Research on Vertical Overlap of the Paired Approach Based on QAR

This paper presents a method to calculate vertical overlap probability based on the position error caused by pilot control. Firstly, a fuzzy correlation model is established and combined with Quick Access Recorder (QAR) data. The correlation rules between QAR parameters and vertical position error are mined, and the relevance is calculated according to the rules. The results show that the correlation between the control column position and the vertical position error is the strongest. According to the flight dynamics principle, the Vertical Attitude Adjustment Model (VAAM) of an aircraft during the approach process is then established. The Pilot Operating Model (POM), which describes different actions taken by pilots when they encounter different position errors, is also created by employing the concepts of the Markov decision process. The VAAM can restore the process of changing the attitude of the aircraft by the pilot operating column and can simulate the position error of the aircraft in the approach process when combined with the POM. Based on the previous simulated result and considering the overlap condition of the Interval Management (IM) aircraft overlap, the vertical overlap process in the paired approach can then be simulated. We employ MATLAB to carry out numerous simulations. Changing the accuracy of pilot operation in the simulations show that the lower the accuracy, the greater the overlap probability and frequency. However, when the accuracy is between 61% and 73% (61%–73% is the range of operational accuracy based on QAR data analysis), the vertical overlap probability and frequency are maintained at about 5% and 20 flights per hour, respectively.


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The concept of the paired approach was first presented at a 20 workshop held at NASA Langley Research Center in 1996 21 [1] and can effectively improve approach efficiency. Four 22 years later, Hammer [2] proposed a 3 • offset approach pro- of the IM aircraft, not only to ensure a safe distance from 28 the target aircraft but also to avoid the wake generated by the 29 The associate editor coordinating the review of this manuscript and approving it for publication was Rosario Pecora . target aircraft. As both conditions will result in operational 30 risks that are different from the traditional approach, many 31 scholars have studied the safety of closely spaced parallel 32 runway paired approaches. Existing research results of paired 33 approach safety can be divided into two categories: the study 34 of wake safety interval and the study of collision risk. 35 In 2005, Teo et al. [3] proposed a real-time dangerous 36 area calculation method to ensure the safety of the paired 37 approach, which could warn an aircraft to take evasive action 38 when a wrong approach occurred, thus avoiding collision. 39 Madden [4] analyzed the effect of two aircraft' speed on 40 safety from the point of view of kinematics and obtained 41 the longitudinal safety interval between the paired aircraft. 42 Guerreiro et al. [ When implementing the paired approach procedure, the lon-87 gitudinal spacing between two aircraft must comply with the 88 following requirements: 89 (1) Avoid airframe contact: the rear aircraft must be kept 90 far enough away from the front aircraft to prevent collision; 91 (2) Avoid wake contact: the rear aircraft shall keep close 92 enough to the front aircraft to avoid the wake of the front 93 aircraft. 94 Because the assessment of collision risk can be regarded 95 as the premise of calculating the safety interval, an accurate 96 calculation method is needed to evaluate the collision risk. 97 Collision risk is usually calculated from three dimensions 98 [18], [20], the basic parameters of which are vertical, lon-99 gitudinal, and lateral overlap probability and frequency. The 100 overlap in the vertical dimension is caused by the vertical 101 position error. The aircraft that deviates from the glide slope 102 to a certain extent may collide with the paired aircraft in the 103 vertical direction. The conflict process is shown in Figure. 1. 104 Previous research has tended to analyze the position error 105 directly from the point of the error distribution without con-106 sidering the effect of pilot operation. 107 In view of this, this paper employs pilot operation pro-108 cess and operation process recording Quick Access Recorder 109 (QAR) data to determine the operating parameters that have 110 the greatest correlation with the vertical position error (glide 111 deviation in the QAR parameters) during an approach. The 112 Vertical Attitude Adjustment Model (VAAM) is established 113 according to the parameters, and the Pilot Operating Model 114 (POM) is established using the concept of the Markov deci-115 sion process based on the parameter statistics. Finally, accord-116 ing to the motion characteristics of the wake and the vertical 117 overlap condition, a simulation model of paired approach 118 vertical overlap is obtained. By running the simulation model, 119 the vertical overlap time and overlap times are counted, 120 and then the overlap probability and frequency are calcu-121 lated. The technical roadmap for this article is shown in 122 Figure. 2. The differences between the research process of 123 this paper and the general methods are shown in Table. 1.

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In this paper, the influence of 20 related factors on ver-125 tical error was comprehensively analyzed using the fuzzy 126 correlation method to find the most relevant parameters, and 127 the internal mechanism of the vertical error was analyzed. 128 Moreover, on the basis of considering human factors, a pilot 129 VOLUME 10, 2022    In the approach segment, the direct cause of the vertical 143 overlap of the paired aircraft is the vertical position error of 144 the target aircraft and IM aircraft; that is, the vertical position 145 deviation from the nominal track. While the position error is 146 caused by pilot operation, it is also influenced by navigation 147 equipment and the environment. A QAR can record the oper-148 ation state of every system completely, accurately recording 149  the data of pilot operation, navigation, and atmosphere envi-  The parameters associated with the above process are iden-156 tified by combining the QAR data. The summarized parame-FCM [21] gives weight to the data and the clusters, which 167 indicates the degree to which the data belongs to a cluster. 168 The specific algorithm of FCM is: In the formula, u ij represents the initial membership 173 degree of data x i belongs to class j, i = 1, 2, . . . p, j = 174 1, 2, . . . , q, p is the number of data, and q is the number of 175 clusters.

