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泊松白噪声激励下强非线性系统的半解析瞬态解

叶文伟 陈林聪 孙建桥

叶文伟, 陈林聪, 孙建桥. 泊松白噪声激励下强非线性系统的半解析瞬态解. 力学学报, 2022, 54(12): 3468-3476 doi: 10.6052/0459-1879-22-381
引用本文: 叶文伟, 陈林聪, 孙建桥. 泊松白噪声激励下强非线性系统的半解析瞬态解. 力学学报, 2022, 54(12): 3468-3476 doi: 10.6052/0459-1879-22-381
Ye Wenwei, Chen Lincong, Sun Jian-Qiao. Semi-analytical transient solutions for strong nonlinear systems excited by Poisson white noise. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 3468-3476 doi: 10.6052/0459-1879-22-381
Citation: Ye Wenwei, Chen Lincong, Sun Jian-Qiao. Semi-analytical transient solutions for strong nonlinear systems excited by Poisson white noise. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 3468-3476 doi: 10.6052/0459-1879-22-381

泊松白噪声激励下强非线性系统的半解析瞬态解

doi: 10.6052/0459-1879-22-381
基金项目: 国家自然科学基金(12072118)、福建省杰出青年科学基金(2021J06024)和厦门青年创新基金(3502Z20206005)资助项目
详细信息
    作者简介:

    陈林聪, 教授, 主要研究方向: 非线性随机振动与控制. E-mail: lincongchen@hqu.edu.cn

  • 中图分类号: O324

SEMI-ANALYTICAL TRANSIENT SOLUTIONS FOR STRONG NONLINEAR SYSTEMS EXCITED BY POISSON WHITE NOISE

  • 摘要: 自然界与工程中都普遍存在着随机扰动, 且大多数呈现出固有的非高斯性质, 若采用高斯激励建模可能会导致巨大的误差. 泊松白噪声作为一种典型且重要的非高斯激励模型, 已引起了广泛的关注. 目前, 泊松白噪声激励下系统的动态特性分析主要集中于稳态响应的研究, 而针对瞬态响应的求解难度仍较大, 需进一步发展. 本文引入径向基神经网络, 提出了一种泊松白噪声激励下单自由度强非线性系统瞬态响应预测的高效半解析方法. 首先将广义Fokker-Plank-Kolmogorov (FPK) 方程的瞬态解表示为一组含时变待定权值系数的高斯径向基神经网络; 然后采用有限差分法离散时间导数项, 并结合随机取样技术构造含时间递推式的损失函数; 最后通过拉格朗日乘子法使得损失函数最小化获得时变最优权值系数. 作为算例, 探究了两个经典强非线性系统, 并采用蒙特卡罗模拟方法对解析结果加以验证. 结果表明: 本文方法所获得的瞬时概率密度函数与蒙特卡罗模拟数据吻合地较好, 并且算法具备较高的计算效率. 在系统响应的整个演化过程中, 本文所提方法能够非常有效地捕捉到系统响应在各个时刻下的复杂非线性特征. 此外, 本文方法所获得的高精度半解析瞬态解, 不仅可作为基准解检验其他非线性随机振动分析方法的精度, 对于结构的优化设计也存在巨大的潜在应用价值.

     

  • 图  1  径向基神经网络算法流程图

    Figure  1.  The flowchart of the RBF-NN scheme

    图  2  不同时刻系统 (26) 的边缘概率密度函数 (实线: 径向基神经网络解, 符号: 蒙特卡罗模拟结果)

    Figure  2.  Marginal PDFs of system (26) at different time (lines: RBF-NN solutions, symbols: MCS results)

    图  3  系统 (26) 的位移概率密度函数演化

    Figure  3.  The displacement PDF evolution of system (26)

    图  4  t = 6 s时系统 (26) 的联合概率密度函数

    Figure  4.  The joint PDF of system (26) at t = 6 s

    图  5  不同中心域网格数对算法的均方根误差与计算时间的影响

    Figure  5.  The effect of different number of meshes in the central domain on the root mean square (RMS) error and CPU time of the algorithm

    图  6  不同时刻系统 (27) 的边缘概率密度函数 (实线: 径向基神经网络解, 符号: 蒙特卡罗模拟结果)

    Figure  6.  Marginal PDFs of system (27) at different time (lines: RBF-NN solutions, symbols: MCS results)

    图  7  系统 (27) 的位移概率密度函数演化

    Figure  7.  The displacement PDF evolution of system (27)

    图  8  t = 80 s时系统 (27) 的联合概率密度函数

    Figure  8.  The joint PDF of system (27) at t = 80 s

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出版历程
  • 收稿日期:  2022-08-18
  • 录用日期:  2022-10-08
  • 网络出版日期:  2022-10-09
  • 刊出日期:  2022-12-15

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