Accurate structural response prediction forms a main driver for structural health monitoring and control applications. This often requires the proposed model to adequately capture the underlying dynamics of complex structural systems. In this work, we utilize a learnable Extended Kalman Filter (EKF), named the Neural Extended Kalman Filter (Neural EKF) throughout this paper, for learning the latent evolution dynamics of complex physical systems. The Neural EKF is a generalized version of the conventional EKF, where the modeling of process dynamics and sensory observations can be parameterized by neural networks, therefore learned by end-to-end training. The method is implemented under the variational inference framework with the EKF conducting inference from sensing measurements. Typically, conventional variational inference models are parameterized by neural networks independent of the latent dynamics models. This characteristic makes the inference and reconstruction accuracy weakly based on the dynamics models and renders the associated training inadequate. In this work, we show that the structure imposed by the Neural EKF is beneficial to the learning process. We demonstrate the efficacy of the framework on both simulated and real-world structural monitoring datasets, with the results indicating significant predictive capabilities of the proposed scheme.

翻译：精确的结构响应预测是结构健康监测与控制应用的主要驱动力。这通常要求所提出的模型能够充分捕捉复杂结构系统的潜在动力学特性。本文采用一种可学习的扩展卡尔曼滤波（EKF）方法，即文中所述的神经扩展卡尔曼滤波（Neural EKF），用于学习复杂物理系统的潜在演化动力学。神经扩展卡尔曼滤波是传统EKF的广义版本，其中过程动力学与传感观测的建模可通过神经网络参数化，从而通过端到端训练进行学习。该方法基于变分推断框架实现，EKF利用传感测量进行推断。通常，传统变分推断模型由独立于潜在动力学模型的神经网络参数化，这一特性使得推断与重建精度对动力学模型的依赖性较弱，并导致相关训练不充分。本文证明，神经扩展卡尔曼滤波所强加的结构对学习过程具有积极影响。我们通过在模拟与真实结构监测数据集上的实验展示了该框架的有效性，结果表明所提方案具备显著的预测能力。