工程科学学报.第42卷.第12期：1664-1673.2020年12月 Chinese Journal of Engineering,Vol.42,No.12:1664-1673,December 2020 https://doi.org/10.13374/j.issn2095-9389.2019.12.09.002;http://cje.ustb.edu.cn 基于多变量混沌时间序列的航班运行风险预测模型 王岩韬四，李景良，谷润平 中国民航大学空管学院，天津300300 通信作者，E-mail:CAUCwyt@126.com 摘要为了提升航班运行风险预测精度，基于某航空公司2016一2018年航班运行风险数据，在验证15个风险时间序列的 混沌特性后，构建基于多变量混沌时间序列的风险预测模型.首先，对15个风险时间序列进行多变量相空间重构，采用主成 分分析法(PCA)对相空间进行降维处理：然后，基于迭代预测的方式，分别采用极限学习机、RBF神经网络、回声状态网络和 Elm神经网络建立风险短期预测模型：最后，以降维后的相空间作为输入.计算并比较分析未来1~7d的风险预测结果.结 果表明：多变量相空间重构后总维数为62维.经PCA降维处理.降至31维：在不同的预测模型中，降维后RBF模型预测效果 最佳：其中，预测第1天结果相对误差<25%出现频数为82.62%.至第5天仍达75%以上：该模型第1天预测结果的修正平均 绝对百分比误差(MAPE)值为11.32%，且前5d均低于20%.满足航空公司使用要求，1~5d预测结果对航班风险管控具有实 践操作价值，证明基于多变量混沌时间序列的风险预测方案可行、有效. 关键词航班运行风险：风险预测：多变量混沌时间序列：相空间重构：神经网络 分类号N945.24;X949U8 Flight operation risk prediction model based on the multivariate chaotic time series WANG Yan-tao,LI Jing-liang.GU Run-ping School of Air Traffic Management,Civil Aviation University of China,Tianjin 300300,China Corresponding author,E-mail:CAUCwyt@126.com ABSTRACT With the development of civil aviation safety management,the flight operation risk of airlines is of increasing concern. Risk prediction technology extracts information from historical and current risk data and uses it to predict short-term trends in the future. thus helping identify emerging risks and providing more time for risk management.Compared with non-dynamic risk assessment,this technology is more substantial for the management and control of flight operation risk.To improve the accuracy of flight operation risk prediction,on the basis of the flight risk data of a certain airline in 2016-2018,the chaotic characteristics of 15 risk time series were verified and a short-term risk prediction model based on the multivariate chaotic time series was constructed.First,multivariate phase space reconstruction was performed on 15 risk time series,and the phase space was reduced by the principal component analysis(PCA) method.Then,four short-term risk prediction models,namely,extreme learning machine,radial basis function(RBF)neural network, echo state network,and Elman neural network,were built on the basis of iterative prediction.Finally,the phase space after dimension reduction was used as the model input,and the risk prediction results for 1-7 d were calculated and compared.Results show that the total number of dimensions after multivariable phase space reconstruction is 62,which is reduced to 31 by PCA dimension reduction.Of the four prediction models,the RBF neural network model after dimension reduction has the best prediction effect.The occurrence frequency of<25%relative error is 82.62%for the first day and 75%for the fifth day.The corrected mean absolute percentage error for the first day is 11.32%,and lower than 20%for the next 4 d.Thus,the calculation results meet the requirements of the airline.The prediction results within 1-5 d have practical value for flight risk management,proving that the risk prediction method based on the 收稿日期：2019-12-09 基金项目：国家自然科学基金资助项目(01933103)基于多变量混沌时间序列的航班运行风险预测模型 王岩韬苣，李景良，谷润平 中国民航大学空管学院，天津 300300 苣通信作者，E-mail：CAUCwyt@126.com 摘    要    为了提升航班运行风险预测精度，基于某航空公司 2016—2018 年航班运行风险数据，在验证 15 个风险时间序列的 混沌特性后，构建基于多变量混沌时间序列的风险预测模型. 首先，对 15 个风险时间序列进行多变量相空间重构，采用主成 分分析法（PCA）对相空间进行降维处理；然后，基于迭代预测的方式，分别采用极限学习机、RBF 神经网络、回声状态网络和 Elman 神经网络建立风险短期预测模型；最后，以降维后的相空间作为输入，计算并比较分析未来 1～7 d 的风险预测结果. 结 果表明：多变量相空间重构后总维数为 62 维，经 PCA 降维处理，降至 31 维；在不同的预测模型中，降维后 RBF 模型预测效果 最佳；其中，预测第 1 天结果相对误差<25% 出现频数为 82.62%，至第 5 天仍达 75% 以上；该模型第 1 天预测结果的修正平均 绝对百分比误差（MAPE）值为 11.32%，且前 5 d 均低于 20%，满足航空公司使用要求. 1～5 d 预测结果对航班风险管控具有实 践操作价值，证明基于多变量混沌时间序列的风险预测方案可行、有效. 关键词    航班运行风险；风险预测；多变量混沌时间序列；相空间重构；神经网络 分类号    N945.24; X949; U8 Flight operation risk prediction model based on the multivariate chaotic time series WANG Yan-tao苣 ，LI Jing-liang，GU Run-ping School of Air Traffic Management, Civil Aviation University of China, Tianjin 300300, China 苣 Corresponding author, E-mail: CAUCwyt@126.com ABSTRACT    With the development of civil aviation safety management, the flight operation risk of airlines is of increasing concern. Risk prediction technology extracts information from historical and current risk data and uses it to predict short-term trends in the future, thus helping identify emerging risks and providing more time for risk management. Compared with non-dynamic risk assessment, this technology is more substantial for the management and control of flight operation risk. To improve the accuracy of flight operation risk prediction, on the basis of the flight risk data of a certain airline in 2016—2018, the chaotic characteristics of 15 risk time series were verified and a short-term risk prediction model based on the multivariate chaotic time series was constructed. First, multivariate phase space reconstruction was performed on 15 risk time series, and the phase space was reduced by the principal component analysis (PCA) method. Then, four short-term risk prediction models, namely, extreme learning machine, radial basis function (RBF) neural network, echo state network, and Elman neural network, were built on the basis of iterative prediction. Finally, the phase space after dimension reduction was used as the model input, and the risk prediction results for 1–7 d were calculated and compared. Results show that the total number of dimensions after multivariable phase space reconstruction is 62, which is reduced to 31 by PCA dimension reduction. Of the four prediction models, the RBF neural network model after dimension reduction has the best prediction effect. The occurrence frequency of <25% relative error is 82.62% for the first day and 75% for the fifth day. The corrected mean absolute percentage error for the first day is 11.32%, and lower than 20% for the next 4 d. Thus, the calculation results meet the requirements of the airline. The prediction results within 1–5 d have practical value for flight risk management, proving that the risk prediction method based on the 收稿日期: 2019−12−09 基金项目: 国家自然科学基金资助项目（U1933103） 工程科学学报，第 42 卷，第 12 期：1664−1673，2020 年 12 月 Chinese Journal of Engineering, Vol. 42, No. 12: 1664−1673, December 2020 https://doi.org/10.13374/j.issn2095-9389.2019.12.09.002; http://cje.ustb.edu.cn