Abstract:The quality of the modeling of essential equipment in the flotation process is paramount to enhancing the operational efficiency of the flotation process simulation platform and is a prerequisite for the subsequent implementation of control optimization strategies in the flotation process. Nevertheless, the direct utilization of multi-source data from the industrial Internet for federated learning modeling may result in the generation of non-independent and identically distributed data due to the varying equipment parameters between clients, leading to local models that deviate from the initial global model. To address these challenges, this paper proposes a flotation equipment modeling method based on personalized federated learning with proximal optimization. The method utilizes a federation learning with personalization layer to train the local personalization layer parameters and the base layer parameters transmitted from the server. It then aggregates the weights of the base layer parameters from the client at the server to construct the personalization model of the equipment in the flotation process. The proximal term is incorporated to optimize non-independently and identically distributed data, thereby constructing a global model with high generalization and uploading it to the cloud for storage. The effectiveness of the proposed method is then verified through experiments on the flotation process. The model constructed by means of personalized federation learning with proximal optimization has a coefficient of determination ranging from 97.47% to 98.51% and a root mean square error ranging from 2.31% to 2.97% for the prediction of flotation machine overflow ash, which is more accurate than the FedAvg and FedProx algorithms, and the method meets the industrial demand for equipment modeling in the flotation process.