A non-probabilistic reliability-based design optimization method via dimensional decomposition-aided Chebyshev metamodel

In high-dimensional interval uncertainty optimization problems, traditional methods often face the challenge of the “curse of dimensionality”. To address this problem, this paper proposes an efficient non-probabilistic reliability-based design optimization method to improve the reliability and safety of the system. First, the coefficients of Chebyshev polynomials are efficiently computed by decomposing the high-dimensional problem into multiple low-dimensional subproblems. A dimensional decomposition-aided Chebyshev metamodel balances the accuracy and efficiency of interval analysis, replacing inner-layer optimization in the traditional two-layer nested optimization framework. Furthermore, the proposed method transforms the uncertainty optimization problem into a deterministic bi-objective optimization problem by using the interval order relation and non-probabilistic reliability theory. Then, the bi-objective optimization problem is reduced to an unconstrained single-objective optimization problem using the linear weighting method and the penalty function approach. To enhance the stability and global convergence of the optimization process, a new meta-heuristic optimization algorithm, the snake optimizer, is introduced in this paper. The effectiveness and accuracy of the proposed method in improving the safety and reliability of engineering systems are verified through numerical examples and an aero-engine dual-rotor system. The proposed method does not depend on the derivative information of the objective function or constraints, which is especially suitable for complex “black-box” engineering uncertainty optimization problems and has a wide range of engineering applications.