A novel ensemble model using PLSR integrated with multiple activation functions based ELM: Applications to soft sensor development

Soft sensor plays a decisive role in making control strategies and production plans. However, the difficulty in establishing accurate and robust soft sensors using an individual model is continuously increasing due to the increasing scale and complexity in modeling data. To handle this problem, an effective ensemble model using partial least squares regression (PLSR) integrated with extreme learning machine (ELM) with multiple activation functions (PLSR-MAFELM) is proposed in this paper. The proposed PLSR-MAFELM is simple in construction: firstly, train several ELM models assigned with different activation functions using the least squares solution; secondly, combine ELM models for enhancing accuracy and stability performance; finally, obtain the optimal ensemble outputs by aggregating the outputs of individual ELM models using PLSR. To test the performance of the proposed PLSR-MAFELM model, a UCI benchmark dataset and two real-world applications are selected to carry out simulation case studies. Simulation results show that PLSR-MAFELM can achieve good stability and accuracy performance, which indicates that the generalization capability of soft sensors can be improved through combining some single models.