Close-distance parallel runway collision risk assessment method based on influence of positive and lateral wind

Abstract

The invention relates to the technical field of aviation safety, in particular to a short-distance parallel runway collision risk assessment method based on influence of front and side wind, which comprises collision risk assessment, Bayesian parameter estimation, linear regression analysis, dynamic front and side wind fitting and Monte Carlo analog simulation. The problem of small sample parameter estimation is solved by introducing a Bayesian parameter estimation method, crosswind parameters are calculated by combining linear regression analysis, positive crosswind data are fitted by applying Weibull distribution, and an influence rule of positive crosswind and an initial interval on collision probability is quantified through Monte Carlo simulation. According to the short-distance parallel runway collision risk assessment method based on the influence of the positive and crosswind, on the basis of a traditional collision model, a re-flight condition is incorporated into the model, complex scenes such as crosswind and re-flight are considered, a dynamic interval adjustment model is fused, and a new collision risk model is established; the crosswind grading minimum interval standard is provided for airline companies and air traffic control operation management, and the runway safety and the airport operation capacity are improved.

Description

Technical Field

[0001] This invention relates to the field of aviation safety technology, specifically to a three-dimensional method for assessing the collision risk of close-range parallel runways under the influence of crosswinds. Background Technology

[0002] In today's increasingly busy air transport environment, the safe operation of closely spaced parallel runways is of paramount importance. Existing collision risk assessment models for closely spaced parallel runways have several limitations. They fail to delve into complex scenarios involving crosswinds and go-arounds, do not consider a comprehensive analysis of meteorological factors and wake turbulence safety separations, rely heavily on large amounts of measured data with high barriers to entry, and incur high data processing costs. Furthermore, current research has not systematically analyzed the complex scenario of crosswind disturbances, go-arounds, and runway isolation operations overlapping. In actual operation, crosswind interference can alter aircraft trajectories, and go-arounds further increase operational uncertainty; the combination of these two factors significantly enhances the collision risk. Therefore, a new collision risk assessment method is urgently needed to address the shortcomings of existing technologies. Summary of the Invention

[0003] The purpose of this invention is to provide a method for assessing the collision risk of close parallel runways under the influence of crosswinds, so as to overcome the limitations of existing close parallel runway collision risk assessment models in complex scenarios and provide better theoretical support and decision support for runway operation safety.

[0004] To establish a collision probability model between aircraft taking off and going around from close runways, this paper breaks through the limitations of traditional static assessment models and constructs a three-dimensional collision risk assessment model for close parallel runways that integrates crosswind disturbances and go-around scenarios. Using Guangzhou Baiyun International Airport as an example, the model quantifies the influence of crosswinds and initial separation on collision probability through Monte Carlo simulation, proposes a crosswind-graded separation standard, and provides data support for air traffic control decision-making.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for assessing the collision risk of close-range parallel runways under the influence of crosswinds, comprising the following steps:

[0006] S1: Construct a collision risk model, which includes a longitudinal collision probability model, a lateral collision probability model, and a vertical collision probability model, decomposing the total risk into the product of independent probabilities of longitudinal, lateral, and vertical collisions;

[0007] S2: Establish a theoretical aircraft spacing model, divide the approach and go-around process of the approaching aircraft and the takeoff process of the taking-off aircraft into different stages, and construct the ideal spacing calculation model between the two aircraft for each stage.

[0008] S3: Construct a dynamic safety separation model, combine the frontal and crosswind speeds to calculate the wake dissipation time, and then obtain the safety separation between the two aircraft;

[0009] S4: Collect and preprocess relevant data, including ADS-B trajectory data and METAR message observation data, and extract random error data;

[0010] S5: Bayesian parameter estimation method is used to estimate the parameters of random error. A relationship model between frontal and crosswind and lateral offset is established through linear regression analysis and verified. Frontal and crosswind data of Baiyun Airport are fitted to determine a suitable distribution model.

[0011] S6: Conduct Monte Carlo simulations to statistically analyze the average collision probability under different initial intervals and crosswind conditions, and propose a standard for classifying crosswind intervals.

[0012] Preferably, in the longitudinal collision probability model, the longitudinal position error of the aircraft follows a normal distribution, the total longitudinal error is the sum of the longitudinal errors of the two aircraft, and the longitudinal collision risk probability is calculated by integrating the normal distribution probability density function within the safe interval, and the calculation can be simplified by standardization transformation using the standard normal distribution.

[0013] Preferably, in the lateral collision probability model, the lateral position error includes a deterministic offset term and a random error term caused by the frontal crosswind. The lateral offset caused by the frontal crosswind is linearly related to the frontal crosswind speed. The mean of the total lateral error is the deterministic offset difference, and the variance is the sum of the variances of the random errors. The lateral collision risk probability is calculated based on this distribution. In the vertical collision probability model, the vertical position error includes a random error term and a systematic deviation term.

[0014] Preferably, in the theoretical interval model of the aircraft, the approaching aircraft's approach go-around process is divided into stages such as uniform level flight, uniform deceleration descent, uniform descent, accelerated go-around climb, and turning and uniform go-around climb after climbing to 200m. The takeoff process of the taking-off aircraft is divided into stages such as accelerated taxiing, accelerated climb, and turning and uniform climb after climbing to 150m. The interval calculation formula for each stage is constructed based on the kinematic equations.

[0015] Preferably, in the dynamic safety interval model, the longitudinal safety interval is calculated based on the wake dissipation time and the speed difference between the two engines. The wake dissipation time is related to the crosswind speed, and the lateral safety distance and vertical safety distance are set to fixed values ​​according to relevant regulations.

[0016] Preferably, the data preprocessing includes applying corresponding interpolation methods to different fields of the ADS-B trajectory data, such as constrained linear interpolation for altitude, boundary-constrained cubic spline interpolation for latitude and longitude coordinates, smoothed spline interpolation for ground speed, and cyclic interpolation for heading, while removing abnormal samples with excessive track deviations.

[0017] Preferably, in the Bayesian parameter estimation, it is assumed that the random position error of the aircraft follows a normal distribution with a mean of 0. The prior distribution is selected as the Inverse-Gamma distribution. The parameters are set based on prior knowledge, and the posterior distribution is calculated through the likelihood function and the prior distribution to obtain the estimated variance.

[0018] Preferably, in the linear regression analysis model of the relationship between crosswind and lateral offset, the relationship expression between lateral offset and crosswind speed is: lateral offset = proportionality coefficient × crosswind speed + intercept. The proportionality coefficient and intercept are calculated using sample data, and the model is verified using mean square error and coefficient of determination.

[0019] Preferably, in the fitting of the crosswind data of Baiyun Airport, the Weibull distribution and the gamma distribution are used for fitting respectively. The fitting effect is judged by the KS test, AIC and BIC criteria, and the Weibull distribution is determined to be the appropriate distribution model.

[0020] Preferably, in the Monte Carlo simulation, the physical parameters, error distribution parameters, and simulation parameters of the aircraft motion are set. Crosswind speeds are simulated using Weibull distribution random sampling. The ideal and safe intervals for each stage are calculated, thus obtaining the collision probability at each time step. The average collision probability is obtained by averaging multiple simulation results. Based on the simulation results, an initial interval of 5550m-9000m, crosswind speeds of 0-15m / s, and the ICAO-specified safe collision probability threshold (5×10⁻⁶ m / s) are used. −9 (times / hour), combined with the FAA wake dissipation time standard, proposes a crosswind classification interval standard.

