A method, apparatus for determining flight parameter safety thresholds for runway excursion risk

Abstract

The application provides a method and device for determining a flight parameter safety threshold of runway overrun risk, and belongs to the field of aviation safety. The method comprises the following steps: (1) determining whether a monotonicity requirement exists for a runway overrun risk factor of an airplane during an approach process; if not, the method proceeds to step (2), and if yes, the method proceeds to step (3); (2) determining a safety threshold at a single height, and then the method proceeds to step (4); (3) determining a safety envelope at multiple heights, wherein the safety envelope is a set of dynamic safety thresholds at multiple heights, and then the method proceeds to step (4); and (4) ending. The application provides a runway overrun risk control system from discrete to continuous and from node to process by combining a single-height safety threshold and a multiple-height safety envelope for flight parameters of the runway overrun risk of an airplane during landing, and provides a scientific operation guidance basis for the flight and training of a pilot.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of civil aviation safety, and in particular to a method and device for determining a flight parameter safety threshold for runway excursion risk. BACKGROUND

[0002] The current researches on the risk of runway excursion can be divided into two categories: one is based on the historical real runway excursion events, and the other is based on the QAR data (including the "black box" flight data recorder data). In terms of historical event data, early research focused on statistical analysis of accident location, such as Khatwa et al. analyzed the key factors of accidents in 1999, pointing out that factors such as pilot operation and weather conditions affect accidents (see Khatwa R, Helmreich R L. Flight safety foundation approach-and-landing accident reduction task force: analysis of critical factors during approach and landing in accidents and normal flight: data acquisition and analysis working group final report [J]. SAE Transactions, 1999, 108: 1173-1266.). Subsequent research developed to use airport data to comprehensively evaluate accident risk, such as Eddowes et al. proposed a risk analysis framework in 2001 (see Eddowes M, Hancox J, MacInnes A. Final report on the risk analysis in support of aerodrome design rules [R]. Warrington, UK: AEA Technologies plc, 2001.), focusing on the correlation between airport design rules and accident risk. Although this type of research has built a relatively complete system, it is mainly post-event analysis and cannot effectively warn real-time risks. The research direction of QAR data mainly revolves around flight parameter analysis and risk assessment model construction.For example, Wang et al. (2014) identified the rate of descent as an important risk factor by analyzing QAR data of long landing events (see Wang L, Wu C, Sun R. An analysis of flight quick access recorder (QAR) data and its applications in preventing landing incidents [J]. Reliability Engineering & System Safety, 2014, 127: 86-96.); Ayra et al. (2019) applied Bayesian network method to analyze the influence of multiple QAR parameters on the risk of overshooting the runway (see Ayra E S, Rios ID, Cano J. Bayesian network for managing runway overruns in aviation safety [J]. Journal of Aerospace Information Systems, 2019, 16(12): 546-558.); Chu et al. (2024) proposed a physical modeling method to calculate the relationship between braking distance and risk, which effectively predicted the risk of overshooting the runway (see Chu L, Liu Y, Fwa T F. Estimating runway overrun risks of landing aircraft [J]. Journal of Infrastructure Systems, 2024, 30(2): 361-385.). The research on the risk of overshooting the runway based on QAR data has covered multiple aspects such as flight performance analysis and risk assessment model.

[0003] In general, existing research on the risk of overshooting the runway mainly focuses on three aspects: (1) identifying the main risk factors, i.e., the flight parameters that have the risk of overshooting the runway; (2) comprehensively assessing the risk of overshooting the runway; (3) establishing a prediction model to predict the risk of overshooting the runway, ground speed, ground distance, etc. However, there are still problems: the safety threshold of specific risk factors is not clearly defined, and the guidance significance of specific pilot operations is relatively limited. For example: during the approach, what is the safe threshold of airspeed at an altitude of 500 feet, and what is the safety envelope composed of different thresholds as the altitude changes, which are difficult to give specific recommendations to pilots. SUMMARY

[0004] The purpose of the present application is to solve the problems existing in the prior art, and to provide a method for determining the safety threshold of the runway overrun risk factor, thereby providing a reference for civil aviation safety risk assessment and prevention and control as well as flight training under different scenarios.

[0005] The present application is realized by the following technical solutions:

[0006] A method for determining the safety threshold of the flight parameter of the runway overrun risk, the method comprising:

[0007] Step (1), for all the runway overrun risk factors of the aircraft during the approach process, it is judged whether there is a monotonicity requirement; if not, go to step (2), if yes, go to step (3);

[0008] Step (2), determine the safety threshold on a single height, and then go to step (4);

[0009] Step (3), determine the safety envelope on multiple heights, the safety envelope being a set of dynamic safety thresholds on multiple heights, and then go to step (4);

[0010] Step (4), end.

