Identification of Mathematical Models for DO and BOD Concentrations in Polluted Streams from Noise Corrupted Measurements

Abstract

The numerical values of parameters in the mathematical model describing the dissolved oxygen (DO) and biochemical oxygen demand (BOD) concentrations (e.g., the reaeratio.n coefficient and the BOD removal coefficient) are determined in a systematic manner so that a best fit to the noise corrupted DO data is obtained asymptotically. The goodness of the estimates is evaluated by the squared difference between measured DO concentrations and concentrations calculated from the mathematical model. A stochastic approximation algorithm of the Robbins‐Monro type is applied for computing the parameter values in a sequential manner. The algorithm converges in the mean square sense to the parameter value that furnishes a local minimum for the average of the error criterion. The procedure is illustrated by several numerical examples. Because of the sequential nature of the algorithm, savings in computer time as well as in the required memory capacity are obtained.