A method for analyzing car-following effect of heterogeneous traffic flow in the air

Abstract

The application discloses an air heterogeneous traffic flow following effect analysis method, first, based on the air heterogeneous traffic flow scene, the basic operation data of the front and rear aircrafts with the following effect are collected, and the motion state and mutual relationship of the front and rear aircrafts at different time are analyzed; in combination with the OVM of the ground traffic flow, the air heterogeneous traffic flow microscopic following model is established according to different situations that whether the rear aircraft needs to form the vertical interval caused by the different initial longitudinal intervals; then, the traffic data of the rear aircraft in the heterogeneous aircraft queue are considered, the following model is improved to stabilize the traffic flow; finally, the relationship between the initial interval of the rear aircraft and the front aircraft and the acceleration after the flight attitude is reestablished is obtained. The application quantifies the flight interval and the motion change condition based on the heterogeneous traffic flow scene, judges whether the two situations that the initial longitudinal interval and the speed difference between the front and rear aircrafts need to establish the vertical interval, constructs the air microscopic following model, and analyzes the air heterogeneous traffic flow following effect.

Description

Technical Field

[0001] This invention belongs to the field of airspace and heterogeneous traffic flow, and specifically relates to a method for analyzing the car-following effect of heterogeneous air traffic flow. Background Technology

[0002] With the continuous development of society and the economy, civil aviation transportation has made great progress, and non-traditional aircraft transportation methods, which are different from traditional civil airliners, have gradually come into people's view. These non-traditional aircraft are intertwined and mutually influential with traditional civil airliners, and the potential safety issues arising from conflicts are gradually attracting people's attention.

[0003] Non-traditional aircraft refer to unmanned aerial vehicles, personal aircraft that do not require airport facilities for takeoff and landing, and supersonic and very slow aircraft that operate over a wide range of altitudes. The traffic flow formed by the interaction and influence of these non-traditional aircraft with traditional commercial airliners in the airspace is called heterogeneous traffic flow.

[0004] To address potential conflicts between aircraft in heterogeneous air traffic flows, which differ from ground traffic in that aircraft fly beyond visual line of sight, pilots must coordinate with ground controllers to adjust the relationship between preceding and following aircraft to ensure the car-following effect of traffic flow platoons. However, existing methods cannot characterize the car-following effect between preceding and following aircraft in heterogeneous air traffic flow scenarios due to numerous issues such as potential flight safety accidents, wasted airspace resources, and unnecessary fuel consumption. Furthermore, existing methods only analyze the car-following effect in single scenarios, resulting in limited applicability to complex air traffic flow scenarios, and their incomplete consideration of factors leads to inaccurate results. Summary of the Invention

[0005] Purpose of the Invention: The purpose of this invention is to fill the technological gap in the current trend of heterogeneous traffic flow, and to address the shortcomings of existing kinematic equations, such as insufficient application prospects, incomplete consideration of factors, and the need for optimization of actual results. This invention proposes a method for analyzing the car-following effect in heterogeneous air traffic flow. This method can accurately and quickly interpret the motion relationships and describe the motion states between heterogeneous aircraft using existing real-time data and based on a model, providing a more feasible solution for controllers' rapid decision-making.

[0006] Technical solution: This invention provides a method for analyzing the car-following effect of heterogeneous air traffic flow, specifically including the following steps:

[0007] (1) Collect basic operating data of front and rear vehicles with car-following effect based on two scenarios: the rear vehicle does not need to establish a vertical separation with the front vehicle and the rear vehicle must establish a vertical separation with the front vehicle.

[0008] (2) Based on the heterogeneous traffic flow scenario, the motion state and interrelationship of the preceding and following vehicles at different times are preprocessed;

[0009] (3) Combine the speed optimization function with the kinematic equations of the front and rear aircraft to determine whether the initial longitudinal interval and the speed difference between the front and rear aircraft need to establish a vertical interval, and construct a micro-car-following model of heterogeneous air traffic flow.

[0010] (4) Consider the impact of the historical speed of the following vehicle on the current speed, and add the speed difference to stabilize the traffic flow;

[0011] (5) The relationship between the initial flight interval of the front and rear aircraft and the acceleration of the rear aircraft was obtained through simulation.

[0012] Furthermore, the implementation process of step (1) is as follows:

[0013] The following aircraft does not need to establish a vertical separation with the preceding aircraft: the initial longitudinal flight separation between the preceding and following aircraft; the flight speed, maximum flight speed, stall speed, and common target speed of the preceding and following aircraft; controller reaction time; pilot reaction time to execute instructions; time for the following aircraft to re-establish flight attitude; and the time required for the preceding aircraft to return to the target speed with constant acceleration from its actual initial speed.

[0014] The following aircraft must establish a vertical separation with the preceding aircraft: the initial longitudinal flight separation between the preceding and following aircraft; the flight speed, maximum flight speed, and stall speed of the preceding and following aircraft; the target speed of the preceding aircraft; the controller's reaction time; the pilot's reaction time to execute instructions; the time for the following aircraft to re-establish its flight attitude; the time required for the preceding aircraft to return to its target speed with constant acceleration from its actual initial speed; and the vertical separation that the following aircraft must establish.