[0011] Further, the operation of determining the safety threshold on a single height in the step (2) comprises:

[0012] Step 21, set a candidate threshold set for a specific risk factor: take the 5% quantile of the risk factor in the flight sample as the lower limit, and the 95% quantile of the risk factor as the upper limit, generate M points in the closed interval formed by the lower limit and the upper limit by uniform sampling, and form the candidate threshold set of the risk factor;

[0013] Step 22, for each candidate threshold, divide the flight sample into two groups of 'high risk' and 'low risk' according to the candidate threshold, and calculate the corresponding KS statistics;

[0014] Step 23, obtain the optimal safety threshold.

[0015] Further, the KS statistics is calculated by the following formula:

[0016]

[0017] Wherein, KS(c) is the KS statistics of the candidate threshold c, representing the maximum difference of the residual runway length distribution functions of the corresponding high-risk flight sample and low-risk flight sample, y l is the residual runway length of the lth flight, is the high-risk flight sample set determined according to the candidate threshold c, n1 is the number of high-risk flight samples, n2 is the number of low-risk flight samples, and a is an independent variable of the distribution function.

[0018] Further, the operation of the step 23 includes: traversing the KS statistics corresponding to all candidate threshold values in the candidate threshold value set, and finding the candidate threshold value c that makes the KS statistics maximum. * The candidate threshold value c is determined according to the following formula: * The optimal safety threshold value of the specific risk factor.

[0019] Further, the operation of determining the safety envelope at multiple altitudes in the step (3) includes:

[0020] Step 31: Obtain grid points, and calculate the KS statistics on the grid points, wherein the grid points are composed of the candidate threshold value sets at different altitudes;

[0021] Step 32: Obtain the safety envelope by using a dynamic programming algorithm.

[0022] Further, the operation of the step 31 includes:

[0023] First, set the candidate threshold value set for the specific risk factor at different altitudes, take the 5% quantile of the risk factor in the flight sample at the specific altitude as the upper limit, take the 95% quantile of the risk factor as the lower limit, generate M points in the closed interval composed of the lower limit and the upper limit by uniform sampling, and form the candidate threshold value set of the risk factor at the specific altitude;

[0024] Combine the candidate threshold value sets at all altitudes to obtain grid points Wherein is the i-th candidate threshold value at the altitude h, h1, …, h N is the different altitudes considered, and M is the number of candidate threshold values at each altitude;

[0025] Finally, for each candidate value in the grid points The KS statistics is calculated by using the following formula:

[0026]

[0027] Wherein is the KS statistics of the candidate threshold value , y l is the residual runway length of the l-th flight, is the high-risk flight sample set determined according to the candidate threshold value , and is the low-risk flight sample set determined according to the candidate threshold value The determined low-risk flight sample set, n1 is the high-risk flight sample number, n2 is the low-risk flight sample number, and a is the independent variable of the distribution function.

[0028] Further, the dynamic programming algorithm of the step 32 is:

[0029] A set of candidate threshold values is found to maximize the sum of KS statistics of all heights; the set of candidate threshold values is obtained by using the following formula:

[0030]

[0031] Wherein, Indicates joint optimization of candidate threshold values for all heights, and a set of candidate threshold values is found to maximize the sum of KS statistics of all heights; Indicates a set of heights to be considered, and N is the number of heights to be considered, and h1 N ; c h Indicates the candidate threshold value corresponding to the height h; KS(c h ) is the KS statistic corresponding to c h , which is calculated by the formula (4) and introduces a monotonicity constraint condition

[0032] Further,

[0033] The operation of the step 32 includes:

[0034] Step 321, initialization stage: selecting the lowest height h1, initializing the optimal cumulative KS statistic of the i-th grid point of the height of the i-th grid point of the height h1, initializing the node path

[0035] Step 322, constraint recursive optimization: processing the optimal cumulative KS statistic of each height from low to high and recording the corresponding predecessor node path, the predecessor node being a grid point satisfying the monotonicity condition: screening the grid points in the previous height h k-1 that satisfy , selecting the maximum value from all cumulative KS statistics as the optimal cumulative KS statistic of the current grid point and recording the corresponding predecessor node path;

[0036] Step 323, generating a safety envelope: when the optimal cumulative KS statistics of all heights are calculated, the calculation is terminated; in all grid points of the highest height h N , the grid point with the maximum optimal cumulative KS statistic is selected The grid point is taken as a backtracking end point, a precursor node path recorded along the grid point is backtracked to the lowest height h1 in turn, and each height h of the backtracking path is collected k The candidate threshold value is taken as the optimal threshold value The safety envelope is arranged in ascending order of height.

