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

Xu Dong Shi, Qi Kang, Jing An, Meng Chu Zhou

Research output: Contribution to journalArticlepeer-review

54 Scopus citations


Extreme learning machine (ELM) is suitable for nonlinear soft sensor development. Yet it faces an overfitting 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 nonconvexity and nonsmoothness of the objective function, this article 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.

Original languageEnglish (US)
Pages (from-to)1009-1017
Number of pages9
JournalIEEE Transactions on Industrial Informatics
Issue number2
StatePublished - Feb 1 2022

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Information Systems
  • Computer Science Applications
  • Electrical and Electronic Engineering


  • Extreme learning machine (ELM)
  • machine learning
  • soft sensing
  • variational Bayesian (VB) inference


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