A probabilistic self-validating soft-sensor with application to wastewater treatment

•A VBPCA-based pretreatment is performed to deal with missing and faulty values before soft-sensor modeling.•The resulting clean data are used for RVM soft-sensor modeling.•The propagation of uncertainty from fault diagnosis model to soft-sensor model is considered.•Dissimilar to traditional soft sensors, the output of the soft-sensor is an interval format.•The results show that the proposed soft-sensor performed well in the highly and lowly equimented wastewater plants.