基于双输出前馈神经网络和鲸鱼优化算法的区间预测方法  

Interval prediction based on double-output feedforward neural network and whale optimization algorithm

作　　者：马宇红 杨梅 孙亚娜 MA Yu-hong;YANG Mei;SUN Ya-na(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China;Editorial Department of the University Journal,Northwest Normal University,Lanzhou 730070,Gansu,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070 [2]西北师范大学学报编辑部,甘肃兰州730070

出　　处：《西北师范大学学报（自然科学版）》2021年第2期23-32,共10页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(51368055)。

摘　　要：结合改进的鲸鱼优化算法(WOA)、双输出前馈神经网络(DFNN)和上下界估计(LUBE)方法设计了一种新的区间预测算法WDL(WOA+DFNN+LUBE).首先,构建双输出前馈神经网络,以较大输出作为预测区间的上界,较小输出作为下界.其次,以区间覆盖宽度准则(CWC)作为网络优化目标,针对其非连续、非可微的特征,通过改进的鲸鱼优化算法优化双输出前馈神经网络.最后,通过10个通用数据集评估WDL算法的预测性能,并与GDL(GA+DFNN+LUBE)算法和PDL(PSO+DFNN+LUBE)算法进行比较;进一步,通过数据集分区技术分析数据分布对WDL算法性能的影响.结果表明:随着置信水平上升,WDL算法的预测区间覆盖率(PICP)快速减小,预测区间归一化平均宽度(PINAW)显著增加,预测性能明显下降;在90%的置信水平下,WDL算法的平均PICP接近1,而GDL和PDL算法的平均PICP只有0.9和0.8,平均PINAW分别为0.5554,0.6811和0.6403,WDL算法具有明显优势;对均值中心区域数据,WDL算法的平均PICP高达0.9860,而均值临近区域和偏远区域数据的平均PICP仅为0.9835和0.8106,对中位数中心区域数据,WDL算法的平均PICP高达0.9873,而中位数低值区域和高值区域数据的平均PICP仅为0.9377和0.8336,但PINAW并无明显差异,说明数据降噪能够显著改善WDL算法的性能.总之,WDL算法能够获得更高的PICP和更窄的PINAW,显著降低数据预测的不确定性,提高预测性能.The WDL(WOA+DFNN+LUBE)algorithm is proposed to interval prediction by combining whale optimization algorithm(WOA),double-output feedforward neural network(DFNN)and lower and upper bound estimation(LUBE)method.First,a DFNN is constructed,in which larger and smaller output is respectively regarded as upper bound and lower bound of prediction interval.Secondly,coverage width-based criterion(CWC)is selected as optimization target of the neural network,and an improved WOA is used to optimize neural network due to non-continuous and non-differentiable characteristics of target function.Finally,the interval prediction performance of WDL algorithm is evaluated with 10 popular data sets,and it is compared with that of GDL(GA+DFNN+LUBE)algorithm and PDL(PSO+DFNN+LUBE)algorithm.Furthermore,the influence of data distribution on interval prediction performance is analyzed by the data set partitioning methods.The results show that with the increase of confidence level,the prediction interval cover probability(PICP)of WDL algorithm decreases rapidly,while prediction interval normalized average width(PINAW)increases rapidly,the prediction performance decreases significantly.At the confidence level of 90%,the average PICP of WDL,GDL and PDL algorithm is respectively 1,0.9 and 0.8,while the average PINAW is 0.5554,0.6811 and 0.6403,so WDL algorithm has obvious advantages;the average PICP of WDL algorithm is up to 0.9860 for these data near the data mean,while average PICP is only 0.9835 and 0.8106 for those data far away from the mean;the average PICP is up to 0.9873 for these data near the data median,while the average PICP is only 0.9377 and 0.8336 for those data far away from the median,but the difference of average PINAW is not obvious,so the noise reduction can significantly improve the prediction performance of WDL algorithm.In conclusion,WDL algorithm can give a higher PICP and a narrower PINAW,which effectively reduces the uncertainty of data prediction and improves prediction performance.

关 键 词：区间预测 双输出前馈神经网络 鲸鱼优化算法 上下界估计 

分 类 号：TM715[电气工程—电力系统及自动化]