Probabilistic optimal control parameters with incomplete information on design variables using a heuristic algorithm

Abstract

Uncertain structural performance and cost ineffectiveness are two major barriers in applying active control. Fuzzy theory is often adopted to handle the difficulty of insufficient statistical information. To fully capture the uncertainty, a probabilistic based optimization framework, 3P3MSOS (3-Parameter 3-Moment Symbiotic Optimization Search), is proposed to find the optimal controller parameters satisfying the predefined reliability target. To overcome the issue of lacking probability distribution function (PDF), only the first three moments from sample data is used. To lessen the computational burden, dimension reduction technique is adopted. To obtain a fast and an accurate reliability index, the limit state is converted to the 3-Parameter Lognormal distribution of an equivalent single variable function. The first three moments of the corresponding function are obtained using Gaussian–Hermite integration. SOS metaheuristic algorithm is adopted to minimize the required control force considering probabilistic constraints. To demonstrate the proposed framework in the absence of PDF, common state feedback such as the pole placement method and linear quadratic regulator (LQR) for a 6-story building with 14 random variables is provided. Accuracy of the calculated reliability is verified with Monte Carlo Simulation. Compared to Monte-Carlo Simulation (MCS), error induced by 3P3M is around 10% if COV is less than 0.15. Meanwhile, the time taken by 3P3M is only 8E-4 times the time taken by MCS. 3P3MSOS takes the least time to find a converged solution that fulfills the constraint requirement (i.e., β=3.0) among three investigated algorithms. Results indicate that the proposed framework is able to deliver a promising controller design, in which the reliability calculation is accurate and affordable.