Conflict risk analysis method for mixed approach operations on parallel runways based on TCAS warnings

Abstract

This invention belongs to the field of air traffic management technology, specifically disclosing a method for calculating the rapid conflict risk of parallel runway mixed approach operations based on TCAS (Traffic Response System). The method includes establishing an aircraft motion model, which involves projecting the aircraft's trajectory onto the runway system plane to establish horizontal and vertical motion models for two aircraft; establishing a track error model, which uses track deviation data to fit the relationship between the normal standard deviation and the track variation, and corrects for the aircraft track changes to obtain the true aircraft position; and establishing an aircraft conflict detection model, which includes obtaining the relative distance and relative speed of the aircraft in the horizontal and vertical directions, and calculating the expected encounter time at each moment; when it is predicted that the intruding aircraft's flight path will penetrate the collision area, the system notifies the crew using visual and audible signals. This method enables the verification of simultaneous approach flight procedures, navigation parameters, and other factors during the planning stage, allowing for a more objective quantitative assessment of the conflict risk of parallel runway operations.

Description

Technical Field

[0001] This invention relates to the field of parallel runway operation conflict risk assessment technology, and mainly provides a conflict risk verification method in parallel runway approach and departure procedure planning and airspace design. Specifically, it involves calculating and analyzing conflict risks during the parallel runway operation planning stage, and analyzing flight procedure types, structures, aircraft speeds, combinations, etc. Background Technology

[0002] ILS (Integrated Lightning Approach) is currently the primary approach method used for simultaneous approaches to parallel runways. However, due to limitations imposed by the working principles of ground-based equipment, it suffers from issues such as long approach five-leg lengths and strict separation requirements, limiting further increases in runway capacity. With the development and maturation of various approach technologies, technologies such as Required Navigation Performance (RNPAR) and Global Landing System (GLS) are now required to support simultaneous approaches to parallel runways. The combined application of these approach technologies in parallel runway operations can achieve shorter five-leg lengths, and simultaneous approaches from both sides can be performed without establishing high and low sides, demonstrating good performance in improving runway capacity. However, the mixing of multiple approach procedures, due to their different structures and applicability to different separation standards, introduces operational complexity, potentially leading to safety issues.

[0003] Currently, air traffic control intervention is the primary means of resolving conflicts arising from simultaneous approaches to dual runways. However, the aforementioned operational complexity directly impacts the work of air traffic controllers. Therefore, based on mixed approaches and their characteristics, studying the conflict risks associated with simultaneous approaches to parallel runways is not only significant for runway system planning and ensuring airport airspace safety, but can also provide corresponding guidance for air traffic controllers.

[0004] Currently, the verification of parallel runway operation schemes mainly focuses on operational safety, capacity, and efficiency. Safety assessments primarily adopt an operational perspective, using collision risk theory as a foundation and expert subjective evaluation as a method. There is no method for verifying conflict risks by limiting flight procedures and aircraft navigation elements. Existing safety assessments are mainly based on collision risk theory and simulation methods. Methods based on collision risk theory using mathematical models are highly dependent on parameters for accuracy and are not suitable for assessing multi-factor and multi-operational scenarios. Simulation methods currently mainly use rapid simulation methods based on simulation software (such as TAAM, Airtop, etc.), but due to insufficient accuracy, they are unsuitable for assessing simultaneous approach conflict risks.

[0005] A crucial task in parallel runway operation planning is validating TCAS (Traffic Collision Avoidance System) warnings and using the results as the basis for approach procedure validation. TCAS can provide different levels of warning information and recommended avoidance information to ensure operational safety. The complexity of mixing different approach procedures can lead to a higher frequency of TCAS warnings, disrupting normal flight operations.

[0006] Therefore, conducting simultaneous approach conflict risk research based on the TCAS warning principle during the approach procedure planning phase serves as a basis for the structural design and planning scheme verification of the approach procedure, providing important theoretical support for the formulation of parallel runway approach operation and control schemes. However, current TCAS verification mainly focuses on nominal flight procedures, fixed flight speeds and positions, without considering operational errors, including track deviation errors and speed errors. This is a relatively static assessment, primarily concentrating on the assessment of conflict risks during simultaneous approaches to two runways using a single procedure, and the purpose of the assessment is merely to identify locations prone to warnings. Some literature uses Monte Carlo simulation methods to perform multiple simulations to verify the conflict risk of simultaneous approaches to two ILSs, but the verification speed is slow when considering multiple errors, and it is not suitable for multi-factor verification under mixed procedures. Summary of the Invention

