Abstract:The ocean is a treasure trove of resources for humanity. With the continuous exploration of ocean resources, the detection and rational development of these resources has become a hot topic of widespread concern for countries around the world. Consequently, the exploration activities of underwater vehicles have been gradually increasing. However, the ocean environment is characterized by strong stochastic uncertainty, posing significant challenges for the operation and trajectory planning of underwater vehicles. Therefore, it is crucial to accurately predict the stochastic response characteristics of underwater vehicles in random ocean environments. In this paper, a new type of underwater vehicle, equipped with a rudderless paddle, is adopted as the research object. Based on the principle of probability conservation, a probability density integration equation of the underwater vehicle in a random ocean environment is established from a new perspective of stochastic integration. Then, a direct probability integration method (DPIM) based on block parallel computing is proposed in this paper. This method decouples the control equations of the underwater vehicle system from the probability density integration equation, and utilizes block-parallel computations, enabling the efficient stochastic dynamic response analysis of the new type of underwater vehicle under the random sea wave excitation. Furthermore, the computational results of the proposed method are compared with those of the original DPIM and Monte Carlo simulation method to further validate its accuracy and efficiency. The final research results reveal that sea wave significant height and flow velocity are the primary stochastic factors affecting the response of underwater vehicles. An increase in the sea wave's significant height and flow velocity will significantly raise the probability of deviation from the predetermined trajectory of underwater vehicles. In addition, it can be found that the higher sea wave flow velocity may induce the random jumping phenomena, thereby reducing the navigation safety of the underwater vehicle.