Comparing A Bayesian and Fuzzy Number Approach to Uncertainty Quantification in Short-Term Dissolved Oxygen Prediction

Abstract

A new autoregressive-type, updating fuzzy linear regression method is proposed to predict daily dissolved oxygen (DO) concentration in a highly urbanized riverine environment. Results of this model are compared to results from an updating Bayesian regression model. Both methods use lagged daily DO (at four different lags) as the independent variable. Uncertainty in the models is represented by a fuzzy number based approach in the first case, and by a Bayesian framework in the second. Real-time data from the Bow River in Calgary, Canada is used to calibrate the models sequentially to mimic a real-time updating model. Four different performance metrics were used to measure the performance of each model. Lastly, the input data resolution is reduced to measure the impact on model performance. Results show that the physical system can be adequately characterized using only one year of data. Both approaches can capture the general trend of daily DO, but the fuzzy number based method can better capture the changes in observed variability. The metrics for both models are comparable, with the one-day lag case categorized as “very goodâ€; however, the performance reduces at higher lags. The fuzzy number method captures more low DO events than the Bayesian approach, with a much lower mean squared error. A possibility to probability transformation is used to highlight the risk of low DO days for the fuzzy case. Lastly, reducing the input data resolution from 96 to 6 points per day has a minimal impact on model performance, suggesting the limited efficacy or utility in increasing sampling rates.

Keywords: dissolved oxygen, Bayesian liner regression, fuzzy linear regression, uncertainty analysis, river water quality