CN111724053B - Aviation network risk propagation identification method - Google Patents
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Abstract
The invention discloses an aviation network risk propagation identification method, which is applied to the field of civil aviation risk assessment and comprises the following steps: determining an airport risk coefficient for the preprocessed airport pair risk time sequence data based on a pre-established airport risk coefficient model; determining a checking order according to the airport risk coefficient, and determining a corresponding residual square sum based on the checking order and the corresponding airport risk time sequence; the residual sum of squares is examined to identify risk propagation relationships between the airport pairs. The method determines the corresponding residual sum of squares based on the inspection order and the corresponding risk time sequence of the airport; and (4) the sum of squares of the residual errors is checked to identify the risk propagation relationship between the airport pairs, so that the judgment of whether risk propagation exists between two airports in the aviation network is realized.
Description
Technical Field
The invention belongs to the field of civil aviation risk assessment, and particularly relates to an aviation network risk propagation identification method.
Background
In the running process of the aircraft network, the propagation and sweep effect of the running risk are extremely strong, and the running safety and efficiency of other airports are influenced and the running risk is increased when some important airports are influenced by sudden weather or accidents, so that the running efficiency and the running safety of the global network are reduced. Therefore, research work on the operation risk propagation of the aviation network is increasingly important, and the operation risk propagation problem of the aviation network is also increasingly required to be paid attention. How to reasonably quantify the operation risk of the aviation network and how to accurately identify the propagation of the operation risk also become important problems in the field of civil aviation.
In terms of aviation network operation risk quantification, the Federal Aviation Administration (FAA) originally proposed a single safety index as a civil aviation operation safety risk index. Other foreign civil aviation institutions and units also make researches on the definition and evaluation of risk indexes through different angles, and the general idea is to adopt a risk evaluation matrix, measure the risk level by calculating risk probability and make different grades on the risk. The risk quantification and the selection of risk indexes are also developed for a great deal of research in China. A risk safety evaluation system is established by the China civil aviation administration based on an accident incentive level, indexes are established mainly from the aspects of people, machines, environment, management and the like, and a risk judgment method of mixed indexes is provided. At present, although a great number of technical methods are available for risk assessment and indexes of the overall level of the civil aviation industry, the technical methods for operation risk indexes and risk quantification of the aviation network level are relatively lacked. Although Ringelnei et al rate risk in the congestion aspect of the aviation network, the risk is limited to the local space embodiment factor of congestion, and a complete operation risk quantification method at the aviation network level is still lacking at present.
Disclosure of Invention
In view of this, the present invention aims to provide an aviation network risk propagation identification method, which is intended to make up for the shortage of an aviation network level operation risk quantification method.
In order to achieve the purpose, the invention provides the following technical scheme:
an aviation network risk propagation identification method comprises the following steps:
determining an airport risk coefficient for the preprocessed airport pair risk time sequence data based on a pre-established airport risk coefficient model;
determining a checking order according to the airport risk coefficient;
determining a corresponding sum of squares of residuals based on the inspection order and the corresponding airport pair risk time series;
the residual sum of squares is examined to identify risk propagation relationships between the airport pairs.
Optionally, determining an airport risk coefficient model includes:
acquiring an average takeoff delay time sequence and an airport saturation sequence of each airport in the historical flight data within a preset time period;
and clustering the average takeoff delay time sequence and the airport saturation time sequence after normalization processing to obtain a corresponding clustering range.
Optionally, the obtaining of the average takeoff delay time sequence and the airport saturation sequence of each airport in the historical flight data within the preset time period includes:
the average takeoff delay time meets the following requirements:
wherein d is i (t) is the average takeoff delay time of the airport i in the time period from t to t +1, D i (t) is the total takeoff delay time of the i airport in the time period from t to t +1, C i (t) the number of flight cancellation of the i airport in the time period from t to t +1, the equivalent takeoff delay time of the flight cancellation in 3 hours, and p i (t) is the total number of scheduled take-off flights of the i airport in the time period from t to t + 1;
airport saturation, satisfies:
wherein s is i (t) is the saturation of i airport in the time period from t to t +1, Q i (t) the arrival traffic at airport i in the time period from t to t +1, C i (t) airport capacity of i airport in time period t to t + 1.
Optionally, clustering the average takeoff delay time sequence and the airport saturation time sequence after the normalization processing includes:
and clustering the takeoff delay time and the airport saturation of all airports in the time period from t to t +1 to obtain a delay interval and a saturation interval.