[0021] Compared with the prior art, the beneficial effects of the present invention are:

[0022] 1. This method for assessing collision risk of closely spaced parallel runways under the influence of crosswinds addresses the shortcomings of traditional risk assessment models that rely on static error distribution and neglect dynamic coupling effects. Specifically, this study proposes a collision risk model that dynamically couples crosswind disturbances, tailored to the crosswind distribution characteristics of Guangzhou Baiyun Airport. This model integrates the systematic impact of crosswinds on the isolated operation of closely spaced parallel runways into a three-dimensional collision risk model. Furthermore, it breaks through the traditional model assumption that only considers aircraft landing scenarios, incorporating go-around scenarios into the entire model construction system. This provides a more comprehensive reference for tower decision-making and represents an innovative breakthrough in theoretical modeling.

[0023] 2. This method for assessing the collision risk of close-range parallel runways under the influence of crosswinds takes the actual operation scenario of Baiyun Airport as the object. Based on a small amount of ADS-B trajectory data and METAR message observation data, it comprehensively utilizes a variety of data processing methods and the programming tool MATLAB to simplify the overall calculation process. It successfully extracts the distribution characteristics of key parameters such as heading deviation and crosswind speed, and introduces the Bayesian parameter estimation method to solve the reliability problem of parameter estimation under small sample conditions.

[0024] When the initial interval is in the range of 9000m-9900m, the collision probability is generally close to 0. Only at an interval of 9000m and a crosswind speed < 2.57m / s does the collision probability show a small positive value, approximately 8.2 × 10⁻⁶. -30 The collision rate is far below the ICAO safety threshold, and as the crosswind speed increases to ≥2.57m / s, the collision probability quickly drops to 0, demonstrating the high safety redundancy under a large initial interval.

[0025] When the initial interval is 7500m, the influence of crosswind speed on the collision probability exhibits a stepwise decreasing characteristic: when the crosswind speed is <2.57m / s, the collision probability is approximately 6.3×10⁻⁶. -11 The crosswind speed increased to 2.57 m / s-5.14 m / s, and the collision probability decreased to 2.1 × 10⁻⁶ m / s due to the wake dissipation time being shortened from 85 s to 35 s. -12 When the crosswind speed is ≥7.71 m / s, the wake dissipation time is only 1 s, and the collision probability is further reduced to 9.5 × 10⁻⁶. -14 The number of times per hour significantly improves safety redundancy.

[0026] When the initial interval was reduced to 6700m, the relationship between crosswind speed and collision probability exhibited a nonlinear relationship of first decreasing and then increasing: as the crosswind speed increased from 0 to 5.14m / s, the collision probability increased from 4.8×10 -9 The frequency decreased to 2.3 × 10⁻⁶ times per hour. -9 The frequency was [number] times per hour; however, the crosswind speed continued to increase to 7.71 m / s, and the trajectory deviation caused by the lateral shift increased, raising the collision probability to 5.9 × 10⁻⁶. -9 The frequency of crosswinds per hour exceeds the safety threshold, highlighting the two-way nature of crosswind influence.

[0027] When the initial clearance is in the 6200m-6250m range, the negative impact of crosswind speed begins to dominate: when the crosswind speed is <2.57m / s, the collision probability is approximately 7.1×10⁻⁶. -9 The frequency of collisions per hour slightly exceeds the threshold; crosswind speed increases to 5.14 m / s, and the probability of collision rises to 1.3 × 10⁻⁶. -8 When the crosswind speed is ≥7.71 m / s, the collision probability exceeds 3.5 × 10⁻⁶. -8 The frequency of incidents per hour is seven times the threshold, leading to a sharp increase in safety risks.

[0028] When the initial spacing is reduced to 5550m, the collision probability is approximately 4.9 × 10⁻⁶ only when the crosswind speed is <2.57m / s. -9 The frequency of collisions per hour is close to the threshold; when the crosswind speed increases slightly to 2.57 m / s-5.14 m / s, the probability of collision immediately rises to 8.6 × 10⁻⁶. -9 When the crosswind speed is ≥7.71 m / s, the collision probability increases to 2.1 × 10⁻⁶ times per hour; when the crosswind speed is ≥7.71 m / s, the collision probability increases to 2.1 × 10⁻⁶ times per hour. -8 At times per hour, even if the initial interval is maintained, strong crosswinds will still significantly reduce the safety margin, and operations must be strictly limited.

[0029] 3. This method for assessing the collision risk of close-range parallel runways under the influence of crosswinds, based on limited ADS-B trajectory data and METAR message observation data, comprehensively utilizes various data processing methods and the programming tool Matlab, simplifying the overall calculation process. It successfully extracts the distribution characteristics of key parameters such as heading deviation and crosswind speed, and introduces Bayesian parameter estimation to solve the reliability problem of parameter estimation under small sample conditions.

[0030] 4. This method for assessing the collision risk of close parallel runways under the influence of crosswinds proposes a minimum crosswind separation standard and a dynamic separation adjustment model based on theoretical models and simulation results. The dynamic separation adjustment model can dynamically correct the safe separation threshold through real-time feedback of crosswind speed, thereby increasing runway capacity while ensuring operational safety. The minimum crosswind separation standard provides a reliable decision support tool for airport operation management. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 This is a schematic diagram of the overall simulation process of the present invention;

[0033] Figure 2 This is a diagram illustrating the Bayesian parameter estimation implementation steps of the present invention;

[0034] Figure 3 This is a diagram illustrating the construction process of the lateral offset and crosswind relationship model of the present invention;

[0035] Figure 4 This is a diagram illustrating the crosswind distribution demonstration process of the present invention;

[0036] Figure 5 This is a diagram showing the stages of the two-machine operation process of the present invention;

[0037] Figure 6 This is a comparison chart of the average flight path and the actual flight path before outlier removal in this invention.

[0038] Figure 7 This is a comparison chart of the average track and the actual track after outlier removal according to the present invention;

[0039] Figure 8 This is a scatter plot of the crosswind offset linear fitting of the present invention;

[0040] Figure 9 This is a comparison chart of the probability density function and data distribution histogram of the present invention;

[0041] Figure 10 This is a graph showing the trend of collision probability variation under different lateral wind speeds when the two aircraft are spaced 9000m apart.

[0042] Figure 11 This is a graph showing the trend of crosswind speed and collision probability when the two engines are spaced 7500m apart, according to the present invention.

[0043] Figure 12 This is a graph showing the trend of wake dissipation time and collision probability when the two engines are 7500m apart.

[0044] Figure 13 This is a graph showing the trend of crosswind speed and collision probability when the two engines are 6700m apart.

[0045] Figure 14 This is a graph showing the trend of wake dissipation time and collision probability when the two engines are 6700m apart.

[0046] Figure 15 This is a graph showing the trend of crosswind speed and collision probability when the two engines are 6100m apart.

[0047] Figure 16 This is a graph showing the trend of wake dissipation time and collision probability when the two engines are 6100m apart.

[0048] Figure 17 This is a graph showing the trend of crosswind speed and collision probability when the two engines are spaced 5550m apart.

[0049] Figure 18 This is a graph showing the trend of wake dissipation time and collision probability when the two engines are spaced 5550m apart. Detailed Implementation

[0050] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] Please see Figures 1-18 This invention provides a technical solution: a method for assessing the collision risk of close-range parallel runways under the influence of crosswinds, comprising the following steps:

[0052] S1: Construct a collision risk model, which includes a longitudinal collision probability model, a lateral collision probability model, and a vertical collision probability model, decomposing the total risk into the product of independent probabilities of longitudinal, lateral, and vertical collisions;

[0053] Longitudinal collision probability model

[0054] Find a fixed reference point A. Taking the vertical position as an example, assume... Let be the longitudinal distance of the aircraft's longitudinal position relative to point A at time t. Let the aircraft taking off be aircraft i, and the aircraft approaching be aircraft j (the same applies below). and These are the longitudinal distances of the taking-off aircraft and the approach aircraft relative to point A, respectively. Because the same reference point was chosen, the ideal longitudinal distance between the two aircraft at time t can be obtained. for:

[0055] (3-1)

[0056] If we consider the random longitudinal error of the aircraft Then the actual longitudinal position of the aircraft is Assuming that the longitudinal position errors of both aircraft follow a normal distribution, the total longitudinal error follows a normal distribution.

