Menghui Xu

Mixed Nonprobabilistic Reliability-Based Optimization Method for Heat Transfer System With Fuzzy and Interval Parameters

By combining the nonprobabilistic reliability theory with optimization design approach, this paper proposes a mixed reliability-based optimization method for the heat transfer system design with both fuzzy and interval parameters in material property, external load, and boundary condition. Fuzzy variables are used to represent subjective uncertainties associated with expert opinions; whereas, interval variables are adopted to quantify objective uncertainties with limited information. Based on the level-cut strategy, the mixed uncertain problem is transformed into a pure interval problem first. Then, a modified reliability analysis method using an interval ranking strategy and integral operation is presented to precisely assess the system safety possibility. Subsequently, a mixed reliability-based optimization model with fuzzy and interval parameters is established, which is a nested optimization problem with huge computational cost. A subinterval perturbation method is eventually presented for temperature field prediction, which can replace the inner loop optimization and improve the computational efficiency. A transient heat conduction example about a three-layer thermal structure verifies the superiority of the proposed model and method for mixed reliability analysis and optimization in practical engineering.

An Iterative Dimension-Wise Approach to the Structural Analysis with Interval Uncertainties

The structural analysis is inevitably surrounded with uncertainties and the interval analysis is a favorable method if insufficient data is available on uncertainties. The accuracy of current interval analysis methods including the interval perturbation method (IPM), subinterval perturbation method (SIPM) and dimension-wise approach (DWA) depends on a reference point (RP), e.g., the expansion point in IPM, for some problems due to ignoring the co-operative effects of multiple interval inputs on the response. To this end, an iterative dimension-wise approach (IDWA) is proposed. Either the minimal or maximal input vector of the response is identified as an RP by a global update in which a novel RP is dimension-wisely assembled by the minimal or maximal points of all sectional curves of the response surface at a previous RP through a local update. The interval response is calculated by deterministic solvers at the minimal and maximal input vectors. An acoustic analysis problem is studied eventually to valida...