Optionally, determining the airport risk coefficient model further includes:
determining a clustering range corresponding to the average takeoff delay time and the airport saturation of each airport in the time period from t to t +1 in the aviation network;
mapping the average takeoff delay time and airport saturation of each airport in the aviation network in the time period from t to t +1 into corresponding delay weight and saturation weight through a mapping function according to the corresponding clustering range;
wherein, the delay weight satisfies:
the saturation weight satisfies:
wherein, W d (k, t) and W s (k, t) are respectively the delay weight and saturation weight of the airport k in the time period from t to t +1, d k (t) and s k (t) the average takeoff delay and the saturation value of the airport k in the time period from t to t +1 respectively, and n is the number of the intervals obtained by clustering;
establishing an airport risk coefficient model according to the delay weight and the saturation weight, and satisfying the following conditions:
R k (t)＝||W d (k，t)+W s (k，t)||
wherein R is k (t) is the risk factor for airport k.
Optionally, determining a checking order according to the airport risk coefficient includes:
performing a granger test on the clustered airport risk coefficients;
the inspection rank is determined for the range of risk classes based on the airport obtained from the grangey inspection.
Optionally, determining a corresponding sum of squares of residuals based on the inspection rank and the corresponding airport pair risk time series includes:
respectively constructing an unconstrained regression model and a constrained regression model according to the inspection order and the corresponding risk time sequence of the airport pair;
and determining the corresponding unconstrained residual sum of squares and constrained residual sum of squares according to the unconstrained regression model and the constrained regression model.
Optionally, the checking the sum of squares of the residuals includes:
and F test, chi-square test and likelihood ratio test are carried out on the unconstrained residual square sum and the constrained residual square sum.
Optionally, identifying a risk propagation relationship between the pair of airports includes:
and if all the inspection results exceed the preset critical value, judging that risk propagation exists between the airport pairs.
Optionally, after identifying the risk propagation relationship between the pair of airports, the method further includes:
all airport pairs within the airline network are inspected to identify overall risk propagation relationships for the airline network.
The invention has the beneficial effects that: the method determines the corresponding residual sum of squares based on the inspection order and the corresponding risk time sequence of the airport; the sum of the squares of the residual errors is checked to identify the risk propagation relationship between the airport pairs, so that the judgment of whether risk propagation exists between two airports in the aviation network is realized, and the purpose of operating risk propagation identification of the aviation network can be achieved according to the identified risk propagation network.
Drawings
In order to make the object, technical scheme and beneficial effect of the invention more clear, the invention provides the following drawings for explanation:
FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is a flow chart of a risk quantification method according to an embodiment of the present invention;
fig. 3 is a flowchart of a risk propagation identification method according to an embodiment of the present invention.
Detailed Description
Preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
The embodiment of the invention provides an aviation network risk propagation identification method, which comprises the following steps of:
determining an airport risk coefficient for the preprocessed airport pair risk time sequence data based on a pre-established airport risk coefficient model;
determining a checking order according to the airport risk coefficient;
determining a corresponding sum of squares of residuals based on the inspection order and the corresponding airport pair risk time series;
the residual sum of squares is examined to identify risk propagation relationships between the airport pairs.
The method determines the corresponding residual sum of squares based on the inspection order and the corresponding risk time sequence of the airport; the sum of the squares of the residual errors is checked to identify the risk propagation relationship between the airport pairs, so that the judgment of whether risk propagation exists between two airports in the aviation network is realized, and the purpose of operating risk propagation identification of the aviation network can be achieved according to the identified risk propagation network.
Optionally, determining an airport risk coefficient model includes:
acquiring an average takeoff delay time sequence and an airport saturation sequence of each airport in the historical flight data within a preset time period;
and clustering the average takeoff delay time sequence and the airport saturation time sequence which are subjected to normalization processing to obtain a corresponding clustering range.
Specifically, the method mainly comprises two parts of contents, namely a first part risk quantification method and a second part risk propagation identification. The second part risk propagation identification requires as input the risk coefficients output by the first part in order to identify risk propagation between airports.