[0057] (3-2)

[0058] in Let be the longitudinal error of machine i at time t; Let J be the longitudinal error of machine j at time t; and These are the mean longitudinal errors of machine i and machine j, respectively; and These are the longitudinal error variances of machine i and machine j, respectively.

[0059] This allows us to determine the actual longitudinal distance between the aircraft. for:

[0060] (3-3)

[0061] And it follows a normal distribution

[0062] (3-4)

[0063] in It is the mean. It is variance.

[0064] Assume the longitudinal safety separation of the aircraft is Then the probability of longitudinal collision risk It can be represented as:

[0065] (3-5)

[0066] From a probabilistic perspective, it is necessary to calculate the normal distribution within that interval. Falling into the safe interval arrive- The probability within a given interval. According to the definition of probability, for a continuous random variable, its probability within a certain interval is equal to the integral of the probability density function over that interval. Therefore, for... The calculation involves applying the probability density function of the normal distribution to... arrive- Integrate over the interval within the range, i.e.

[0067] (3-6)

[0068] Where x represents the integration variable, arrive- The value of x corresponds to the possible longitudinal position of the aircraft. The theoretical longitudinal distance between the two aircraft at time t is determined by the aircraft's flight trajectory and operating status. and These are the mean longitudinal errors of machine i and machine j, respectively; and These are the longitudinal error variances of machine i and machine j, respectively.

[0069] To simplify the calculation, a standardization transformation can be performed using the standard normal distribution, let...

[0070] (3-7)

[0071] Will and Substituting into equation (3-7), we get and

[0072] (3-8)

[0073] (3-9)

[0074] Then, transform equation (3-7), separate the constant term, and extract x to obtain...

[0075] (3-10)

[0076] Differentiating both sides of equation (3-10) yields

[0077] (3-11)

[0078] Finally, substituting equations (3-11), (3-8), and (3-9) into the original probability integral formula (3-6) yields...

[0079] (3-12)

[0080] The cumulative distribution function of the standard normal distribution is known to be:

[0081] (3-13)

[0082] in It is the standard normal distributed cumulative distribution function, and t is the integral variable, so Therefore, the longitudinal collision risk probability can be expressed as:

[0083] (3-14)

[0084] in Let be the mean of the longitudinal random error of machine i. Let be the mean of the longitudinal random error of machine j.

[0085] Lateral collision probability model

[0086] In the traditional model, the lateral position errors of machine i and machine j and It follows a normal distribution. and This assumption cannot accurately reflect the dynamic changes in the model caused by crosswinds. Therefore, this study adds lateral offsets caused by crosswind disturbances to the lateral error. Assume crosswind speeds... It is an observable and has a linear relationship with the offset, based on the crosswind speed. Calculate the lateral offset :

[0087] (3-15)

[0088] in It is a proportionality coefficient (unit: m / s → m), which represents the average lateral displacement caused by a unit crosswind speed. It is the intercept, which represents the offset when there is no wind. The derivation of this coefficient and the intercept will be given later.

[0089] After incorporating crosswind disturbances, the lateral position error must include a deterministic offset term. and random error term Therefore, the lateral error is updated as follows:

[0090] (3-16)

[0091] Assuming the random error follows a normal distribution, the total lateral error is:

[0092] (3-17)

[0093] in Let t be the lateral deviation of aircraft j caused by the crosswind at time t. Let be the random lateral error of machine i at time t. Let be the random lateral error at time t.

[0094] Since the random errors remain independent and follow a normal distribution, the mean becomes a deterministic deviation. The variance is still the sum of the variances of random errors.

[0095] (3-18)

[0096] (3-19)

[0097] Therefore, the actual lateral distance is:

[0098] (3-20)

[0099] (3-21)

[0100] in Let t be the ideal lateral distance between the two aircraft. Qualitative deviation caused by crosswinds

[0101] Let the standard positive cumulative distribution function be... The safety interval is The probability of a lateral collision is:

[0102] (3-22)

[0103] Vertical collision probability model

[0104] Similarly, the formula for the vertical collision probability is:

[0105] (3-23)

[0106] in For vertical safety spacing, Let t be the ideal vertical distance between the two machines. Let i be the vertical random error variance of the machine. Let j be the vertical random error variance of machine j. Let i be the mean vertical random error of machine i. Let J be the mean of the vertical random error of machine j.

[0107] For complex scenarios in the terminal area, the total risk is decomposed into a product of independent probabilities in the vertical, lateral, and longitudinal directions:

[0108] (3-24)

[0109] S2: Establish a theoretical aircraft spacing model, divide the approach and go-around process of the approaching aircraft and the takeoff process of the taking-off aircraft into different stages, and construct the ideal spacing calculation model between the two aircraft for each stage.

[0110] Introduction to Baiyun Airport's "One Takeoff and One Landing Operation Mode"

[0111] According to AIP data from Baiyun International Airport, runway 02L / 20R is mainly used for departure, while runway 02R / 20L is mainly used for approach. Therefore, this study uses runway 02R / 20L as the approach and landing runway. To simplify the calculation model, the following assumptions are made regarding the aircraft's motion: after accelerating to the programmed altitude, both aircraft begin a constant indicated airspeed climb. Since the meteorological parameters of the two aircraft's environment are basically the same at the same airport, the constant indicated airspeed climb is approximated as a uniform climb.

[0112] Based on this assumption, after analyzing the ADS-B data of the target aircraft during the approach phase and the approach and approach procedures at Baiyun Airport, it can be concluded that the approach and go-around process of the approaching aircraft j can be divided into 5 stages:

[0113] 1. Maintain constant speed and level flight before reaching the FAF point.

[0114] 2. After reaching the FAF point, it decelerates uniformly during descent.

[0115] 3. After decelerating to landing speed, descend at a constant speed.

[0116] 4. After reaching the go-around point, accelerate and climb for a go-around.

[0117] 5. After climbing to the designated altitude (200m), turn (40°) and then climb again at a constant speed.

[0118] Similarly, the takeoff process of an aircraft can be divided into the following three stages:

[0119] 1. Accelerate from a standstill during the gliding run.

[0120] 2. Takeoff acceleration and climb along the runway direction

[0121] 3. Climb to the prescribed altitude (150m), turn (15°) and take off at a constant speed.

[0122] This study sets the variable as the initial longitudinal separation between the two aircraft when aircraft i begins takeoff. This is because the initial longitudinal distance between the two aircraft is determined before aircraft j reaches the FAF point. Equal to the distance from the FAF point to the runway exit Including the distance between the approaching aircraft and the FAF point, and the staggered distance between the 02L and 02R runway entrances, among which =9.9km, so the longitudinal distance between aircraft j and aircraft i exceeds 9.9km. RECAT-CN requires that when the preceding aircraft is a medium-sized aircraft and the following aircraft is a light-sized aircraft, the distance between the two aircraft should exceed 9.3km. In other words, the safety margin in this case is significantly higher than the basic requirement of RECAT-CN. Therefore, this paper only studies the case where aircraft j has passed the FAF point and has begun to decelerate.

[0123] Aircraft interval calculation model during operation

[0124] In a close-proximity parallel runway takeoff and landing scenario, when aircraft i begins takeoff, aircraft j is in the uniform deceleration approach phase after the final approach fix (FAF). Based on a detailed description of each phase of the two aircraft's operation, and considering the differences in the aircraft's motion states at different phases, this study divides the formula for calculating the distance between the two aircraft throughout the entire operation into multiple time periods according to chronological order, as follows: Figure 5 As shown.