[0007] To address the shortcomings of current parallel runway operation conflict risk verification technologies in my country, this invention aims to propose a method based on the TCAS (Traffic Response System) collision principle, analyzing conflict risks from the perspectives of procedure structure and operational control parameters for mixed operations with different procedures. Based on the flight procedure type used for parallel runways, horizontal and vertical aircraft operation models are established, comprehensively considering trajectory and speed uncertainties. Based on the TCAS warning principle and an improved gradient descent method, a rapid simultaneous approach operation verification method applicable to multiple scenarios and multi-factor parallel runway conflict risks is proposed. This method overcomes the current limitations of simultaneous approach risk assessment, which cannot perform comprehensive operational assessments and suffers from poor accuracy.

[0008] The complete technical solution of this invention includes:

[0009] A method for calculating the conflict risk of parallel runway mixed approach operations based on TCAS includes the following steps:

[0010] (1) Establish an aircraft motion model, including projecting the aircraft motion trajectory onto the runway system plane and establishing horizontal and vertical motion models of the two aircraft. The horizontal motion model includes a turning motion model and a straight motion model.

[0011] (2) Establish a trajectory error model, use trajectory deviation data to fit the relationship between the normal standard deviation and the trajectory, and correct the trajectory change to obtain the true position of the aircraft.

[0012] (3) Establish an aircraft conflict detection model, including obtaining the relative distance and relative speed of the aircraft in the horizontal and vertical directions, and calculating the expected horizontal encounter time τ. hor The expected encounter time τ between the two sides is vertical. ver ;

[0013] (4) The extreme values ​​of the horizontal and vertical approach times of the two aircraft are calculated using the target-based gradient descent method, alarm judgment is made, and the risk of conflict is calculated.

[0014] (5) Based on the alarm judgment result of step (4), when it is expected that the flight path of the intruding aircraft will penetrate the collision area, the system will notify the crew with visual and auditory signals.

[0015] Furthermore, the aircraft motion model is as follows:

[0016] (1) Horizontal direction

[0017] Projecting the aircraft's trajectory onto the runway system plane, the horizontal motion model of the two aircraft is established as follows:

[0018] 1) EoR program RF turning motion model:

[0019]

[0020] Δx=r-rcos(wΔt)(2)

[0021] Δy=rsin(wΔt) (3)

[0022] In the formula: w is the turning angular velocity, in degrees / s; IAS is the aircraft's vacuum speed, in km / s; r is the turning radius of the RF segment, in km; Δx is the displacement in the x-axis direction, in km; Δy is the displacement in the y-axis direction, in km; Δt is the time taken for the aircraft to fly in the RF turning section, in seconds.

[0023] 2) Linear motion model:

[0024] Δx=IASΔt (4)

[0025] (2) Vertical direction

[0026] Δz=KΔt (5)

[0027] In the formula: Δz is the displacement of the aircraft in the z-axis direction, in km; K is the descent rate of the aircraft, in m / s.

[0028] Furthermore, in the aforementioned track error model, the relationship between the normal standard deviation and the track variation is derived from the track deviation data fitting as follows:

[0029] σ lat (x') = 0.0028x' + 9.02 (6)

[0030] σ ver (x') = 0.0004x' + 2.89 (7)

[0031] Where, σ lat σ represents the lateral normal standard deviation in meters. ver is the vertical normal standard deviation, in meters; x′ is the distance from the aircraft to the runway landing point, in meters.

[0032] Furthermore, the aircraft conflict detection model includes:

[0033] The estimated time of encounter between the aircraft at each moment is:

[0034]

[0035]

[0036] In the formula, τ hor The estimated time of encounter in the horizontal direction, in seconds; τ ver The estimated time of encounter is vertical, in seconds. The relative speed of the aircraft in the horizontal direction of relative distance is expressed in km / s.

[0037] The horizontal relative distance d(t) between the two machines at time t is expressed as:

[0038]

[0039] Where x 入侵 (t) represents the x-coordinate of the intruder at time t, and y-coordinate... 入侵 (t) represents the y-coordinate of the intruder at time t, x 本机 (t) represents the x-coordinate of the machine at time t, and y-coordinate... 本机 (t) represents the coordinate of the machine in the y-axis direction at time t.

