Flexible control method and system for aircraft departure pushback based on probabilistic taxiing time

Abstract

The present invention relates to a method for flexible control of aircraft pushback time, and in particular to a method and system for flexible control of aircraft departure pushback time based on probabilistic taxi time. The method for flexible control of aircraft departure pushback time based on probabilistic taxi time includes: obtaining a probability density function of taxi time; determining an ideal taxi time buffer time based on the probabilistic taxi time, generating a flexible pushback moment for departing aircraft; and / or generating a flexible pushback time slot for departing aircraft based on the probabilistic taxi time, a planned runway arrival time range, and a required runway arrival time range. It can achieve the allocation of departure pushback time based on the optimal trade-off between the departure taxi time and the probability of arriving at the runway on time, and achieve the best match between the pushback time range and the probability of arriving at the runway within the planned time range.

Description

Technical Field

[0001] The present invention relates to a method for flexible control of aircraft pushback time, and in particular to a method and system for flexible control of aircraft departure pushback time based on probabilistic taxiing time. Background Art

[0002] Airport surface departure activities generally consist of processes such as wheel block removal, pushback, taxiing, waiting, and takeoff. This process is highly complex, dynamic, and easily disturbed, and is very likely to cause intensive surface conflicts and continuous congestion delays. It is a key stage in the "gate-to-gate" operation of flights. Departure flight delays include waiting at the parking stand, pushback waiting, apron waiting, and departure queue waiting. In this context, how to scientifically predict and control flight departure activities and transform high-cost taxiing waiting and runway head waiting into low-cost stand waiting as much as possible has become a key problem that the current aviation transportation industry and academia need to solve urgently. However, the surface taxiing process is easily affected by internal and external factors such as airport facility conditions, resource allocation plans, flight transit support, and external flow control restrictions. The taxiing time has strong randomness and uncertainty, and it is difficult to accurately predict it. Inaccurate predictions make departure pushback control decisions lack scientific basis, which in turn leads to relatively poor surface departure operation performance. If a flight is launched too late, it may be delayed because it cannot take off at the scheduled time; if a flight is launched too early, it may cause unnecessary queuing, fuel consumption and aviation emissions due to conflicts in the use of ground resources.

[0003] Although the current research work has achieved a series of remarkable results, it still has the following shortcomings: First, the current prediction results of the taxi time on the surface mainly focus on the "point value" estimation of the individual taxi time and the "distribution" estimation of the taxi time of the group, and it is impossible to give a probabilistic "range" estimation of the individual taxi time, and it is not possible to better reflect the highly dynamic and random disturbance characteristics of the taxiing process of a single aircraft; second, the current research results on departure pushback control mainly focus on the "pushback rate" control from the perspective of "traffic volume" and the "pushback time" control from the perspective of "delay conversion", and the control process of the pushback time does not consider the disturbance problem caused by taxiing uncertainty, and it is not possible to achieve the best trade-off between taxi time and take-off delay; third, the current control decision on the "pushback time" is too rigid, and does not fully consider the flexible pushback control problem under uncertain taxi time, and it is impossible to give a more reasonable and more practical departure pushback time range, which is very likely to cause more surface conflicts and delays in the pushback to take-off process. Summary of the invention

[0004] The present invention provides a method and system for flexible control of aircraft departure pushback time based on probabilistic taxiing time.

[0005] In a first aspect, the present invention provides a method for flexible control of aircraft departure pushback time based on probabilistic taxi time, comprising: obtaining a probability density function of taxi time; determining an ideal taxi time buffer time based on the probabilistic taxi time, and generating a flexible pushback moment for the departing aircraft; and / or generating a flexible pushback time slot for the departing aircraft based on the probabilistic taxi time, a planned runway arrival time range, and a probability of arrival within a runway arrival time range that needs to be met.

[0006] Furthermore, the method of obtaining the probability density function of the taxiing time includes: analyzing the factors affecting the taxiing time, selecting characteristic variables, using random sampling and 5-fold cross validation to divide and construct a training set and a test set, using a random forest regression prediction method to predict the taxiing time, and obtaining a set of deterministic prediction values ​​of the taxiing time for each decision tree; using the deterministic prediction value of the taxiing time of each decision tree as a random sample, and using a kernel density estimation method to obtain the probability density function of the taxiing time.

