最近，机器学习方法逐渐在水利工程中得到广泛运用。本研究将采用最小二乘支持向量机（LSSVM）方法，建立阶梯式溢洪道各种流态下复氧率的预测模型。采用粒子群优化算法（PSO）优化了LSSVM算法的参数（惩罚函数γ和核函数常数σ2），新的PSO-LSSVM模型预测精度相对于常用的BP模型明显提高。误差分析表明，在测试集上PSO-LSSVM模型的平均绝对百分比误差MAPE、均方差RMSE和平方相关系数R2分别为1.1000×10-3, 4.8996×10-4和9.9986×10-1。最后，采用平均影响值法评价了输入参数对复氧率的影响程度。
Abstract
Recently, machine learning methods have been widely used in hydraulic engineering. In this study, the least squares support vector machine (LSSVM) algorithm was used to establish a prediction model for the re-aeration rate of stepped spillway under various flow regimes. Particle swarm optimization (PSO) was used to optimize the parameters (the penalty parameter γ and kernel constant σ2) of the LSSVM algorithm. The prediction accuracy of the new PSO-LSSVM model was significantly improved compared with the commonly used BP model. Error analysis showed that the average absolute percentage error MAPE, root-mean-square error RMSE and square correlation coefficient R2 of PSO-LSSVM model on test set were 1.1000×10-3, 4.8996×10-4 and 9.9986×10-1, respectively. Finally, the effect of input parameters on the re-aeration rate was evaluated by means of the mean impact value method.
关键词
机器学习 /
最小二乘支持向量机 /
复氧率 /
粒子群优化 /
平均影响值
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Key words
machine learning /
least squares support vector machine /
re－aeration rate /
particle swarm optimization /
mean impact value
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