[0040] Horizontal proximity rate is the relative speed of two aircraft relative to their relative distance. express:

[0041]

[0042] In the formula, θ is the angle between the speed of the intrusion machine and the relative distance, in degrees; α is the angle between the speed of the machine and the relative distance, in degrees.

[0043] The vertical relative distance Z is represented as:

[0044] Z(t) = |z入侵 (t)-z 本机 (t)| (12)

[0045] Vertical proximity rate is calculated using the relative vertical speeds of the two aircraft. express:

[0046]

[0047] In the formula K 本机 K represents the local descent rate. 入侵机 The rate at which the intrusion machine decreases.

[0048] Furthermore, τ is revised to converge to a non-zero range, and the horizontal encounter time τ is predicted. hor The corrected formula is:

[0049] d'(t)=d(t)-DMOD (14)

[0050]

[0051] d′(t) is the corrected horizontal relative distance between the two machines at time t; DMOD is a fixed range threshold. Let t be the relative velocity of the two machines in the horizontal relative distance direction at time t.

[0052] Make corrections in the vertical direction:

[0053] Z'(t)=Z(t)-ZTHR (16)

[0054]

[0055] Where Z′(t) is the corrected vertical relative distance between the two aircraft at time t, and ZTHR is the non-zero range of vertical convergence of τ, which is related to the altitude interval and is a constant within different altitude intervals. Let t be the vertical relative velocity of the two machines.

[0056] Furthermore, step (4) includes:

[0057] The conflict risk calculation method for the aircraft conflict detection model in step (4) is as follows:

[0058] Step 1: Set the simultaneous approach flight procedure, the initial position range of the two aircraft, the velocity error range, the RNP AR / ILS accuracy parameters and range, and the number of simulations N;

[0059] Step 2: Generate the two-machine path equations, as well as the horizontal and vertical approach time functions;

[0060] Step 3: Calculate the vertical and horizontal approach time extremes f respectively. l (xmin ), f v (x min The alarm value is compared with the corresponding threshold. The alarm is determined by whether the vertical and horizontal extreme values ​​are both less than the standard value, and the alarm count n is recorded.

[0061] Step 4: Calculate the alarm probability.

[0062] The advantages of this invention over the prior art are:

[0063] 1. With the aim of meeting the actual needs of airport and air traffic control operations and based on the actual TCAS requirements, the factors affecting the risk of simultaneous approach conflicts of parallel runways were comprehensively considered, and the verification of simultaneous approach flight procedures, navigation parameters and other factors was achieved in the planning stage.

[0064] 2. This invention takes into account the randomness of key parameters during operation and uses an improved gradient descent algorithm, which can achieve faster and more objective quantitative evaluation than existing methods;

[0065] 3. This invention is the first to realize the analysis of factors such as flight procedure structure, different procedure combinations, flight parameters during operation, and runway layout in the planning stage based on conflict risk. It is also the first to conduct research on the relationship between static factors such as flight procedures and runways and dynamic elements such as operating parameters and risks, and conducts a more in-depth study of airspace design elements. Attached Figure Description

[0066] Figure 1 This is a flowchart of the alarm detection cycle.

[0067] Figure 2 This is a schematic diagram of a simulation scenario.

[0068] Figure 3 This is a flowchart of the TCAS II system simulation.

[0069] Figure 4 This is a schematic diagram of the ILS+RNP hybrid approach.

[0070] Figure 5 The flowchart of the conflict risk calculation method based on gradient descent Detailed Implementation

[0071] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only illustrative and are not intended to limit this application.

[0072] A method for calculating the operational conflict risk of parallel runways based on TCAS, the specific steps of which are as follows:

[0073] S1: Construct a running scenario with two parallel runways

[0074] Let the runway spacing be D, and the two runways be R1 and R2. Establish a spatial rectangular coordinate system with the approach entrance of one of the runways as the origin. The relevant parameters are shown in Table 1.

[0075] Table 1 Parameter List

[0076]

[0077] During the approach, regardless of the approach procedure used, once both aircraft are stable in the segment where they are finally aligned with the runway, the possibility of them continuing to approach under stable flight conditions is very small because the two aircraft are heading in the same direction. Conflicts mainly occur when the two aircraft converge on the runway centerline.

[0078] S2: Establish the aircraft's motion model from both horizontal and vertical perspectives.

