具有统一稀疏先验和模型不确定性的贝叶斯动力系统辨识
Bayesian Dynamical System Identification With Unified Sparsity Priors And Model Uncertainty
摘要：
本文研究降阶动力系统辨识中的不确定性量化问题。降阶系统动力学模型在设计和控制应用中无处不在，最近的努力集中在其数据驱动的建设。我们的出发点是稀疏识别的非线性动力学（SINDy）的框架，重新制定系统辨识作为一个回归问题，其中未知的功能近似从一个稀疏的子集的基础库。在这篇手稿中，我们制定这个系统辨识方法在贝叶斯框架来处理参数和结构模型的不确定性。我们提出了一个一般的方法来执行稀疏性，这是建立在最近推出的类神经元先验。我们在不同的变体之间进行比较，例如Lasso，马蹄铁，以及spike和slab先验，它们都是通过修改单个激活函数获得的。我们还概述了如何状态观测噪声可以与概率状态空间模型。由此产生的贝叶斯回归框架是强大的，易于实现。我们将该方法应用于两个通用的数值应用，摆和洛伦兹系统，和一个空气动力学应用实验测量。
英文摘要：
This work is concerned with uncertainty quantification in reduced-order dynamical system identification. Reduced-order models for system dynamics are ubiquitous in design and control applications and recent efforts focus on their data-driven construction. Our starting point is the sparse-identification of nonlinear dynamics (SINDy) framework, which reformulates system identification as a regression problem, where unknown functions are approximated from a sparse subset of an underlying library. In this manuscript, we formulate this system identification method in a Bayesian framework to handle parameter and structural model uncertainties. We present a general approach to enforce sparsity, which builds on the recently introduced class of neuronized priors. We perform comparisons between different variants such as Lasso, horseshoe, and spike and slab priors, which are all obtained by modifying a single activation function. We also outline how state observation noise can be incorporated with a probabilistic state-space model. The resulting Bayesian regression framework is robust and simple to implement. We apply the method to two generic numerical applications, the pendulum and the Lorenz system, and one aerodynamic application using experimental measurements.
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