[0037] Further, the precursor node path is obtained through the following formula:

[0038]

[0039] Wherein, j * is the optimal precursor node index, that is, the j that makes the maximum in all j satisfying .

[0040] The second aspect of the application also provides a terminal device, comprising: at least one processor and a memory;

[0041] The memory stores a computer program; and the at least one processor executes the computer program stored in the memory to realize the method for determining the flight parameter safety threshold of the runway overrun risk.

[0042] Compared with the prior art, the application has the following beneficial effects:

[0043] (1) The safety threshold of each key risk factor at a specified flight height is determined by optimizing the KS statistical quantity index. For a single height point, the optimal safety threshold of each key risk factor at a single height is determined, which can give a clear “high risk” or “low risk” prompt to the actual approach process.

[0044] (2) The joint optimization of the optimal threshold value at different heights is proposed to construct the safety envelope of the risk factor (i.e., a set of optimal safety thresholds). For the risk factor required to be monotonic at different heights, a set of dynamic safety thresholds is established through the joint optimization model, so that the risk factor at different heights can follow a decreasing (increasing) relationship, and the safety envelope formed by the optimal safety threshold changing with height in accordance with the monotonicity requirement is determined.

[0045] In summary, the application can determine the safety threshold of the flight parameter (risk factor) causing the airplane to overrun the runway at different heights during the approach process. The single-height safety threshold and the multi-height safety envelope jointly construct a full-range risk control system from discrete to continuous and from node to process, which is a key technical path for upgrading the aviation safety from experience management to data-driven decision-making, provides a scientific operation guidance basis for the flight and training of pilots, and improves the safety operation level of the airline. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 Flow chart of the method for determining the safety threshold in the present application.

[0047] Figure 2 Optimization schematic diagram of the dynamic programming algorithm constraint recursion in the second embodiment of the present application.

[0048] Figure 3 Safety envelope schematic diagram of the airspeed safety factor in the second embodiment of the present application. DETAILED DESCRIPTION

[0049] The present application will be further described in detail below with reference to the accompanying drawings:

[0050] To achieve the above object, the present application provides a method for determining the safety threshold of the flight parameter of the risk of aircraft running off the runway, i.e. the risk factor, which is referred to as the risk factor below. The method is based on QAR data and divided into two cases: for the risk factor without monotonicity requirement, only the safety threshold corresponding to the representative node height (single height) needs to be found to directly block the high-risk state; for example, if the runway deviation exceeds a certain range at 300 feet, it indicates that the aircraft is not stable and aligned with the runway, and immediate reflight can avoid subsequent accumulated deviation leading to running off the runway. For the risk factor with monotonicity requirement, a set of dynamic safety thresholds at multiple heights needs to be constructed, and the safety threshold needs to be dynamically decreased or increased with the decrease of height to construct the height-threshold decrease (increase) curve to force the aircraft to gradually adjust the state during the descent, which is the formation of the safety envelope. The dynamic safety envelope cuts off the risk transmission path through the threshold sequence, and at the same time meets the requirement of the pilot that "the lower the height, the more cautious the operation"; for example, the airspeed envelope requires the airspeed to decrease with the decrease of height to prevent high airspeed from entering the runway to cause landing risk.

[0051] Specifically, the method comprises the following steps:

[0052] Step (1), for the risk factor of the aircraft running off the runway during the approach, it is judged whether it has monotonicity requirement. If the risk factor does not have monotonicity requirement, go to step (2), and after the operation of step (2) is completed, the process is ended; if the risk factor has monotonicity requirement, go to step (3), and after the operation of step (3) is completed, the process is ended. The monotonicity of the risk factor refers to that the value of the risk factor changes in a single direction with the decrease of height during the approach of the aircraft. For example, the airspeed of the aircraft should decrease with the decrease of height.

[0053] Preferably, step (0) is added before step (1) to pre-process the parameter of the flight sample data to eliminate abnormal data caused by sensor noise or operation error.

[0054] Step (2), determining the safety threshold at single height

[0055] The single height refers to the height value of a representative node in the descent process. For a specific node height value, the safety threshold at a representative flight height (such as 500, 300, 200, 100, and 50 feet) is determined using the KS (Kolmogorov-Smirnov) statistic for a given risk factor (such as airspeed). First, a candidate threshold set is set for each risk factor, and the flight sample is divided into "low risk" and "high risk" groups according to the candidate threshold. The flight sample is a batch of flight data included in the calculation. The KS statistic of the difference in the residual runway length (defined as the distance from the runway end when the ground speed of the aircraft decreases to 80 feet after landing) distribution of the two groups of flights is calculated, and the threshold that maximizes the KS statistic is selected as the optimal safety threshold.

