Optimization of fuzzy membership function of runoff forecasting error based on the optimal closeness - Jiang, Zhiqiang; Wu, Wenjie; Qin, Hui; Hu, Dechao; Zhang, Hairong (Journal of hydrology (Amsterdam), 2019)
•A fuzzy membership function optimization model of runoff forecast error is proposed.•Multiple closeness criterions and fuzzy distribution functions are used in this model.•Normal, Cusp Γ and Cauchy distributions are used to find the best membership function.•Cusp Γ distribution is the better than others, its average closeness can reach 0.979. The forecasted runoff is an important input data for the daily operation of hydropower station, and the forecast accuracy directly affects its operation efficiency. However, the forecasting error is inevitable, and it is influenced by the input, the structural parameters and many human factors, it is not only random, but also has great fuzziness. Therefore, it is very important to study the fuzziness of runoff forecasting error and reveal its fuzzy distribution law to guide the actual operation of hydropower station. In view of this, this paper has carried out research work in the following two aspects. At the theoretical level, in order to make the establishment of fuzzy set more objective and scientific, based on different theoretical fuzzy distribution functions and the parameter optimization method, an overall framework of fuzzy membership function optimization model is proposed by coupling the optimal closeness criterion, which can make full use of the guiding role of practical experience and at the same time effectively avoid the difficulty of subjective choice. At the practical level, in order to quantify the fuzzy characteristics of runoff forecasting error, a quantification method for runoff forecasting error in fuzzy environment is proposed based on the Hamming closeness, Cauchy distribution, Normal distribution and Cusp Γ distribution. Taking the Jinxi hydropower station of Yalong River basin as the research object, the fuzzy membership functions of the fuzzy sets of runoff forecasting error under different flow intervals are calculated and optimized by the proposed method. The results show that the optimized Cusp Γ distribution can fit the actual data points better compared with Cauchy distribution and Normal distribution, and its average closeness can reach 0.979. So, the accurate mathematical expression of the fuzzy distribution law of runoff forecasting error under different flow intervals is well realized, which provides a good basis for the fuzzy risk analysis of hydropower station operation.