基于多维gPC的船舶电力推进系统仿真不确定性分析

Uncertainty Analysis for Simulation of Shipboard Electric Propulsion System Based on Multi-Dimensional gPC

为了解决在船舶电力推进系统设计研发过程中面临不确定性因素较多的问题,将广义多项式混沌(gPC)应用到系统仿真的不确定性分析中,并通过张量积将一维的gPC扩展到了多维。通过在一阶随机微分方程中的应用,验证了方法的有效性。在此基础上,对船舶电力推进系统在多个随机变量共同影响下的响应进行了建模、仿真和不确定性分析,得到了系统响应的统计特性。研究结果表明,构建的多维广义多项式混沌能够有效地对船舶电力推进系统在多个不确定因素共同影响下的响应进行定量的不确定性分析。在多个随机变量的共同影响下,系统的动态过程和稳态过程都将受到影响,在过渡过程中将会出现影响最严重的时刻,从而为设计研发提供参考。

In order to analyze the influence of many uncertain factors on the design stage of shipboard electric propulsion systems, gPC was applied in the uncertainty analysis of system simulation. A method to construct multi-dimensional gPC from one-dimension gPC by tensor product was adopted in this paper. By applying the method in the first-order stochastic differential equation, the efficiency of the proposed method was validated. Then, uncertainty analysis of the simulation for the shipboard electric propulsion systems arising from two independent random variables was analyzed. The statistical properties of variables were obtained. The results showed that the proposed method can simulate and analyze the performance of the shipboard electric propulsion system affected by multiple uncertain factors effectively. The dynamic and steady-state performance of the system will be affected by the random variables. The largest impact appears when the system is about to steady-state from dynamic process, which can provide reference for design and development.