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

Xudong Shi, Qi Kang, Mengchu Zhou, Jing An, Abdullah Abusorrah

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish (US)
JournalIEEE Transactions on Industrial Informatics
StateAccepted/In press - 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

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


  • Bayes methods
  • Extreme learning machine
  • Extreme learning machines
  • Inference algorithms
  • Linear programming
  • Machine learning
  • Neurons
  • Optimization
  • Soft sensing
  • Training
  • Variational Bayesian inference


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