[0015] Furthermore, the implementation process of step (2) is as follows:

[0016] (21) Two dissimilar aircraft i and j are flying in the same direction with a longitudinal spacing S in the airspace, where S should be greater than the specified value of longitudinal spacing. m The flight speeds of the front and rear aircraft are V respectively. i and V j At time t0, the leading aircraft i changes speed due to an emergency and reports to the controller. At this time, the speed of the leading aircraft i is set to V. i (t0), the speed of the rear machine j is V. j (t0); The time taken for the controller's reaction time, the time for issuing operational instructions to the subsequent controller, and the time for the subsequent pilot to react and implement operations until the start of flight attitude establishment are defined as the reaction time T. r V j (t0) and V j (t0+T r ) are the subsequent machine j at time t0 and t0+T respectively.r The same speed at any given moment;

[0017] (22) Describe the motion state of the fore-engine:

[0018]

[0019] In the formula, a i V is the acceleration of the preceding machine i when it begins uniform acceleration motion from time t0; d V represents the target velocity after the changes in the velocities of aircraft i and j; i (t0) represents the actual speed of the preceding machine i at time t0; T i For the preceding machine i, from time t0 until it finally reduces to the target speed V d Time required;

[0020] V i (t0+T r ) = V i (t0)+a i ·T r

[0021] S i (t0+T r )=(V i 2 (t0+T r )-V i 2 (t0)) / (2a i )

[0022]

[0023] In the formula, T r V represents the time interval from when the preceding aircraft begins to change its flight attitude at time t0 until the following aircraft re-establishes its flight attitude; i (t0+T r ) is the preceding machine i at t0+T r Speed ​​at a given moment; S i (t0+T r Let ) represent the time interval i from time t0 to t0+T. r The distance traveled at any given moment; S i For the preceding machine i from time t0 to t0+T i The distance traveled during the entire deceleration process at any given moment;

[0024] (23) The flight distance of the rear aircraft during the uniform motion phase within the reaction time cannot be ignored; describe the motion state of the rear aircraft under different scenarios:

[0025] The rear machine does not need to be perpendicular to the front machine:

[0026] S j (t0+Tr ) = V j (t0+T r )·T r

[0027]

[0028] In the formula, S j (t0+T r ) is the reaction time T of the subsequent machine j. r Flight distance within; V j (t0) represents the reaction time T of the subsequent machine j. r speed; V j (t0+T r ) is the rear machine j at t0+T r The speed at a given moment is actually related to V. j (t0) are equal; S j For the rear machine j from t0+T r The distance traveled from the moment the speed begins to change until it reaches the target speed; a j Let J be the acceleration of the rear aircraft j as its velocity changes;

[0029] The following aircraft must establish a vertical separation with the preceding aircraft: Considering the vertical separation standards for different types of airspace, assuming the vertical separation standard for the airspace is L m The rate of ascent or descent of the rear aircraft is β. L :

[0030] L m =β L ·(T i -T r )

[0031] The movement of the rear aircraft J during the climb phase is shown as follows:

[0032]

[0033]

[0034] V d =V j (t0+T r )+a j ·(T i -T r )

[0035] In the formula, L m β is the vertical spacing standard for airspace; r S represents the initial climb / descent rate of the rear aircraft j; j (T i -T r () represents the distance traveled by aircraft j during the climb / descent phase;

[0036] (24) Analyze and establish the relationship between the preceding and following machines i and j at different times:

[0037] (241) At time t0, the initial longitudinal flight interval between the leading and trailing aircraft i,j is S;

[0038] S = s i (t0)-s j (t0)

[0039] Differentiate with respect to both sides t:

[0040] S'=V i (t0)-V j (t0)

[0041] In the formula, s i (t0) represents the position of the preceding machine i at time t0; s j (t0) represents the position of the rear machine j at time t0;

[0042] (242) at t0+T r At time i, j, the distance relationship between the preceding and following machines is:

[0043]

[0044] Differentiate with respect to both sides t:

[0045] V i (t0)-V j (t0)+S′ i (t0+T r )-S' j (t0+T r )>0

[0046] In the formula, △S(t0+T) r ) is t0+T r The distance between aircraft i and j ahead and behind at any given time should be greater than the minimum longitudinal flight separation value S specified for the aircraft ahead and behind. m The specific decision depends on whether the car-following effect involves acceleration or deceleration; the situation should be considered accordingly.

