Natural frequency-based robust design optimization of clamp-pipe systems via an integrated sequential Kriging approach

The position of clamps is critical to achieve desired natural frequency characteristics of a clamp-pipe system (CPS) in aero-engines. Due to inherent uncertainties in terms of the stiffness coefficient and positional deviation of a clamp, natural frequency results of the CPS become random variables. In contrast to the deterministic scenario, the uncertainty-based design optimization has to effectively balance the trade-off between the mean-value maximization of the variance minimization of the natural frequency response. This motivates the clamp position-based robust design optimization (CP-RDO) of the CPS in this paper. A critical challenge is to recursively deal with the computationally demanding uncertainty analysis embedded in the CP-RDO routine. The multiplicative dimensional reduction method (M-DRM) is employed to obtain statistical moments of the uncertain natural frequency based only on a small number of functional evaluations. Then, a sequential Kriging technique is followed to obtain global optima of the clamp position for the robust concern of the CPS. Numerical examples based on an L-shape and a spatial CPSs are presented to examine performance of the proposed approach. Results have shown that a combination of the M-DRM and the sequential Kriging scheme is able to effectively obtain robust solutions of the design optimization problem, whereas the total number of model evaluations has been significantly reduced as compared to the benchmark algorithm in the literature. The integrated sequential Kriging approach has potentials to deal with the CP-RDO of various CPSs in general.