·1672 工程科学学报.第42卷，第12期 表7各模型降维前后预测相对误差频数 Table 7 RE frequency of each prediction model before and after dimension reduction RE frequency of prediction model before dimension reduction RE frequency of prediction model after dimension reduction Model Prediction range <259% 25%-50% >50% <25% 25%-50% >50% Day 1 131168.95% 41/21.58% 1819.47% 127166.84% 43/22.63% 20/10.53% ELM Day3 107156.32% 55/28.95% 28/14.74% 109/57.37% 46/24.21% 35/18.42% Day 5 115/60.53% 45/23.68% 30/15.79% 113/59.47% 46/24.21% 31/16.32% Day 1 157/82.63% 22/11.58% 11/5.79% 151/79.479% 27/14.21% 12/6.329% RBF Day 3 150/78.95% 20/10.53% 20/10.53% 138/72.63% 32/16.84% 20/10.53% Day 5 143/7526% 19/10.00% 21/11.05% 129/67.89% 28/14.74% 24/12.63% Day 1 111158.42% 53127.89% 26/13.68% 108/56.84% 56/29.47% 26/13.68% ESN Day 3 102/53.68% 58/30.53% 30115.79% 99152.11% 61/32.11% 30/15.79% Day 5 106155.79% 52/27.37% 32/16.84% 105/55.26% 46/24.21% 39/20.53% Day 1 142/74.74% 32/16.84% 16/8.42% 142/74.74% 35/18.42% 13/6.84% Elman Day3 116/61.05% 47/24.74% 27/14.21% 129/67.89% 31/16.329% 30/15.79% Day 5 109/57.37% 54/28.42% 27/14.21% 111/58.42% 47124.749% 32/16.84% 300 samples 500 samples 至第5天MAPE值仍为18.21%，说明未来5d的预 600 samples …700 samples --◆--800 samples -900 samples 测结果均可满足航空公司实践操作要求.从预测 35 30 精度和周期两个角度综合评判，多变量时间序列 方法对航班运行风险的预测可行且有效 国内航空公司以周为单位制定航班计划，因 10 此可在文中结果基础上，最早于5d前从飞机调配 5 和人员调度等方面调整计划编排，提前降低运行 0 Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 风险.该方案还可扩展至其他领域，适用于结果受 Prediction range 多变量综合影响的、各变量为混沌时间序列的短 图9训练样本数量与预测精度 期预测问题，其预测周期随多变量的混沌时间序 Fig.9 Number of training samples and prediction accuracy 列特性而定 30 25.44 25 2284 参考文献 15.1416.35 18.21 [Feng Z L.Promote the high-quality development of civil aviation 15 11.32 13.42 with the new development concept.People's Forum,2019(5):6 10 8 (冯正霖.以新发展理念引领新时代民航高质量发展.人民论坛 2019(5):6) 0 Day I Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 [2]Bowen B D,Headley D E,Luedtke J R.A quantitative Prediction range methodology for measuring airline quality.J Aviation/Aerospace 图10RBF降维后的多变量预测精度 Educ Res,.1992,2(2):27 Fig.10 Prediction accuracy of the RBF model after dimension reduction [3]Lower M.Magott J,Skorupski J.Analysis of air traffic incidents using event trees with fuzzy probabilities.Fy Sets Syst,2016, 4结论 293(C:50 [4] Kokangu A,Polat U,Dagsuyu C.A new approximation for risk 通过混沌识别和相空间重构，构建的4种风险 assessment using the AHP and Fine Kinney methodologies.Saf 预测模型在迭代预测后发现：在降维前后的ELM、 Sci,2017,91:24 RBF、ESN和Elman预测模型中，降维后的RBF预 [5]FAA.Flight risk assessment tool[EB/OL].Federal Aviation Administration Online (2007-08-02)[2018-08-31].https://www.faa 测模型效果最佳；其未来第1天预测结果RE<25% gov/news/safety_briefing/2016/media/SE_Topic_16-12.pdf 的频数可达到82.62%，修正MAPE值仅为11.32%； [6]NATA.NATA 's risk assessment tool -RA Check[EB/OL].4    结论 通过混沌识别和相空间重构，构建的 4 种风险 预测模型在迭代预测后发现：在降维前后的 ELM、 RBF、ESN 和 Elman 预测模型中，降维后的 RBF 预 测模型效果最佳；其未来第 1 天预测结果 RE<25% 的频数可达到 82.62%，修正 MAPE 值仅为 11.32%； 至第 5 天 MAPE 值仍为 18.21%，说明未来 5 d 的预 测结果均可满足航空公司实践操作要求. 