[0007] Furthermore, the analyzing the factors affecting taxiing time and selecting characteristic variables includes: performing feature selection based on correlation analysis, and selecting push-off time related variables, surface flight related variables, and traffic flow related variables as characteristic variables.

[0008] Furthermore, the launch time-related variables include: launch month, launch period; the field flight-related variables include: flight number, aircraft model, parking position; the traffic flow-related variables include: field departure instantaneous flow, field departure cumulative flow, departure time slot demand index, departure queue index, and arrival queue index.

[0009] Furthermore, determining the ideal taxiing time buffer time according to the probabilistic taxiing time and generating the flexible pushback time of the departing aircraft includes: calculating the control pushback time:

[0010] t ControlledPush =t runway -t taxi -t buffer ;

[0011] Among them, t ControlledPush To control the launch time, t runway is the planned arrival time at the runway, t taxi is the deterministic prediction value of the taxiing time, t buffer buffer time for taxi time;

[0012] Calculate the probability of arriving at the runway on time:

[0013]

[0014] Among them, p ontime is the probability of arriving at the runway on time, is the probability sliding time, let Φ f () represents the cumulative distribution function;

[0015] Let the estimated taxiing time t Etaxi =t runway -t push , t EPush For a given expected launch time, t push You can take t ControlledPush or EPush , and the launch delay t pushdelay =t ControlledPush -t EPush ;

[0016] Analysis ontime Follow buffer The trend of size change, according to t Etaxi With p ontime The trade-off relationship between the two is to determine the ideal buffer time t IdealBuffer The value of

[0017] Based on the ideal buffer time t IdealBuffer Generate flexible pushback times for departing aircraft.

[0018] Further, generating a flexible pushback time slot for a departing aircraft according to the probabilistic taxi time, the planned runway arrival time range, and the arrival probability within the runway arrival time range to be met includes:

[0019] Establish the runway arrival time opportunity constraint:

[0020] (1) Indicates t runway The probability of reaching the runway within the previous x minutes is greater than or equal to p ad ;

[0021] (2) Indicates t runway The probability of reaching the runway within y minutes is greater than or equal to p de ;

[0022] in, is the probabilistic taxiing time of the departing flight, t runway For a given planned arrival time at the runway, the maximum allowed advance and delay times for arrival at the runway are x and y respectively, and the minimum probability of controlling the arrival time at the runway within the maximum allowed advance time and the maximum allowed delay time are p respectively. ad and p de ;

[0023] Convert the two chance constraints into deterministic constraints. represents the inverse function of the cumulative distribution function. The corresponding deterministic constraint for constraint (1) is The corresponding deterministic constraint of constraint (2) is The flexible pushback time slot for departing aircraft can be generated as follows:

[0024] In a second aspect, the present invention provides an aircraft departure pushback time flexible control system based on probabilistic taxi time, comprising: a probability density function acquisition module, used to acquire the probability density function of taxi time; a flexible pushback moment acquisition module, used to determine the ideal taxi time buffer time according to the probabilistic taxi time, and generate a flexible pushback moment for the departing aircraft; and / or a flexible pushback time slot acquisition module, which generates a flexible pushback time slot for the departing aircraft according to the probabilistic taxi time, the planned runway arrival time range, and the arrival probability within the runway arrival time range that needs to be met.

[0025] In a third aspect, the present invention provides a flexible control system for aircraft departure pushback time based on probabilistic taxi time, comprising: a data storage module for storing data; a processor module, electrically connected to the data storage module, suitable for using the flexible control method for aircraft departure pushback time based on probabilistic taxi time as described above to generate a flexible pushback moment for a departing aircraft and / or generate a flexible pushback time slot for a departing aircraft.

[0026] The beneficial effects of the present invention are:

[0027] (1) The probabilistic taxi time prediction model based on the combination of random forest regression algorithm and kernel density estimation method can effectively predict the probabilistic taxi time of a single flight;

[0028] (2) The proposed flexible control method for departure pushback timing based on buffer time can achieve the optimal trade-off between departure taxi time and the probability of arriving at the runway on time by optimally setting the buffer time length;

[0029] (3) The proposed flexible control method of departure pushback slot based on opportunity constraints can achieve the best match between the pushback time range and the probability of reaching the runway within the planned time range by controlling the feasible pushback time slot of the departing flight;

[0030] (4) The above two push-out time control methods are based on different perspectives such as push-out "moment" and "time slot", respectively. The proposed push-out time control method has good flexibility.

