基于稀疏Bayes学习算法的无约束结构荷载重构方法  

An Unconstrained Structural Dynamic Load Reconstruction Method Based on the Sparse Bayesian Learning Algorithm

作　　者：陈先智 周新元 曾耀祥 张亚辉[1] CHEN Xianzhi;ZHOU Xinyuan;ZENG Yaoxiang;ZHANG Yahui(State Key Laboratory of Structural Analysis for Industrial Equipment,Dalian University of Technology,Dalian,Liaoning 116024,P.R.China;Beijing Institute of Astronautical System Engineering,Beijing 100076,P.R.China)

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,辽宁大连116024 [2]北京宇航系统工程研究所,北京100076

出　　处：《应用数学和力学》2023年第8期931-943,共13页Applied Mathematics and Mechanics

基　　金：国家自然科学基金项目(12032008)。

摘　　要：为快速准确重构含有未知初始条件的无约束结构外激励,提出了一种基于稀疏Bayes学习算法的荷载重构方法.结合函数拟合的思想建立控制方程,以噪声服从Gauss分布为先验,在Bayes模型中使用快速算法,稀疏重构未知荷载.为合理表达分段拟合中的初始条件,提出了改进的分段拟合手段,以上一分段末状态响应作为可能初始条件,并辅以低阶振型作为初始位移和初始速度的补充.算例以简化运载火箭模型为研究对象,考虑不同等级噪声和不同初始条件表达形式的影响,验证方法的精度和效率.For rapid and exact reconstruction of dynamic loads on unconstrained structures with unknown initial conditions,a dynamic load reconstruction method was proposed based on the sparse Bayesian learning algorithm.With the idea of the function fitting technique,the control equations were built.The noise was assumed to obey the Gaussian distribution,and the fast algorithm was used in the sparse Bayesian learning model.An improved piecewise fitting method was formulated to rationally express the initial conditions in the piecewise fitting,the end state response of the previous segment was used as the possible initial condition,and the low-order vibration modes were applied as the supplement to the initial displacements and initial velocities.The numerical simulations of simplified launch vehicle models prove the accuracy and efficiency of the proposed method,under the effects of different noise levels and different expressions of initial conditions.

关 键 词：函数拟合 稀疏Bayes学习算法 改进分段拟合 荷载重构 

分 类 号：O32[理学—一般力学与力学基础]