[0079] (1) Horizontal direction

[0080] Projecting the aircraft's trajectory onto the runway system plane, the horizontal motion model of the two aircraft is established as follows:

[0081] 1) EoR program RF turning motion model:

[0082]

[0083] Δx=r-rcos(wΔt) (2)

[0084] Δy=rsin(wΔt) (3)

[0085] In the formula: w is the turning angular velocity, in degrees / s; IAS is the aircraft vacuum speed, in km / s; r is the turning radius of the RF segment, in km; Δx is the aircraft displacement in the x-axis direction, in km; Δy is the aircraft displacement in the y-axis direction, in km; Δt is the calculation step size, in s.

[0086] 2) Aircraft linear motion model:

[0087] Δx=IASΔt (4)

[0088] (2) Vertical direction

[0089] Δz=KΔt (5)

[0090] In the formula: Δz is the displacement of the aircraft in the z-axis direction, in km; K is the descent rate of the aircraft, in m / s.

[0091] S3: Establish a trajectory error model

[0092] Due to factors such as airborne receiving equipment, ground transmitting devices, and approach guidance lights, the aircraft is susceptible to interference when receiving signals, preventing it from following the planned trajectory during approach. Therefore, a deviation in the aircraft's trajectory occurs during actual flight. Based on trajectory deviation data fitting, the pattern of normal standard deviation variation along the trajectory is derived:

[0093] σ lat (x') = 0.0028x' + 9.02 (6)

[0094] σ ver (x') = 0.0004x' + 2.89 (7)

[0095] Where, σ lat σ represents the lateral normal standard deviation in meters. ver denoted as the vertical normal standard deviation, in meters; x′ is the distance from the aircraft to the runway landing point, in meters. Since the means of both lateral and vertical deviation distributions are small, their means are taken as 0.

[0096] S4: Establish an aircraft conflict detection model

[0097] The estimated time of encounter between the aircraft at a certain moment is:

[0098]

[0099]

[0100] In the formula, τ hor The estimated time of encounter in the horizontal direction, in seconds; τ ver The estimated time of encounter is vertical, in seconds. The relative speed of the aircraft in the horizontal direction of relative distance is expressed in km / s.

[0101] The horizontal relative distance d(t) between the two machines at time t is expressed as:

[0102]

[0103] Where x 入侵 (t) represents the x-coordinate of the intruder at time t, and y-coordinate... 入侵 (t) represents the y-coordinate of the intruder at time t, x 本机 (t) represents the x-coordinate of the machine at time t, and y-coordinate... 本机 (t) represents the coordinate of the machine in the y-axis direction at time t.

[0104] The horizontal approach rate of two aircraft is measured by their relative speeds relative to the relative distance. express:

[0105]

[0106] In the formula, θ is the angle between the speed of the intrusion machine and the relative distance, in degrees; α is the angle between the speed of the machine and the relative distance, in degrees.

[0107] The vertical relative distance Z is represented as:

[0108] Z(t) = |z 入侵 (t)-z 本机 (t)| (12)

[0109] z 入侵 (t) represents the z-axis coordinate of the intruder at time t, where z 本机 (t) represents the coordinate of the machine in the z-axis direction at time t.

[0110] Vertical proximity rate is calculated using the relative vertical speeds of the two aircraft. express:

[0111]

[0112] K 本机 K represents the local descent rate. 入侵机 The rate at which the intrusion machine decreases.

[0113] At low speeds, the approach speeds of the two aircraft are relatively small, and the τ value may not reach the alarm range, but the distance between the two aircraft may already be very close, even posing a possibility of collision. To prevent this from happening, τ needs to be revised. That is, at lower approach rates, the calculation method for the τ value needs to be corrected to make it converge and allow TCAS to issue TA and RA at or before the fixed DMOD range threshold in this situation. The horizontal estimated encounter time τ... hor The corrected formula is:

[0114] d'(t)=d(t)-DMOD (14)

[0115]

[0116] d′(t) is the corrected horizontal relative distance between the two machines at time t; DMOD is a fixed range threshold. Let t be the relative velocity of the two machines in the horizontal relative distance direction at time t.

[0117] Similarly, make a similar correction in the vertical direction:

[0118] Z'(t)=Z(t)-ZTHR (16)

[0119]

[0120] Where Z′(t) is the corrected vertical relative distance between the two aircraft at time t, and ZTHR is the non-zero range of vertical convergence of τ, which is related to the altitude interval and is a constant within different altitude intervals. Let t be the vertical relative velocity of the two machines.