[0125] The diagram assumes the aircraft takes off at the following time: Meanwhile, the approaching aircraft has passed the FAF point and is decelerating. The two horizontal lines in the diagram represent the total flight time of aircraft J and I during the entire operation. The duration of each stage, From t The total time elapsed until the end of phase i is shown. The triangles on the straight line represent changes in the aircraft's motion state at that moment. The time segments enclosed in curly braces at the top and bottom of the figure represent aircraft j and i maintaining a certain motion state during that time period. The following will be based on... Figure 5The phase divisions in the model are used to construct calculation models for the ideal interval between the two aircraft at different stages.

[0126] In phase 1, aircraft i accelerates from rest, while aircraft j is approaching with uniform deceleration. Given an initial longitudinal distance... Let the glide angle be... Then the initial vertical distance Since the J aircraft is already making a straight approach to the runway, the initial lateral distance is set to the runway spacing. m. Based on the kinematic equations, the formulas for calculating the intervals in the three directions of stage 1 are as follows:

[0127] (3-25)

[0128] in Let be the horizontal component of the initial velocity of machine j, and t be the running time. Let J be the horizontal component of the acceleration during deceleration and descent. The acceleration of the i-plane during takeoff. , , These represent the longitudinal, lateral, and vertical intervals between the two machines within time t in the first stage (the formulas for the other stages below are similar).

[0129] During Phase 2, while aircraft I was still in the takeoff roll, aircraft J had already decelerated and begun to move at landing speed. The descent proceeds at a constant speed, and the total duration of the first stage is... The formula for calculating the stage interval is:

[0130] (3-26)

[0131] in This represents the total running time of the preceding stage. Since there was only stage 1 preceding the preceding stage, therefore... .

[0132] During Phase 3, the aircraft completes its takeoff roll and lifts off at a horizontal takeoff speed. Horizontal acceleration along the runway direction As the aircraft accelerates its ascent, it remains in a constant descent at its landing speed. The interval calculation formula is as follows:

[0133] (3-27)

[0134] In phase 4, aircraft i accelerates and climbs along the runway to the programmed height, then turns 15° and begins a constant-speed climb, while aircraft j continues a constant-speed descent. Let the climb angle be... The formula for calculating the stage interval is:

[0135] (3-28)

[0136] in This represents the total running time of the first three stages. .

[0137] During Phase 5, the J aircraft reached the go-around point and began to accelerate horizontally. If the aircraft accelerates uniformly along the runway direction for a go-around, and its motion remains unchanged during this period, then the formula for calculating this phase interval is:

[0138] (3-28)

[0139] During Phase 6, aircraft i maintains its motion state, while aircraft j reaches the required go-around altitude, turns 40°, and continues climbing at a constant speed. The formula for calculating the interval of this phase is:

[0140] (3-29)

[0141] In phase 6, both aircraft complete the procedures for takeoff and go-around in the near-ground zone. After that, the probability of collision will decrease as the distance between the two aircraft increases. The entire operation is considered to end 5 seconds after the two aircraft enter phase 6.

[0142] S3: Construct a dynamic safety separation model, combine the frontal and crosswind speeds to calculate the wake dissipation time, and then obtain the safety separation between the two aircraft;

[0143] Dynamic safety interval model

[0144] To ensure the safety of aircraft landing in isolated operation mode, Baiyun Airport control generally requires that when a landing aircraft reaches the approach of runway 02R, the taking-off aircraft has already taken off and departed from the exit of runway 02L. Assuming aircraft J lands at the runway approach, the distance between aircraft I and J at this point is at least the runway length (3800m) plus the staggered distance between the two runway exits (600m), which is 4400m. Considering the possibility of a go-around, aircraft J must remain outside the wake turbulence range generated by aircraft I. Assume that at time t, the speed of aircraft J is... The speed of the i machine is Then the speed difference between the two machines is If the time required for the wake to dissipate is Therefore, the safe distance between the two engines before the wake dissipates is: Therefore, the longitudinal safety margin at this time is:

[0145] (3-30)

[0146] The time it takes for the wake to dissipate is related to the crosswind speed. Table 3-1 below shows the relationship between wake dissipation speed and time, as summarized by the FAA after extensive practical observation.

[0147] Table 3-1 Relationship between wake dissipation velocity and time

[0148]

[0149] Regarding lateral and vertical safety distances, according to the International Civil Aviation Organization (ICAO) regulations, at altitudes below 10,000 feet (approximately 3,048 meters), the vertical safety separation between aircraft is typically 1,000 feet (approximately 305 meters). Therefore, the vertical safety distance is set to a fixed value of 305 meters, and the lateral safety distance is set to a fixed value of 400 meters based on the runway spacing between runways 02R and 02L.

[0150] The safety separation model constructed above for the "quasi-isolated operation" scenario of close-proximity parallel runways is highly scientific and rigorous. It accurately captures the key dynamic characteristic that aircraft speeds are not constant during takeoff and landing, but are constantly adjusting, and fully considers the dynamic changes in the speeds of the two aircraft during actual operation. Simultaneously, crosswind speed, a key factor affecting wake dissipation time, is also included in the model's considerations. Combined with data on the relationship between wake dissipation speed and time summarized by the FAA after extensive practical observation, the model can accurately obtain the wake dissipation time under different crosswind speed conditions, and then directly calculate the safe separation between the two aircraft based on the wake dissipation time. For example, if the speed of the preceding aircraft i is much lower than that of the following aircraft j and the wake dissipation time is longer, the model will automatically increase the longitudinal safety separation to ensure that the following aircraft is completely outside the influence range of the preceding aircraft's wake; conversely, if the speed of the preceding aircraft i is greater than that of the following aircraft j and the wake dissipation time is shorter, the longitudinal safety separation will be appropriately reduced, but still maintain a safety baseline.

[0151] Compared with the traditional fixed safety interval setting method, this dynamic safety interval adjustment model is theoretically more in line with the complexity and variability of actual flight scenarios, effectively avoiding safety risks caused by unreasonable safety interval settings; making the simulation model results more reliable; and in practice, it can maximize runway utilization efficiency while ensuring safety, providing strong support for the efficient and safe operation of airports.

[0152] S4: Collect and preprocess relevant data, including ADS-B trajectory data and METAR message observation data, and extract random error data;

[0153] The ADS-B trajectory data of the ARJ21 aircraft during the straight approach phase (from altitude ≤900m to touchdown) on runway 02R at Baiyun Airport was collected through the FlightADSB website, and comprehensive data preprocessing was performed on it.

[0154] First, the data content and characteristics need to be analyzed. The data includes fields such as UTC time (seconds), barometric altitude (m), ground speed (km / h), true heading angle (°), and latitude and longitude coordinates (WGS84). The precision is not high, but the content is relatively comprehensive. Then, interpolation was performed on different types of data (at 1-second intervals). Altitude was interpolated using constrained linear interpolation, a method that adapts to relatively stable altitude changes while avoiding unreasonable negative values ​​through constraints. Latitude and longitude coordinates were interpolated using boundary-constrained cubic spline interpolation, ensuring curve smoothness while adjusting interpolation results outside the Earth's longitude (-180° to 180°) and latitude (-90° to 90°) ranges to boundary values. Ground speed was interpolated using smoothed spline interpolation, which first calculates the mean and standard deviation of the speed, corrects outliers deviating from the mean by a certain multiple of the standard deviation, and then performs interpolation to control curve smoothness and avoid abnormal speed fluctuations. Heading was interpolated using a cyclic interpolation method, converting the heading to coordinates on a unit circle, interpolating in a two-dimensional plane, and then returning to the angle, avoiding discontinuous jumps near 0° and 360°. These interpolation methods were matched to the characteristics of different data sequences to minimize data errors caused by interpolation.