[0047] At time t0, the longitudinal separation between aircraft i and j should be greater than the minimum longitudinal flight separation specified for the preceding and following aircraft. m S m is a constant, representing the minimum longitudinal flight interval specified between aircraft i and j;

[0048] (243) At t=t0+T i At time i, j, assume that the longitudinal distance between the front and rear machines i and j is exactly the minimum specified value S. mThen we have:

[0049] The rear machine does not need to be perpendicular to the front machine:

[0050]

[0051] The above formulas are rearranged, and the derivative of t on both sides of the equation is taken:

[0052] V i (t0)-V j (t0)=a j ·T r +S' j -S′ i

[0053] S' j -S′ i =V j (t0+T r )·V′ j (t0+T r ) / a j -V i (t0)·V′ i (t0) / a i

[0054] Here, let the proportionality coefficient α be:

[0055] (α+1)[V i (t0)-V j [(t0)]=a j T r

[0056] Let λ = (α+1) / T r ,have to:

[0057] a j =λ[V i (t0)-V j (t0)]

[0058] In the formula, α is the proportionality coefficient; λ is the reaction intensity coefficient / sensitivity (unit: h). -1 This indicates quantities related to controller workload and pilot activity intensity;

[0059] The rear machine must maintain a perpendicular distance from the front machine:

[0060] The longitudinal spacing between the front and rear engines is as follows: In cases where the rear engine must change height, if the actual direction of movement of the rear engine is considered as longitudinal, the difference from case one is that the rear engine's T in this case... i -T r The sailing distance is longer during the time period, that is, in t0+T iThe longitudinal distance between the front and rear machines will be less than S. m ;

[0061] The vertical spacing between the front and rear units is as follows:

[0062] L j -L i =L m

[0063] In the formula, L j For the rear machine j at t0+T i Location at any given moment; L i For the front machine i at t0+T i The location at any given moment.

[0064] Furthermore, the implementation process of step (3) is as follows:

[0065] Introducing the optimized velocity function V(△S(t0+T) r Establish the change in the interval between the front and rear engines ΔS(t0+T) r The velocity V of the preceding machine i at time t0 i The connection of (t0) in (t0+T) r At time V i (t0) and △S(t0+T) r The relationship is:

[0066] △S(t0+T r ) = S + S i (t0+T r )-S j (t0+T r )

[0067] S i (t0+T r It can also be expressed as:

[0068]

[0069] Then we have:

[0070]

[0071] Based on the above relationships, a microscopic car-following model applicable to heterogeneous air traffic flow scenarios is established, and the calculation formula is as follows:

[0072] a j =λ[V(△S(t0+T)] r ))-V j (t0+T r )]

[0073] in:

[0074]

[0075] In the formula, V(△S(t0+T) r )) is t0+T r The optimized velocity function for the time difference between the pre- and post-moment points; tanhC(S) is the hyperbolic tangent function with S as the independent variable, which can characterize the fluctuation range of tanhC(S) caused by the change of S within a certain interval; ΔS(t0+T) r ) is t0+T r The distance between the front and rear machines at any given moment; V max This is the maximum speed that the rear aircraft j can reach during the cruise phase.

[0076] Furthermore, the implementation process of step (4) is as follows:

[0077] (41) Considering the impact of the historical speed of the following aircraft on the current speed, add the speed difference to stabilize traffic flow:

[0078] a j =λ[V(△S(t0+T)] r ))-V j (t0+T r )]+μ[V j (t0+T i )-V j (t0+T r )]

[0079] In the formula, μ is the self-stabilizing coefficient;

[0080] (42) Considering that the speed change phase of the rear engine is a continuous process, the speed difference between the current speed and the historical speed is expressed in the form of calculus, and the calculation formula is as follows:

[0081]

[0082] in, Able to [t0+T r ,t0+T i The speed difference between the current speed and the historical speed within a given time period will be described more accurately.

[0083] Beneficial Effects: Compared with existing technologies, the beneficial effects of this invention are as follows: Based on heterogeneous traffic flow scenarios, this invention studies the influence of an aircraft's historical speed on its current speed by quantifying flight intervals and changes in motion, overcoming the shortcomings of existing kinematic equations that cannot describe the nonlinear motion of aircraft. Following aircraft adjust accordingly based on the actual motion of preceding aircraft, providing a theoretical model for achieving autonomous car-following effects and avoiding airspace resource waste or flight safety issues caused by excessively large or small flight intervals. It transforms the application scenario of heterogeneous traffic flow from ground traffic to air traffic. The air heterogeneous traffic flow car-following model can assist air traffic controllers in more accurately judging the approach trends of preceding and following aircraft and quickly deciding whether intervention is necessary. This model can also provide a theoretical method for the post-event analysis of unsafe air traffic car-following incidents. Attached Figure Description

[0084] Figure 1 This is a flowchart of the present invention;

[0085] Figure 2 A schematic diagram of a flight following aircraft in an air traffic flow scenario where a vertical separation is not required;

[0086] Figure 3 A schematic diagram illustrating the flight following maneuver where vertical spacing must be established for following aircraft in an air traffic flow scenario;

[0087] Figure 4 The graph shows the relationship between the initial longitudinal flight distance between the preceding and following aircraft and the acceleration of the following aircraft, as represented by the kinematic equations, under different conditions.

