Construction of a Probabilistic Model Describing Deterioration of Pumping Wells and Its Verification Using Actual Data

Abstract

A probabilistic model is newly proposed for describing random deterioration of pumping wells, in consideration of application to efficient management of pumping wells using a concept of asset management procedure. First, introducing a health index for quantifying specific capacity, we formulate a differential equation describing mean deterioration of the helth index. Next, it is extended to a random differential equation, in which a Gaussian white noise is introduced for representing intensive fluctuation around the mean deterioration behavior, so that intensively random variation of the health index can be well reproduced. A probability distribution of the health index is then derived in an analytical form. Finally, the obtained probability distribution is compared with actual data of the health index for active eight pumping wells in Joyo area, Kyoto prefecture, Japan. It is clarified that the scatter of health index of actual pumping wells is quite well reproduced by the theoretically derived probability distribution from the newly proposed probabilistic model.