Instantaneous Water Demand Parameter Estimation from Accumulated Readings

Abstract

RESIDENTIAL WATER DEMAND IS A HIGHLY UN STEADY STOCHASTIC PROCESS, DEFINED STATISTICALLY BY THE FREQUENCY OF WATER USE, AND INTENSITY AND DURATION OF STOCHASTIC DEMAND PULSES. KNOWN PROCEDURES FOR OBTAINING THOSE PARAMETERS ARE BASED ON DIRECT OBSERVATION OF THE INSTANTANEOUS WATER DEMAND BY REGISTERING IT EVERY SECOND. THAT DIRECT TECHNIQUE TURNS OUT TO BE IMPRACTICAL BECAUSE OF THE ENORMOUS AMOUNT OF DATA GENERATED AND TO BE PROCESSED. A NEW METHOD FOR ESTIMATING THE NECESSARY PARAMETERS FOR SIMULATING THE INSTANTANEOUS WATER DEMAND FROM LARGER THAN ONE SECOND METER READINGS IS PRESENTED IN THIS PAPER. THE PROPOSED METHOD CONSIDERS PRINCIPLES FROM THE NEYMAN-SCOTT (N-S) PROCESS, SUCH AS THE DISAGGREGATION OF THE ACCUMULATED WATER VOLUME, BASED ON A COMPARISON BETWEEN THE STATISTICAL MOMENTS OF THE OBSERVED LARGER INTERVAL DEMAND SERIES AND THE THEORETICAL MOMENTS OF THE INSTANTANEOUS WATER DEMAND. AN OBJECTIVE FUNCTION EXPRESSING THE RELATION BETWEEN BOTH THEORETICAL AND OBSERVED MOMENTS IS FORMULATED AND MINIMIZED BY A NON LINEAR PROGRAMMING TECHNIQUE OBTAINING THE INTENSITY, DURATION AND ARRIVAL RATE OF THE INSTANTANEOUS DEMAND PULSES. USING THESE RESULTS INSTANTANEOUS WATER DEMAND SERIES, OR DEMAND SERIES WITH ANY AVERAGING INTERVAL, CAN BE GENERATED. THE METHOD IS VALIDATED BY COMPARING THE GENERATED DEMAND SERIES WITH OBSERVED DEMAND SERIES