[0155] Random error data extraction

[0156] To obtain the random errors of each aircraft in various directions during the approach phase, this study assumes that the average track of all samples is the standard track during the approach. By performing polynomial fitting on the latitude, longitude, and altitude at each time point, the fitting polynomial coefficients for that time series are obtained. Based on these coefficients, the fitted longitude, latitude, and altitude for each point are calculated. Then, the spherical distance formula is used to calculate the distance and azimuth between the actual point and the fitted point. Lateral and longitudinal errors are then calculated based on the track direction, while the vertical error is directly calculated from the difference between the fitted altitude and the actual altitude. All of the above processes are implemented using a MATLAB program.

[0157] For sample data, excessive track deviation may lead to significant offsets in the fitted track. Therefore, it is necessary to first plot the actual trajectory of all samples through programming to eliminate outliers. For example... Figures 6-7 As shown, one of the sample tracks has an excessively large deviation ( Figure 6 To prevent large errors in the fitting results, they were removed, and then the remaining tracks were compared. Figure 7It was found that the aircraft's altitude was highly concentrated in the average track within the 700m-100m range. Based on the 600m altitude of the FAF point at Baiyun Airport, it was estimated that the aircraft entered the final approach phase within the 700m-100m range. The latitude, longitude, and altitude values ​​of the average track during this phase were extracted and the time was aligned to obtain the longitudinal, lateral, and vertical error data for the final approach phase.

[0158] S5: Bayesian parameter estimation method is used to estimate the parameters of random error. A relationship model between frontal and crosswind and lateral offset is established through linear regression analysis and verified. Frontal and crosswind data of Baiyun Airport are fitted to determine a suitable distribution model.

[0159] Prior distribution setting

[0160] In a precision approach and landing scenario, assume that the random position error of the aircraft at time t follows a mean of . variance is normal distribution .

[0161] Because the aircraft has a strong heading-maintaining capability after entering the localizer (the horizontal guidance signal of the ILS instrument landing system), the mean error is set to 0. Based on existing data, the standard deviations for three aircraft classes can be obtained. The standard deviation decreases as the aircraft size decreases. This variation reflects that light aircraft are more flexible and have smaller deviation fluctuations in acceleration / deceleration (longitudinal) and heading adjustments (lateral), while heavy aircraft, due to their larger mass and slower handling response, have a wider deviation range. The length, height, and wingspan of an aircraft are key factors affecting its maneuverability. Therefore, as shown in Table 4-1, based on the differences in length, height, and wingspan between the ARJ21 and medium-sized aircraft, the standard deviations of its deviations from the expected position in the three directions are estimated, and these are used as the prior standard deviations for parameter estimation.

[0162] Table 4-1 Aircraft Dimensional Parameters and Standard Deviation

[0163]

[0164] Taking the longitudinal direction as an example, within the framework of Bayes' theorem, when the estimated parameter is the variance of a normal distribution, the conjugate prior is usually chosen to be an inverse-Gamma distribution. Therefore, let the prior be:

[0165] (4-1)

[0166] in, The variance to be estimated is the longitudinal error. For shape parameters, As a scale parameter, it needs to be set based on prior knowledge. When When the prior mean does not exist, the mean cannot be used to describe the central tendency. At this time, the prior mean exists but the variance does not exist; only when... Both prior mean and variance exist, and as... Increasing the value of prior information increases its weight. To balance the influence of prior information, a certain percentage is generally set. This facilitates subsequent integration with measured data.

[0167] The prior standard deviation has been obtained in Table 4-1. Then the prior variance is Therefore, the mean of the prior Inverse-Gamma distribution is:

[0168] (4-2)

[0169] Will Substituting into the mean formula (4-2) yields the following result. Therefore, the prior distribution is:

[0170] (4-3)

[0171] Therefore, the prior probability density function (PDF) is further obtained as follows:

[0172] (4-4)

[0173] Given the gamma function Then, by substituting the known parameters, we obtain the prior distribution.

[0174] (4-5)

[0175] Likelihood function establishment

[0176] Taking the x-direction as an example, for n independent and identically distributed position error samples... Then its probability density function (PDF) is:

[0177] (4-6)

[0178] in Let be the variance parameter to be estimated. Let be the value of the i-th sample. Since the samples are independent and identically distributed, meaning that the errors of each observation do not affect each other and follow the same distribution, the overall likelihood function is the product of the densities of the n samples.

[0179] (4-7)

[0180] That is, the likelihood function is:

[0181] (4-8)

[0182] To simplify calculations, the constant and variable terms of the likelihood function are separated, resulting in...

[0183] (4-9)

[0184] Sum of squares of all error samples Therefore, the exponent part is abbreviated as In Bayesian inference, since the posterior only needs to be proportional to the likelihood prior, the constant part of the likelihood function does not affect the posterior distribution, thus yielding...

[0185] (4-10)

[0186] in It is the likelihood function, a core concept in Bayesian parameter estimation, used to quantify the degree to which data supports the parameters, representing the likelihood of a given parameter being supported by other data. The probability of; is the standard deviation of the position error in the x-direction, used to measure the range of fluctuation in the position error in that direction; D is the observation dataset. ,in It is the position error in the x-direction (actual position - expected position) in the i-th observation, for example... This indicates that the lateral offset of the third observation was +25 meters (deviating from the right side of the runway centerline).

[0187] Posterior distribution calculation

[0188] By Bayes' theorem, the posterior distribution is proportional to the product of the likelihood function and the prior distribution.

[0189] (4-11)

[0190] in It is a posterior distribution. It is the likelihood function. It is a prior distribution

[0191] Substituting the likelihood function (4-10) and the prior distribution (4-5) into the equation, we obtain...

[0192] (4-12)

[0193] Combining the power term and exponent term in equation (4-12) yields...

[0194] (4-13)

[0195] From equation (4-13), based on conjugacy, we can obtain the posterior distribution. In the middle, the shape parameters are The scale parameter is ,Right now

[0196] (4-14)

[0197] Finally, the estimated variance is obtained using the formula for the posterior distribution mean.

[0198] (4-15)

[0199] Similarly, the posterior distribution functions for the lateral and vertical directions can be obtained. Then, by substituting the error data of the aircraft during the approach process obtained earlier into the formula and rounding the estimated variance, the data in Table 4-2 below can be obtained.

[0200] Table 4-2 Parameter Estimation Calculation Results

[0201]

[0202] Comparing the prior variance and estimated variance in Table 4-2, it can be seen that the variances in all three directions have decreased to varying degrees. This reflects the direct impact of the measured error data and demonstrates the role of Bayesian parameter estimation. The estimated variance for the lateral error has decreased significantly, indicating that the ARJ21 aircraft has a high track accuracy maintenance capability, which is consistent with the high requirements for heading deviation under precision approach conditions.

[0203] Linear regression analysis of crosswind offset coefficient

[0204] Lateral offset and corresponding crosswind data collection

[0205] First, raw ADS-B data of ARJ-21 aircraft approaching Baiyun Airport was collected. A segment of data from their straight approach (heading adjusted to 14°) was extracted and interpolated. Then, a track map was drawn based on latitude and longitude coordinates. The line connecting the latitude and longitude coordinates was used as the actual track, and the track angle at each coordinate point was obtained. The difference between the track angle and the nominal track was then calculated to obtain the heading deviation at each positioning point. Finally, the lateral displacement was obtained based on the trigonometric relationship between the distance between two positioning points and the heading deviation angle. .

[0206] Because METAR messages can only collect wind speed and direction information at 30-minute intervals, they cannot accurately describe the dynamic impact of crosswinds on lateral displacement during approach. Therefore, this study focuses on each flight... The average value is taken to obtain the systemic lateral displacement during this approach. Then, the crosswind speed during this approach period is calculated based on the METAR report for this approach period, thus obtaining the data of systemic lateral displacement and crosswind.

