<p>The centrifugal pumps have been widely used in aviation engine for delivering fuel with desired pressure and flow capacity, but their performance has been shown to fluctuate under typical operational conditions, due to some intrinsic randomness. This has motivated the study of robust design optimization for centrifugal pumps, but the state-of-the-art methods may face challenges in terms of numerical efficiency due to the high cost of simulating the fluid field. To fill this gap, a highly efficient sequential algorithm, which combines Bayesian optimization and Bayesian integration, is first developed for decoupling and solving the nested problems for robust design optimization. The constrained problem is first transformed into a non-constrained one. The method then involves training a Gaussian process regression (GPR) model in the augmented space of design and random variables, enabling performing Bayesian queries in the two marginal spaces sequentially. For each iteration, only one deterministic simulation of the fluid field is required, making it numerically efficient in terms of the number of simulator calls. After addressing its effectiveness with a numerical example, it is applied to real-world centrifugal pumps, and results show an improvement in mean performance, meanwhile, an obvious reduction of the variation of the performance.</p>