基于“回归+马尔可夫”组合模型的民用航空事故症候数预测

doi:10.12305/j.issn.1001-506X.2023.07.22

摘要/Abstract

摘要：

民航事故症候数预测对于民航安全具有重要的意义。准确的预测民航事故症候数的发展趋势可以指导采取合适的事故预防措施, 从而尽可能地减少民航事故数。本文在回归模型的基础上, 发展了“回归+马尔可夫”组合模型来进行民用航空事故症候数的预测。其中回归模型用于发展趋势项的预测, 马尔可夫模型用于随机干扰项的预测。通过中国民航局以及国家统计局发布的2006~2020年的历史统计数据, 计算了回归模型、GM(1, 1)灰色模型和“回归+马尔可夫”组合模型的拟合及测试误差。结果表明, “回归+马尔可夫”组合模型的拟合精度以及测试精度相比单一模型均得到了有效提高。

关键词: 民航, 事故症候预测, 回归+马尔可夫, 灰色模型

Abstract:

Prediction of the number of civil aviation accident symptoms is of great significance to civil aviation safety. Accurate prediction of the development trend of the number of civil aviation accident symptoms can guide the adoption of appropriate accident prevention measures, so as to reduce the number of civil aviation accidents as much as possible. Based on the regression model, this paper develops a combined model of "regression+Markov" to predict the number of accident symptoms in civil aviation. The regression model is used to predict the trend term and the Markov model is used to predict the random disturbance term. Based on the historical statistical data of Civil Aviation Administration of China (CAAC) and National Bureau of Statistics from 2006 to 2020, the fitting and test errors of regression model, GM (1, 1) and "regression+Markov" combined model are calculated. The results show that the fitting goodness and test accuracy of "regression+Markov" combined model are improved effectively compared with the single model.

Key words: civil aviation, prediction of accident symptoms, regression+Markov, grey model

中图分类号:

王华友, 张诚诚, 薛海红, 刘轶斐. 基于“回归+马尔可夫”组合模型的民用航空事故症候数预测[J]. 系统工程与电子技术, 2023, 45(7): 2114-2120.

Huayou WANG, Chengcheng ZHANG, Haihong XUE, Yifei LIU. Prediction of the number of accident symptoms in civil aviation based on "regression+Markov" combined model[J]. Systems Engineering and Electronics, 2023, 45(7): 2114-2120.

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年份	事故症候数	飞行小时 (×10⁴)/h	飞行架次 (×10⁴)	人均GDP/元
2006	117	342.83	197.17	16 738
2007	117	397.28	221.86	20 494
2008	119	422.96	236.76	24 100
2009	161	481.48	278.42	26 180
2010	221	551.33	303.74	30 808
2011	233	612.51	348.78	36 277
2012	302	680.67	392.09	39 771
2013	302	754.49	437.62	43 497
2014	344	835.94	490.86	46 912
2015	394	933.66	539.67	49 922
2016	545	1 029.79	558.41	53 783
2017	601	1 149.74	617.02	59 592
2018	608	1 253.21	672.30	65 534
2019	584	1 343.10	739.11	70 328
2020	466	979.03	601.98	72 000

自变量	年份	飞行小时	飞行架次	人均GDP
拟合误差	9.00	14.27	12.88	10.61
测试误差	79.75	11.95	7.90	77.37

年份	y(k)	ŷ(k)	相对残差/%	状态空间
2006	117	127.13	-7.97	3
2007	117	138.25	-15.37	3
2008	119	145.43	-18.17	4
2009	161	167.53	-3.90	3
2010	221	182.58	21.05	1
2011	233	212.76	9.51	2
2012	302	246.48	22.53	1
2013	302	287.70	4.97	2
2014	344	344.73	-0.21	3
2015	394	406.89	-3.17	3
2016	545	433.63	25.68	1
2017	601	529.15	13.58	2
2018	608	638.44	-4.77	3
2019	584	801.08	-27.10	4

年份	实际值	回归模型			回归+马尔可夫模型
年份	实际值	预测值	相对误差/%	平均误差/%	预测值	相对误差/%	平均误差/%
2006	117	127.13	-8.66	12.88	115.69	1.12	4.14
2007	117	138.25	-18.16		125.81	-7.53
2008	119	145.43	-22.21		110.53	7.12
2009	161	167.53	-4.06		152.45	5.31
2010	221	182.58	17.39		226.39	-2.44
2011	233	212.76	8.69		231.91	0.47
2012	302	246.48	18.39		305.63	-1.20
2013	302	287.70	4.74		313.59	-3.84
2014	344	344.73	-0.21		313.70	8.81
2015	394	406.89	-3.27		370.27	6.02
2016	545	433.63	20.44		537.70	1.34
2017	601	529.15	11.96		576.77	4.03
2018	608	638.44	-5.01		580.98	4.44
2019	584	801.08	-37.17		608.82	-4.25

年份	实际值	回归模型		回归+马尔可夫模型
年份	实际值	预测值	相对误差/%	预测值	相对误差/%
2020	466	502.79	-7.90	457.54	1.81