[0088] Figure 5 This is a graph showing the relationship between the initial longitudinal flight distance between the preceding and following aircraft and the acceleration of the following aircraft, as represented by the car-following model of heterogeneous air traffic flow under different conditions. Detailed Implementation

[0089] The present invention will now be described in further detail with reference to the accompanying drawings.

[0090] This invention provides a method for analyzing the car-following effect of heterogeneous air traffic flow, such as... Figure 1 As shown, it includes the following steps:

[0091] Step 1: Collect basic operating data of the front and rear vehicles with car-following effect, based on two scenarios: the rear vehicle does not need to establish a perpendicular distance with the front vehicle and the rear vehicle must establish a perpendicular distance with the front vehicle.

[0092] Scenario 1 (No vertical separation required between the following aircraft and the preceding aircraft): Initial longitudinal flight separation between the preceding and following aircraft, their respective flight speeds, maximum flight speeds and stall speeds, as well as the common target speed, controller reaction time, pilot reaction time to execute instructions and time for the following aircraft to re-establish flight attitude, and the time required for the preceding aircraft to reach the target speed from its actual initial speed with constant acceleration.

[0093] Scenario 2 (If Scenario 1 is not met, the following aircraft must establish a vertical separation with the preceding aircraft): the initial longitudinal flight separation between the preceding and following aircraft, their respective flight speeds, maximum flight speeds and stall speeds, the target speed of the preceding aircraft, the controller's reaction time, the pilot's reaction time to execute instructions and the time for the following aircraft to re-establish its flight attitude, and the time required for the preceding aircraft to reach its target speed from its actual initial speed with constant acceleration, and the vertical separation that the following aircraft must establish.

[0094] The criteria for determining whether a vertical separation is needed are as follows: First, use the data for calculations where a vertical separation is not needed (Scenario 1). If one of the following conditions is met, a vertical separation must be established (Scenario 2): 1) The calculated acceleration exceeds the acceleration range that the rear engine can achieve; 2) Although the rear engine can theoretically achieve the calculated acceleration, after comprehensively considering safety and economy (fuel consumption) factors, it is considered that establishing a vertical separation is a more reasonable decision; otherwise, Scenario 1 is adopted.

[0095] This embodiment takes the flight situation of heterogeneous aircraft flying in the same direction at the same flight altitude in a certain airspace as an example. The motion of the preceding and following aircraft is analyzed using the air traffic flow following model established by this invention. Figure 2 , Figure 3 As shown, the specific steps are as follows:

[0096] This embodiment simulates the flight data of two heterogeneous aircraft i and j at the same altitude in the simulated airspace. The flight data includes the actual initial longitudinal flight interval S between the heterogeneous aircraft i and j, and their actual flight speeds V. i V j Maximum flight speed V max and stall speed V s And the common target velocity V after the change d The total time for controller reaction time, pilot reaction time to execute instructions, and aircraft attitude establishment time is called reaction time T. r And the time T required for the preceding machine to accelerate from its actual initial velocity to the target velocity at a constant acceleration. i wait.

[0097] Step 2: Based on the heterogeneous traffic flow scenario, preprocess the data on the motion status and interrelationships of the vehicles before and after at different times.

[0098] S2.1: Scenario: Two dissimilar aircraft i and j are flying in the same direction in airspace with a longitudinal separation S (km), where S should be greater than the specified value of longitudinal separation. m (km), the flight speeds of the front and rear aircraft are respectively: V i V j At time t0, the leading aircraft i changes speed due to an unforeseen situation and reports to the controller. At this time, the speed of the leading aircraft i is set to V. i (t0), the speed of the rear machine j is V. j (t0). The time taken for the controller's reaction time, the time for issuing operational instructions to the subsequent controller, and the time for the subsequent pilot to react and implement operations until the flight attitude is established are defined as the reaction time T. r .

[0099] The specific scenario is as follows: Assume that in a certain airspace, two dissimilar aircraft are flying in the same direction at the same flight altitude with a longitudinal spacing of S (km) (this spacing is greater than the 10km interval required for en-route flight under current radar control conditions). Both aircraft i and j have a speed of 850 km / h. At time t0, aircraft i suddenly decelerates due to detecting a hazard; the target speed is 500 km / h, which is greater than V. S (Aircraft stall speed). The pilot of the preceding aircraft notifies air traffic control of this situation as soon as it begins to decelerate; the communication lasts 9 seconds. Air traffic control reacts for 6 seconds and then instructs the following aircraft to decelerate; this communication also lasts 9 seconds. The pilot of the following aircraft receives the air traffic control instruction and reacts for 6 seconds before initiating deceleration. Assuming the aircraft attitude establishment time is 6 seconds, the total time from when the preceding aircraft begins decelerating to when the following aircraft begins decelerating is 36 seconds. The preceding aircraft takes 3 minutes to decelerate to its target speed, and the following aircraft's maximum cruise speed is V. max = 945 km / h.