[0207] Linear regression model construction

[0208] Assuming lateral offset With crosswind offset coefficient Satisfies a linear relationship:

[0209] (4-16)

[0210] is the slope, which is the crosswind offset coefficient, and b is the intercept, representing the offset when there is no wind.

[0211] Given n sample points ,in Let be the crosswind speed at the i-th sample point. Let be the lateral offset of the i-th sample point, then the formula for calculating the parameters of the linear regression is:

[0212] (4-17)

[0213] in Covariance Cov and The variances Var are respectively:

[0214] (4-18)

[0215] (4-19)

[0216] in The mean crosswind speed for all samples. The mean of the lateral offset for all samples

[0217] Substituting equations (4-17) and (4-18) into equation (4-19), we obtain the slope as:

[0218] (4-20)

[0219] The intercept obtained is:

[0220] (4-21)

[0221] Crosswind offset model validation

[0222] To verify the rationality of the simulation, it is necessary to calculate the mean square error of this model. )for:

[0223] (4-22)

[0224] Coefficient of determination for:

[0225] (4-23)

[0226] in Let MSE be the predicted value for the i-th sample; a smaller MSE indicates a more accurate model. RSS is the Residual Sum of Squares, representing the fluctuations unexplained by the model, and TSS is the Total Sum of Squares, representing the total fluctuations in the data. This represents "the volatility that the model can explain / total volatility", which is the reliability of the model.

[0227] The final calculation yielded a regression coefficient k≈0.0461, indicating that for every 1 m / s increase in crosswind speed, the average lateral displacement increases by approximately 0.0461 m; the intercept b≈0.1105, indicating that in the absence of crosswinds, the predicted lateral displacement is approximately 0.1105 m; the mean square error MSE≈0.000567, indicating that the average error between the predicted and actual values ​​is 0.000567 square units, which is relatively small; the coefficient of determination... The value is approximately 0.5732, indicating that the model can explain about 57.32% of the data fluctuations, which is considered a moderate fit.

[0228] To visualize the fit more clearly, we plotted a scatter plot of the linear regression function and the actual data. Figure 8 The study found that when the crosswind speed was low (less than 2 m / s), the linear regression equation could better fit the relationship between crosswind and lateral displacement. However, as the crosswind gradually increased, the rate of increase in lateral displacement decreased significantly. Based on the analysis of the actual scenario, it is speculated that this may be because when the crosswind was low, the aircraft's sensitivity to crosswind correction was low. As the crosswind gradually increased, the aircraft's sensitivity to crosswind correction gradually increased. Therefore, it shows that as the wind speed increased to more than 2 m / s, the increment of lateral displacement gradually decreased. Considering that the crosswind speed at Baiyun Airport is generally low, the fitting results are accepted.

[0229] Baiyun Airport crosswind data fitting

[0230] METAR (Airport Weather Report) messages, as an important source of meteorological information in the aviation field, are updated every 30 minutes. For meteorological elements such as airport wind speed and direction, which have high-frequency dynamic changes, relying solely on a single day's message is insufficient to accurately capture their patterns of fluctuation over time. Therefore, this study innovatively extends the time dimension by extracting wind speed and direction messages from Baiyun Airport for the same time period each day from April 2023 to April 2025, and then calculating the crosswind speed relative to the approach direction of Baiyun Airport (hereinafter, crosswind refers to positive crosswind). This long-term data collection method effectively avoids the randomness and bias of single-day data, and can more comprehensively and objectively reflect the changing trends of wind speed and direction at Baiyun Airport. Based on previous research experience with crosswind data at Baiyun Airport, it was found that crosswind data has a right-skewed characteristic at low wind speeds. In the field of statistics, the two-parameter Weibull distribution and the Gamma distribution are more suitable for non-negative right-skewed data and are often used in data modeling and analysis in meteorology, engineering, and other fields.

[0231] The following sections will use these two distributions to fit the wind measurement data, aiming to accurately characterize the distribution pattern of crosswind data at Baiyun Airport through a scientific and reasonable mathematical model, and to provide a data foundation and theoretical support for subsequent simulation of close-range parallel runway operation involving crosswind influence.

[0232] Weibull distribution fitting

[0233] Assuming that the crosswind volume x during this time period follows a Weibull distribution with shape parameter k and scale λ, its probability density function (PDF) is:

[0234] (4-24)

[0235] The maximum likelihood estimation method is used to obtain the log-likelihood function by taking the logarithm of the PDF.

[0236] (4-25)

[0237] Where n represents the number of samples. Since the process of calculating the log-likelihood is complex, the subsequent process will be completed by programming in MATLAB.

[0238] Gamma distribution fitting

[0239] Assume that the cross-flow volume x during this time period follows a shape parameter. Scale parameters If the gamma distribution is such that its probability density function (PDF) is:

[0240] (4-26)

[0241] in It is the gamma function, defined by equation (4-27), where the parameter t is the integral variable of the gamma function.

[0242] (4-27)

[0243] The maximum likelihood estimation method is used to obtain the log-likelihood function by taking the logarithm of the PDF.

[0244] (4-28)

[0245] Where n represents the number of samples. Since the process of calculating the log-likelihood is complex, the subsequent process is also completed by programming in MATLAB.

[0246] Fitting results and tests

[0247] To determine the fit, the first step is to assess whether the sample data conforms to a specific distribution. The KS test is a commonly used method in current research. Its core idea is to evaluate the goodness of fit between the empirical cumulative distribution function (ECDF) and the theoretical cumulative distribution function (CDF) by comparing their maximum vertical deviations. The smaller the deviation, the more likely the data is to follow the target distribution. Generally, a p-value > 0.05 is considered acceptable for the hypothesis.

[0248] If both parameters pass the KS test, it is necessary to determine whether the distribution fits the data better. This paper introduces AIC (Akaike Information Criterion) and BIC (Bayesian Information Criterion) as evaluation criteria.

[0249] (4-29)

[0250] (4-30)

[0251] Where m is the number of parameters in the distribution, and the number of parameters in both the Weibull and Gamma distributions is 2; The log-likelihood function value is typically used to represent and measure the ability of a distribution to fit data; n is the number of data samples. Smaller values ​​for AIC and BIC indicate a better fit. The MATLAB code calculation results are shown in Table 4-3 below.

[0252] Table 4-3 Comparison of Fitting Standards

[0253]

[0254] As shown in Table 4-3, both the Weibull and Gamma distributions passed the KS test. By comparing the AIC and BIC, it is concluded that the wind measurement data is more consistent with the Weibull distribution, in which the shape parameter... Scale parameters , Figure 9 This is a comparison between probability density functions and data distribution histograms.

[0255] S6: Conduct Monte Carlo simulations to statistically analyze the average collision probability under different initial intervals and crosswind conditions, and propose a standard for classifying crosswind intervals.

[0256] The previous section established a model for calculating the ideal interval and collision probability of two aircraft within time t. First, the physical parameters, error distribution parameters, and Monte Carlo simulation parameters of the aircraft motion were set. The physical parameters include the aircraft's speed, acceleration, and turning angle. The error distribution parameters include the mean and variance in each direction (the variance of the two aircraft has been calculated in advance according to the collision probability formula). The Monte Carlo simulation parameters include the number of simulations, the Weibull distribution parameters of the wind speed, and the time step.

[0257] To study the variation in collision probability under different crosswind speeds, the simulation code uses Weibull distribution random sampling to simulate the uncertainty of crosswind speed during each run. It then calculates the lateral offset caused by the crosswind based on the sampled crosswind components, using this as the mean of the lateral deviation. Simultaneously, the code determines the wake dissipation time using the randomly sampled crosswind speed to calculate the safe interval time, stores the calculation results, and uses them for subsequent safe distance calculations of aircraft positions.