[0031] Other features and advantages of the present invention will be described in the following description, and partly become apparent from the description, or understood by practicing the present invention. The purpose and other advantages of the present invention are realized and obtained by the structures particularly pointed out in the description, claims and drawings.

[0032] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, preferred embodiments are given below and described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0034] Figure 1 A relationship diagram of various components of aircraft departure pushback flexible control based on probabilistic taxi time according to an embodiment of the present invention is shown;

[0035] Figure 2 A step diagram of a probabilistic taxiing time prediction method according to an embodiment of the present invention is shown;

[0036] Figure 3 A graph showing a probabilistic taxiing time prediction result according to an embodiment of the present invention is shown;

[0037] Figure 4 An explanatory diagram showing the calculation of the push-out time and the probability of arriving at the runway on time according to the set buffer time according to an embodiment of the present invention;

[0038] Figure 5 The figure shows the changing trend of the probability of arriving at the runway on time under different values ​​of the taxiing buffer time under the embodiment of the present invention. DETAILED DESCRIPTION

[0039] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0040] Example

[0041] In this embodiment, the relationship between the components of the aircraft departure pushback flexible control method based on probabilistic taxiing time is as follows: Figure 1As shown in Figure 2, the historical data required for probabilistic taxi time prediction uses the actual operation data of departure flights from a large domestic airport from September 1, 2019 to December 31, 2019. The probabilistic taxi time prediction steps can be as follows: Figure 2 shown.

[0042] In this embodiment, the method for flexible control of aircraft departure pushback time based on probabilistic taxi time includes: obtaining the probability density function of taxi time; determining the ideal taxi time buffer time according to the probabilistic taxi time, and generating a flexible pushback moment for the departing aircraft; and / or generating a flexible pushback time slot for the departing aircraft according to the probabilistic taxi time, the planned runway arrival time range, and the arrival probability within the runway arrival time range that needs to be met.

[0043] Optionally, the method of obtaining the probability density function of the taxiing time includes: analyzing the factors affecting the taxiing time, selecting characteristic variables, using random sampling and 5-fold cross validation to divide and construct a training set and a test set, using a random forest regression prediction method to predict the taxiing time, and obtaining a set of deterministic prediction values ​​of the taxiing time for each decision tree; using the deterministic prediction value of the taxiing time of each decision tree as a random sample, and using a kernel density estimation method to obtain the probability density function of the taxiing time.

[0044] In specific application scenarios, feature selection can be performed based on correlation analysis, and variables related to push-out time (pull-out month / pull-out period), surface flight related variables (flight number / aircraft model / parking position), and traffic flow related variables (surface departure instantaneous flow / surface departure cumulative flow / departure time slot demand index / departure queue index / arrival queue index) are selected as feature variables. The training set and test set are constructed using the random sampling method, and the taxi time is predicted using the random forest regression prediction method to obtain the taxi time prediction result set of each decision tree. The specific process of dividing the training set and the test set is as follows. By comparing the prediction effects of different division ratios, 80% of the data is selected as the training set, with a sample number of 45,120, and the remaining 20% ​​is the test set, with a sample number of 11,280. The preprocessing operation process of the original data mainly includes screening and deleting outliers, filling missing values ​​with the median, and processing text and category attributes. The Person correlation coefficient is used for feature selection to obtain 10 characteristic variables in three categories, including push-out time related variables (pull-out month / pull-out period), surface flight related variables (flight number / aircraft model / parking position), and traffic flow related variables (surface departure instantaneous flow / surface departure cumulative flow / departure time slot demand index / departure queue index / arrival queue index).

[0045] Furthermore, the taxiing time prediction results of each decision tree are used as random samples, and the probability density function of the taxiing time is obtained by using the kernel density estimation method. The probability taxiing time prediction results are as follows: Figure 3shown.

[0046] In this embodiment, if Figure 4 As shown, the departing aircraft will obtain a given planned arrival time t runway , given the expected launch time t EPush .

