Stochastic Sampling Design for Water Distribution Model Calibration

Abstract

A novel approach to determine optimal sampling locations under parameter uncertainty in a water distribution system (WDS) for the purpose of its hydraulic model calibration is presented. The problem is formulated as a multi-objective optimisation problem under calibration parameter uncertainty. The objectives are to maximise the calibrated model accuracy and to minimise the number of sampling devices as a surrogate of sampling design cost. Model accuracy is defined as the average of normalised traces of model prediction covariance matrices, each of which is constructed from a randomly generated sample of calibration parameter values. To resolve the computational time issue, the optimisation problem is solved using a multi-objective genetic algorithm and adaptive neural networks (MOGA-ANN). The verification of results is done by comparison of the optimal sampling locations obtained using the MOGA-ANN model to the ones obtained using the Monte Carlo Simulation (MCS) method. In the MCS method, an equivalent deterministic sampling design optimisation problem is solved for a number of randomly generated calibration model parameter samples.The results show that significant computational savings can be achieved by using MOGA-ANN compared to the MCS model or the GA model based on all full fitness evaluations without significant decrease in the final solution accuracy.