A hybrid polynomial-based optimization method for underwater gliders with parameter uncertainty

As a type of enduring platform for ocean exploration, underwater glider usually contains some uncertain parameters in actual engineering applications, which are related to manufacturing errors, assembly errors, and sensor measurement errors. Uncertain parameters will make the glider performance show uncertain characteristics, so it is necessary to consider their effects in the design optimization process for an underwater glider. In this paper, a hybrid polynomial-based optimization method is proposed to solve optimization problems of underwater gliders with parameter uncertainty. The hybrid polynomial consists of power function terms and trigonometric function terms, and it is used for fitting surrogate models of the glider dynamic models. The fitted surrogate models are used for quickly calculating the performance evaluation parameters of underwater gliders. Specifically, power function terms and trigonometric function terms correspond to optimization design variables and uncertain parameters, respectively. The hybrid polynomial method covers the convenience of the traditional response surface method and the advantage of the Chebyshev polynomial in interval analysis. Based on surrogate models and interval analysis, we can estimate boundary functions of performance evaluation parameters, and they are employed to construct optimization objective functions. Then, the optimization iteration calculation can be carried out. Here, the proposed method is used for determining the optimal control parameter values of the Petrel-II glider with the uncertainty of some configuration and measurement parameters. The optimization objectives are to minimize the specific energy consumption and maximize the average advance velocity simultaneously. Finally, some laws of the glider performance are summarized.