[0100] If the following aircraft cannot ultimately reach the same speed at the same altitude, it is assumed that the following aircraft will perform a climb maneuver to establish a vertical separation, with the standard vertical separation being L. m =600m. Considering the complexity of airflow and maneuvering that affects the subsequent aircraft in establishing vertical separation, we set the actual flight distance to increase by 1km when changing altitude. V j (t0) and V j (t0+T r ) are the subsequent machine j at time t0 and t0+T respectively. r The same speed at every moment.

[0101] S2.2: Calculate the motion of the preceding machine.

[0102] For the preceding machine i:

[0103]

[0104] In the formula, a i V is the acceleration of the preceding machine i when it begins uniform acceleration motion from time t0; d V represents the target velocity after the changes in the velocities of aircraft i and j; i (t0) represents the actual speed of the preceding machine i at time t0; T i For the preceding machine i, from time t0 until it finally reduces to the target speed V d The time required.

[0105] V i (t0+T r ) = V i (t0)+a i ·T r

[0106] S i (t0+T r )=(V i 2 (t0+T r )-V i 2 (t0)) / (2a i )

[0107]

[0108] In the formula, T r V represents the time interval from when the preceding aircraft begins to change its flight attitude at time t0 until the following aircraft re-establishes its flight attitude; i (t0+T r ) is the preceding machine i at t0+T r Speed ​​at a given moment; S i (t0+T r Let ) represent the time interval i from time t0 to t0+T. r The distance traveled at any given moment; S i For the preceding machine i from time t0 to t0+T i The distance traveled during the entire deceleration process at any given moment.

[0109] S2.3: Calculate the motion of the rear mechanism.

[0110] Scenario 1:

[0111] S j (t0+T r ) = V j (t0+T r )·T r

[0112]

[0113] In the formula, S j (t0+Tr ) is the reaction time T of the subsequent machine j. r Flight distance within; V j (t0) represents the reaction time T of the subsequent machine j. r speed; V j (t0+T r ) is the rear machine j at t0+T r The speed at a given moment is actually related to V. j (t0) are equal; S j For the rear machine j from t0+T r The distance traveled from the moment the speed begins to change until it reaches the target speed; a j Let J be the acceleration of the rear engine j as its velocity changes.

[0114] Scenario 2: Considering the vertical separation standards for different types of airspace, assuming the vertical separation standard for the airspace is L. m The climb / descent rate of the rear aircraft is β L , Unit: km / h.

[0115] L m =β L ·(T i -T r )

[0116] The movement of the rear aircraft J during the climb phase is shown as follows:

[0117]

[0118]

[0119] V d =V j (t0+T r )+a j ·(T i -T r )

[0120] In the formula, L m β is the vertical spacing standard for airspace; r S represents the initial climb / descent rate of the rear aircraft j; j (T i -T r () represents the flight distance of the rear aircraft j during the climb / descent phase.

[0121] S2.4: Analyze and establish the relationship between the preceding and following machines i and j at different times.

[0122] ①At time t0, the initial longitudinal flight interval between the leading and trailing aircraft i and j is S;

[0123] S = s i (t0)-sj (t0)

[0124] Differentiating with respect to both sides t, we can obtain,

[0125] S'=V i (t0)-V j (t0)

[0126] In the formula, s i (t0) represents the position of the preceding machine i at time t0; s j (t0) represents the position of the subsequent machine j at time t0.

[0127] ② at t0+T r At time i, j, the distance relationship between the preceding and following machines is:

[0128]

[0129] Differentiating with respect to both sides t, we can obtain,

[0130] V i (t0)-V j (t0)+S′ i (t0+T r )-S' j (t0+T r )>0

[0131] In the formula, △S(t0+T) r ) is t0+T r The distance between aircraft i and j ahead and behind at any given time should be greater than the minimum longitudinal flight separation value S specified for the aircraft ahead and behind. m The specific decision depends on whether the aircraft accelerates or decelerates during the follow-along operation; at time t0, the longitudinal separation between aircraft i and j should be greater than the minimum longitudinal flight separation specified for the preceding and following aircraft. m S m is a constant, representing the minimum longitudinal flight interval specified between aircraft i and j.

[0132] ③ At t=t0+T i At time i, j, assume that the longitudinal distance between the front and rear machines i and j is exactly the minimum specified value S. m Then there is,

[0133] Scenario 1:

[0134]

[0135] By rearranging the above formulas and differentiating t on both sides of the equation, we can obtain:

[0136] V i (t0)-V j (t0)=aj ·T r +S' j -S′ i

[0137] S' j -S′ i =V j (t0+T r )·V j '(t0+T r ) / a j -V i (t0)·V′ i (t0) / a i

[0138] Here, we set a proportionality constant α, and we get...

[0139] (α+1)[V i (t0)-V j [(t0)]=a j ·T r

[0140] Let λ = (α+1) / T r ,have to

[0141] a j =λ[V i (t0)-V j (t0)]

[0142] In the formula, α is the proportionality coefficient; λ is the reaction intensity coefficient / sensitivity (unit: h). -1 ), which represents the quantity related to controller workload and pilot intensity.