Optionally, the obtaining of the average takeoff delay time sequence and the airport saturation sequence of each airport in the historical flight data within the preset time period includes:
the average takeoff delay time meets the following requirements:
wherein, d i (t) is the average takeoff delay time of the airport i in the time period from t to t +1, D i (t) is the total takeoff delay time of the i airport in the time period from t to t +1, C i (t) is t to t +Number of cancelled flights at i airport in 1 time period, equivalent takeoff delay time for cancelling flights in 3 hours, P i (t) is the total number of scheduled take-off flights of the i airport in the time period from t to t + 1;
airport saturation, satisfies:
wherein s is i (t) is the saturation of i airport in the time period from t to t +1, Q i (t) airport arrival traffic at i airport in time period t to t +1, C i (t) airport capacity of i airport in time period from t to t + 1.
In this embodiment, the first part of risk quantification method is described, and in a specific embodiment, the determining an airport risk coefficient model includes:
and acquiring the average takeoff delay time and the time sequence of the airport saturation of each airport in a specific time period according to historical flight data. The time sequence may be one time unit of 1 hour, and the 1 hour is divided into 12 time intervals, so that the average takeoff delay time and the airport saturation can be calculated every 5 minutes. The average takeoff delay time and the airport saturation are calculated according to the following formula:
wherein d is i (t) is the average takeoff delay time of the airport i in the time period from t to t +1, D i (t) is the total takeoff delay time of the i airport in the time period from t to t +1, C i (t) the number of flight cancellation of the i airport in the time period from t to t +1, the equivalent takeoff delay time of the flight cancellation in 3 hours, P i (t) is the total number of scheduled takeoff flights for the i airport during the time period t to t + 1.
Wherein s is i (t) is the saturation of i airport in the time period from t to t +1, Q i (t) airport arrival traffic at i airport in time period t to t +1, C i (t) airport capacity of i airport in time period t to t + 1.
Optionally, clustering the average takeoff delay time sequence and the airport saturation time sequence after the normalization processing includes:
and clustering the takeoff delay time and the airport saturation of all airports in the time period from t to t +1 to obtain a delay interval and a saturation interval.
Specifically, in the present example, as shown in fig. 2, the data normalization processing is further performed on the obtained average takeoff delay and saturation, respectively. Clustering the takeoff delay time of all airports in the time period from t to t +1 to obtain 4 delay intervals ([0, lambda ] d，1 ]，[λ d，1 ，λ d，2 ]，[λ d，2 ，λ d，3 ]，[λ d，3 ，max(d i (t))]) With a 3 interval boundary value (lambda) d，1 ，λ d，2 ，λ d，3 ) And simultaneously clustering the saturation of all airports to obtain 4 saturation intervals ([0, lambda ] 3，1 ]，[λ s，1 ，λ s，2 ]，[λ s，2 ，λ s，3 ]，[λ s，3 ，max(s i (t))]) With a 3 interval boundary value (lambda) s，1 ，λ s，2 ，λ s，3 )。
Optionally, determining the airport risk coefficient model further includes:
determining a clustering range corresponding to the average takeoff delay time and the airport saturation of each airport in the time period from t to t +1 in the aviation network;
mapping the average takeoff delay time and airport saturation of each airport in the aviation network in the time period from t to t +1 into corresponding delay weight and saturation weight through a mapping function according to the corresponding clustering range;
wherein, the delay weight satisfies:
and the saturation weight satisfies the following conditions:
wherein, W d (k, t) and W s (k, t) are respectively the delay weight and saturation weight of the airport k in the time period from t to t +1, d k (t) and s k (t) the average takeoff delay and the saturation value of the airport k in the time period from t to t +1 respectively, and n is the number of the intervals obtained by clustering;
establishing an airport risk coefficient model according to the delay weight and the saturation weight, and satisfying the following conditions:
R k (t)＝||W d (k，t)+W s (k，t)||
wherein R is k (t) is the risk factor for airport k.
Specifically, in this embodiment, according to the obtained delay interval and saturation interval, the average takeoff delay and saturation of each airport in the network in the time period from t to t +1 are mapped to the corresponding interval, and are mapped to the corresponding delay weight and saturation weight through the corresponding mapping function based on the gaussian kernel function.
Delay weight mapping function:
saturation weight mapping function:
wherein, W d (k, t) and W s (k, t) are respectively the delay weight and saturation weight of k airport in the time period from t to t +1, d k (t) and s k (t) mean takeoff at k airports over a period of t to t +1, respectivelyDelay and saturation values, n is the number of intervals obtained by clustering, and n is 4 according to step 2.
Risk factor R of last airport k k (t) may be determined as a modulus of a two-dimensional plane vector synthesized by the delay weight vector and the saturation weight vector:
R k (t)＝||W d (k，t)+W s (k，t)||
based on the risk quantification coefficient of the airport k in the time period from t to t + 1. Calculating risk coefficient R for all time intervals of all airports in the network within 1 hour time period respectively k (t) forming a corresponding risk time series for the corresponding airport.
