CN110889543A - RTA sequence allocation method based on four-dimensional track operation - Google Patents

RTA sequence allocation method based on four-dimensional track operation Download PDF

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CN110889543A
CN110889543A CN201911137980.9A CN201911137980A CN110889543A CN 110889543 A CN110889543 A CN 110889543A CN 201911137980 A CN201911137980 A CN 201911137980A CN 110889543 A CN110889543 A CN 110889543A
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李广文
黄彭辉
李梦涵
翟少博
吴果
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Northwestern Polytechnical University
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Abstract

The invention provides an RTA sequence allocation method based on four-dimensional track operation. And adding time constraint to the three-dimensional flight path to obtain the four-dimensional flight path. Calculating ETA and ETA boundaries according to the requirements of an air traffic control department, meteorological conditions, an airplane performance database and the like to obtain an initial RTA sequence; and (3) constructing a mathematical model for reallocating the RTA sequence, and reallocating the RTA sequence to the intermediate waypoint by adopting an interior point method according to the RTA tolerance given by the air traffic control department and the ETA and ETA boundaries obtained by calculation to obtain the reallocating RTA sequence. The method provides a new technical scheme for the flight management system to realize accurate 4D guidance, so that the airplane can have more accurate timed arrival capability.

Description

RTA sequence allocation method based on four-dimensional track operation
Technical Field
The invention belongs to the technical field of civil aviation, and particularly relates to an RTA sequence distribution method based on four-dimensional flight path operation.
Background
With the increase of the number of civil aircrafts and the continuous expansion of the scale of airlines, available airspace resources become less and less, and the pressure of flight operation and scheduling becomes greater and greater. In order to meet the requirements of future air traffic and enable civil aviation flight to be safer and more efficient, and meanwhile, to improve airspace flow and reduce operation cost, four-dimensional track-based operation (4D-TBO) is provided. The European Union and the U.S. both propose a specific 4D-TBO project on the basis of the air transportation system of the European Union and the U.S. China. The European union proposed a Single European Sky project (Single European Sky, ATM Research, SESAR), and the united states proposed a Next Generation Air transport System (Next Generation Air transport System, NextGen). These projects propose a number of related concepts, solutions and air-ground data interaction standards for supporting future air transport systems.
The four-dimensional flight path increases the Time dimension requirement relative to the general three-dimensional flight path, i.e., increases the Arrival Time Requirement (RTA) for the waypoints on the flight path. The track-based mode of operation is based on the prediction of the 4D track of the aircraft, sharing dynamic track information between air traffic controllers, airlines, aircraft flight management systems, and making air-to-ground collaborative decisions. The position precision and the time precision of the four-dimensional flight path have higher requirements than those of the three-dimensional flight path. Track-based operations (TBO) are based on the knowledge of the precise four-dimensional tracks of all aircraft in the airspace and ensure safety separation requirements between aircraft, particularly the knowledge of future tracks, by ensuring track accuracy.
According to the current development trend of the aviation industry, a 4D flight management system (4D-FMS) supporting TBO is a key avionic device which must be equipped for advanced civil aircraft in the future. The 4D-FMS should have 4D flight path planning, 4D flight path prediction and 4D flight guidance functions. The RTA sequence allocation method provided by the invention can provide a scheme for developing the 4D-FMS in China.
Disclosure of Invention
In order to realize four-dimensional track planning and four-dimensional guidance, the invention provides an RTA sequence distribution method based on four-dimensional track operation, which realizes the purpose of obtaining the four-dimensional track on the basis of a three-dimensional track. Calculating an Estimated Time of Arrival (ETA) and an ETA boundary according to requirements of an air traffic control department, benefits of an airline company, meteorological conditions, an airplane performance database and the like; and (3) constructing a mathematical model for reallocating the RTA sequences, and reallocating the RTA sequences to the intermediate waypoints by adopting an interior point method according to RTA tolerances (earliest time and latest time for reaching the waypoints) given by an air traffic control department to obtain the reallocating RTA sequences.