[0143] Scenario 2:

[0144] ① The longitudinal spacing between the front and rear machines is as follows:

[0145] In cases where the rear aircraft must change altitude, if the actual direction of movement of the rear aircraft is considered as longitudinal, the difference from case one is that the rear aircraft's T in this case... i -T r The sailing distance is longer during the time period, that is, in t0+T i The longitudinal distance between the front and rear machines will be less than S. m .

[0146] The difference from scenario one is that the rear machine is at t0+T r The velocity at time t0+T i The speed of time, and S m The value of .

[0147] ②The vertical spacing between the front and rear machines is as follows:

[0148] L j -L i =L m

[0149] In the formula, L j For the rear machine j at t0+T i Location at any given moment; L i For the front machine i at t0+T i The location at any given moment.

[0150] In this embodiment, a flight scenario is selected where the preceding aircraft decelerates due to a sudden situation, and the following aircraft also decelerates to ensure safety and maintain the following flight effect. Wherein:

[0151] Scenario 1: The acceleration of the front aircraft i is -7000 km / h 2 The first aircraft, i, has a speed of 780 km / h at 36 seconds and a flight distance of 8.15 km. Its total flight distance over the 3 minutes is 33.75 km. The second aircraft, j, has a speed of 850 km / h at 36 seconds and a flight distance of 8.5 km. Its total flight distance over the 3 minutes is 35.5 km. The corresponding S... m It is 10km.

[0152] Scenario 2: The acceleration of the front aircraft i is -7000 km / h 2 The leading aircraft i had a speed of 780 km / h at 36 seconds, and a flight distance of 8.15 km. Its total flight distance over the 3 minutes was 33.75 km. The following aircraft j, after re-establishing its flight attitude at 36 seconds, had a speed of [missing information] km / h, and a flight distance of 8.5 km. Its total flight distance over the 3 minutes was [missing information]. The corresponding S m for

[0153] Step 3: Introduce a velocity optimization function to describe the nonlinear relationship in the actual scenario.

[0154] To more accurately describe the instability and nonlinear motion of air traffic flow in real-world scenarios, an optimized velocity function V(ΔS(t0+T)) is introduced. r Establish the change in the interval between the front and rear engines ΔS(t0+T) r The velocity V of the preceding machine i at time t0 i The relationship between (t0) and (t0) can be determined from the analysis. r At that moment, V i (t0) and △S(t0+T) r The relationship is:

[0155] △S(t0+T r ) = S + S i (t0+Tr )-S j (t0+T r )

[0156] S i (t0+T r It can also be expressed as:

[0157]

[0158] Then there is,

[0159]

[0160] Based on the above relationships, a microscopic car-following model applicable to heterogeneous air traffic flow scenarios is established, and the calculation formula is as follows:

[0161] a j =λ[V(△S(t0+T)] r ))-V j (t0+T r )]

[0162] in,

[0163]

[0164] In the formula, V(△S(t0+T) r )) is t0+T r The optimized velocity function for the time difference between the pre- and post-moment points; tanhC(S) is the hyperbolic tangent function with S as the independent variable, which can characterize the fluctuation range of tanhC(S) caused by the change of S within a certain interval; ΔS(t0+T) r ) is t0+T r The distance between the front and rear machines at any given moment; V max Let C be the maximum speed that the rear aircraft j can reach during the cruise phase. In this embodiment, C is set to 0.8, and V... max The speed is 945 km / h, in scenario one, S m Take the value 10km, S in case two m for

[0165] Step 4: Consider the impact of the following vehicle's historical speed on the current speed, and incorporate the speed difference to stabilize traffic flow. The calculation formula is:

[0166] a j =λ[V(△S(t0+T)] r ))-V j (t0+T r )]+μ[V d -V j (t0+T r )]

[0167] In the formula, μ is the self-stability coefficient (unit: h). -1 ).

[0168] Considering that the speed change phase of the rear aircraft is a continuous process, the speed difference between the current speed and the historical speed is expressed in the form of calculus. The calculation formula is:

[0169]

[0170] in, Able to [t0+T r ,t0+T i The speed difference between the current speed and the historical speed within a given time period will be described more accurately.

[0171] In this embodiment, the value of μ is 0.8h. -1 The historical time range is [t0+0.01, t0+0.05].

[0172] S5: The relationship between the initial flight interval of the leading and trailing aircraft and the acceleration of the trailing aircraft is derived.

[0173] In this embodiment, the acceleration a of the rear machine j is finally obtained. j The relationship between the initial flight interval S of the aircraft in front and behind is as follows:

[0174] Scenario 1:

[0175]

[0176] Unit: km / h 2 .

[0177] Scenario 2:

[0178]

[0179] Unit: km / h 2 .

