基于最大熵方法的水下航行体结构动力响应概率建模

水下航行体结构承受的水动力外载荷具有显著的时空分布不确定性,其引发的结构动力响应,诸如结构最大内力、最大内力发生时刻、最大内力发生位置等也由此产生了不确定性;同时,水下航行体的动力响应还会因其连接或分离结构的拉压刚度不同而出现非线性特征. 为了在水动力外载荷样本有限的基础上,分析水下航行体结构连接非线性对动力响应统计特性的影响, 利用水下航行体结构的简化动力学模型,计算了水动力横向载荷作用下响应的样本统计矩,采用最大熵方法实现了动力响应的概率建模. 在分别求出结构最大内力、最大内力发生时刻、最大内力发生位置的概率密度函数后,通过与蒙特卡洛模拟结果对比验证了最大熵方法拟合的响应概率密度函数精度;而后,基于这些结构响应概率密度曲线讨论了系统连接非线性参数变化对结构动力响应的影响. 最终得出如下结论:连接非线性会导致结构在只有横向力的作用时产生的轴力响应,并且最大轴力概率密度函数峰值会因连接结构非线性程度增大而逐渐增大;连接非线性对不确定性传播有显著影响,当连接非线性比较强时,输入正态分布的载荷所得到的内力响应不是正态分布的;最大内力响应的发生位置也会受到连接非线性程度的影响. 上述结果可以为结构优化提供技术支持. 

PROBABILISTIC MODELLING OF DYNAMIC RESPONSE OF UNDERWATER VEHICLE STRUCTURE VIA MAXIMUM ENTROPY METHOD

Hydrodynamic loads of underwater vehicle structure have a high degree of randomness in time and space, which leads to random responses of structure such as maximum internal forces, time and position they taking place, etc. Dynamic response of underwater vehicle will also be nonlinear due to different tension and compression stiffness of its connecting or separated structures. To analyse the influence of nonlinearity of connection on statistics of response of underwater vehicle based on limited sample data of hydrodynamic external load, probabilistic modelling of dynamic response of underwater vehicle is completed by using maximum entropy method in which statistical moments of response samples are obtained from a simplified dynamic model of the structure. Probability density functions of maximum internal forces, time and position they taking place, are proposed separately to predict the most dangerous cases of the underwater vehicle. Accuracy of results proposed here is verified through Monte Carlo simulation. Effects of nonlinear parameters of connections on dynamic response are studied and discussed. Final conclusions are as follows: Nonlinearity of connection leads to axial force response of structures under transverse loads; peak of probabilistic density function of maximum axial force of the structure increases with nonlinear degree of connections which leads to significant effect of propagation of uncertainty; internal force response of structure with nonlinear connections under normal random loads is non-normal; position of maximum internal force response of underwater vehicle structure is influenced by degree of nonlinearity of connections. These findings can provide technical support for structural optimization.