An RTA sequence allocation method based on four-dimensional track operation is characterized by comprising the following steps:
step 1: selecting optimization indexes according to flight plans, altitude and speed constraints raised by an air management department, an airplane performance database, meteorological conditions and operation requirements of an airline company, and selecting a climbing mode and a descending mode; the optimization index is the minimum cost or the minimum fuel saving or the longest endurance time; the climbing or descending modes include a constant-surface-speed climbing or descending mode, a constant-Mach-number climbing or descending mode, a constant-surface-speed and constant-Mach-number climbing or descending mode, and a constant-surface-speed and constant-Mach-number and constant-surface-speed climbing or descending mode.
Step 2: and within the height and speed constraints of the flight plan, inquiring the airborne performance database according to the selected optimization indexes to obtain the optimal cruise height, the optimal cruise speed and the cruise speed interval.
And step 3: according to the selected climbing mode and the selected descending mode, the time, the distance and the fuel consumption data of a climbing section and a descending section are inquired and obtained in an airborne performance database, and the longitude and latitude of the TOC point are calculated and obtained by utilizing the climbing distance and a climbing starting point provided in an original flight plan and adopting an equiangular course forward solution formula; calculating the longitude and latitude of the TOD point by using the descending distance and a descending destination provided in the original flight plan and adopting an equiangular flight path forward solution formula; taking the optimal cruising altitude as the altitude of the TOC point and the TOD point; and adding the obtained longitude and latitude and the height of the TOC point and the TOD point into the original flight plan to obtain an updated flight plan.
And 4, step 4: ETA and ETA boundaries of each waypoint in the updated flight plan are calculated as follows:
Figure BDA0002280068280000021
Figure BDA0002280068280000022
Figure BDA0002280068280000023
wherein i is the waypoint number, i is 1,2, n-1, n is the total number of waypoints, LresFor remaining voyage, VTASAt the current airspeed, VwindForecasting wind speed, ETA, for weatheriETA for ith waypoint, when i is 11For the takeoff time of the aircraft, VTAS,maxAt a maximum value in the cruise speed interval, VTAS,minAt the minimum value of the cruise speed interval, ETAi+1Estimated time of arrival, ETA, for the i +1 st waypointi+1,minPredicted earliest time of arrival, ETA, for the i +1 st waypointi+1,maxThe predicted latest arrival time for the (i + 1) th waypoint.
And 5: if the air traffic control department does not have an arrival time requirement for each waypoint in the updated flight plan, RTAiIf the value of i ═ 2, ·, n is arbitrary, the ETA and ETA boundary of each waypoint obtained in step 4 constitute an initial RTA sequence, and the initial allocation of the RTA sequence is completed; otherwise, go to step 6.
Step 6: judging the arrival time RTA of the last waypoint given by the air traffic control departmentnWhether it is at the ETA boundary [ ETA ] of the waypointn,min,ETAn,max]If the number of the intermediate waypoints is within the range, performing RTA sequence reallocation on the intermediate waypoints by adopting an interior point method according to RTA tolerance of each waypoint provided by the air traffic control; otherwise, abandoning the optimization indexes selected in the step 1, reselecting one from other optimization indexes as the optimization index, keeping the climbing mode and the descending side unchanged, returning to the step 2 for calculation again, and if all the calculation results of the optimization indexes cannot meet the arrival time RTA of the last waypointnETA boundary [ ETA ] at the waypointn,min,ETAn,max]And (3) proposing an RTA reassignment requirement to the empty pipe, giving a new RTA requirement and an RTA tolerance to the empty pipe according to the altitude-speed performance limit of the airplane, and returning to the step 1 for recalculation.