[0180] The relationship between the initial longitudinal flight distance between the preceding and following aircraft and the acceleration of the following aircraft, as characterized by the kinematic equations and the car-following model of heterogeneous air traffic flow established in this embodiment, are as follows: Figure 4 , Figure 5 As shown. In heterogeneous air traffic flow, while the original kinematic equations can simply describe the motion between aircraft, they cannot characterize the nonlinear motion relationship existing in the following aircraft's car-following effect. During the motion of aircraft at different longitudinal intervals, the acceleration of the following aircraft remains constant with respect to the longitudinal interval between the preceding and following aircraft, which is inconsistent with real-world scenarios, such as... Figure 4As shown; by introducing a speed optimization function, a car-following model for heterogeneous air traffic flow is established, which can effectively characterize the strength of the car-following effect under different longitudinal intervals and describe the nonlinear motion relationship between preceding and following aircraft, such as... Figure 5 As shown.

[0181] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for analyzing the car-following effect of heterogeneous air traffic flow, characterized in that, Includes the following steps: (1) Collect basic operating data of front and rear vehicles with car-following effect based on two scenarios: the rear vehicle does not need to establish a vertical separation with the front vehicle and the rear vehicle must establish a vertical separation with the front vehicle. (2) Based on the heterogeneous traffic flow scenario, the motion state and interrelationship of the preceding and following vehicles at different times are preprocessed; (3) Combine the speed optimization function with the kinematic equations of the front and rear aircraft to determine whether the initial longitudinal interval and the speed difference between the front and rear aircraft need to establish a vertical interval, and construct a micro-car-following model of heterogeneous air traffic flow. (4) Consider the impact of the historical speed of the following vehicle on the current speed, and add the speed difference to stabilize the traffic flow; (5) The relationship between the initial flight interval of the leading and trailing aircraft and the acceleration of the trailing aircraft was obtained through simulation; The implementation process of step (3) is as follows: Introducing the optimized velocity function V(ΔS(t0+T)) r Establish the change in the interval between the front and rear engines ΔS(t0+T) r The velocity V of the preceding machine i at time t0 i The connection of (t0) in (t0+T) r At time V i (t0) and ΔS(t0+T) r The relationship is: ΔS(t0+T r )=S+S i (t0+T r )-S j (t0+T r ) S i (t0+T r It can also be expressed as: Then we have: Based on the above relationships, a microscopic car-following model applicable to heterogeneous air traffic flow scenarios is established, and the calculation formula is as follows: a j =λ[V(ΔS(t0+T r ))-V j (t0+T r )] in: In the formula, V(ΔS(t0+T) r )) is t0+T r The optimized velocity function for the time difference between the pre- and post-moment points; tanhC(S) is the hyperbolic tangent function with S as the independent variable, which can characterize the fluctuation range of tanhC(S) caused by the change of S within a certain interval; ΔS(t0+T) r ) is t0+T r The distance between the front and rear machines at any given moment; V max This is the maximum speed that the rear aircraft J can reach during the cruise phase; The implementation process of step (4) is as follows: (41) Considering the impact of the historical speed of the following aircraft on the current speed, add the speed difference to stabilize traffic flow: a j =λ[V(ΔS(t0+T r ))-V j (t0+T r )]+μ[V j (t0+T i )-V j (t0+T r )] In the formula, μ is the self-stabilizing coefficient; (42) Considering that the speed change phase of the rear engine is a continuous process, the speed difference between the current speed and the historical speed is expressed in the form of calculus, and the calculation formula is as follows: in, Able to [t0+T r ,t0+T i The speed difference between the current speed and the historical speed within a given time period will be described more accurately.

2. The method for analyzing the car-following effect of heterogeneous air traffic flow according to claim 1, characterized in that, The implementation process of step (1) is as follows: The following aircraft does not need to establish a vertical separation with the preceding aircraft: the initial longitudinal flight separation between the preceding and following aircraft; the flight speed, maximum flight speed, stall speed, and common target speed of the preceding and following aircraft; controller reaction time; pilot reaction time to execute instructions; time for the following aircraft to re-establish flight attitude; and the time required for the preceding aircraft to return to the target speed with constant acceleration from its actual initial speed. The following aircraft must establish a vertical separation with the preceding aircraft: the initial longitudinal flight separation between the preceding and following aircraft; the flight speed, maximum flight speed, and stall speed of the preceding and following aircraft; the target speed of the preceding aircraft; the controller's reaction time; the pilot's reaction time to execute instructions; the time for the following aircraft to re-establish its flight attitude; the time required for the preceding aircraft to return to its target speed with constant acceleration from its actual initial speed; and the vertical separation that the following aircraft must establish.