Optionally, determining a checking order according to the airport risk coefficient includes:
performing a granger test on the clustered airport risk coefficients;
the inspection rank is determined for the range of risk classes based on the airport obtained from the grangey inspection.
The embodiment includes the content of the second part of risk propagation identification, specifically, the acquired risk time series of the airport pairs a and B in the aviation network are preprocessed, as shown in fig. 3, where the preprocessing includes performing Z-Score standardization, removing data trend and average value, performing ADF inspection, verifying data stationarity after standardization, and performing first-order difference operation on the data if the data is not stable.
After obtaining the stationary data, the overall risk factor for each airport for 1 hour is calculated according to the airport risk factor model, as shown in fig. 3, and the maximum lag period maxlag of the granger test is the average of the risk level of the airport a and the risk level of the airport B. And finally, in the range of 1 to maxlag, selecting the order with the minimum AIC value in each regression as the order of final inspection, and recording the order as L.
Optionally, determining a corresponding sum of squares of residuals based on the inspection rank and the corresponding airport pair risk time series includes:
respectively constructing an unconstrained regression model and a constrained regression model according to the inspection order and the corresponding risk time sequence of the airport pair;
and determining the corresponding unconstrained residual sum of squares and constrained residual sum of squares according to the unconstrained regression model and the constrained regression model.
Specifically, in this embodiment, risk time series R from airport A, B A (t) and R B (t) constructing two regression models, and obtaining the unconstrained residual square sum RSS according to the two regression models u And constrained Residual Sum of Squares (RSS) r 。
Unconstrained regression model (u):
constrained regression model (r):
in the present embodiment, an initial assumption H 0 : the B airport risk time series is not the Glanberg cause of the A airport risk, i.e. in unconstrained regression (u), B 1 ＝b 2 ＝...＝b L ＝0。
Optionally, the checking the sum of squares of the residuals includes:
and F test, chi-square test and likelihood ratio test are carried out on the unconstrained residual square sum and the constrained residual square sum.
Specifically, in the present embodiment, F test, chi-square test, and likelihood ratio test are performed on the sum of squared residuals of the two regression models.
More specifically, the conventional granger test is an F-test on the sum of the squared residuals of two models, namely:
where n is the length of each risk time series and L is the lag chosen by the AIC criterionThe number of last steps. If the calculated F-value at a selected significance level alpha exceeds the critical F a Value, then refuse H 0 Assuming that the B airport risk time series is the Greenger reason for the A airport risk, B propagates the risk to A.
The traditional regression analysis F test is limited to the test of a regression coefficient, and only can be used for simply determining whether the airport B risk time series is helpful to improve the prediction of the airport A risk time series, but the overall fitting effect of a complex model introducing B parameters and the significance of model difference can not be ensured to meet the requirement of statistical credibility. Furthermore, there is a large error in the condition of regression coefficients or model nonlinearity. In a few cases, the B airport sequences can help to improve the prediction of the A airport sequences due to accidental factors, but the significance and the fitting effect of the complex model introducing the B parameters do not meet the statistically credible standard.
Therefore, in this embodiment, the chi-square test and the likelihood ratio test model are further introduced, so that the occurrence of the few cases can be effectively avoided, the significance of the regression model difference (the greater the significance is, the better the effect of the free regression model introduced into the airport B parameters is) and the model fitting effect are verified, and the test accuracy is improved. The chi-square test can check and correct the misjudgment condition of the traditional F test under some nonlinear conditions, the likelihood ratio test can verify the significance of the difference of the regression model, and the effect of the unconstrained regression model introduced with the airport B parameters is obviously better than the fitting effect of the constrained regression model.
Specifically, in this embodiment, the chi-square test based on the sum of squared residuals satisfies:
calculated χ at selected significance level α 2 Whether the value exceeds the critical χ a 2 Value, if exceeded, reject H 0 It is assumed.
Further, in the present embodiment, a likelihood ratio test (LR) is introduced, which satisfies:
LR＝2*(ln(L u )-ln(L r ))
wherein L is u For the maximum likelihood value of the unconstrained regression model, L r Is the constrained model maximum likelihood value. Whether the calculated LR value at a selected significance level alpha exceeds the critical LR α Value, if exceeded, reject H 0 It is assumed.