The specific process for reallocating the RTA sequence by adopting the interior point method is as follows:
step a: constructing an intermediate waypoint RTA adjustment quantity constraint optimization function as follows:
Figure BDA0002280068280000031
where the index i denotes the ith waypoint, Δ tiFor RTA adjustment of ith waypoint, RTAiRTA requirement value for ith waypoint, RTAi,minIs the RTA margin minimum for the ith waypoint, RTAi,maxAn RTA margin maximum for the ith waypoint;
the penalty function for constructing the interior point method is as follows:
Figure BDA0002280068280000032
wherein Δ t is represented byiI is a vector consisting of 1,2, …, n, r is a penalty factor, f (Δ t) is an objective function,
Figure BDA0002280068280000033
for the penalty term, the calculation formula is respectively as follows:
Figure BDA0002280068280000034
Figure BDA0002280068280000035
step b: initializing, including: let the iteration count variable k equal to 0, the initial value of penalty factor 1 < r(0)< 50, adjustment threshold εΔt∈(10-9,10-11) The objective function threshold ε ∈ (10)-5,10-7) Initial sequence ofColumn(s) of
Figure BDA0002280068280000036
In (1),
Figure BDA0002280068280000041
step c: using golden section method to J (delta t, r)(k)) Performing one-dimensional line search, and calculating to obtain the product satisfying minJ (delta t, r)(k)) Δ t of (1), noted as Δ t(k+1)If, | | f (Δ t) is satisfied(k+1))-f(Δt(k)) | | < epsilon or | Δ t(k+1)-Δt(k)||＜εΔtThen the iteration is stopped, at this time(k+1)I.e. the optimal solution deltat*Go to step d; otherwise, let r(k+1)＝Cr(k)K is k +1, and the procedure is repeated, where C is a decreasing coefficient, preferably in the range of [0.1, 0.5%]。
Step d: according to
Figure BDA0002280068280000042
Calculating to obtain the reassigned RTA sequence, wherein the RTA sequencei,newRTA, RTA representing the ith waypoint in the reassigned RTA sequenceiIndicating the RTA of the ith waypoint in the original RTA sequence given by the empty pipe,
Figure BDA0002280068280000043
represents the optimal solution Δ t*The ith component.
The invention has the beneficial effects that: the technical scheme is provided for realizing accurate 4D guidance of a future airborne 4D flight management system, and the aircraft can realize more accurate timed arrival capability on the basis of accurate three-dimensional flight path guidance by adding time constraint to the three-dimensional flight path; because the flight path planning is carried out by taking the minimum cost, the most fuel-saving and the longest endurance time as the optimization indexes, the flight path planning method can fully give consideration to the air traffic control management and the operation requirements of an airline company, reduce the flight cost of civil aviation, improve the management efficiency of an air traffic control department, reduce the management pressure of the air traffic control department and fully utilize limited airspace resources.
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FIG. 1 is a flow chart of an RTA sequence allocation method based on four-dimensional track operation according to the present invention.
Fig. 2 is a schematic diagram of RTA sequence reallocation principle of the present invention.
FIG. 3 is a diagram illustrating the movable range of the ETA window when the adjusted waypoint RTA is between the ETA windows.
FIG. 4 is a diagram illustrating the movable range of the ETA window when the adjusted waypoint RTA is less than the left boundary of the ETA window.
FIG. 5 is a diagram illustrating the movable range of the ETA window when the adjusted waypoint RTA is greater than the right boundary of the ETA window.
FIG. 6 is a flow chart of RTA sequence reallocation by interior point method according to the present invention.
Detailed Description
The present invention will be further described with reference to the following drawings and examples, which include, but are not limited to, the following examples.
As shown in fig. 1, the present invention provides an RTA sequence allocation method based on four-dimensional track operation. The method comprises an RTA sequence initial allocation technology and an RTA reallocation technology based on an interior point method. Wherein the RTA sequence initial assignment is a result of trade-off optimization between air traffic control requirements, airline benefits, and aircraft performance databases for four-dimensional trajectory planning to complete profile optimization prior to takeoff. RTA sequence reallocation is to perform 4D track re-planning according to RTA tolerance (earliest time and latest time of arriving at a waypoint), ETA and ETA boundary given by an air traffic control department. Aiming at RTA sequence reallocation, firstly, a mathematical model of RTA sequence reallocation is established, and then an interior point method is applied to the mathematical model to adjust the RTA sequence. The specific implementation process is as follows:
1. the method comprises the steps of selecting an optimization index (with the minimum cost, or most fuel oil saving, or longest endurance time) according to the flight plan, the altitude and speed constraint provided by the air traffic control, an airplane performance database, meteorological conditions and the operation requirement of an airline company, and selecting a climbing mode and a descending mode, wherein the climbing mode and the descending mode comprise a constant-surface-speed climbing or descending mode, a constant-Mach-number climbing or descending mode, a constant-surface-speed-before-constant-Mach-number climbing or descending mode, and a constant-surface-speed-before-constant-Mach-number climbing or descending mode.