[0047] Preferably, determining the ideal taxiing time buffer time according to the probabilistic taxiing time and generating the flexible pushback time of the departing aircraft comprises:

[0048] First, calculate the control push-out moment:

[0049] t ControlledPush =t runway -t taxi -t buffer ;

[0050] Among them, t ControlledPush To control the launch time, t runway is the planned arrival time at the runway, t taxi is the deterministic prediction value of the taxiing time, t buffer buffer time for taxi time;

[0051] Second, calculate the probability of arriving at the runway on time:

[0052]

[0053] Among them, p ontime is the probability of arriving at the runway on time, is the probability sliding time, let Φ f () represents the cumulative distribution function;

[0054] Let the estimated taxiing time t Etaxi =t runway -t push , t EPush For a given expected launch time, t push You can take t ControlledPush or EPush , and the launch delay t pushdelay =t ControlledPush -t EPush ;

[0055] Analysis ontime Follow buffer The trend of size change, according to t Etaxi With p ontime The trade-off relationship between the two is to determine the ideal buffer time t IdealBuffer The value of

[0056] Based on the ideal buffer time tIdealBuffer Generate flexible pushback times for departing aircraft.

[0057] In this embodiment, if Figure 5 As shown in the figure, as the buffer time increases, the probability of arriving at the runway on time also increases; however, when the buffer time increases to a certain extent, the increase in the probability of arriving at the runway on time is no longer obvious.

[0058] In addition, the increase of buffer time will lead to the increase of overall sliding time, so it is necessary to consider t Etaxi With p ontime The trade-off relationship between the two is to determine the ideal buffer time t IdealBuffer The value of .

[0059] In a specific application scenario, the changing trend of the probability of flight a arriving at the runway on time under different taxi buffer time values ​​is as follows: Figure 5 As shown in the figure, when the buffer time is set to 1 minute, 1.5 minutes, and 2 minutes respectively, the probability of arriving at the runway head on time is 88%, 96.9%, and 98% respectively. If the buffer time is further increased, the probability of arriving at the runway head on time will no longer increase significantly, indicating that increasing the taxi time buffer time of flight a cannot continuously reduce takeoff delays. 1.5 minutes and 2 minutes are relatively ideal taxi time buffer times.

[0060] In this embodiment, t Etaxi With p online The trade-off relationship can be:

[0061] If the buffer time is set to a small value and the push-off time is later, the probability of arriving at the runway on schedule becomes smaller, and the estimated taxiing time t Etaxi Based on t ControlledPush Calculation based on t EPush The calculated value decreases greatly, that is, (t runway -t Epush )-(t runway -t Controlledpush ) is larger; if the buffer zone is set larger and the push-out time is earlier, the probability of the flight arriving at the runway head on schedule increases, and the estimated taxiing time t Etaxi Based on t ControlledPush Calculation based on t EPush The calculated value decreases less, that is, (t runway -t Epush )-(t runway -t Controlledpush ) has a smaller value.

[0062] In determining the ideal buffer time t IdealBuffer After the value of t runway -t taxi -t IdealBufferGenerate flexible pushback times for departing aircraft.

[0063] In this embodiment, preferably, generating a flexible pushback time slot for a departing aircraft according to the probabilistic taxiing time, the planned runway arrival time range, and the arrival probability within the runway arrival time range to be met includes:

[0064] Establish the runway arrival time opportunity constraint:

[0065] (1) Indicates t runway The probability of reaching the runway within the previous x minutes is greater than or equal to p ad ;

[0066] (2) Indicates t runway The probability of reaching the runway within y minutes is greater than or equal to p de ;

[0067] in, is the probabilistic taxiing time of the departing flight, t runway For a given planned arrival time at the runway, the maximum allowed advance and delay times for arrival at the runway are x and y respectively, and the minimum probability of controlling the arrival time at the runway within the maximum allowed advance time and the maximum allowed delay time are p respectively. ad and p de ;

[0068] Convert the two chance constraints into deterministic constraints. represents the inverse function of the cumulative distribution function. The corresponding deterministic constraint for constraint (1) is The corresponding deterministic constraint of constraint (2) is The flexible pushback time slot for departing aircraft can be generated as follows:

[0069] In a specific application, the maximum allowable advance x and the maximum allowable delay y of the planned runway arrival time are both set to 3 minutes, and the minimum probability p of the runway arrival time within the maximum allowable advance / delay time x / y minutes is set to 90%. The feasible push-out time slots obtained by selecting flights at different times of the day are shown in the following table:

[0070]

[0071] The present embodiment also provides an aircraft departure pushback time flexible control system based on probabilistic taxi time, including: a probability density function acquisition module, used to acquire the probability density function of taxi time; a flexible pushback moment acquisition module, used to determine the ideal taxi time buffer time according to the probabilistic taxi time, and generate a flexible pushback moment for the departing aircraft; and / or a flexible pushback time slot acquisition module, which generates a flexible pushback time slot for the departing aircraft according to the probabilistic taxi time, the planned runway arrival time range, and the arrival probability within the runway arrival time range that needs to be met.