[0258] The core of the simulation model is the calculation of the distance between the two aircraft and the probability of collision. After calculating and storing the duration of each stage and the time point of stage transition, the aircraft motion is divided into multiple stages according to the interval calculation model described above. Then, using an if loop, the ideal interval and the corresponding safe interval in three directions are calculated and stored for each stage, with the stored time point as the transition standard. Finally, the safe interval standard and ideal interval calculated at each time step in the entire simulation process are substituted into the collision probability calculation module to obtain the collision probability at each step. These probabilities are then discretely summed and integrated to obtain the collision probability for the current cycle. Finally, the collision probabilities of multiple runs are obtained through Monte Carlo simulation, and the average collision probability at a certain initial interval is obtained by averaging.

[0259] Parameter data settings

[0260] To better reflect the actual operational situation at Baiyun Airport, the B738 aircraft, which has a high number of takeoffs at Baiyun Airport, was selected as the takeoff aircraft, and the domestically produced ARJ21-700 aircraft was selected as the approach and go-around aircraft. Based on the analysis of ADS-B operational data and Baiyun Airport's go-around procedures, the following fixed parameter data were set.

[0261] Table 5-1 Fixed Simulation Parameter Settings

[0262]

[0263] Based on the results of Bayesian parameter estimation and frontal and lateral wind speed fitting mentioned above, the following random parameters are set.

[0264] Table 5-2 Random Simulation Parameter Settings

[0265]

[0266] Analysis of Simulation Experiment Results

[0267] To clearly observe how the collision probability changes throughout the entire operation of the two aircraft with variations in the initial distance between them and the crosswind strength, the number of Monte Carlo cycles was set to [number missing]. Next, the simulation will start with an initial interval of 9900m (the distance between the FAF point and the 02R runway entrance), and gradually reduce the initial interval until the safe threshold of the initial interval during operation is obtained.

[0268] 1. The initial interval is between 9900m and 9000m.

[0269] Simulation results show that, at this initial interval, the collision probability between the two aircraft is almost zero regardless of the crosswind strength. The model only recorded a collision probability greater than zero when the interval was 9000m and the crosswind speed was less than 5kt. Figure 10 As shown, as the crosswind speed increases, the wake dissipation time decreases, and the collision probability gradually decreases.

[0270] 2. The initial interval is between 9000m and 6800m.

[0271] Under these conditions, simulation results show that the collision probability between the two aircraft exhibits a clear stepwise decrease with increasing crosswind speed, such as... Figures 11-12 As shown, this pattern is most pronounced when the distance is 7500m. Combining the calculation models for safe distance and collision probability, it can be found that this simulation result occurs because as the crosswind speed increases, the wake dissipation time decreases, and the required safe distance between the two aircraft also decreases accordingly. Therefore, the probability that the actual distance between the two aircraft is less than the safe distance will also decrease, and the probability of collision will decrease accordingly.

[0272] Figure 11 In the diagram, the vertical dashed line represents the threshold value for wake dissipation time as a function of crosswind speed, obtained from FAA statistics; the solid line represents the probability of a collision between the two aircraft; and the horizontal dashed line represents the safety standard stipulated by the International Civil Aviation Organization, i.e., the probability of a collision in three directions is less than [a certain value]. For each flight hour, the horizontal axis represents crosswind speed and the vertical axis represents collision probability, respectively. Figure 12 In the diagram, the solid line represents the probability of a collision between the two aircraft, while the horizontal and vertical axes represent the collision probability and the wake dissipation time, respectively.

[0273] Table 5-3 below shows the simulation results for 8000m, 7800m, 7100m, and 6800m. Because the collision probability varies considerably, for ease of data comparison and analysis, the simulated collision probability is uniformly taken as the exponent of 10 in scientific notation (i.e.,...). In value).

[0274] Table 5-3 Simulation results at different intervals

[0275]

[0276] Analysis of the data in Table 5-3 above reveals that when the initial interval is 8000m, under crosswind conditions...

[0277] Within the speed range of >5.14 m / s (10 kt), the collision probability is 0. This result confirms the previously proposed rule that the greater the initial separation and crosswind speed, the more sufficient the safety redundancy, indicating that aircraft operation at separations far exceeding the conventional safety threshold is insufficient to cause a collision risk. Simultaneously, the data shows that the collision probability gradually increases as the initial separation and crosswind speed decrease, a pattern that also confirms the collision probability calculation mechanism analyzed earlier.

[0278] 3. The initial interval is between 6800m and 6250m.

[0279] Simulation results show that when the initial distance between the two aircraft is less than 6800m, the relationship between the change in crosswind speed and collision probability begins to change.

[0280] like Figures 13-14 As shown, in the simulation, when the initial interval was set to 6700 m, the collision probability reached its lowest value throughout the entire observation period as the crosswind speed gradually increased to 5.14 m / s. This phenomenon indicates that, under a specific initial interval, a moderate increase in crosswind speed can reduce wake dissipation time and thus lower the collision risk. However, when the crosswind speed exceeded 5.14 m / s, the collision probability showed an upward trend as the crosswind speed continued to increase, reflecting that the influence of crosswind speed on the safety interval has a nonlinear threshold characteristic. After exceeding the critical value, the positive effect of wake dissipation may be offset by factors such as increased airflow disturbance. To further verify the correlation between the initial interval and the collision probability, simulation experiments were conducted on five groups of decreasing initial intervals: 6600 m, 6500 m, 6400 m, 6300 m, and 6250 m. The collision probability obtained from the simulation was taken as the exponential part of scientific notation 10. The specific results are shown in Table 5-4 below.

[0281] Table 5-4 Simulation results at different intervals

[0282]

[0283] A longitudinal comparison of the results reveals that the collision probability increases under all crosswind conditions as the initial distance decreases. Let crosswind speeds greater than 7.71 m / s (15 kt) be considered strong crosswinds, and crosswind speeds less than 2.57 m / s (5 kt) be considered weak crosswinds. A horizontal comparison further shows that the collision probability under strong crosswinds gradually changes from less than that under weak crosswinds to greater than that under weak crosswinds. This indicates that the impact of strong crosswinds on operational safety gradually intensifies as the initial distance decreases. Combining the collision probability calculation model and the safety separation calculation model reveals that when the initial distance is between 6250 m and 6800 m, the positive benefits of strong crosswinds (such as reduced wake dissipation time) gradually weaken compared to their negative impacts (such as the impact on aircraft lateral position error and the increased safety separation when the following aircraft's speed is greater than the preceding aircraft's). Therefore, after the initial distance falls below a certain threshold, the collision probability increases with increasing crosswind speed.

[0284] 4. Initial interval less than 6250m

[0285] When the initial distance between the two machines is less than 6250m, such as Figures 15-16 As shown, the change pattern of the collision probability will completely change to increasing with the increase of crosswind.

[0286] Further simulations were performed on five decreasing initial intervals of 6200m, 6000m, 5900m, 5800m, 5700m, 5600m, and 5550m. The collision probabilities obtained from the simulations were taken as the exponent of 10 in scientific notation. The results are shown in Table 5-5 below.

[0287] Table 5-5 Simulation results at different intervals

[0288]

[0289] like Figures 17-18 As shown, when the initial interval of the simulation is set to 5550 meters, the collision probability shows a significant increasing trend with increasing crosswind. Only when the crosswind is less than 2.57 m / s is the collision probability lower than the local safety standard. ).

[0290] Simulation Experiment Summary and Practical Application

[0291] By setting an initial decreasing interval from 9000 meters to 5550 meters, and dividing the crosswind speed ranges (covering four levels: <2.57 m / s, <5.14 m / s (2.57-5.14 m / s), <7.71 m / s (5.14-7.71 m / s), and ≥7.71 m / s) with a step size of 2.57 m / s (5 kt), cross-simulation analysis was conducted to quantify the collision probability (times / hour) under different conditions. Combined with the previous research on data and calculation mechanisms, the following core laws can be deduced:

[0292] 1. As the initial interval decreases, the probability of a collision between the two aircraft will inevitably increase under the same crosswind conditions.

