This paper presents a novel approach called physics-informed probabilistic slow feature analysis. The probabilistic slow feature analysis method has been employed to extract slowly varying latent patterns from high-dimensional measured data. The extracted slow features have proven effective in industrial applications such as soft sensing and process monitoring. However, industrial processes come with various physical constraints that must be taken into account, such as energy requirements, equipment limitations, and safety considerations. The conventional black-box nature of the slow feature model often leads to physically inconsistent or unacceptable results. To address this issue, we propose integrating physics principles into the probabilistic slow feature model, ensuring that the extracted features adhere to physics laws. Our formulation incorporates two types of physical constraints: linear algebraic equality and inequality constraints. Through an industrial case study, we demonstrate the effectiveness of our methodology, showcasing the advantages of incorporating physics in feature extraction. These advantages include improved interpretability, reduced data dimensionality, and enhanced generalization performance.

中文翻译：

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基于物理的概率慢特征分析


本文提出了一种称为物理信息概率慢特征分析的新颖方法。采用概率慢特征分析方法从高维测量数据中提取缓慢变化的潜在模式。提取的慢速特征已被证明在软传感和过程监控等工业应用中有效。然而，工业过程具有必须考虑的各种物理限制，例如能源要求、设备限制和安全考虑。慢速特征模型的传统黑盒性质通常会导致物理上不一致或不可接受的结果。为了解决这个问题，我们建议将物理原理集成到概率慢特征模型中，确保提取的特征遵循物理定律。我们的公式包含两种类型的物理约束：线性代数等式和不等式约束。通过工业案例研究，我们证明了我们方法的有效性，展示了将物理学纳入特征提取的优势。这些优点包括提高可解释性、降低数据维度和增强泛化性能。