[0056] The specific implementation process is as follows:

[0057] Step 21, construction of the candidate threshold set: for the target risk factor (as shown in Table 2), the 5th percentile of the risk factor in the flight sample is taken as the lower limit, the 95th percentile is taken as the upper limit, and then evenly take points in the closed interval between the upper limit and the lower limit, finally obtain M segmentation points, form the candidate threshold set of the risk factor.

[0058] Step 22, for each candidate threshold c in the candidate threshold set, the flight sample is divided into "high risk" and "low risk" two groups, and the specific division of the high risk and low risk flight sample is related to the selected specific risk factor. Taking the airspeed of 500 feet as an example, the flight sample data with airspeed of 500 feet exceeding c is called "high risk" sample, and the flight sample data with airspeed of 500 feet lower than c is called "low risk" sample; taking the heading deviation of 500 feet as an example, since the heading deviation has left-right symmetry, the "high risk" sample is defined as the absolute value of the heading deviation being greater than or equal to c. Further, the value of the candidate threshold c may be different at different heights.

[0059] For each candidate threshold c in the candidate threshold set, the KS statistic is calculated: according to the data of the flight sample, the KS statistic of the "residual runway length" (defined as the distance from the runway end when the ground speed of the aircraft decreases to 80 knots after landing) distribution of the two groups of flights is calculated, such as formula:

[0060]

[0061] Where y l is the residual runway length of the lth flight, and are the sample sets of high-risk flights and low-risk flights determined according to the candidate threshold c, and n1 and n2 are the numbers of high-risk flights and low-risk flights in the samples, respectively; and The definition of KS(c) is related to the candidate threshold c; a is the independent variable of the distribution function, which is a continuous variable, and is uniformly selected from the value range of the flight sample set of the risk factor.

[0062] For the candidate threshold c, the KS(c) statistic index is the maximum difference between the residual runway length distribution functions of the corresponding high-risk and low-risk flights, which measures the overall maximum deviation of the residual runway length distributions of high-risk and low-risk flights. Specifically, the empirical distribution function of the residual runway length of high-risk flights is:

[0063]

[0064] The empirical distribution function of the residual runway length of low-risk flights is:

[0065]

[0066] a is the independent variable of the distribution function, and the difference between the two is F1(a)-F2(a), and KS(c) is obtained by taking the upper limit value of a through the sup function, as shown in formula (1).

[0067] Step 23, obtaining the optimal safety threshold: traversing all candidate thresholds in the candidate threshold set, finding the threshold that maximizes the KS statistic by solving the optimization problem max c KS(c), and determining the threshold c * that maximizes the KS statistic as the optimal safety threshold of the risk factor under this condition, and realizing the quantitative definition of the influence of the risk factor.

[0068] At this point, the safety threshold of single height is output, the calculation is completed, and the operation is ended.

[0069] Step (3), determining the safety envelope for multiple heights

[0070] For risk factors with monotonicity requirements (for example: in the process of final approach, airspeed should gradually decrease, and the safety threshold at different heights should also decrease with height), construct a safety envelope that meets the monotonicity requirements. Specifically, take the sum of the KS statistics at all heights as the objective function, and add the monotonicity constraint condition. Use the grid algorithm and dynamic programming algorithm to solve the optimization problem, and construct the optimal threshold combination at different heights, which forms a safety envelope based on flight height. If the flight exceeds the envelope, there is a high risk.

[0071] The selection of the candidate threshold set is the same as the operation of step 21 in step (2). For the flight sample data, by finding a set of candidate thresholds, so that the sum of KS statistics of all altitudes is maximum, the function is as follows:

[0072]

[0073] wherein is the set of altitudes to be considered (h1< h2< … h N ), N is the number of altitudes to be considered, c h represents the candidate threshold corresponding to the altitude h, and KS(c h ) is converted into the following formula by formula (1):

[0074]

[0075] The KS statistics corresponding to c h is calculated, and the constraint condition is introduced to ensure that the candidate threshold strictly follows the rule of decreasing with the decrease of altitude; represents the joint optimization of the candidate threshold c h for all altitudes. The final goal is to find the value of c h , so that the sum of KS statistics at all altitudes is maximum, so as to determine a set of optimal safety thresholds, i.e. safety envelope.

