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In this research, the propulsion of the proposed jellyfish-inspired mantle undulated propulsion robot (MUPRo) is optimized. To reliably predict the hydrodynamic forces acting on the robot, the proposed non-intrusive reduced-order model (NIROM) based on proper orthogonal decomposition (POD) additionally considers the POD basis that has an important contribution to the features on the specified boundary. The proposed model establishes a mapping between the parameter-driven motion of the mantle and the evolution of the fluid characteristics around the swimmer. Moreover, to predict new cases where the input needs to be updated, the input of the proposed model is taken from the kinematics of the robot rather than extracted from full-order high-fidelity models. In this paper, it takes approximately 950s to perform a simulation using the full-order high-fidelity model. However, the computational cost for one prediction with the proposed POD-NIROM is around 0.54s, of which about 0.2s is contributed by preprocessing. Compared with the NIROM based on the classic POD method, the proposed POD-NIROM can effectively update the input and reasonably predict the characteristics on the boundary. The analysis of the hydrodynamic performance of the MUPRo pinpoints that, under a certain period and a certain undulation amplitude, the hydrodynamic force generated by swinging-like mantle motion (k<0.5) is greater, outperforming Aequorea victoria in startup acceleration. It is demonstrated that considering a certain power loss and a certain tail beat amplitude, the wave-like mantle motion (k>0.5) can produce greater propulsion, which means higher propulsion efficiency.

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The present study is intended to develop a new method for analyzing nonlinear stochastic dynamic response of the Preisach hysteretic systems based on covariance and switching probability analysis of a nonlocal memory hysteretic constitutive model. A nonlinear algebraic covariance equation is formulated for the single-degree-of-freedom Preisach hysteretic system subjected to stationary Gaussian white noise excitation, from which the stationary mean square response of the system is obtained. The correlation coefficients of hysteretic restoring force with response in the covariance equation are evaluated by using the second moments and switching probabilities that are derived from the disjoint event probability and the mathematical machinery of an exit problem. In recognizing the symmetry of the classical Preisach weighting function, an approximation of equal “up” and “down” switching probabilities is introduced, which greatly simplifies the evaluation of the correlation coefficients. An example of the Preisach hysteretic system with Gaussian distribution weighting function is presented and the analytical results are compared with the digital simulation findings to verify the accuracy of the derived formulas. Computation results show that there exists a sharp drop in the mean square responses with the increase of a hysteresis parameter, and the mean square responses are affected only in a certain range of the Preisach weighting function.

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