基于 RBFNN 方法的具有惯性非线性的高斯白噪声激励振荡器的响应

IF 3 3区 工程技术 Q2 ENGINEERING, MECHANICAL Probabilistic Engineering Mechanics Pub Date : 2024-07-01 DOI:10.1016/j.probengmech.2024.103637
Yongqi Hu , Gen Ge
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引用次数: 0

摘要

虽然随机平均法已被证明能有效解决具有强刚度项的非线性振荡器在宽带噪声激励下的响应问题,但在处理具有强惯性非线性项(也称为坐标相关质量)或多个势阱的振荡器时,这些方法似乎并不奏效。为了解决这一局限性,我们采用径向基函数神经网络(RBFNN)算法来预测具有强惯性非线性项和多个势阱的振荡器的响应。在该模型中,选择了众所周知的高斯函数作为径向基函数。然后,将近似静态概率密度函数(PDF)表示为带权重的高斯基函数(GBF)之和。使用拉格朗日乘法最小化 Fokker-Plank-Kolmogorov (FPK) 函数近似解的平方误差,从而确定最佳权系数。本文列举了三个例子来说明惯性非线性项和电位井对响应的影响。提供了蒙特卡罗模拟(MCS)与 RBFNN 预测之间的均方误差。结果表明,RBFNN 预测结果与蒙特卡罗模拟结果完全一致。
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Response of Gaussian white noise excited oscillators with inertia nonlinearity based on the RBFNN method

Although stochastic averaging methods have proven effective in solving the responses of nonlinear oscillators with a strong stiffness term under broadband noise excitations, these methods appear to be ineffective when dealing with oscillators that have a strong inertial nonlinearity term (also known as coordinate-dependent mass) or multiple potential wells. To address this limitation, a radial basis function neural network (RBFNN) algorithm is applied to predict the responses of oscillators with both a strong inertia nonlinearity term and multiple potential wells. The well-known Gaussian functions are chosen as radial basis functions in the model. Then, the approximate stationary probability density function (PDF) is expressed as the sum of Gaussian basis functions (GBFs) with weights. The squared error of the approximate solution for the Fokker-Plank-Kolmogorov (FPK) function is minimized using the Lagrange multiplier method to determine optimal weight coefficients. Three examples are presented to demonstrate how inertia nonlinearity terms and potential wells affect the responses. The mean square errors between Monte Carlo simulations (MCS) and RBFNN predictions are provided. The results indicate that RBFNN predictions align perfectly with those obtained from MCS.

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来源期刊
Probabilistic Engineering Mechanics
Probabilistic Engineering Mechanics 工程技术-工程:机械
CiteScore
3.80
自引率
15.40%
发文量
98
审稿时长
13.5 months
期刊介绍: This journal provides a forum for scholarly work dealing primarily with probabilistic and statistical approaches to contemporary solid/structural and fluid mechanics problems encountered in diverse technical disciplines such as aerospace, civil, marine, mechanical, and nuclear engineering. The journal aims to maintain a healthy balance between general solution techniques and problem-specific results, encouraging a fruitful exchange of ideas among disparate engineering specialities.
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