[0076] The specific implementation process is as follows:

[0077] Step 31, calculate the KS statistics on the grid points (i.e. the numerical grid composed of candidate thresholds c h at each altitude): first, at each altitude h, take the 5% quantile of the risk factor at this altitude in the flight sample as the lower limit, and the 95% quantile as the upper limit, then take points uniformly in the closed interval between the upper limit and the lower limit, finally obtain M segmentation points at this altitude, forming the candidate threshold set of the risk factor. Combine the candidate threshold sets at all altitudes to obtain the grid points wherein is the i-th candidate threshold at altitude h, h1,…,h N is the different altitudes to be considered, and M is the number of candidate thresholds at each altitude. In this way, it is ensured that the grid points uniformly cover the distribution area of the flight sample data.

[0078] Then, for each grid point , based on the sample data and formula (1) conversion calculation Specifically, as follows:

[0079]

[0080] wherein, and Based on candidate thresholds The identified high-risk and low-risk flight sample sets, where n1 and n2 are the number of medium-high risk flights and low-risk flights, respectively.

[0081] Calculate the KS statistic up to all grid points at all heights. Once everything is confirmed, the algorithm ends. This provides the basic data for subsequent solutions.

[0082] Step 32: Dynamic Programming Algorithm Optimization to Obtain the Safety Envelope: Based on dynamic programming, the optimal cumulative KS value at each height is calculated recursively to avoid exhaustively searching all possible path combinations. A greedy piecewise maximization algorithm is used to select the current optimal path at each step, and the optimal solution is obtained through cumulative calculation. Thus, among the candidate thresholds generated by the grid algorithm, a path is found that strictly increases (decreases) with increasing height and has the largest sum of KS statistics. The algorithm steps are as follows:

[0083] Step 321, Initialization Phase: Select the lowest height h1 and calculate the grid points at that height. The optimal cumulative KS statistic is equal to the KS statistic corresponding to the grid point since there is no preceding path at the lowest altitude. Initialize node path

[0084] Step 322, Constraint Recursive Optimization: Process each height h sequentially from low to high. k , for h k Each candidate threshold Filter the previous height h k-1 China satisfies From the grid points that meet the conditions, select the path with the largest optimal cumulative KS statistic, update the optimal cumulative KS value of the current candidate point, and update the node path.

[0085] Specifically, for k = 2, ..., N, for h k All grid points below (in h) k The following algorithm is applied sequentially to the i-th candidate threshold point at the height:

[0086] 1) Filtering by criteria: Find the previous height h k-1 All grid points j that satisfy the monotonicity condition are taken as predecessor nodes, such that... Its threshold is This ensures the monotonicity constraint that the threshold increases with height.

[0087] 2) Select the optimal path: in the precursor node meeting the monotonicity condition, calculate its cumulative contribution, that is, the cumulative KS statistics, using the formula:

[0088] Cumulative

[0089] Where, is the KS statistics calculated alone for the current threshold, is the maximum cumulative KS statistics recorded for the precursor node threshold.

[0090] From the cumulative KS statistics of the effective precursor node, select the maximum value as the optimal cumulative KS statistics of the current grid point:

[0091]

[0092] Select the path with the optimal cumulative KS statistics, specifically, select the maximum value from the cumulative KS statistics of all effective precursor nodes as the optimal cumulative KS statistics of the current grid point , and record the corresponding precursor node path, the path expression is:

[0093]

[0094] Where, j * is the optimal precursor node index.

[0095] 3) Update the optimal loss: update the optimal statistics of all paths, the update formula is:

[0096]

[0097] For each grid point of the next height , the above conditions are screened, the optimal path is selected, and the optimal loss is updated.

[0098] Step 323, generate the safety envelope: when all heights of are calculated, the calculation is terminated. After processing all heights, in all grid points of the highest height h N , select the grid point with the maximum optimal cumulative KS statistics as the backtracking end point, along the precursor node path recorded by the grid point, backtrack to the lowest height layer h1 in turn, collect the threshold of each height h k on the backtracking path as the optimal threshold , and arrange them in ascending order according to the height to form the safety envelope sequence.

[0099] At this point, the multi-height safety envelope is output, the calculation is exited, and the operation is ended.

[0100] The technical solutions will be described clearly and completely by examples in combination with the drawings of the application. The data used in the examples is the QAR data of A320 aircraft at Dali Airport from 2019 to 2020, and the flight sample contains 3123 flights. After feature extraction and dimension reduction processing of flight parameters, and removing outliers, the target risk factor in the examples is determined as airspeed, pitch angle, glide path deviation, and heading deviation.

