Adaptive just-in-time and relevant vector machine based soft-sensors with adaptive differential evolution algorithms for parameter optimization

•A Just-in-time (JIT) and Relevant-vector-machine (RVM) to perform perditions.•Nature-inspired optimized algorithm that ensures optimal parameters selection for JIT and RVM.•A JADE evolution algorithm to optimize parameters for JIT and RVM without hyper-parameter setting.•A moving window methodology for improvement of the JIT and RVM model.•Proposed method is efficiently attractive in a wastewater plant monitoring.

Just-in-time (JIT) and Relevant vector machine (RVM) are two of commonly used models for soft-sensors modeling, the efficiency of which is governed by few critical parameters and hyper-parameters significantly. These parameters are routinely selected by trial and error or experience, thus leading to over- or under-fitting for the prediction. Adaptive differential evolution with optional external archive (JADE) has been used to optimize the parameters of JIT and RVM in this paper. The resulted JADE-JIT and JADE-RVM based soft-sensors are further enhanced into an adaptive format by the moving window (WM) technique. The proposed methodologies are applied to prediction of hard-to-measured variables in the wastewater treatment plants (WWTPs) and successful results are obtained.