[0072] The present embodiment also provides an aircraft departure pushback time flexible control system based on probabilistic taxi time, comprising: a data storage module for storing data; a processor module, electrically connected to the data storage module, suitable for using the aircraft departure pushback time flexible control method based on probabilistic taxi time as described above to generate a departure aircraft flexible pushback moment and / or generate a departure aircraft flexible pushback time slot.

[0073] In summary, the probabilistic taxi time prediction adopted in the present invention can not only predict the taxi time itself, but also quantify the uncertainty of the taxi time. The aircraft departure pushback method based on probabilistic taxi time includes flexible control of the pushback "moment" and flexible control of the pushback "time slot", which can effectively promote the flexible transformation of traditional pushback control rigid constraints to multi-perspective flexible control.

[0074] Based on the above ideal embodiments of the present invention, the relevant staff can make various changes and modifications without departing from the technical concept of the present invention through the above description. The technical scope of the present invention is not limited to the contents of the specification, and its technical scope must be determined according to the scope of the claims.

Claims

1. A method for flexible control of aircraft departure pushback time based on probabilistic taxiing time, characterized in that: include: Get the probability density function of the taxiing time; Determine the ideal taxi time buffer time based on the probabilistic taxi time and generate the flexible pushback time for departing aircraft; and / or Generate the flexible pushback time slot for departing aircraft based on the probabilistic taxi time, the planned runway arrival time range, and the arrival probability within the runway arrival time range that needs to be met; The probability density function for obtaining the taxiing time includes: The factors affecting taxiing time were analyzed, characteristic variables were selected, random sampling and 5-fold cross validation were used to divide and construct training and test sets, and the taxiing time was predicted using the random forest regression prediction method to obtain the set of deterministic prediction values ​​of taxiing time for each decision tree. The deterministic prediction value of the taxiing time of each decision tree is used as a random sample, and the probability density function of the taxiing time is obtained by using the kernel density estimation method; Determining the ideal taxiing time buffer time according to the probabilistic taxiing time and generating the flexible push-out time of the departing aircraft includes: Calculate the control launch time: t ControlledPush =t runway -t taxi -t buffer ; Among them, t ControlledPush To control the launch time, t runway is the planned arrival time at the runway, t taxi is the deterministic prediction value of the taxiing time, t buffer buffer time for taxi time; Calculate the probability of arriving at the runway on time: Among them, p ontime is the probability of arriving at the runway on time, is the probability sliding time, let Φ f ( ) represents the cumulative distribution function; Let the estimated taxiing time t Etaxi =t runway -t push , t EPush For a given expected launch time, t push You can take t ControlledPush or EPush , and the launch delay t pushdelay =t ControlledPush -t EPush ; Analysis ontime Follow buffer The trend of size change, according to t Etaxi With p ontime The trade-off relationship between the two is to determine the ideal buffer time t IdealBuffer The value of Based on the ideal buffer time t IdealBuffer Generate flexible pushback time for departing aircraft; The generating of the flexible pushback time slot for the departing aircraft according to the probabilistic taxiing time, the planned runway arrival time range, and the arrival probability within the runway arrival time range to be met comprises: Establish the runway arrival time opportunity constraint: (1) Indicates t runway The probability of reaching the runway within the previous x minutes is greater than or equal to p ad ; (2) Indicates t runway The probability of reaching the runway within y minutes is greater than or equal to p de ; in, is the probabilistic taxiing time of the departing flight, t runway For a given planned arrival time at the runway, the maximum allowed advance and delay times for arrival at the runway are x and y respectively, and the minimum probability of controlling the arrival time at the runway within the maximum allowed advance time and the maximum allowed delay time are p respectively. ad and p de ; Convert the two chance constraints into deterministic constraints. represents the inverse function of the cumulative distribution function. The corresponding deterministic constraint for constraint (1) is The corresponding deterministic constraint of constraint (2) is The flexible pushback time slot for departing aircraft can be generated as follows:

2. The method for flexible control of aircraft departure pushback time based on probabilistic taxiing time according to claim 1, characterized in that: The analysis of the factors affecting the taxiing time is as follows: The selected feature variables include: Feature selection is performed based on correlation analysis, and launch time related variables, surface flight related variables, and traffic flow related variables are selected as feature variables.

