Modeling of adaptive multi-output soft-sensors with applications in wastewater treatments

Jing Wu, Hongchao Cheng, Yiqi Liu, Bin Liu, Daoping Huang

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)
19 Downloads (Pure)


Given the multivariable coupling, strong nonlinearity and time-varying features in the wastewater treatment processes, adaptive strategies, including just-in-time learning (JITL), time difference (TD), and moving window (MW) methods have been chosen in this paper to enhance multi-output soft-sensor models to ensure online prediction for a variety of hard-to-measure variables simultaneously. In the proposed adaptive multi-output soft-sensors, multi-output partial least squares (MPLS), multi-output relevant vector machine (MRVM) and multi-output Gaussian process regression (MGPR) served as the multi-output models. The integration of adaptive strategies and multi-output models not only provides a solution for multi-output prediction, but also offers a potential to alleviate the degradation of multi-output soft-sensors. To further improve the adaptive ability, four adaptive soft-sensors, termed TD-MW, TD-JIT, JIT-MW, and TD-JIT-MW, have been proposed by mixing the three aforementioned adaptive strategies to upgrade multi-output softsensors. All the adaptive multi-output soft-sensors are analyzed and compared in terms of simulation data and practical industrial data, which exhibit stationary and nonstationary behaviors, respectively.
Original languageEnglish
Pages (from-to)161887-161898
Number of pages12
JournalIEEE Access
Publication statusPublished - 29 Oct 2019


  • adaptive soft sensor
  • multiple-output
  • wastewater treatment plants
  • multiple adaptive mechanisms


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