标题： 学习，快速与缓慢：一种基于数据的模型自适应的双阶段算法 显示英文标题

标题： Learning, fast and slow: a two-fold algorithm for data-based model adaptation

摘要： 本文解决了随时间变化的数据模型适应性挑战。 我们提出了一种新颖的两阶段建模架构，旨在纠正由于两种类型的不确定性引起的植物模型不匹配。 域外不确定性发生在系统在初始训练数据集未表示的条件下运行时，而域内不确定性则源于现实世界的变异性以及模型结构或训练过程中的缺陷。 为了处理域外不确定性，一个缓慢学习组件，受人类大脑缓慢思维过程的启发，在未探索的操作条件下学习系统动态，并且仅当监控策略认为有必要时才被激活。 该组件由一组模型组成，具有（i）一种基于其训练数据与当前操作条件之间统计接近性的个体模型加权规则，以及 （ii）一种基于统计控制图的监控算法，用于监督集成的可靠性，并在检测到新操作条件时触发新模型的离线训练和集成。 为了解决域内不确定性，一个快速学习组件，受人类大脑快速思维过程的启发，实时连续补偿缓慢学习模型的不匹配。 该组件被实现为高斯过程（GP）模型，在每次迭代中使用最新数据进行在线训练，同时丢弃旧样本。 所提出的方法在文献中引用的基准能源系统上进行了测试，结果表明，结合使用缓慢和快速学习组件比标准适应方法提高了模型精度。 显示英文摘要

摘要： This article addresses the challenge of adapting data-based models over time. We propose a novel two-fold modelling architecture designed to correct plant-model mismatch caused by two types of uncertainty. Out-of-domain uncertainty arises when the system operates under conditions not represented in the initial training dataset, while in-domain uncertainty results from real-world variability and flaws in the model structure or training process. To handle out-of-domain uncertainty, a slow learning component, inspired by the human brain's slow thinking process, learns system dynamics under unexplored operating conditions, and it is activated only when a monitoring strategy deems it necessary. This component consists of an ensemble of models, featuring (i) a combination rule that weights individual models based on the statistical proximity between their training data and the current operating condition, and (ii) a monitoring algorithm based on statistical control charts that supervises the ensemble's reliability and triggers the offline training and integration of a new model when a new operating condition is detected. To address in-domain uncertainty, a fast learning component, inspired by the human brain's fast thinking process, continuously compensates in real time for the mismatch of the slow learning model. This component is implemented as a Gaussian process (GP) model, trained online at each iteration using recent data while discarding older samples. The proposed methodology is tested on a benchmark energy system referenced in the literature, demonstrating that the combined use of slow and fast learning components improves model accuracy compared to standard adaptation approaches.