established based on analytical justifications. Secondly, an analytical method and a one-dimensional optimization algorithm for getting the non-probabilistic reliability index are developed to replace approaches. Finally, traditional Response Surface Method is incorporated into the analytical method and the one-dimensional optimization algorithm, which brings up a new response surface method with different theoretical principle from the former. The main ideas of this paper are as follows:1. Based on the discrete weighted average formula for the fuzzy random reliability, a continuous one is developed. Equivalences between the continuous weighted average formula both the fuzzy event formula and the weighted average formula are proved. The two equivalences illustrate that the three formula are coherent in theory, which enable us to select the most efficient one for calculating fuzzy random reliability of a structure, and the most efficient one is undoubtedly the continuous weighted average formula.2. An equivalent transformation implicated in the three formulas for fuzzy random reliability is pointed out definitely, which enable us to determine the mean for a normal random variable equivalent to a fuzzy variable. And then, a method by which a fuzzy variable can be transformed into its equivalent normal random variable is put forward, and the method follows the entropy conservation principle.3. A new methodology for constructing an impersonality membership function is developed founded on three specialities requisite for a membership function which objectively characterizes the ambiguity of a structure's performance. The impersonality membership function can be obtained from a definite integral of probability density function of random subset's boundary point, under the condition that the boundary point is regarded as linear function of performance function.4. Founded on a functional proof that 2 norm of a non-zero vector invariably less than its l_∞norm, an analytical method and a one-dimensional optimization algorithm for getting the non-probabilistic reliability index are developed. Moreover, the of the...