[0121] By analyzing the motion model of the aircraft approach process and the relative positional relationships and trends, the expected horizontal encounter time τ can be calculated. hor The expected encounter time τ between the two sides is vertical. ver TCAS alarm judgment is based on sensitivity level.

[0122] S5: Conflict Risk Calculation Based on Improved Gradient Descent Method

[0123] The approach and descent of an aircraft is a complex, dynamic, and stochastic process. Therefore, traditional mathematical derivations and single-scenario demonstrations are insufficient to uncover general patterns in the approach of two aircraft. Extensive simulations are required to arrive at a relatively objective conflict risk during the program planning and design phase. In this invention, speed error is based on air traffic control scheduling, considering a large error range. Furthermore, it considers not only the errors of RNP AR aircraft but also those of ILS aircraft, resulting in a massive computational burden. Currently, most related studies use the Monte Carlo algorithm for model verification and simulation. This method is sufficient when considering only limited speed and trajectory positioning errors, but becomes computationally intensive and slow to converge when considering complex error terms. Therefore, this invention calculates conflict risk using an improved gradient descent method.

[0124] The calculation of the horizontal and vertical τ values ​​can be regarded as an extreme value problem, that is, the closest time is the minimum value of the approach time during the movement of the two machines. The alarm situation can be judged by comparing the minimum value with the alarm threshold.

[0125] S5.1 horizontal ι hor Calculation method

[0126] Based on the preceding analysis and description, the horizontal approach time function ι(t) of the two aircraft (hereinafter referred to as aircraft A and aircraft B) can be expressed as:

[0127]

[0128] Where x A (t) represents the x-coordinate of aircraft A at time t, where x is the x-axis coordinate. B (t) represents the x-coordinate of aircraft B at time t, and y-coordinate... A (t) represents the y-coordinate of aircraft A at time t, where y B (t) represents the y-coordinate of aircraft B at time t; IAS A Indicates the vacuum velocity of aircraft A, IAS B This indicates the vacuum speed of aircraft B.

[0129] The approach time is related to the distance between the two aircraft and their relative approach speeds, and is a nonlinear equation for time t. During simultaneous approach, due to the difference in aircraft speeds, the two aircraft may undergo changes in their relative positions, such as overtaking or moving away, and their motion states may change from turning to straight-line motion. Therefore, the approach time function is a discontinuous function, but it is continuously differentiable within the piecewise intervals. Furthermore, the approach time is related to the relative positions and angles of the two aircraft (see...). Figure 4 ),from Figure 4 It can be seen that the possible alarm location generally starts from the position where the tangent arc is perpendicular to the pentagon, and only extends to the end of the turn within a 90-degree range. Therefore, the function within the segmented interval is a convex function.

[0130] Define β as the angle between the line connecting the two machines and the Y-axis:

[0131]

[0132] When the aircraft turns (x(t)>xIF), and aircraft A acts as the intruding aircraft, we have:

[0133] x A (t) <x B (t),θ=W*t+β

[0134] x A (t)=x B (t),θ=W*t

[0135] x A (t)>x B (t),θ=|β-W*t|

[0136] When the aircraft turns (x(t)>xIF), and aircraft B acts as the intruding aircraft, we have:

[0137] x A (t) <x B (t), α=|β-W*t|

[0138] x A (t)=x B (t), α=W*t

[0139] x A (t)>x B (t), α=W*t+β

[0140] When the aircraft is flying in a straight line, and aircraft A is the intruding aircraft, then:

[0141] x A (t) <x B (t), θ=90+β

[0142] x A (t)=x B (t), θ=90

[0143] x A (t)>x B (t), θ=90-β

[0144] When the aircraft is flying in a straight line, and aircraft B is the intruding aircraft, then:

[0145] x A (t) <x B (t), α=90-β

[0146] x A (t)=x B (t), α=90

[0147] x A (t)>x B (t), α=90+β

[0148] Finding the extrema of a function can be viewed as finding the saddle point of the objective function, i.e., the point where the first derivative of the function is zero. However, the two-machine approach time function is a complex function, making direct solution difficult and slow. Therefore, for the above problem, gradient descent (GD) is used, with an initial solution s0, and the extrema are obtained by iterative optimization.

[0149]

[0150] Where η∈R is the iteration step size. For the gradient operator, s t For the current solution, s t+1 For the next iteration solution, t is the iteration time, f(s) t Let η be the objective function. η and the initial solution s0 determine the efficiency of the algorithm.

