摘要
It is widely accepted that Prediction Interval (PI) can provide more accurate and precise information than deterministic forecast when the uncertainty level increases in flood forecasting. Coverage probability and PI width are two main criteria used to assess the constructed PI, rarely has there been an index to quantify the symmetry between target value and PI. This study extends a newly proposed PI estimation method called Lower Upper Bound Estimation (LUBE) method, which adopts an Artificial Neural Network (ANN) with two outputs to directly generate the upper and lower bounds of PI without making any assumption about the data distribution. A new Prediction Interval Symmetry (PIS) index is introduced and a new objective function is developed for the comprehensive evaluation of PI considering their coverage probability, width and symmetry. Furthermore, Shuffled Complex Evolution algorithm (SCE-UA) is used to minimize the objective function and optimize ANN parameters in the LUBE method. The proposed method is applied to a real world flood forecasting case study of the upper Yangtze River Watershed. The result shows that the SCE-UA based LUBE method with new objective function is very efficient, meanwhile, the midpoint forecasting of the PI obtains excellent performance by evidently improving the symmetry of PI. Keywords Prediction interval Symmetry Artificial neural networks Uncertainty Flood forecasting Shuffled complex evolution