A EWC-Based Online-Learning Algorithm for Ordinary Differential Equation Network

In industrial processes, changes in operational conditions, including variations in raw materials, lead to concept drift in process data, thereby affecting the performance of soft sensor models trained offline. To address this issue, this study introduces an online-learning method for soft sensor modeling, by utilizing a Lipschitz ordinary differential equation recurrent neural network. This method combines two fundamental components: threshold detection and online incremental fine-tuning. Firstly, the base model is established through offline training using the initial dataset, designed for predicting data within a sliding window. Then, the method adaptively adjusts the threshold or initiates online model updates by comparing the prediction error against a preset threshold. This process not only improves the efficiency of online updates but also minimizes unnecessary adjustments. The online update phase incorporates an incremental fine-tuning approach, integrated with elastic weight consolidation technology, to boost the model adaptability and mitigate catastrophic forgetting during updates, thereby enhancing the efficiency of the model updating. Finally, the performance of the developed approach is validated through simulations on both an artificial dataset and a real-world industrial dataset, comparing it with other online-learning algorithms.