日径流预报贝叶斯回声状态网络方法

回声状态网络（ESN）相比传统递归神经网络，具有模型简单、参数训练速度快的特点．针对标准ESN因常采用线性回归率定模型参数容易出现过拟合问题，提出了基于贝叶斯回声状态网络（BESN）的日径流预报模型．该模型将贝叶斯理论与ESN模型相结合，通过权重后验概率密度最大化而获得最优输出权重，提高了模型的泛化能力．通过安砂和新丰江两座水库日径流预测实例表明，BESN模型是一种有效、可行的预测方法，与传统BP神经网络和ESN模型对比，进一步表明BESN模型具有更好的预测精度．

Daily rainfall-runoff forecasting using Bayesian echo state network

The echo state network （ESN） is simpler and costs less training time than traditional recurrent neural networks. Due to linear regression algorithm usually adopted by standard ESN to calibrate model parameters, the over-fitting phenomenon easily occurs. To overcome this shortcoming, a Bayesian echo state network （BESN） model is proposed for daily rainfall-runoff forecasting. The BESN model combined Bayesian theory and ESN obtains the optimal output weights via maximizing posterior probabilistic density and improves its generalization ability. Two Case studies on daily inflow forecasting for Ansha Reservoir and Xinfengjiang Reservoir show that the BESN model is effective and feasible and can provide better forecast accuracy than the traditional BP neural network and ESN models.