Kuo-Wei Liao, Nophi Ian Delos Reyes Biton
The computational cost of an optimization considering probabilistic constraints is often expensive due to the reliability analysis performed inside the optimization loop. This study computes reliability using an equivalent single variable Pearson's distribution system. To retain the accuracy without sacrificing efficiency, dimension reduction method is used to reduce the required number of points in Gaussian–Hermite integration. In addition, four advance machine learning techniques are used to construct a hyper-probability density function to solve the singularity issue in the Pearson distribution system. The ε-constrained is utilized in a metaheuristic optimization algorithm (PSO/SOS) to consider the probabilistic constraints. The proposed algorithm is verified with several literature studies. Results shown that it is able to find an optimal design for problems having linear, highly nonlinear, and implicit probabilistic constraint functions with normal or non-normal variables. It is found that increasing number of variates in dimension reduction can provide a more accurate estimation of moments of the performance functions and enhance the solution accuracy. To demonstrate the applicability of the proposed algorithm to a practical problem, a platform of the SAP2000 Open Application Programming Interface (OAPI) is developed to find an optimal design for a three story steel frame under nonlinear time history analysis. © 2019
Department of Bioenvironmental Systems Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei, 10617, Taiwan; University of San Carlos, Cebu, Philippines
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