2. And within the height and speed constraints of the flight plan, the optimal cruising height, the optimal cruising speed and the cruising speed interval of the aircraft are obtained by inquiring in an airborne performance database according to the selected optimization indexes.
3. And according to the selected climbing mode and the selected descending mode, inquiring and obtaining the time, the distance and the fuel consumption data of the climbing section and the descending section from an onboard climbing/descending performance database, calculating the data of the positions, the heights, the time and the like of the climbing vertex TOC and the descending vertex TOD, and updating the flight plan.
4. Calculating ETA and ETA boundaries of flight plan waypoints according to the updated flight plan, specifically as follows:
Figure BDA0002280068280000051
Figure BDA0002280068280000052
Figure BDA0002280068280000053
wherein i is the waypoint number, i is 1,2, n-1, n is the total number of waypoints, LresFor remaining voyage, VTASAt the current airspeed, VwindForecasting wind speed, ETA, for weatheriETA for ith waypoint, when i is 11For the takeoff time of the aircraft, VTAS,maxAt a maximum value in the cruise speed interval, VTAS,minAt the minimum value of the cruise speed interval, ETAi+1Estimated time of arrival, ETA, for the i +1 st waypointi+1,minPredicted earliest time of arrival, ETA, for the i +1 st waypointi+1,maxThe predicted latest arrival time for the (i + 1) th waypoint.
The ETA and ETA boundaries of all waypoints form an ETA sequence.
5. And judging whether the blank pipe has a requirement on the arrival time of the waypoint, if not, directly taking the ETA sequence obtained by the previous calculation as an initial RTA sequence, finishing the initial allocation of the RTA sequence and finishing the allocation process. If so, step 6 is performed.
6. If the empty pipe has the arrival time requirement on the navigation point, whether the total time requirement for reaching the terminal point is within the ETA boundary of the calculated terminal point is judged. If so, performing RTA sequence reallocation on the intermediate waypoints under the waypoint RTA constraint of the air traffic control. If not, the optimization index is reselected, and the ETA and ETA boundaries of the flight plan waypoint are recalculated according to the process. And if all the optimization indexes are traversed, and the calculated ETA and ETA boundaries still cannot meet the total time requirement for reaching the terminal, proposing an RTA redistribution requirement to the air traffic control according to the performance data of the air traffic control, giving a new RTA requirement and an RTA tolerance by the air traffic control according to the altitude-speed performance limit of the airplane, calculating the ETA and ETA boundaries of the flight planning waypoint again according to the process under the new arrival time requirement, and carrying out RTA sequence distribution.
The RTA sequence reallocation principle is as follows: the relationship between RTA sequence reallocation and ETA is shown in FIG. 2, where RTAi-1RTA for the i-1 st waypoint, i is waypoint number, i ═ 1,2,3, ·, n, [ RTA ·i-1,min,RTAi-1,max]RTA tolerance, Δ t, for the i-1 st waypointi-1,L and Δti-1,RThe magnitude of the left and right shift of the RTA for the i-1 st waypoint within the RTA tolerance, RTAnew,i-1,L and RTAnew,i-1,RFor the i-1 st waypoint RTAi-1The new RTA after moving left and right. As can be seen, the RTA increment of the ith-1 st waypoint affects the ETA boundary of the ith waypoint, i.e., the left boundary of the ETA window of the ith waypoint moves to the left by Δ ti-1,LOr to the right by Δ ti-1,RThe left boundary of which is ETA in the figurenew,i,min,L and ETAnew,i,min,R. Setting RTAi-1With a positive right shift and a negative left shift, the effect of the RTA change for the ith-1 waypoint on the ETA boundary for the ith waypoint may be expressed as ETAnew,i,min＝ETAi,min+Δti-1,ETAnew,i,max＝ETAi,max+Δti-1, wherein ETAnew,i,min，ETAnew,i,maxRTA for ith waypoint for left and right boundaries of ETA for ith waypoint after movementiAfter moving, change to RTAnew,iThe remaining waypoints are similar.
