Arbitrary polynomial chaos expansion for uncertainty analysis of the one-dimensional hindered-compression continuous settling model

Secondary settling tank (SST) models play a significant role in the simulation of a wastewater treatment system. They can estimate effluent and underflow quality and thus help with the design, management, and optimization of wastewater treatment systems. SST modeling consists of an empirical settling velocity function where parameter uncertainty could raise. The performance of an SST model could suffer from parameter uncertainty, which makes parameter uncertainty assessment valuable for SST modeling. Monte Carlo simulation (MCS) is a classical technique for assessing uncertainty, but it requires parameter distribution information and is computationally expensive. To overcome these limitations, arbitrary polynomial chaos expansion (aPCE), a novel approach has been adopted for the first time in this study. The well-recognized Bürger-Diehl SST model is used and the uncertainties originating from five essential model parameters are assessed by the novel aPCE method with the MCS technique being used as a benchmark. Probabilistic estimations of the model output, i.e., sludge blanket height (SBH), are generated by both aPCE and MCS. The comparison results between aPCE and MCS suggest that the aPCE approach can be as effective as MCS in quantifying the uncertainties associated with SST model parameters, while significantly reducing approximately 90 % computational requirements. This study explicitly quantifies the uncertainties associated with SST model parameters in an efficient manner, which can provide robust support for the design, management, and optimization of wastewater treatment systems.