A Comparative Study of Stochastic and Deterministic Sampling Design for Model Calibration

This paper presents and compares two approaches, stochastic and deterministic sampling design, for the purpose of calibrating water distribution system model. Both approaches use a multi-objective genetic algorithm known as NSGA-II to identify the whole Pareto-optimal front of optimal solutions. The relevant objective functions are to maximize the calibrated model accuracy and to minimize the number of sampling devices as a surrogate of sampling design cost. In the deterministic approach, optimal solutions are identified based on the assumed values for calibration parameters. However, the uncertainty of calibration parameters is taken into account in the stochastic approach with some pre-defined probability density functions. Two different stochastic approaches, including noisy fitness function and Monte Carlo simulation, are considered in this study. The efficacy of considering stochastic sampling design rather than deterministic one is assessed by evaluating their objective functions in the simulation of 10000 sampling design problems, each of which is constructed with randomly generated calibration parameters. The stochastic approach is first test on an artificial case study. Then it is applied to a real world water distribution system known as Mahalat model in the central part of Iran. The results of comparison show significant improvements in optimal solutions when using stochastic approaches of sampling design.