Based on the above analysis, the RTA movement of the previous waypoint can be utilized to bring the ETA boundary of the next or subsequent waypoint into coincidence with the RTA tolerance, achieving that the RTA of each waypoint is within the calculated ETA boundary. Now, a mathematical model for RTA sequence adjustment is established, which can be totally divided into three cases, respectively: 1) RTAnew,iWithin the ETA boundary of the ith waypoint, i.e. RTAnew,i∈[ETAi,min,ETAi,max]；2)RTAnew,iETA left boundary, i.e. RTA, less than ith waypointnew,i＜ETAi,min；3)RTAnew,iETA Right boundary greater than ith waypoint, i.e. RTAnew,i＞ETAi,max. For case 1, the ETA window allowable range for the aircraft to reach the ith waypoint is shown in FIG. 3. Because the ETA allowed movement range reaching the ith waypoint is also the RTA of the (i-1) th waypointi-1So that the allowable adjustment increment at for the i-1 st waypoint is Δ ti-1Comprises the following steps:
Δti-1∈[RTAnew,i-ETAi,max,RTAnew,i-ETAi,min](11)
for case 2, the ETA window allowable range for the aircraft to reach the ith waypoint is shown in FIG. 4. Allowable time increment of the i-1 st waypoint Δ ti-1Comprises the following steps:
Δti-1∈[RTAnew,i-ETAi,max,RTAnew,i-ETAi,min](12)
for case 3, the ETA window allowable range for the aircraft to reach the ith waypoint is shown in FIG. 5. Allowable time increment of the i-1 st waypoint Δ ti-1Comprises the following steps:
Δti-1∈[RTAnew,i-ETAi,max,RTAnew,i-ETAi,min](13)
in addition, Δ ti-1Cannot be moved arbitrarily, and also satisfies the RTA tolerance of itself, i.e.
Δti-1∈[RTAi-1,min-RTAi,RTAi-1,max-RTAi],i＝2,3,···,n (14)
To summarize the above, the following mathematical model description may be used:
setting the existence of a sequence RTAiI.e. 1,2, n, each number in the series satisfying an interval associated therewith, namely RTAi∈[RTAi,min,RTAi,max]When the ith value is adjusted within its range, i.e. RTAnew,i＝RTAi+Δti, wherein ,ΔtiTo adjust the increment, the increment can be positive or negative, while also meeting the following RTA requirements:
Figure BDA0002280068280000071
another group of ETA intervals [ ETAi,min,ETAi,max]Requires a Δ t to be obtainediI 1,2, n, satisfying RTAnew,i-ETAi,max≤Δti-1≤RTAnew,i-ETAi,minWherein, RTAnew,iIs the adjusted RTA. I.e. ati and Δti-1Need to satisfy the relation RTAi+Δti-ETAi,max≤Δti-1≤RTAi+Δti-ETAi,min. Only one set of sequences, { Δ t, { needs to be foundi1,2, so that the cost function is
Figure BDA0002280068280000072
The minimum is the calculated RTA reassigned increment sequence, the significance of the cost function is to make the RTA shift quantity absolute value of each waypoint minimum, and the delta t is formed by delta tiAnd adding an increment sequence on the basis of the original RTA sequence to the formed vector to obtain the redistributed RTA sequence, namely completing the establishment of the RTA redistributing mathematical model.
