Deep learning (DL) has become an essential tool in prognosis and health management (PHM), commonly used as a regression algorithm for the prognosis of a system's behavior. One particular metric of interest is the remaining useful life (RUL) estimated using monitoring sensor data. Most of these deep learning applications treat the algorithms as black-box functions, giving little to no control of the data interpretation. This becomes an issue if the models break the governing laws of physics or other natural sciences when no constraints are imposed. The latest research efforts have focused on applying complex DL models to achieve a low prediction error rather than studying how the models interpret the behavior of the data and the system itself. In this paper, we propose an open-box approach using a deep neural network framework to explore the physics of degradation through partial differential equations (PDEs). The framework has three stages, and it aims to discover a latent variable and corresponding PDE to represent the health state of the system. Models are trained as a supervised regression and designed to output the RUL as well as a latent variable map that can be used and interpreted as the system's health indicator.

中文翻译：

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通过深度神经网络框架揭示退化系统行为的潜在物理学：剩余使用寿命预测案例

深度学习 (DL) 已成为预后和健康管理 (PHM) 的重要工具，通常用作预测系统行为的回归算法。一个特别感兴趣的指标是使用监控传感器数据估计的剩余使用寿命 (RUL)。大多数这些深度学习应用程序将算法视为黑盒函数，几乎没有控制数据解释。如果模型在没有强加约束的情况下违反了物理或其他自然科学的支配规律，这就会成为一个问题。最新的研究工作集中在应用复杂的 DL 模型来实现低预测误差，而不是研究模型如何解释数据和系统本身的行为。在本文中，我们提出了一种使用深度神经网络框架的开箱方法，通过偏微分方程 (PDE) 探索退化的物理学。该框架分为三个阶段，旨在发现一个潜在变量和相应的 PDE 来表示系统的健康状态。模型作为监督回归进行训练，旨在输出 RUL 以及可用作和解释为系统健康指标的潜在变量图。