Multiscale fuzzy system identification

One of the biggest challenges in constructing empirical models is the presence of measurement errors in the data. These errors (or noise) can have a drastic effect on the accuracy and prediction of estimated models, and thus need to be removed for improved models accuracy. Multiscale representation of data has shown great noise-removal ability when used in data filtering. In this paper, this advantage of multiscale representation is exploited to improve the accuracy of the nonlinear Takagi-Sugeno (TS) fuzzy models by developing a multiscale fuzzy (MSF) system identification algorithm. The developed algorithm relies on constructing multiple TS fuzzy models at multiple scales using the scaled signal approximations of the input-output data, and then selecting the optimum multiscale model that maximizes the signal-to-noise ratio of the model prediction. The developed algorithm is shown to outperform the time domain fuzzy model, NARMAX model, and fuzzy model estimated from pre-filtered data using an Exponentially weighted Moving Average (EWMA) filter through a simulated shell and tube heat exchanger modeling example. The reason for this improvement is that the developed MSF modeling algorithm improves the model accuracy by integrating modeling and data filtering using a filter bank, from which the optimum filter (for modeling purposes) is selected.