Uncertain optimal design using non-probabilistic interval set-theoretic based method and probabilistic method for dynamic response problem

Most applications of uncertain optimal design have been concerned with static performance in practical engineering, and applications in structural dynamics are rare. The uncertain optimal design of dynamic response problems is studied using non-probabilistic interval set-theoretic based method and probabilistic method in this paper. During the design process, only the upper and lower bounds of uncertain design parameters need to be known. By the dynamic finite element analysis and interval mathematics, the non-probabilistic interval analysis method for dynamic optimization problem under uncertainty is developed. In addition, probabilistic optimal design using Chebyshev point method is presented for comparison. In probabilistic optimal design Chebyshev point method is used to access the probabilistic constraint, and the objective function is to minimize simultaneously the mean and standard variance of structural dynamic response. In non-probabilistic optimal design, the objective function is to minimize simultaneously the nominal value and variation of structural dynamic response. Numerical examples of a vibration absorber and a 25-bar space truss subject to uncertain excitation are used to illustrate the feasibility and superiority of the presented method. The superiority can be shown especially under the condition of lacking data information. The results show that the non-probabilistic optimization is more reliable than the probabilistic optimization.