Reliability-based Design Of Mechanical With The Mixture Of Fuzzy And Interval Variables

Structural analysis and design model is usually built on determinate physical significance and treats with factors as certain variables in analysis process. However, some unavoidable uncertainties exist in actual engineering structural reliability analysis and design, such as that of material and geometrical properties, loads, and so on. If we consider these uncertain factors as determinate ones, incompatible or unreasonable results often come into being, it means that structural analysis of the project had to consider these uncertainties.For there are uncertainties consist in practical engineering, the paper attempts to address this issue by proposing a RBD(Reliability-Based Design) method to deal with the uncertain variables characterized by the mixture of fuzzy and intervals. First, transformation the fuzzy variable into equivalent normal random variables, introduce the approach to determining the expected values of an equivalent normal random variable in transforming a fuzzy variable with an arbitrary universe of discourse into its equivalent normal random variable in a mechanical system.With reliability as a constraint condition,establishing the Reliability Optimization Design Model with the mixed variables ,and the model is a double-loop procedure. As the reliability is considered under the condition of the worst combination case of interval variables, the computational demand of RBD with random and interval mixture variables may increase dramatically for identifying the worst case of interval variables. To lower the computational burden, a sequential single-loop procedure is employed to replace the computationally expensive double-loop procedure when the worst case scenario is applied directly. With the proposed method, the RBD is conducted within a series of cycles of deterministic optimization and reliability analysis. The optimization model in every cycle is built on the most probable point under the worst combination case of the interval variables obtained from the reliability analysis in the previous cycle. Since the optimization is decoupled from the probabilistic analysis, the computational amount for reliability analysis is decreased to the minimum extent. In this paper, the Max-min ant colony optimization algorithm is used to optimize the objective function. Two engineering examples show the feasibility and validity of the proposed method.