[0151] Gradient descent is a numerical optimization method with good convergence and strong stability. However, it requires setting appropriate initial solutions and iteration step sizes, otherwise the search efficiency is low. Therefore, this invention adopts a target-based gradient descent algorithm (TBGD) to improve the algorithm by understanding the rules of the objective function in advance, determining the initial value and iteration step size, narrowing the search range, and improving the algorithm efficiency.

[0152] The objective function for the two machines to approach is a piecewise function, but it is a gradually changing function within each segment. Utilizing the principle that the derivative of the objective function is 0 at convex points, the derivative value of the objective function is calculated with a certain step size. The positions of the two points closest to 0, i.e., s, are then determined. 0- and s 0+Then, take the midpoint between these two points as the initial value x0 for the GD algorithm.

[0153] The iteration step size of the gradient descent method determines the efficiency and speed of the algorithm. The position of the initial solution roughly determines the range of the optimal solution; that is, the optimal solution must be generated at x. 0- and x 0+ Between, therefore during the iteration process x t+1 The value should be within ±T (where T is the iteration step size), and the change should be smaller as the target is approached.

[0154]

[0155] The algorithm flow for finding the horizontal approach time extrema of two machines is as follows: Figure 5 .

[0156] S5.2 Vertical ι ver calculate

[0157] After entering the intermediate approach segment, the aircraft descends vertically strictly according to the gradient prescribed by the flight procedure. The altitude equation is a linear function based on distance. For ease of calculation, the turning portion of the EoR track is treated as a straight line. Therefore, the altitude equations for both aircraft can be established:

[0158]

[0159]

[0160] Z A (t) represents the altitude of aircraft A at time t. The initial altitude of aircraft A. Let x(t) be the vertical descent rate of aircraft A, and x(t) be the distance the aircraft has flown at time t. This is the initial position of aircraft A. This is the location of the runway entrance for aircraft A.

[0161] The vertical height difference Z(t) between the two machines is:

[0162]

[0163] Since the aircraft's descent gradient remains constant, the vertical approach rate is constant, therefore ι ver Alarm judgment can be transformed into the calculation of the extreme value of a linear function Z(t).

[0164] 5.3 Conflict Risk Calculation Process

[0165] Step 1: Set the simultaneous approach flight procedure, the initial position range of the two aircraft, the speed error range, the RNP AR / ILS accuracy parameters and range, and the number of simulations N.

[0166] Step 2: Generate the two-machine path equations, as well as the horizontal and vertical approach time functions;

[0167] Step 3: Calculate the vertical and horizontal approach time extremes f respectively. l (x min ), f v (x min The alarm value is compared with the corresponding threshold. The alarm is determined by whether the vertical and horizontal extreme values ​​are both less than the standard value, and the alarm count n is recorded.

[0168] Step 4: Calculate the alarm probability.

[0169] S5: Alarm Judgment

[0170] Because TCAS is a time-based system, the size and shape of the collision zone vary with the approach speed and relative orientation of the intruding aircraft. If the intruding aircraft's trajectory is expected to penetrate the collision zone, the system will simultaneously notify the crew with visual and audible signals. TCAS generates two levels of alerts: TA (Traffic Advisory) and RA (Decision Advisory). Table 2 provides the thresholds for TA and RA alerts under different SLs.

[0171] Table 2 Sensitivity Level Definitions and Alarm Thresholds

[0172]

[0173] At a certain sensitivity level, an alarm is triggered only when both the horizontal and vertical τ values ​​are less than a specific threshold. The workflow diagram for an alarm detection cycle of the TCAS II system is as follows: Figure 3 As shown.

[0174] S6: Conflict risk calculation and parameter verification based on gradient descent method

[0175] The approach and descent of an aircraft is a complex, dynamic, and stochastic process. Therefore, traditional mathematical derivations and single-scenario demonstrations are insufficient to uncover general patterns, requiring extensive computation to arrive at a relatively objective conflict risk during the program planning and design phase. Due to the numerous factors considered in mixed approaches, the computational load for TCAS alarm judgment and overall risk calculation is substantial. To improve computational speed, an improved gradient descent method is used for risk calculation. This implementation uses a domestic airport as an example to verify and simulate the method using gradient descent.

