Abstract Summary
Structural optimization is the process of identifying the optimal set of design parameters for a structural system. Optimization technique provides an effective approach for rationally improving engineering structural design, both for structural system with deterministic and uncertain parameters. Moreover, it is unanimously agreed that in engineering design applications, knowledge about a planned system is never comprehensive. Therefore, these uncertainties resulting from incomplete information are often assessed probabilistically. In this probabilistic framework, the system design process is referred to as stochastic system design, and the concomitant design optimization problem is alluded to as stochastic optimization. The stochastic optimization process has been widely used in civil, mechanical, and aeronautical engineering designs. Available stochastic system optimization approaches include two stage approaches where initially the performance measure is approximated either by Taylor series approximation or the metamodels and in second stage the approximated performance function is optimized by implementing the available optimization techniques such as nonlinear programming methods, gradient based methods, metaheuristic methods, etc. These aforementioned approaches can effectively take into account the uncertainties but still, achieving higher accuracy and lower computational cost remains a challenging task for designing complex and realistic structural systems. This is also true for the complex deterministic structural systems. To obliviate these aforementioned limitations, an iterative simulation-based approach know as Stochastic Subset Optimization (SSO) is adopted and improved to more effectively determine the optimal design parameter of the system in the present study. The basic principle in original SSO is the formulation of an augmented problem where the design variables are artificially considered as uncertain. Then the design space size is reduced by iteratively identifying a subset of the original design space that has high plausibility of containing the optimal design variables. However, the success of the approach depends on the shape selection of the design space while implementing the SSO. Therefore, in the present study the dependency of the original SSO over the selection of the shape of the design subset is obviated by implementing the novel idea of Voronoi Tessellation for the exploration of the design space rather than presuming its shape as Hyper-Rectangle or Hyper-Ellipse. This improves the applicability of the SSO to the complex realistic problem where the later fails to identify the global minima. The improved SSO can be employed to perform the optimal design of structures in a probabilistic framework: Reliability-Based Design Optimization (RBDO) and Robust Design Optimization (RDO) as well as in the deterministic framework. To demonstrate the efficiency of the proposed approach, three optimization problems: quadratic function and Sinc function for deterministic optimization and 10-bar truss structure for RDO. The results obtained illustrates the efficiency and accuracy of the proposed approach.