3. The method for analyzing the car-following effect of heterogeneous air traffic flow according to claim 1, characterized in that, The implementation process of step (2) is as follows: (21) Two dissimilar aircraft i and j are flying in the same direction with a longitudinal spacing S in the airspace, where S should be greater than the specified value of longitudinal spacing. m The flight speeds of the front and rear aircraft are V respectively. i and V j At time t0, the leading aircraft i changes speed due to an emergency and reports to the controller. At this time, the speed of the leading aircraft i is set to V. i (t0), the speed of the rear machine j is V. j (t0); The time taken for the controller's reaction time, the time for issuing operational instructions to the subsequent controller, and the time for the subsequent pilot to react and implement operations until the start of flight attitude establishment are defined as the reaction time T. r V j (t0) and V j (t0+T r ) are the subsequent machine j at time t0 and t0+T respectively. r The same speed at any given moment; (22) Describe the motion state of the fore-engine: In the formula, a i V is the acceleration of the preceding machine i when it begins uniform acceleration motion from time t0; d V represents the target velocity after the changes in the velocities of aircraft i and j; i (t0) represents the actual speed of the preceding machine i at time t0; T i For the preceding machine i, from time t0 until it finally reduces to the target speed V d Time required; V i (t0+T r )=V i (t0)+a i ·T r S i (t0+T r )=(V i 2 (t0+T r )-V i 2 (t0)) / (2a i ) In the formula, T r V represents the time interval from when the preceding aircraft begins to change its attitude at time t0 until the following aircraft re-establishes its flight attitude; i (t0+T r ) is the preceding machine i at t0+T r Speed ​​at a given moment; S i (t0+T r Let ) represent the time interval i from time t0 to t0+T. r The distance traveled at any given moment; S i For the preceding machine i from time t0 to t0+T i The distance traveled during the entire deceleration process at any given moment; (23) The flight distance of the rear aircraft during the uniform motion phase within the reaction time cannot be ignored; describe the motion state of the rear aircraft under different scenarios: The rear machine does not need to be perpendicular to the front machine: S j (t0+T r )=V j (t0+T r )·T r In the formula, S j (t0+T r ) is the reaction time T of the subsequent machine j. r Flight distance within; V j (t0) represents the reaction time T of the subsequent machine j. r speed; V j (t0+T r ) is the rear machine j at t0+T r The speed at a given moment is actually related to V. j (t0) are equal; S j For the rear machine j from t0+T r The distance traveled from the moment the speed begins to change until it reaches the target speed; a j Let J be the acceleration of the rear aircraft j as its velocity changes; The following aircraft must establish a vertical separation with the preceding aircraft: Considering the vertical separation standards for different types of airspace, assuming the vertical separation standard for the airspace is L m The rate of ascent or descent of the rear aircraft is β. L : L m =β L ·(T i -T r ) The movement of the rear aircraft J during the climb phase is shown as follows: V d =V j (t0+T r )+a j ·(T i -T r ) In the formula, L m β is the vertical spacing standard for airspace; r S represents the initial climb / descent rate of the rear aircraft j; j (T i -T r () represents the distance traveled by aircraft j during the climb / descent phase; (24) Analyze and establish the relationship between the preceding and following machines i and j at different times: (241) At time t0, the initial longitudinal flight interval between the leading and trailing aircraft i,j is S; S=s i (t0)-s j (t0) Differentiate with respect to both sides t: S'=V i (t0)-V j (t0) In the formula, s i (t0) represents the position of the preceding machine i at time t0; s j (t0) represents the position of the rear machine j at time t0; (242) at t0+T r At time i, j, the distance relationship between the preceding and following machines is: Differentiate with respect to both sides t: V i (t0)-V j (t0)+S i '(t0+T r )-S' j (t0+T r )>0 In the formula, ΔS(t0+T) r ) is t0+T r The distance between aircraft i and j ahead and behind at any given time should be greater than the minimum longitudinal flight separation value S specified for the aircraft ahead and behind. m The specific decision depends on whether the car-following effect involves acceleration or deceleration; the situation should be considered accordingly. At time t0, the longitudinal separation between aircraft i and j should be greater than the minimum longitudinal flight separation specified for the preceding and following aircraft. m S m is a constant, representing the minimum longitudinal flight interval specified between aircraft i and j; (243) At t=t0+T i At time i, j, assume that the longitudinal distance between the front and rear machines i and j is exactly the minimum specified value S. m Then we have: The rear machine does not need to be perpendicular to the front machine: The above formulas are rearranged, and the derivative of t on both sides of the equation is taken: V i (t0)-V j (t0)=a j ·T r +S' j -S i ' S' j -S i '=V j (t0+T r )·V j '(t0+T r ) / a j -V i (t0)·V i '(t0) / a i Here, let the proportionality coefficient α be: (α+1)[V i (t0)-V j (t0)]=a j T r Let λ = (α+1) / T r ,have to: a j =λ[V i (t0)-V j (t0)] In the formula, α is the proportionality coefficient; λ is the reaction intensity coefficient / sensitivity (unit: h). -1 This indicates quantities related to controller workload and pilot activity intensity; The rear machine must maintain a vertical distance from the front machine: The longitudinal spacing between the front and rear engines is as follows: In cases where the rear engine must change height, if the actual direction of movement of the rear engine is considered as longitudinal, the difference from case one is that the rear engine's T in this case... i -T r The sailing distance is longer during the time period, that is, in t0+T i The longitudinal distance between the front and rear machines will be less than S. m ; The vertical spacing between the front and rear units is as follows: L j -L i L m In the formula, L j For the rear machine j at t0+T i Location at any given moment; L i For the front machine i at t0+T i The location at any given moment.

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