Recursive System Identification for Real-Time Sewer Flow Forecasting

Abstract

On-line sewer flow forecasting is simulated in this study using an autoregressive transfer function rainfall-runoff model and a recursive procedure for parameter estimation. Reliable off-line estimates of the model parameters are assumed to be unavailable. Three recursive estimation algorithms are used: the time-invariant and time-varying versions of the recursive least-squares algorithm, and the Kalman filter interpretation of this algorithm. The sensitivity of the forecasting accuracy to the model order and to the initial conditions of the algorithm is studied using sewer flow data from the Milwaukee Metropolitan Sewerage District. It is observed that increasing the number of model parameters does not automatically improve the on-line forecasting results, although it does improve the off-line results. Also, the asymptotic properties of the recursive estimates appear to be better for the low-order models. It is observed that using the off-line identification results as the initial conditions for the recursive procedure produces more accurate forecasts than the (unreliable) model identified off-line without parameter updating. Forecasting results achieved using the time-invariant recursive least-squares algorithm are compared with those obtained for the time-varying approaches.