Optionally, identifying a risk propagation relationship between the pair of airports includes:
and if all the inspection results exceed the preset critical value, judging that risk propagation exists between the airport pairs.
Specifically, based on the aforementioned F-test, chi-square test and likelihood ratio test, in this embodiment, when all the test results show rejection of H 0 Assuming that, the B airport risk time series can be considered the Greenger's cause of the A airport risk, B propagates the risk to A. As long as one does not satisfy rejection H 0 Assuming the conditions, B is considered to not propagate the risk to a. And conversely, whether the A is helpful to predict the risk time series of the B is also checked, and finally, the risk propagation relation between the airport A and the airport B is identified.
Optionally, after identifying the risk propagation relationship between the pair of airports, the method further includes:
all airport pairs within the airline network are inspected to identify overall risk propagation relationships for the airline network.
Specifically, in this embodiment, the inspection is performed on all airports within the aviation network, and the overall risk propagation condition in the aviation network is finally identified. And finally, establishing a directed risk propagation network by taking the airports as nodes and the propagation relation as directed edges, connecting the two airports if the risk propagation relation exists between the two airports, and pointing the arrows from the risk source airport to the propagated airport.
In summary, the invention comprises two major components of an aviation network operation risk quantification method and a risk propagation identification technology. The first partial risk quantification method is the basis of the second partial risk propagation identification technique. The second part risk propagation identification requires as input the risk coefficients output by the first part in order to identify risk propagation between airports.
An aviation network is a complex network in which airports or waypoints serve as nodes of the network and the routings between the airports serve as edges of the network. At present, in the field of civil aviation, the research on the quantification of the operation risk value of the aviation network is less, and the first part of the invention is to provide a novel clustering algorithm-based aviation network risk quantification method. The method starts from two angles of operation efficiency and operation safety, two local risk factors of airport average takeoff delay and airport saturation are selected according to two dimensions of time dimension and space dimension, and a clustering algorithm and mapping coupling are applied to quantify macroscopic risk coefficients. The average takeoff delay can improve the operation efficiency of an airport and a network, the saturation can show the load condition of the airport, and the operation safety state of the airport is indirectly shown.
The second part of the invention is to propose an improved granger test based on chi-square and likelihood ratio tests for risk propagation identification between two airports. Principle of the glange test: in the time series case, the granger causal relationship between two variables X, Y is defined as: x is said to be the Greenwich cause of Y if it helps to predict another variable Y, i.e., in the regression of Y with respect to the past values of Y, adding the past values of X as independent variables can significantly increase the interpretability of the regression. In the aviation network, two airports A and B are assumed, whether the past value of the risk coefficient time series of B is used for judging whether the prediction of the risk coefficient time series of A is improved or not is facilitated, and if the prediction of the risk coefficient time series of A is facilitated, B is considered to be the Glanberg reason of A, namely B spreads risks to A. In fixed time, firstly, calculating the risks of two object airports according to a designated time interval by using a risk quantification method, finally forming a risk time sequence in the unit time, then taking the risk time sequences of the two objects airports as input, and identifying whether a risk propagation relation exists between the two airports and the direction of risk propagation by using an improved Glanby test based on a chi-square test and a likelihood ratio test. And finally, carrying out propagation identification on all airports in the aviation network pairwise, and finally constructing a risk propagation network to achieve the purpose of the propagation identification of the operation risk of the aviation network.
The method has the beneficial effects that:
1. the method of the invention makes up the deficiency that the prior art lacks specific risk quantification, so that the operation state and the safety efficiency of each airport in the aviation network have more intuitive embodiment and more specific evaluation result, and the method is favorable for risk control and operation monitoring of the aviation network.
2. The method is helpful for deeply excavating the distribution characteristics and the propagation mechanism of the operation risk of the aviation network, understanding the propagation process of the operation risk, contributing theoretical experience to the operation mechanism of the aviation network and having reference value for the decision of relevant civil aviation departments.
3. The method is beneficial to analyzing the actual operation safety and the operation efficiency of the aviation network, finding out a risk source in the network, reducing the potential accident rate of the aviation network, controlling the propagation of risks, enhancing the network load capacity and adapting to the rapid development of aviation transportation.
4. The method can be used for constructing the risk propagation network, displaying the operation state and the risk condition of the aviation network in a specific time period from the global perspective, more intuitively displaying the risk hidden danger in the aviation network and predicting the risk spread range in the aviation network.