3. The method for flexible control of aircraft departure pushback time based on probabilistic taxiing time according to claim 2, characterized in that: The launch time related variables include: launch month, launch period; The surface flight related variables include: flight number, aircraft type, and parking position; The traffic flow related variables include: instantaneous departure flow, cumulative departure flow, departure time slot demand index, departure queue index, and arrival queue index.

4. A flexible control system for aircraft departure pushback time based on probabilistic taxi time, characterized in that: include: A probability density function acquisition module is used to obtain the probability density function of the taxiing time; A flexible pushback time acquisition module is used to determine the ideal taxi time buffer time according to the probabilistic taxi time and generate a flexible pushback time for the departing aircraft; and / or The flexible pushback time slot acquisition module generates the flexible pushback time slot of the departing aircraft according to the probabilistic taxiing time, the planned runway arrival time range, and the arrival probability within the runway arrival time range that needs to be met; The probability density function for obtaining the taxiing time includes: The factors affecting taxiing time were analyzed, characteristic variables were selected, random sampling and 5-fold cross validation were used to divide and construct training and test sets, and the random forest regression prediction method was used to predict taxiing time, and the set of deterministic prediction values ​​of taxiing time for each decision tree was obtained. The deterministic prediction value of the taxiing time of each decision tree is used as a random sample, and the probability density function of the taxiing time is obtained by using the kernel density estimation method; Determining the ideal taxiing time buffer time according to the probabilistic taxiing time and generating the flexible push-out time of the departing aircraft includes: Calculate the control launch time: t ControlledPush =t runway -t taxi -t buffer ; Among them, t ControlledPush To control the launch time, t runway is the planned arrival time at the runway, t taxi is the deterministic prediction value of the taxiing time, t buffer buffer time for taxi time; Calculate the probability of arriving at the runway on time: Among them, p ontime is the probability of arriving at the runway on time, is the probability sliding time, let Φ f ( ) represents the cumulative distribution function; Let the estimated taxiing time t Etaxi =t runway -t push , t EPush For a given expected launch time, t push You can take t ControlledPush or EPush , and the launch delay t pushdelay =t ControlledPush -t EPush ; Analysis ontime Follow buffer The trend of size change, according to t Etaxi With p ontime The trade-off relationship between the two is to determine the ideal buffer time t IdealBuffer The value of Based on the ideal buffer time t IdealBuffer Generate flexible pushback time for departing aircraft; The generating of the flexible pushback time slot for the departing aircraft according to the probabilistic taxiing time, the planned runway arrival time range, and the arrival probability within the runway arrival time range to be met comprises: Establish the runway arrival time opportunity constraint: (1) Indicates t runway The probability of reaching the runway within the previous x minutes is greater than or equal to p ad ; (2) Indicates t runway The probability of reaching the runway within y minutes is greater than or equal to p de ; in, is the probabilistic taxiing time of the departing flight, t runway For a given planned arrival time at the runway, the maximum allowed advance and delay times for arrival at the runway are x and y respectively, and the minimum probability of controlling the arrival time at the runway within the maximum allowed advance time and the maximum allowed delay time are p ad and p de ; Convert the two chance constraints into deterministic constraints. represents the inverse function of the cumulative distribution function. The corresponding deterministic constraint for constraint (1) is The corresponding deterministic constraint of constraint (2) is The flexible pushback time slot for departing aircraft can be generated as follows:

5. A flexible control system for aircraft departure pushback time based on probabilistic taxi time, characterized in that: include: A data storage module, used for storing data; The processor module is electrically connected to the data storage module and is suitable for generating a flexible pushback moment of a departing aircraft and / or generating a flexible pushback time slot of a departing aircraft by using the flexible control method of the aircraft departure pushback time based on the probabilistic taxiing time as described in any one of claims 1 to 3.

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