Abstract 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.

中文翻译：

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基于最优接近度的径流预测误差模糊隶属函数优化

摘要 预测径流是水电站日常运行的重要输入数据，预测精度直接影响其运行效率。然而，预测误差是不可避免的，它受输入、结构参数和许多人为因素的影响，不仅是随机的，而且具有很大的模糊性。因此，研究径流预测误差的模糊性，揭示其模糊分布规律，对指导水电站实际运行具有重要意义。鉴于此，本文从以下两个方面开展了研究工作。在理论层面，为了使模糊集的建立更加客观、科学，基于不同的理论模糊分布函数和参数优化方法，通过耦合最优接近度准则，提出了模糊隶属函数优化模型的总体框架，可以充分利用实践经验的指导作用，同时有效避免主观选择的困难。在实践层面，为了量化径流预测误差的模糊特征，提出了一种基于汉明接近度、柯西分布、正态分布和Cusp Γ分布的模糊环境下径流预测误差的量化方法。以雅砻江流域锦西水电站为研究对象，采用该方法计算并优化了不同流量区间下径流预测误差模糊集的模糊隶属度函数。结果表明，优化后的Cusp Γ分布与Cauchy分布和正态分布相比，能够更好地拟合实际数据点，其平均贴近度可达0.979。因此，较好地实现了不同流量区间下径流预测误差模糊分布规律的精确数学表达式，为水电站运行的模糊风险分析提供了良好的基础。