从预测 精度和周期两个角度综合评判，多变量时间序列 方法对航班运行风险的预测可行且有效. 国内航空公司以周为单位制定航班计划，因 此可在文中结果基础上，最早于 5 d 前从飞机调配 和人员调度等方面调整计划编排，提前降低运行 风险. 该方案还可扩展至其他领域，适用于结果受 多变量综合影响的、各变量为混沌时间序列的短 期预测问题，其预测周期随多变量的混沌时间序 列特性而定. 参    考    文    献 Feng Z L. Promote the high-quality development of civil aviation with the new development concept. People's Forum, 2019（5）: 6 （冯正霖. 以新发展理念引领新时代民航高质量发展. 人民论坛, 2019（5）：6） [1] Bowen B D, Headley D E, Luedtke J R. A quantitative methodology for measuring airline quality. J Aviation/Aerospace Educ Res, 1992, 2（2）: 27 [2] Lower M, Magott J, Skorupski J. Analysis of air traffic incidents using event trees with fuzzy probabilities. Fuzzy Sets Syst, 2016, 293（C）: 50 [3] Kokangül A, Polat U, Dagsuyu C. A new approximation for risk assessment using the AHP and Fine Kinney methodologies. Saf Sci, 2017, 91: 24 [4] FAA. Flight risk assessment tool[EB/OL]. Federal Aviation Administration Online (2007-08-02)[2018-08-31]. https://www.faa. gov/news/safety_briefing/2016/media/SE_Topic_16-12.pdf [5] [6] NATA. NATA ’s risk assessment tool ‒RA Check[EB/OL]. 表 7 各模型降维前后预测相对误差频数 Table 7 RE frequency of each prediction model before and after dimension reduction Model Prediction range RE frequency of prediction model before dimension reduction RE frequency of prediction model after dimension reduction <25% 25%‒50% >50% <25% 25%‒50% >50% ELM Day 1 131 / 68.95% 41 / 21.58% 18 / 9.47% 127 / 66.84% 43 / 22.63% 20 / 10.53% Day 3 107 / 56.32% 55 / 28.95% 28 / 14.74% 109 / 57.37% 46 / 24.21% 35 / 18.42% Day 5 115 / 60.53% 45 / 23.68% 30 / 15.79% 113 / 59.47% 46 / 24.21% 31 / 16.32% RBF Day 1 157 / 82.63% 22 / 11.58% 11 / 5.79% 151 / 79.47% 27 / 14.21% 12 / 6.32% Day 3 150 / 78.95% 20 / 10.53% 20 / 10.53% 138 / 72.63% 32 / 16.84% 20 / 10.53% Day 5 143 / 75.26% 19 / 10.00% 21 / 11.05% 129 / 67.89% 28 / 14.74% 24 / 12.63% ESN Day 1 111 / 58.42% 53 / 27.89% 26 / 13.68% 108 / 56.84% 56 / 29.47% 26 / 13.68% Day 3 102 / 53.68% 58 / 30.53% 30 / 15.79% 99 / 52.11% 61 / 32.11% 30 / 15.79% Day 5 106 / 55.79% 52 / 27.37% 32 / 16.84% 105 / 55.26% 46 / 24.21% 39 / 20.53% Elman Day 1 142 / 74.74% 32 / 16.84% 16 / 8.42% 142 / 74.74% 35 / 18.42% 13 / 6.84% Day 3 116 / 61.05% 47 / 24.74% 27 / 14.21% 129 / 67.89% 31 / 16.32% 30 / 15.79% Day 5 109 / 57.37% 54 / 28.42% 27 / 14.21% 111 / 58.42% 47 / 24.74% 32 / 16.84% 0 5 10 15 20 25 30 35 Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Modified MAPE/ % Prediction range 300 samples 500 samples 600 samples 700 samples 800 samples 900 samples 图 9 训练样本数量与预测精度 Fig.9 Number of training samples and prediction accuracy Prediction range 11.32 13.42 15.14 16.35 18.21 22.84 25.44 0 5 10 15 20 25 30 Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Modified MAPE/ % 图 10 RBF 降维后的多变量预测精度 Fig.10 Prediction accuracy of the RBF model after dimension reduction · 1672 · 工程科学学报，第 42 卷，第 12 期