[0101] The core of the application is to determine the safety threshold of the target risk factor at a specified height by considering the remaining runway length when the ground speed of the aircraft after landing is reduced to 80 knots, and by using the KS statistic.

[0102] Example 1, determining the safety threshold at a single height

[0103] The present example provides a method for determining a single-height safety threshold. At a specified height, all flights are divided into “high-risk” and “low-risk” categories using the threshold value of the specified risk factor as the split node, and the threshold value that maximizes the difference in remaining runway length distribution between “high-risk” and “low-risk” flight data is found as the optimal safety threshold. The specific steps include:

[0104] Step 11, candidate threshold set setting and grouping

[0105] At a specified height h (as shown in Table 2, the heights are 50, 100, 200, 300, and 500 feet), the value range of the risk factor is determined according to the flight sample, such as the airspeed, pitch angle, glide path deviation, and heading deviation data in Table 2.

[0106] The 5th percentile of the specified risk factor in the flight sample is taken as the lower bound, and the 95th percentile is taken as the upper bound. Then, evenly take points in the closed interval between the lower bound and the upper bound, and finally obtain M split points to form a candidate threshold set. For each candidate threshold c, the flight sample is divided into high-risk flights and low-risk flights. For example, flights with airspeed values greater than or equal to c at height h are classified as high-risk, and the rest are classified as low-risk.

[0107] Step 12, calculate the KS index for candidate threshold c

[0108] I. Calculate the cumulative distribution functions of the remaining runway lengths of the high-risk and low-risk flight samples according to formulas (2) and (3), and denote them as F1(a) and F2(a) respectively, and substitute them into formula (1);

[0109] II. Calculate the KS statistic of the candidate threshold using formula (1):

[0110]

[0111] Step 13, optimal value threshold solving

[0112] The threshold that maximizes KS(c) is selected as the optimal safety threshold at this height. Take the airspeed at 50 feet as an example. In the flight sample data, the 5% quantile of airspeed at 50 feet is 123.10, and the 95% quantile is 148.60. From 123.10 to 148.60, there are M = 51 candidate thresholds with an interval of 0.5. And the KS(c) corresponding to each c is calculated, as shown in Table 1. It can be seen that when c = 138.10, KS(c) takes the maximum value 0.44, so 138.10 is determined as the safety threshold at 50 feet (under the condition of not considering the monotonicity constraint).

[0113] Table 1: Candidate threshold c of airspeed at 50 feet and its corresponding KS(c)

[0114]

[0115]

[0116]

[0117] By the same method, without the monotonicity constraint, the safety threshold of the four key risk factors at the five representative heights can be output in turn by using steps 11, 12, and 13, respectively, as shown in Table 2. Take the airspeed at 50 feet as an example. The safety threshold is 138.10, the number of low-risk flights (flights with airspeed at 50 feet lower than 138.10) is 2717, and the number of high-risk flights (flights with airspeed at 50 feet higher than 138.10) is 406; the average remaining runway of low-risk flights is 4766.00 feet, and the average remaining runway of high-risk flights is 4179.59 feet; the average difference in remaining runway length is 4766.00-4179.59 = 586.41 feet.

[0118] Table 2: Safety threshold of four key risk factors at five heights

[0119]

[0120]

[0121] Example Two: Obtain a multi-height safety envelope

[0122] This example provides a method for determining a multi-height safety envelope. For parameters that need to be monotonically changed (for example, airspeed should decrease with height), a set of safety thresholds that satisfy the monotonicity constraint is constructed to maximize the overall risk discrimination ability. The specific steps include:

[0123] Step 21, Calculate KS statistics of grid points

[0124] Pre-set representative height sequence h1 = 50 feet, h2 = 100 feet, h3 = 200 feet, h4 = 300 feet, h5 = 500 feet, i.e. N = 5, Perform initialization phase: for each height Determine the value range of airspeed according to flight sample data, and divide it into M grid points according to the quantile point method

[0125] For each grid point Based on sample data and formula (5) Calculate Until the statistics of all grid points at all heights are determined, the algorithm ends.

[0126] Step 23, Dynamic programming algorithm obtains safety envelope

[0127] I. Initialization state: record the lowest height h1 = 50, initialize the optimal cumulative statistics of the i-th grid point at this height

[0128] II. Constraint recursive optimization: traverse all heights {h2,..., h N}(all heights in the example are 100, 200, 300, 500) from low to high, for all grid points at h k Perform the following operations:

[0129] 1) Conditional screening: find all grid points j at the previous height h k-1 that satisfy the monotonicity condition as predecessor nodes, so that Its threshold is

[0130] 2) Select the optimal path: among the predecessor nodes that satisfy the monotonicity condition, calculate their cumulative contribution, i.e. cumulative KS statistics, using formula (6) to calculate.

