Impact of Data Collection and Calibration of Water Distribution Models on Model-Based Decisions

Abstract

Mathematical models of water distribution systems (WDS) serve as tools to represent the real systems for many different purposes. Calibration is the process of fine tuning the model parameters so that the real system is well-represented. In practice, calibration is performed considering all information is deterministic. Recent researches have incorporated uncertainties caused by field measurements into the calibration process. Parameter (D-optimality) and predictive (I-optimality) uncertainties have been used as indicators of how well a system is calibrated.This study focuses on a methodology that extends previous work by considering the impact of uncertainty on decisions that are made using the model. A new sampling strategy that would take into account the accuracy needed for different model objectives is proposed.The methodology uses an optimization routine that minimizes square differences between the observed and model calculated head values by adjusting the model parameters. Given uncertainty in measurements, the parameters from this nonlinear regression are imprecise and the model parameter uncertainties are computed using a first order second moment (FOSM) analysis. Parameter uncertainties are then propagated to model prediction uncertainties through a second FOSM analysis. Finally, the prediction uncertainty relationships are embedded in optimization problems to assess the effect of the uncertainties on model-based decisions. Additional data is collected provided that the monetary benefits of reducing uncertainties can be addressed.The proposed procedure is first applied on a small hypothetical network for a system expansion design problem using a steady state model. It is hypothesized that the model accuracy and data required calibrating WDS models with different objectives would require different amount of data. A real-scale network for design and operation problems is studied using the same methodology for comparison. The effect of a common practice, grouping pipes in the system, is also examined in both studies.Results suggest that the cost reductions are related to the convergence of the mean parameter estimates and the reduction of parameter variances. The impact of each factor changes during the calibration process as the parameters become more precise and the design is modified. Identification of the cause of cost changes, however, is not always obvious.