[0176] The airport has an elevation of 2103.5m and currently has two parallel runways, with runways 21 and 22 serving as the main landing runways. Runway 21 is 4000m long, with its runway threshold shifted inward by 540m. Runway 22 is 4500m long. Both runways are equipped with RNP AR and ILS approach procedures, and the current RNP AR procedure for simultaneous approaches requires an accuracy of 0.2.

[0177] See scene illustration Figure 2 Since the scenario is mainly set up for the final approach phase, with little difference in altitude on both sides and the same sensitivity level and alarm threshold, the alarm situation of the aircraft executing the EoR procedure is analyzed during the simulation (as the local unit).

[0178] The verification parameters are shown in Tables 3 and 4. The aircraft number, initial position, and corresponding time are set to ensure adaptability to all operational scenarios.

[0179] Table 3 Simulation data of aircraft initial velocity

[0180]

[0181] Table 4 Simulated data of initial positioning error

[0182]

[0183]

[0184] Note: The vertical errors of RNP AR and ILS are small and can be ignored.

[0185] Initial scenario settings: Runway 21 uses RNP AR approach, with a straight-line length of 14.8km; Runway 22 uses ILS approach, with a straight-line length of 22.6km. See... Figure 2 During the approach, the close proximity of the two aircraft mainly occurred when the RF turn intersected the fifth approach. Based on Table 2 and the actual operational conditions at Kunming Airport, the RNP AR aircraft category was set as Category C, and the ILS aircraft category as Categories C and D. The simulation was set to 100,000 runs. The simulation results showed that the RA alarm probability (RA alarm probability) for the aircraft using the EOR procedure was 0, indicating that the existing procedure meets the RA alarm probability requirement and is consistent with reality. The TA alarm probabilities for the aircraft using the EOR procedure were 4.8e-4 and e-5, respectively.

[0186] Based on actual needs, risk trend charts for different scenarios were derived. It was found that the larger the EoR program is used, the greater the probability of alarms, which increases by orders of magnitude. Furthermore, the probability of alarms is even greater when the EoR program is larger than the ILS program.

[0187] Keeping the initial parameters unchanged in Scenario 1, the pentagonal length of the EOR program (hereinafter referred to as pentagonal length) was changed, starting from 14.8km (the existing length), and increasing in 500m intervals for 10 sets of experiments to verify the impact of the pentagonal length difference on the alarm probability. Each set was run 100,000 times to calculate the TCAS alarm probability. It was found that as the pentagonal length increased, the initial relative longitudinal distance between the two aircraft continuously decreased. The TA alarm probability for Category C and Category D aircraft using the ILS program showed a trend of first increasing and then decreasing.

[0188] Keeping the initial parameters unchanged in Scenario 1, the runway spacing was varied, with 10 sets of experiments conducted at 500m intervals, each set running 100,000 times. The TCAS alarm probability was calculated, revealing that as runway spacing decreased, the lateral relative distance between the two aircraft decreased, and both RA and TA alarms increased. When using ILS procedures, for Category C aircraft, the RA alarm probability decreased to 0 when the runway spacing was greater than or equal to 1.72km; when using ILS procedures, for Category D aircraft, the RA alarm probability was 0. The TA alarm probability was generally high for both types of aircraft, and increased as runway spacing decreased.

[0189] The above results indicate that the method disclosed in this embodiment can provide a strong theoretical basis for decision-making for airports and air traffic control.

[0190] The above-described embodiments are merely some implementation methods of this application. For those skilled in the art, various modifications and improvements can be made without departing from the inventive concept of this application, and these all fall within the protection scope of this application.