[0131] From the cumulative KS statistics of the effective predecessor nodes, select the maximum value as the optimal cumulative KS statistics of the current node, and use formula (7) to calculate.

[0132] Select the path with the optimal cumulative KS statistics, specifically, select the maximum value from the cumulative KS statistics of all effective predecessor nodes as the optimal cumulative KS statistics of the current node , and use formula (8) to record the corresponding predecessor node path.

[0133] ​​3) Update the optimal loss: update the optimal statistics of all paths, update formula (9)

[0134] For each grid point of the next height The above conditions are screened, the optimal path is selected, and the optimal loss is updated.

[0135] III. Calculation termination: when all heights are calculated, the calculation is terminated. After processing all heights, in all grid points of the highest height h N , the grid point with the maximum optimal cumulative KS statistic is selected as the backtracking end point, and the predecessor node path recorded along the grid point is backtracked in turn to the lowest height h1, and the threshold value of each height h k on the backtracking path is collected as the optimal threshold value , which is arranged in ascending order of height to form a sequence.

[0136] After executing the above steps, a set of optimal threshold combinations is output to form a safety envelope, as shown in Figure 3 The safety envelope generated based on the above optimization method shows a gradually decreasing airspeed safety threshold curve as the flight height decreases. This curve starts from a higher height, with a higher airspeed safety threshold, and as the height decreases, the airspeed safety threshold gradually decreases, showing a clear decreasing trend. According to test calculations, after adding the monotonicity constraint, the optimal airspeed safety thresholds at 500 feet, 300 feet, 200 feet, 100 feet, and 50 feet are 147.56, 143.41, 142.58, 142.24, and 138.08 knots, respectively. Without the monotonicity constraint, the optimal airspeed safety thresholds at 500 feet, 300 feet, 200 feet, 100 feet, and 50 feet are (as shown in Table 2) 146.50, 141.12, 139.07, 142.50, and 138.10 feet, respectively, which obviously do not meet the actual requirements of the airspeed process. The results obtained after adding the monotonicity constraint are more reasonable.

[0137] Figure 3 Each point on the curve represents the optimal airspeed safety threshold at a specific height, which is obtained through the joint optimization algorithm, ensuring that the airspeed safety threshold at different heights satisfies the monotonic decreasing constraint condition. Specifically, when the airspeed is higher than the optimal safety threshold, the remaining runway distance decreases significantly, and the risk of running off the runway increases; when the airspeed is lower than the optimal safety threshold, the remaining runway distance increases significantly, and the risk of running off the runway decreases. Therefore, this can be used to further dynamically adjust the flight strategy, providing more accurate decision support for pilots, and ensuring the safety of flights under various flight conditions.

[0138] The above technical solution is only one embodiment of the present application, and for those skilled in the art, on the basis of the disclosed principles, various types of improvements or modifications can be easily made, and the technical solution described in the above specific embodiments is not limited. Therefore, the above description is only preferred, and is not limited in meaning.

Claims

1. A method of determining a flight parameter safety threshold for a runway overrun risk, characterized by: The method comprises: Step (1), judging whether there is monotonicity requirement for the risk factor of the aircraft running off the runway in all approach processes; if not, going to step (2), if yes, going to step (3); The monotonicity is that the value of the risk factor of the aircraft running off the runway in the approach process changes in a single direction as the height decreases; Step (2), determining the safety threshold at a single height, and then going to step (4); The single height is the height value of a representative node of the aircraft in the descending process; Step (3), determining the safety envelope at multiple heights, wherein the safety envelope is a set of dynamic safety thresholds at multiple heights, and then going to step (4); Step (4), ending.

2. The method of determining flight parameter safety thresholds for runway overrun risk according to claim 1, characterized in that: The operation of determining the safety threshold at a single height in step (2) comprises: Step 21, setting a candidate threshold set for a specific risk factor: taking the 5% quantile of the risk factor in the flight sample as the lower limit, and taking the 95% quantile of the risk factor as the upper limit, generating M points in the closed interval formed by the lower limit and the upper limit by uniform sampling, and forming the candidate threshold set of the risk factor; Step 22, for each candidate threshold, dividing the flight sample into two groups of "high risk" and "low risk" according to the candidate threshold, and calculating the corresponding KS statistics; Step 23, obtaining the optimal safety threshold.

