含隐式哈密顿函数随机振动系统概率密度的两步数据驱动辨识  

Two-step data-driven identification of probability densities for random vibrating systems with implicit Hamiltonian functions

作　　者：陈钰瑛 王神龙 焦古月 Yuying Chen;Shenlong Wang;Guyue Jiao(School of Mechanical Engineering,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]不详

出　　处：《Acta Mechanica Sinica》2024年第5期150-160,共11页力学学报（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China(Grant No.12172226).

摘　　要：更非线性随机振动是一种常见现象,预测其概率密度是振动工程的重要组成部分.本文提出了一种数据驱动的方法,用于识别具有隐式哈密顿函数的随机振动系统中响应概率密度的显式表达式.该过程包括两个步骤,一是识别哈密顿函数,二是计算稳态响应的概率密度,前者利用拟哈密顿系统的运动微分方程,从模拟数据中识别出哈密顿函数;后者则从识别出的哈密顿函数估计出概率密度的对数,并获取显式表达式.它们的未知系数可通过求解一组待定方程得到.该方法适用于不能简单导出哈密顿函数的系统,如具有复杂刚度的系统.本文给出了两个例子以证明我们提出方法的适用性和有效性,即非线性振动能量采集器和具有LuGre摩擦的杜芬振子。结果表明,我们所提出的方法在效率上优于蒙特卡罗模拟,对参数变化不敏感,可以用于瞬态概率密度分析,且其应用范围比随机平均法更广.Nonlinear random vibration is a common phenomenon,and predicting its probability density is an essential component of vibration engineering.This paper proposes a data-driven method for identifying explicit expressions of response probability densities in random vibrating systems with implicit Hamiltonian functions.The process concludes with two steps,identifying the Hamiltonian function and calculating the probability density of the stationary response.The former uses the differential equations of the motion of the quasi-Hamiltonian systems to identify Hamiltonian functions from the simulated data,while the latter estimates the logarithm of the probability density from the identified Hamiltonian functions and acquires an explicit expression.Their unknown coefficients can be attributed to the solution of a set of undetermined equations.The proposed method is applied to systems in which the Hamiltonian functions cannot be simply derived,such as those with complicated stiffness.Two examples are presented to demonstrate the applicability and effectiveness of our method,i.e.,the nonlinear vibration energy harvester(VEH)and the Duffing oscillator with LuGre friction.The proposed technique outperforms Monte Carlo simulations(MCSs)in efficiency.The results show that our method is insensitive to parameters and can be used for identifying transient probability density.Its application scope is wider than the stochastic averaging method.

关 键 词：哈密顿函数 概率密度 显式表达式 非线性随机振动 随机平均法 蒙特卡罗模拟 拟哈密顿系统 未知系数 

分 类 号：O32[理学—一般力学与力学基础] O174[理学—力学]