According to the RTA sequence allocation principle and the established mathematical model, the specific process of reallocating the RTA sequence by using the interior point method is shown in FIG. 6, and the steps are as follows:
(1) constructing an intermediate waypoint RTA adjustment quantity constraint optimization function as follows:
Figure BDA0002280068280000073
where the index i denotes the ith waypoint, Δ tiFor RTA adjustment of ith waypoint, RTAiRTA requirement value for ith waypoint, RTAi,minIs the RTA margin minimum for the ith waypoint, RTAi,maxAn RTA margin maximum for the ith waypoint;
the penalty function for constructing the interior point method is as follows:
Figure BDA0002280068280000081
wherein Δ t is represented byiI is a vector consisting of 1,2, …, n, r is a penalty factor, f (Δ t) is an objective function,
Figure BDA0002280068280000082
for the penalty term, the calculation formula is respectively as follows:
Figure BDA0002280068280000083
Figure BDA0002280068280000084
(2) initializing, including: let the iteration count variable k equal to 0, the initial value of penalty factor 1 < r(0)< 50, adjustment threshold εΔt∈(10-9,10-11) The objective function threshold ε ∈ (10)-5,10-7) For the initial sequence
Figure BDA0002280068280000085
Is selected from
Figure BDA0002280068280000086
I.e., within the feasible domain of the objective function, wherein,
Figure BDA0002280068280000087
(3) starting iteration, each iteration using 0.618 (golden section) method to J (delta t, r)(k)) Performing one-dimensional line search to obtain a penalty function J (delta t, r)(k)) Minimum Δ t, noted Δ t(k+1)If, | | f (Δ t) is satisfied(k+1))-f(Δt(k)) | | < epsilon or | Δ t(k+1)-Δt(k)||＜εΔtThen the iteration is stopped, at this time(k+1)I.e. the optimal solution deltat*Go to step d; otherwise, let r(k+1)＝Cr(k)The iterative counting variable is added with 1, and the step is repeated, wherein C is a decreasing coefficient and can be in a range of [0.1,0.5 ]]。
(4) Sequence Δ t obtained by interior point method*The redistributed RTA sequence is obtained by superimposing the original RTA sequence, i.e.
Figure BDA0002280068280000088
RTAnew,iRTA, RTA representing the ith waypoint in the reassigned RTA sequenceiIndicating the RTA of the ith waypoint in the original RTA sequence given by the empty pipe,
Figure BDA0002280068280000089
represents the optimal solution Δ t*The ith component.

Claims (1)

1. An RTA sequence allocation method based on four-dimensional track operation is characterized by comprising the following steps:
step 1: selecting optimization indexes according to flight plans, altitude and speed constraints raised by an air management department, an airplane performance database, meteorological conditions and operation requirements of an airline company, and selecting a climbing mode and a descending mode; the optimization index is the minimum cost or the minimum fuel saving or the longest endurance time; the climbing or descending modes comprise a constant-surface-speed climbing or descending mode, a constant-Mach-number climbing or descending mode, a constant-surface-speed and constant-Mach-number climbing or descending mode, and a constant-Mach-number and constant-surface-speed climbing or descending mode;
step 2: within the height and speed constraints of the flight plan, the optimal cruise height, the optimal cruise speed and the cruise speed interval are obtained by inquiring in an airborne performance database according to the selected optimization indexes;
and step 3: according to the selected climbing mode and the selected descending mode, the time, the distance and the fuel consumption data of a climbing section and a descending section are inquired and obtained in an airborne performance database, and the longitude and latitude of the TOC point are calculated and obtained by utilizing the climbing distance and a climbing starting point provided in an original flight plan and adopting an equiangular course forward solution formula; calculating the longitude and latitude of the TOD point by using the descending distance and a descending destination provided in the original flight plan and adopting an equiangular flight path forward solution formula; taking the optimal cruising altitude as the altitude of the TOC point and the TOD point; adding the longitude and latitude and the height of the TOC point and the TOD point into the original flight plan to obtain an updated flight plan;
