Equation discovery for nonlinear dynamical systems: A Bayesian viewpoint
Equation discovery for nonlinear dynamical systems: A Bayesian viewpoint
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DOI：
10.1016/j.ymssp.2020.107528
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发表时间：
2021-06
影响因子：
8.4
通讯作者：
R. Fuentes;R. Nayek;P. Gardner;N. Dervilis;T. Rogers;K. Worden;E. Cross
中科院分区：
文献类型：
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作者：
R. Fuentes;R. Nayek;P. Gardner;N. Dervilis;T. Rogers;K. Worden;E. Cross
本文提出了一种新的贝叶斯方程发现方法-结合结构检测和参数估计-用于非线性结构动力学的系统识别（SI）。结构检测是通过相关向量机（RVM）框架内的稀疏诱导先验完成的;先验确保对模型没有贡献的项被驱动到零系数值。受压缩感知（CS）思想和机器学习社区最近在稀疏线性回归方面的成果的启发，本文采用了使用过完备字典来表示描述系统的方程的大量候选项。与其他稀疏学习器不同，如Lasso及其衍生物，它们可能对超参数选择敏感，所提出的方法利用了通过分层贝叶斯方法固定先验和超先验的原则方法。该方法通过一些常见的单自由度（SDOF）非线性动力学系统的模拟案例研究，并在两个具有挑战性的实验数据集上成功地证明和验证。
This paper presents a new Bayesian approach to equation discovery – combined structure detection and parameter estimation – for system identification (SI) in nonlinear structural dynamics. The structure detection is accomplished via a sparsity-inducing prior within a Relevance Vector Machine (RVM) framework; the prior ensures that terms making no contribution to the model are driven to zero coefficient values. Motivated by the idea of compressive sensing (CS) and recent results from the machine learning community on sparse linear regression, the paper adopts the use of an over-complete dictionary to represent a large number of candidate terms for the equation describing the system. Unlike other sparse learners, like the Lasso and its derivatives, which are potentially sensitive to hyperparameter selection, the proposed method exploits the principled means of fixing priors and hyperpriors that are available via a hierarchical Bayesian approach. The approach is successfully demonstrated and validated via a number of simulated case studies of common Single-Degree-of-Freedom (SDOF) nonlinear dynamic systems, and on two challenging experimental data sets.