A Two Stage Optimization Approach for Calibrating Water Distribution Systems

Abstract

BWCN is a competition for calibrating pipe roughness coefficients and demand pattern multipliers of CTown Water Distribution System (WDS) to measured SCADA (hourly tank levels and pump flows) and fire flow test data in a 1-week operation. In a pre-calibration step, quality of the data is assessed, base demands for the fire flow tests are estimated, by mass balance, and pipes are grouped and their nominal values and variation range are determined. In this study, the calibration problem is solved in two stages, each of which tunes a portion of decision variables (DVs) that significantly impact the corresponding objectives while other DVs are set to their nominal (or calibrated) values. Dynamically Dimensioned Search based optimization algorithms are used in both stages because the default algorithm parameter setting is robust. Stage-1 aims to fit the fire flow test measurements that are highly affected by pipe roughness coefficients. Also, demand pattern multipliers for hour-1 SCADA must be calibrated in this stage because the base demand during the fire flow tests is roughly the same as those in hour 1. Ideally, a single solution must minimize the calibration error for all the measurements simultaneously. However, since no perfect model and/or data set exist, objective functions (error metrics) are usually in conflict. Therefore, this stage is set up as a bi-objective optimization problem to minimize the calibration error in simulating fire flow test measurements versus simulating hour-1 SCADA measurements. At the end of this stage, multi-criteria decision making is utilized to select candidate solutions to be evaluated in stage-2. In stage-2 demand pattern multipliers are calibrated to fit the SCADA (tank levels and pump flows). The WDS model performance in each hour is independent from subsequent hours; therefore, stage-2 is set up to calibrate demand pattern multipliers hour by hour starting from the hour 2 to 168 (1 week). All candidate solutions from stage-1 are evaluated in stage-2 and one of them is selected as the final solution to the C-Town calibration problem based on multi-criteria decision making. On average, the final calibrated model estimates static pressure, fire flow tests, tank levels and pumping flow rates of SCADA to within 3.5%, 1.5%, 1.0%, and 2.5% of the measured data respectively.