and 4, step 4: ETA and ETA boundaries of each waypoint in the updated flight plan are calculated as follows:
Figure FDA0002280068270000011
Figure FDA0002280068270000012
Figure FDA0002280068270000013
wherein i is the waypoint number, i is 1,2, n-1, n is the total number of waypoints, LresFor remaining voyage, VTASAt the current airspeed, VwindForecasting wind speed, ETA, for weatheriETA for ith waypoint, when i is 11For the takeoff time of the aircraft, VTAS,maxAt a maximum value in the cruise speed interval, VTAS,minAt the minimum value of the cruise speed interval, ETAi+1Estimated time of arrival, ETA, for the i +1 st waypointi+1,minPredicted earliest time of arrival, ETA, for the i +1 st waypointi+1,maxThe estimated latest arrival time of the (i + 1) th waypoint;
and 5: if the air traffic control department does not have an arrival time requirement for each waypoint in the updated flight plan, RTAiIf the value of i ═ 2, ·, n is arbitrary, the ETA and ETA boundaries of each waypoint obtained in step 4 constitute the initial RTA sequence and the RTA tolerance, and the initial allocation of the RTA sequence is completed; otherwise, turning to step 6;
step 6: judging the arrival time RTA of the last waypoint given by the air traffic control departmentnWhether it is at the ETA boundary [ ETA ] of the waypointn,min,ETAn,max]If the number of the intermediate waypoints is within the range, performing RTA sequence reallocation on the intermediate waypoints by adopting an interior point method according to RTA tolerance of each waypoint provided by the air traffic control; otherwise, abandoning the optimization indexes selected in the step 1, reselecting one from other optimization indexes as the optimization index, keeping the climbing mode and the descending side unchanged, returning to the step 2 for calculation again, and if all the calculation results of the optimization indexes cannot meet the arrival time RTA of the last waypointnETA boundary [ ETA ] at the waypointn,min,ETAn,max]If so, proposing an RTA redistribution requirement to the empty pipe, giving a new RTA requirement and an RTA tolerance to the empty pipe according to the altitude-speed performance limit of the airplane, and returning to the step 1 to calculate again;
the specific process for reallocating the RTA sequence by adopting the interior point method is as follows:
step a: constructing an intermediate waypoint RTA adjustment quantity constraint optimization function as follows:
Figure FDA0002280068270000021
where the index i denotes the ith waypoint, Δ tiFor RTA adjustment of ith waypoint, RTAiRTA requirement value for ith waypoint, RTAi,minIs the RTA margin minimum for the ith waypoint, RTAi,maxAn RTA margin maximum for the ith waypoint;
the penalty function for constructing the interior point method is as follows:
Figure FDA0002280068270000022
wherein Δ t is represented byiI is a vector consisting of 1,2, …, n, r is a penalty factor, f (Δ t) is an objective function,
Figure FDA0002280068270000023
for the penalty term, the calculation formula is respectively as follows:
Figure FDA0002280068270000024
Figure FDA0002280068270000025
step b: initializing, including: let the iteration count variable k equal to 0, the initial value of penalty factor 1 < r(0)< 50, adjustment threshold εΔt∈(10-9,10-11) The objective function threshold ε ∈ (10)-5,10-7) Initial sequence
Figure FDA0002280068270000026
In (1),
Figure FDA0002280068270000027
step c: using golden section method to J (delta t, r)(k)) Performing one-dimensional line search, and calculating to obtain the product satisfying minJ (delta t, r)(k)) Δ t of (1), noted as Δ t(k+1)If, | | f (Δ t) is satisfied(k+1))-f(Δt(k)) | | < epsilon or | Δ t(k+1)-Δt(k)||＜εΔtThen the iteration is stopped, at this time(k+1)I.e. the optimal solution deltat*Go to step d; otherwise, let r(k+1)＝Cr(k)K is k +1, and the procedure is repeated, where C is a decreasing coefficient, preferably in the range of [0.1, 0.5%]；
Step d: according to
Figure FDA0002280068270000031
Calculated to be redistributedRTA sequence, wherein RTAi,newRTA, RTA representing the ith waypoint in the reassigned RTA sequenceiIndicating the RTA of the ith waypoint in the original RTA sequence given by the empty pipe,
Figure FDA0002280068270000032
represents the optimal solution Δ t*The ith component.
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