基于多峰分布的大尺度变形翼机构时变可靠性分析

Time-Varying Reliability Analysis of Large-Scale Morphing Wing Mechanism Based on Multimodal Distribution

针对机构可靠性的工程问题,提出了一种基于多峰分布的时变可靠性分析方法(iTRPD),并应用于大尺度变形翼机构的可靠性分析。首先,将变形翼结构模型离散为几个瞬时功能函数,并将其转换为独立正态变量。然后,计算出不同时刻的瞬间可靠度与各向量间的自相关系数矩阵,得到对应的概率密度函数。最后,根据协方差特性与各向量间的相关性,利用1次高维高斯积分将独立标准正态空间的时变可靠度简化为大尺度变形翼机构整体的时变可靠度。结果表明:iTRPD在分析大尺度变形翼时变可靠性时,与蒙特卡洛仿真法(MCS)的相对误差仅为-2.842%,比常规方法TRPD好;对功能函数调用次数为415,远小于MCS的1×10^(9)次;对高维高斯积分的调用,常规时变可靠性方法为35次,iTRPD仅为1次。可见,iTRPD对涉及多模态分布的时变可靠性分析具有较高的计算精度和计算效率。

A time-varying reliability analysis method(iTRPD)based on multi-peak distribution is proposed to address the engineering problem of mechanism reliability,with this method applied to the reliability analysis of largescale morphing wing mechanism.First,the morphing wing structural model is discretized into several instantaneous functional functions and converted into independent normal variables.Then,the instantaneous reliabilities at different moments are calculated,while the autocorrelation coefficient matrix between each vector is calculated to get the corresponding probability density function.Finally,according to the covariance property and the correlation between the vectors,only one high-dimensional Gaussian integral needs to be calculated.The time-varying reliability of the independent standard normal space is simplified to the time-varying reliability of the large-scale morphing wing mechanism as a whole.The results show that:the relative error between iTRPD and Monte Carlo simulation(MCS)in analyzing the time-varying reliability of large-scale morphing wing is only-2.842%,better than that of the conventional method TRPD.The number of invocations of the function is 415,much smaller than that of the MCS(1×10°times).The number of invocations of high-dimensional Gaussian integrals is thirty-five times for the conventional time-varying reliability method,but only one time for iTRPD.It can be seen that iTRPD has high computational accuracy and computational efficiency for time-varying reliability analysis involving multimodal distributions.