Flight operation risk prediction model based on the multivariate chaotic time series
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摘要: 為了提升航班運行風險預測精度，基于某航空公司2016—2018年航班運行風險數據，在驗證15個風險時間序列的混沌特性后，構建基于多變量混沌時間序列的風險預測模型。首先，對15個風險時間序列進行多變量相空間重構，采用主成分分析法（PCA）對相空間進行降維處理；然后，基于迭代預測的方式，分別采用極限學習機、RBF神經網絡、回聲狀態網絡和Elman神經網絡建立風險短期預測模型；最后，以降維后的相空間作為輸入，計算并比較分析未來1～7 d的風險預測結果。結果表明：多變量相空間重構后總維數為62維，經PCA降維處理，降至31維；在不同的預測模型中，降維后RBF模型預測效果最佳；其中，預測第1天結果相對誤差<25%出現頻數為82.62%，至第5天仍達75%以上；該模型第1天預測結果的修正平均絕對百分比誤差（MAPE）值為11.32%，且前5 d均低于20%，滿足航空公司使用要求。1～5 d預測結果對航班風險管控具有實踐操作價值，證明基于多變量混沌時間序列的風險預測方案可行、有效。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 multivariate chaotic time series is feasible and effective.
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圖 8 預測結果示例。（a）第1天；（b）第3天；（c）第5天
Figure 8. Example of prediction results: (a) day 1; (b) day 3; (c) day 5
圖 10 RBF降維后的多變量預測精度
Figure 10. Prediction accuracy of the RBF model after dimension reduction
表 1 ICAO風險矩陣與中國民航局（CAAC）風險值
Table 1. ICAO risk matrix and CAAC risk value
Likelihood Severity Catastrophic,
AHazardous,
BMajor,
CMinor,
DNegligible,
EFrequent, 5 5A / 10 5B / 10 5C / 10 5D / 7 5E / 6 Occasional, 4 4A / 10 4B / 8 4C / 8 4D / 6 4E / 5 Remote, 3 3A / 9 3B / 8 3C / 7 3D / 5 3E / 2 Improbable, 2 2A / 8 2B / 7 2C / 6 2D / 4 2E / 1 Extremely improbable, 1 1A / 7 1B / 4 1C / 3 1D / 1 1E / 1 
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表 2 航班運行風險統計數據
Table 2. Risk assessment statistical data
Risk item Statistical meaning A1 Statistics of captain (non-instructor) and second co-pilot match times A2 Statistics of crew duty time or flight time less than 1 h times A3 Statistics of quick access recorder (QAR) blue and yellow warnings times after flight A4 Statistics times of captain’s experience less than 200 h and the total flight experience less than 3000 h A5 Statistics of the crew first match times to special airport in 12 calendar months A6 Statistics of temporary airborne failures times A7 Number of minimum equipment list (MEL)/configuration discrepancy list (CDL) reservations or MEL reservations affecting near landings A8 Statistics times of flights with special cargo or dangerous goods A9 Statistics of ground handling error times A10 Statistics of low fuel, yaw, abnormal altitude, etc. in flight monitoring A11 Statistics of times the airport failed to meet or on the edge of the weather criteria A12 Statistics of navigation equipment degradations, operating standards and obstacles temporary changes A13 Statistics of special weather (icing, thunderstorms, etc.,) which need to divert A14 Statistics of special operations (polar operations, re-dispatch flights, extended-range operations (ETOPS),
extended cross-water, overflying unmanned areas)A15 Statistics of route closure, flow control, height limit, etc. Total risk Comprehensive assessment from the above risk items
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表 3 航班運行風險時間序列局部數據樣本
Table 3. Time series sample data of flight operation risk
Sequence number/d A1 A2 A3 A4 A5 …… A13 A14 A15 Total risk 1 7 7 9 7 10 …… 8 10 8 8.5 2 6 7 9 6 9 …… 6 9 6 8 3 4 4 6 4 7 …… 3 6 3 5 4 4 4 6 1 4 …… 2 5 2 3 …… …… …… …… …… …… …… …… …… …… …… 1096 6 6 8 3 6 5 6 3 5 5
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表 4 時間序列的時間延遲、嵌入維和最大Lyapunov指數
Table 4. Time delay, embedding dimension, and maximum Lyapunov exponent of the time series
Risk item Time delay, $\tau $ Embedding dimension, $m$ Maximum Lyapunov
exponent, $\lambda $Risk item Time delay, $\tau $ Embedding dimension, $m$ Maximum Lyapunov
exponent, $\lambda $A1 3 4 0.5440 A9 2 9 0.2039 A2 4 2 0.9583 A10 3 3 0.9572 A3 3 4 0.5973 A11 2 8 0.2010 A4 6 3 0.9419 A12 2 4 0.2723 A5 4 2 0.8864 A13 3 4 0.7508 A6 4 3 0.9689 A14 3 4 0.6747 A7 4 2 1.1224 A15 2 4 0.3707 A8 3 6 0.2631 Total risk 4 5 0.3289
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表 5 主成分分析的方差貢獻率
Table 5. Partial variance contribution rate of PCA
Principal component Variance contribution/% Accumulative contribution rate/% Principal component Variance contribution/% Accumulative contribution rate/% 1 15.5907 15.5907 30 0.8018 89.8892 2 11.5223 27.1131 31 0.7893 90.6785 3 7.5821 34.6952 32 0.7054 91.3839 4 6.3632 41.0583 … … … … … … 62 0.0092 100.0000
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表 6 預測模型的參數優化結果
Table 6. Parameter optimization results of the prediction models
Parameter Value Parameter Value Hidden layer sizes of ELM 75 Leaking rate of ESN 0.80 Spread of RBF 1 Layer delays of Elman 4 Reservoir sizes of ESN 18 Hidden layer sizes of Elman 152
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表 7 各模型降維前后預測相對誤差頻數
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%
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