Claims

1. A method for calculating the conflict risk of parallel runway mixed approach operations based on TCAS, characterized in that, Includes the following steps: (1) Establishing an aircraft motion model, including projecting the aircraft's trajectory onto the runway system plane, and establishing horizontal and vertical motion models for the two aircraft. The horizontal motion model includes a turning motion model and a straight-line motion model. The aircraft motion model is as follows: Horizontal direction: Projecting the aircraft's trajectory onto the runway system plane, the horizontal motion model of the two aircraft is established as follows: 1) EoR program RF turning motion model: Δx=r-rcos(wΔt)(2) Δy=rsin(wΔt)(3) In the formula: w is the turning angular velocity, in degrees / s; IAS is the aircraft's vacuum speed, in km / s; r is the turning radius of the RF segment, in km; Δx is the displacement in the x-axis direction, in km; Δy is the displacement in the y-axis direction, in km; Δt is the time taken for the aircraft to fly in the RF turning section, in seconds. 2) Linear motion model: Δx=IASΔt(4) Vertical direction: Δz=KΔt (5) In the formula: Δz is the displacement of the aircraft in the z-axis direction, in km; K is the descent rate of the aircraft, in m / s. (2) Establish a trajectory error model, use trajectory deviation data to fit the relationship between the normal standard deviation and the trajectory, and correct the trajectory change to obtain the true position of the aircraft. (3) Establish an aircraft conflict detection model, including obtaining the relative distance and relative speed of the aircraft in the horizontal and vertical directions, and calculating the expected horizontal encounter time τ. hor The expected encounter time τ between the two sides is vertical. ver ; The aircraft conflict detection model includes: The estimated time of encounter between the aircraft at each moment is: In the formula, τ hor The estimated time of encounter in the horizontal direction, in seconds; τ ver The estimated time of encounter is vertical, in seconds. Let be the relative velocity of the two machines in the horizontal direction relative to each other at time t, in km / s. Let t be the vertical relative velocity of the two machines at time t, in km / s; The horizontal relative distance d(t) between the two machines at time t is expressed as: In the formula, x 入侵 (t) represents the x-coordinate of the intruder at time t, and y-coordinate... 入侵 (t) represents the y-coordinate of the intruder at time t, x 本机 (t) represents the x-coordinate of the machine at time t, and y-coordinate... 本机 (t) represents the y-coordinate of the machine at time t; Horizontal proximity rate is the relative speed of two aircraft relative to their relative distance. express: In the formula, θ is the angle between the speed of the intrusion machine and the relative distance, in degrees; α is the angle between the speed of the machine and the relative distance, in degrees. The vertical relative distance Z is represented as: Z(t)=|z 入侵 (t)-z 本机 (t)| (12) Vertical proximity rate is calculated using the relative vertical speeds of the two aircraft. express: In the formula, Let K be the vertical relative velocity of the two machines at time t. 本机 K represents the local descent rate. 入侵机 The rate at which the intruder descends; (4) The extreme values ​​of the horizontal and vertical approach times of the two aircraft are calculated using the target-based gradient descent method. Perform alarm assessments and calculate conflict risks; (5) Based on the alarm judgment result of step (4), when it is expected that the flight path of the intruding aircraft will penetrate the collision area, the system will notify the crew with visual and auditory signals.

2. The method for calculating the risk of conflict in parallel runway mixed approach operations based on TCAS according to claim 1, characterized in that, In the aforementioned track error model, the relationship between the normal standard deviation and the track variation, derived from the track deviation data fitting, is as follows: s lat (x')=0.0028x'+9.02 (6) s ver (x')=0.0004x'+2.89 (7) In the formula, σ lat σ represents the lateral normal standard deviation in meters. ver denoted as the vertical normal standard deviation, in meters; x' is the distance from the aircraft to the runway landing point, in meters.

3. The method for calculating the risk of conflict in parallel runway mixed approach operations based on TCAS according to claim 1, characterized in that, The τ is revised to converge to a non-zero range, and the horizontal predicted meeting time τ is calculated. hor The corrected formula is: d'(t)=d(t)-DMOD (14) d′(t) is the corrected horizontal relative distance between the two machines at time t; DMOD is a fixed range threshold. Let be the relative velocity of the two machines in the horizontal relative distance direction at time t; Make corrections in the vertical direction: Z'(t)=Z(t)-ZTHR (16) Where Z′(t) is the corrected vertical relative distance between the two aircraft at time t, and ZTHR is the non-zero range of vertical convergence of τ, which is related to the altitude interval and is a constant within different altitude intervals. Let t be the vertical relative velocity of the two machines.

4. The method for calculating the risk of conflict in parallel runway mixed approach operations based on TCAS according to claim 3, characterized in that, Step (4) includes: The conflict risk calculation method for the aircraft conflict detection model in step (4) is as follows: Step 1: Set the simultaneous approach flight procedure, the initial position range of the two aircraft, the velocity error range, the RNP AR / ILS accuracy parameters and range, and the number of simulations N; Step 2: Generate the two-machine path equations, as well as the horizontal and vertical approach time functions; Step 3: Calculate the vertical and horizontal approach time extremes f respectively. l (x min ), f v (x min The alarm value is compared with the corresponding threshold. The alarm is determined by whether the vertical and horizontal extreme values ​​are both less than the standard value, and the alarm count n is recorded. Step 4: Calculate the alarm probability.

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