Finally, it is noted that the above-mentioned preferred embodiments illustrate rather than limit the invention, and that, while the invention has been described in detail with reference to the above-mentioned preferred embodiments, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the scope of the invention as defined by the appended claims.
Claims (4)
1. An aviation network risk propagation identification method is characterized by comprising the following steps:
determining an airport risk coefficient for the preprocessed airport pair risk time sequence data based on a pre-established airport risk coefficient model;
determining a checking order according to the airport risk coefficient, and determining a corresponding residual square sum based on the checking order and the corresponding airport risk time series data;
examining the sum of squared residuals to identify risk propagation relationships between the airport pairs;
determining an airport risk coefficient model comprising:
acquiring an average takeoff delay time sequence and an airport saturation time sequence of each airport in the historical flight data within a preset time period;
clustering the average takeoff delay time sequence and the airport saturation time sequence after normalization processing to obtain a corresponding clustering range;
the method for acquiring the average takeoff delay time sequence and the airport saturation sequence of each airport in the historical flight data in the preset time period comprises the following steps:
the average takeoff delay time meets the following requirements:
wherein d is i (t) is the average takeoff delay time of the airport i in the time period from t to t +1, D i (t) is the total takeoff delay time of the i airport in the time period from t to t +1, C i (t) the number of flight cancellation of the i airport in the time period from t to t +1, the equivalent takeoff delay time of the flight cancellation in 3 hours, P i (t) is the total number of scheduled take-off flights of the i airport in the time period from t to t + 1;
airport saturation, satisfies:
wherein s is i (t) is the saturation of i airport in the time period from t to t +1, Q i (t) airport arrival traffic at i airport in time period t to t +1, C i (t) airport capacity of i airport in time period from t to t + 1;
clustering the average takeoff delay time sequence and the airport saturation time sequence after normalization processing, wherein the clustering comprises the following steps:
clustering the average takeoff delay time and airport saturation of all airports in the time period from t to t +1 to obtain a delay interval and a saturation interval;
determining an airport risk coefficient model, further comprising:
determining a clustering range corresponding to the average takeoff delay time and the airport saturation of each airport in the time period from t to t +1 in the aviation network;
mapping the average takeoff delay time and the airport saturation of each airport in the aviation network in the time period from t to t +1 to corresponding delay weight and saturation weight through a mapping function according to the corresponding clustering range;
wherein, the delay weight satisfies:
and the saturation weight satisfies the following conditions:
wherein, W d (k, t) and W S (k, t) are respectively the delay weight and saturation weight of the airport k in the time period from t to t +1, d k (t) and sk (t) are respectively the average takeoff delay time and airport saturation value of the airport k in the time period from t to t +1, and n is the number of the intervals obtained by clustering;
establishing an airport risk coefficient model according to the delay weight and the saturation weight, and satisfying the following conditions:
R k (t)＝‖W d (k,t)+W s (k,t)‖
wherein R is k (t) risk coefficient for airport k;
determining a checking order according to the airport risk coefficient, comprising:
performing a granger test on the clustered airport risk coefficients;
determining a checking order according to the airport pair risk grade range obtained by the Glange check;
determining a corresponding sum of squares of residuals based on the inspection rank and the corresponding airport pair risk time-series data, comprising:
respectively constructing an unconstrained regression model and a constrained regression model according to the inspection order and the corresponding risk time sequence data of the airport;
determining a corresponding unconstrained residual sum of squares and a constrained residual sum of squares according to the unconstrained regression model and the constrained regression model;
determining a corresponding sum of squares of residuals based on the inspection rank and the corresponding airport pair risk time-series data comprises: time series of risks R from airport A, B A (t) and R B (t) constructing two regression models, and obtaining the unconstrained residual square sum RSS according to the two regression models u And constrained Residual Sum of Squares (RSS) r ；
Wherein:
where L denotes the hysteresis order chosen by the AIC criterion.
2. The method of claim 1, wherein checking the sum of squares of the residuals comprises:
and F test, chi-square test and likelihood ratio test are carried out on the unconstrained residual square sum and the constrained residual square sum.
3. The method of claim 2, wherein identifying risk propagation relationships between the pair of airports comprises:
and if all the inspection results exceed the preset critical value, judging that risk propagation exists between the airport pairs.
4. The method of any one of claims 1-3, wherein after identifying a risk propagation relationship between the pair of airports, the method further comprises:
all airport pairs within the airline network are inspected to identify overall risk propagation relationships for the airline network.
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