[0293] 2. When the initial interval is greater than 6800 meters, under the same initial interval conditions, the probability of collision between the two aircraft will decrease as the wake dissipation time decreases due to the increase in crosswind speed.

[0294] 3. When the initial separation is between 6800 meters and 6200 meters, under the same initial separation condition, the probability of collision between the two aircraft first decreases and then increases as the crosswind increases.

[0295] 4. When the initial spacing is less than 6200 meters, under the same initial spacing conditions, the probability of collision between the two aircraft increases monotonically, and the increase in collision probability also increases with the increase in crosswind speed. This phenomenon indicates that the combined risk of a small spacing and strong crosswinds is very prominent, and the negative impact it brings will compress the safety margin, causing the collision probability to show a sharp increase trend or tend to stabilize at a high level.

[0296] Based on simulation data, the following initial crosswind separation standards are set: When the crosswind speed is below 2.57 m / s (5 kt), the separation between two aircraft during takeoff should be at least 5550 m. Because the runway threshold 02L is offset forward by 600 m from the runway threshold 02R, under these crosswind conditions, the aircraft taking off should begin takeoff roll at least 4950 m from the landing runway threshold; otherwise, takeoff should be prohibited. Similarly, when the crosswind speed is below 5.14 m / s (10 kt), the taking-off aircraft should begin takeoff when the landing aircraft is at least 5050 m from the runway threshold; when the crosswind speed is below 7.71 m / s (15 kt), the taking-off aircraft should begin takeoff when the landing aircraft is at least 5250 m from the runway threshold; when the crosswind speed is above 7.71 m / s (15 kt), the taking-off aircraft should begin takeoff when the landing aircraft is at least 5450 m (5420 rounded up by 50 m) from the runway threshold.

[0297] Then, the random error before Bayesian parameter estimation was used for simulation, and the obtained initial interval standard was compared with the standard after parameter estimation optimization in this study, as shown in Table 5-6 below.

[0298] Table 5-6 Comparison of initial intervals before and after optimization

[0299]

[0300] After optimization using Bayesian parameter estimation, the initial operational intervals between landing and takeoff for the ARJ21 aircraft were reduced to varying degrees while meeting safety requirements, thus increasing airport operational efficiency to some extent.

[0301] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0302] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for assessing the collision risk of closely spaced parallel runways under the influence of crosswinds, characterized in that, Includes the following steps: S1: Construct a collision risk model, which includes a longitudinal collision probability model, a lateral collision probability model, and a vertical collision probability model, decomposing the total risk into the product of independent probabilities of longitudinal, lateral, and vertical collisions; S2: Establish a theoretical aircraft spacing model, divide the approach and go-around process of the approaching aircraft and the takeoff process of the taking-off aircraft into different stages, and construct the ideal spacing calculation model between the two aircraft for each stage. S3: Construct a dynamic safety separation model, combine the frontal and crosswind speeds to calculate the wake dissipation time, and then obtain the safety separation between the two aircraft; S4: Collect and preprocess relevant data, including ADS-B trajectory data and METAR message observation data, and extract random error data; S5: Bayesian parameter estimation method is used to estimate the parameters of random error. A relationship model between frontal and crosswind and lateral offset is established through linear regression analysis and verified. Frontal and crosswind data of Baiyun Airport are fitted to determine a suitable distribution model. S6: Conduct Monte Carlo simulations to statistically analyze the average collision probability under different initial intervals and crosswind conditions, and propose a standard for classifying crosswind intervals.

2. The method for assessing the collision risk of close-range parallel runways under the influence of crosswinds as described in claim 1, characterized in that: In the longitudinal collision probability model, the longitudinal position error of the aircraft follows a normal distribution, and the total longitudinal error is the sum of the longitudinal errors of the two aircraft. The longitudinal collision risk probability is calculated by integrating the normal distribution probability density function within the safe interval, and the calculation can be simplified by standardizing the calculation using the standard normal distribution.

3. The method for assessing the collision risk of close-range parallel runways based on the influence of crosswinds as described in claim 1, characterized in that: In the lateral collision probability model, the lateral position error includes a deterministic offset term and a random error term caused by the frontal crosswind. The lateral offset caused by the frontal crosswind is linearly related to the frontal crosswind speed. The mean of the total lateral error is the deterministic offset difference, and the variance is the sum of the variances of the random errors. The lateral collision risk probability is calculated based on this distribution. In the vertical collision probability model, the vertical position error includes a random error term and a systematic deviation term.

4. The method for assessing the collision risk of close-range parallel runways under the influence of crosswinds as described in claim 1, characterized in that: In the theoretical separation model of the aircraft, the approaching aircraft's approach and go-around process is divided into stages such as uniform level flight, uniform deceleration descent, uniform descent, accelerated go-around climb, and turning and uniform go-around climb after climbing to 200m. The takeoff process of the aircraft is divided into stages such as accelerated taxiing, accelerated climb, and turning and uniform climb after climbing to 150m. The separation calculation formula for each stage is constructed based on the kinematic equations.

5. The method for assessing the collision risk of close-range parallel runways based on the influence of crosswinds as described in claim 1, characterized in that: In the dynamic safety interval model, the longitudinal safety interval is calculated based on the wake dissipation time and the speed difference between the two engines. The wake dissipation time is related to the crosswind speed, and the lateral and vertical safety distances are set to fixed values ​​according to relevant regulations.

6. The method for assessing the collision risk of close-range parallel runways based on the influence of crosswinds according to claim 1, characterized in that: The data preprocessing includes applying corresponding interpolation methods to different fields of the ADS-B trajectory data. For example, constrained linear interpolation is used for altitude, boundary-constrained cubic spline interpolation is used for latitude and longitude coordinates, smooth spline interpolation is used for ground speed, and cyclic interpolation is used for heading. Abnormal samples with excessive track deviations are also removed.

7. The method for assessing the collision risk of close-range parallel runways based on the influence of crosswinds according to claim 1, characterized in that: In the Bayesian parameter estimation, it is assumed that the random position error of the aircraft follows a normal distribution with a mean of 0. The prior distribution is selected as the Inverse-Gamma distribution. Parameters are set based on prior knowledge, and the posterior distribution is calculated through the likelihood function and the prior distribution, thereby obtaining the estimated variance.

8. The method for assessing the collision risk of close-range parallel runways based on the influence of crosswinds according to claim 1, characterized in that: In the linear regression analysis model of the relationship between crosswind and lateral offset, the relationship between lateral offset and crosswind speed is expressed as: lateral offset = proportionality coefficient × crosswind speed + intercept. The proportionality coefficient and intercept are calculated using sample data, and the model is validated using mean square error and coefficient of determination.

9. The method for assessing the collision risk of close-range parallel runways based on the influence of crosswinds according to claim 1, characterized in that: In the fitting of the crosswind data of Baiyun Airport, Weibull distribution and gamma distribution were used for fitting respectively. The fitting effect was judged by KS test, AIC and BIC criteria, and Weibull distribution was determined to be the appropriate distribution model.

10. The method for assessing the collision risk of close-range parallel runways based on the influence of crosswinds according to claim 1, characterized in that: In the Monte Carlo simulation, physical parameters, error distribution parameters, and simulation parameters of the aircraft motion are set. Crosswind speeds are simulated using Weibull distribution random sampling. Ideal and safe intervals are calculated for each stage, thus obtaining the collision probability at each time step. The average collision probability is obtained by averaging multiple simulation results. Based on the simulation results, an initial interval of 5550m-9000m, crosswind speeds of 0-15m / s, and the ICAO-specified safe collision probability threshold (5×10⁻⁶ m / s) are used. −9 (times / hour), combined with the FAA wake dissipation time standard, proposes a crosswind classification interval standard.

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