Novel L1 Regularized Extreme Learning Machine for Soft-sensing of an Industrial Process

Extreme learning machine (ELM) is suitable for nonlinear soft sensor development. Yet it faces an over-fitting problem. To overcome it, this work integrates bound optimization theory with Variational Bayesian (VB) inference to derive novel L1 norm-based ELMs. An L1 term is attached to the squared sum cost of prediction errors to formulate an objective function. Considering the non-convexity and non-smoothness of the objective function, this work uses bound optimization theory, and constructs a proper surrogate function to equivalently convert a challenging L1 norm-based optimization problem into easy one. Then, VB inference is adopted for optimizing the converted problem. Thus an L1 norm-based ELM can be efficiently optimized by an alternating optimization algorithm with a proved convergence. Finally, a soft sensor is developed based on the proposed algorithm. An industrial case study is carried out to demonstrate that the proposed soft sensor is competitive against recent ones.