3. The method of determining flight parameter safety thresholds for runway overrun risk according to claim 2, characterized in that: The KS statistics is calculated by the following formula: Equation (1) wherein, is a KS statistic representing the maximum difference of the residual runway length distribution functions of the corresponding high-risk flight samples and low-risk flight samples, is the residual runway length of the i-th flight, is the high-risk flight sample set determined according to the candidate threshold value is the low-risk flight sample set determined according to the candidate threshold value is the number of high-risk flight samples, is the number of low-risk flight samples, is the independent variable of the distribution function.​​​​ 4. The method of determining a flight parameter safety threshold for a runway excursion risk according to claim 2 or 3, characterized in that: The operation of the step 23 comprises: finding the candidate threshold value corresponding to the maximum KS statistics in all candidate threshold values in the candidate threshold set The candidate threshold value The optimal safety threshold value as a specific risk factor.

5. The method of determining flight parameter safety thresholds for runway overrun risk of claim 1, wherein, The operation of determining the safety envelope at multiple heights in step (3) comprises: Step 31, obtaining grid points and calculating the KS statistics on the grid points, wherein the grid points are formed by the candidate threshold sets at different heights; Step 32, obtaining the safety envelope by using a dynamic programming algorithm.

6. The method of determining flight parameter safety thresholds for runway overrun risk according to claim 5, wherein: The operation of step 31 comprises: First, for a specific risk factor at different heights, set a candidate threshold set, take the 5% quantile of the risk factor in the flight sample at a specific height as the upper limit, and take the 95% quantile of the risk factor as the lower limit, generate M points in the closed interval formed by the lower limit and the upper limit by uniform sampling, and form the candidate threshold set of the risk factor at the specific height; Set up the candidate thresholds at all heights and obtain the grid points. ,in For height The first One candidate threshold, For the different heights considered, The number of candidate thresholds for each height; Finally, for each candidate value in the grid The KS statistic is calculated using the following equation: Equation (5) in Candidate threshold KS statistic, For the first The remaining runway length for each flight To be based on candidate threshold The identified high-risk flight sample set, To be based on candidate threshold The identified low-risk flight sample set, The number of samples from high-risk flights. The number of samples for low-risk flights. is the independent variable of the distribution function.

7. The method of determining flight parameter safety thresholds for runway overrun risk according to claim 6, characterized in that: The dynamic programming algorithm of step 32 is: Find a set of candidate thresholds that maximize the sum of KS statistics at all heights; The set of candidate thresholds is obtained by the following formula: wherein, represents jointly optimizing the candidate thresholds for all heights, finding a set of candidate thresholds such that the sum of KS statistics for all heights is maximized; represents the set of heights to be considered, is the number of heights to be considered, and ; represents the height corresponding candidate threshold; is corresponding KS statistic, calculated from the formula (4) and introducing the monotonicity constraint : Formula (4) wherein, is the remaining runway length for the flight, is the sample set of high-risk flights determined according to the candidate threshold , is the sample set of low-risk flights determined according to the candidate threshold , is the number of high-risk flight samples, is the number of low-risk flight samples.

8. The method of determining flight parameter safety thresholds for runway overrun risk according to claim 7, characterized in that: The operation of step 32 comprises: Step 321, initialization stage: select the lowest height , initialize the optimal cumulative KS statistics of the first grid point at the height , , is the KS statistics of the first grid point at the height , initialize the node path Path { } }; Step 322, constraint recursive optimization: process the optimal cumulative KS statistics of each height in turn from low to high , and record the corresponding predecessor node path, the predecessor node being a grid point satisfying the monotonicity condition: screen the grid points in the previous height that satisfy , select the maximum value from all the cumulative KS statistics as the optimal cumulative KS statistics of the current grid point , and record the corresponding predecessor node path; Step 323, Generate safety envelope: When the optimal cumulative KS statistic for all altitudes is obtained. The calculation terminates when all values ​​are calculated; at the highest altitude. Among all grid points, select the one with the largest optimal cumulative KS statistic. Using the grid point as the backtracking endpoint, the process backtracks sequentially along the predecessor node path recorded at that grid point to the lowest height. Collect each height on the backtracking path The candidate threshold is used as the optimal threshold The safety envelope is formed by arranging the lines in ascending order of height.

9. The method for determining the flight parameter safety threshold of the risk of running off the runway according to claim 8, characterized in that: The predecessor node path is obtained by the following formula: Path = Path ∪{ } Equation (8) wherein, is the optimal predecessor node index, i.e., for all .​​​ 10. A terminal device, comprising: Comprise: At least one processor and a memory; The memory stores a computer program; The at least one processor executes the computer program stored in the memory to realize the method for determining the flight parameter safety threshold of the risk of running off the runway according to any one of claims 1-9.

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