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(2) Compute the Cluster Center c here, k represents the k-th iteration, and m is the weighted 179 index of the membership matrix.

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(3) The iteration of the membership matrix U (k) and U (k+1) 181 is where U (k) is the membership matrix after the k-th iteration, 184 and * is the measure of distance.

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(4) Iterative judgment. If U (k+1) − U (k) < ε, the itera-186 tion ends; otherwise, the result will be substituted back into 187 step 2, where ε is the error threshold.  where the membership in u ij requires: The QAR parameter dataset is recorded as B = b x,y N ×n , 192 where b x,y is the value of the x-th sample on the attribute 193 z 1 , z 2 , . . . , z n ; the fuzzy membership degree is represented by The support of the fuzzy term sets Sup Z | R is In the formula, a x (z r ) is the corresponding membership

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The support for correlation rules is The confidence of correlation rules is The support indicates the importance of the rules, and the 213 confidence indicates the reliability of the rules. When the sup-214 port and the confidence of the correlation rules satisfy both 215 the minimum set of support and confidence, the correlation 216 rules are called strong rules.

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The process of mining correlation rules using the Apriori 218 algorithm [9] is shown in Figure. 4. Firstly, the frequency of 219 occurrence of a fuzzy item set C1 is counted, the support is 220 calculated, the fuzzy item sets smaller than the minimum set 221 of support are deleted, and a frequent fuzzy set is obtained 222 as L1. The next operation is the connection, where L1 and 223 L1 are connected to obtain the candidate two fuzzy sets C2. 224 The candidate fuzzy sets with subsets that are infrequent 225 items in C2 are deleted. If the result of the deleted is an 226 empty set, then L1 is the largest fuzzy frequent item set; 227 otherwise, the frequent fuzzy set L2 with two items is derived. 228 The above steps are looped until the result is an empty set. 229 Finally, the confidence of the correlation rule is calculated by 230 Equation (8) from the fuzzy frequent set.

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The correlation between parameters can be quantified by 232 Equation (9), as shown at the bottom of the next page, with the 233 help of the support and confidence correlation rules, where q 234 is the number of clusters.

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The QAR data of the same B737-800 aircraft landing at 236 the same airport within a week was selected as the research 237 data set. The approach segment studied was from the time 238 the aircraft intercepted the glide path to the landing gear 239 touching the ground, and a total of 1694 data sets were 240 obtained. According to the 20 QAR parameters related to 241 vertical position errors identified in the previous paper, the 242 FCM algorithm was used to operate fuzzy pre-processing. 243 The number of clusters was 3, which corresponded to small, 244 medium, and large fuzzy terms, respectively; the weighted 245 index of the membership matrix m was set to 2. The clustering 246 results are shown in Table 3.

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The clustering results were input into the Apriori algo-248 rithm, and the confidence was set to 60%. When the minimum 249 support was 40%, a total of 6,635 correlation rules were  Table 4.  Table 2 describe the reason for this. In fact, the ''Small 266 glide deviation'' data is not closer to the location of the 267 glide path but is the location below the glide path. When the 268 glide deviation is less than 0, the smaller the value is, the 269 farther the aircraft is under the glide path. All ''Medium glide 270 deviation value'' data is approximately 0, which records the 271 time when the aircraft approaches the glide path. According 272 to the set of support in the Apriori algorithm, events with the 273 support of more than 40% can be output, which shows that the 274 probability of a large glide deviation produced by the aircraft 275 is very small.

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It can be observed more intuitively in Table 3 that among 277 the QAR parameters related to pilot operation, the control 278 column position has the highest frequency of occurrence. 279 Equation 9 can be used to calculate the maximum correlation 280 between the control column position and the glide deviation, 281 which is 51.17%. Therefore, the control column factor is the 282 focus when analyzing the vertical overlap probability.

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In order to study the effect of the control column on the 285 vertical position error, the mapping relationship between the 286 control column and the pitching attitude of the aircraft must 287 first be determined. This is because, in the approach process, 288 the change of aircraft pitch attitude will cause the change 289 of glide deviation, which affects the calculation of overlap 290 probability.

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(1) The push/pull of the control column causes the elevator to 293 experience a downward/upward deflection;

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(2) The downward/upward deflection of the elevator causes 295 an increase/decrease of the horizontal tail lift;

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(3) The change of the horizontal tail lift will produce a 297 pitching moment to the center of gravity of the aircraft, which 298 will change the pitch angle of the aircraft.

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In Process (1), there is a corresponding relationship 300 between the control column and the elevator: When the aircraft is stationary, an angle of the control column 302 corresponds to an angle of the elevator. This rule is called the 303 direct correspondence rule of the elevator and control column. 304 Figure 5 shows the corresponding rule fitted from the QAR 305 data. It can be seen that the control column angle is positive 306 and the elevator angle is negative when the pilot pushes the 307 control column. The elevator angle is about 4.5 • when the 308 control column position is 0 • . This is because the moment 309 generated by the engine thrust is the lift moment when the 310 aircraft is in a smooth configuration and is also due to the 311 (9) VOLUME 10, 2022   The change of the attack angle is caused by the change 329 of the moment. When calculating the pitching moment due 330 to the aerodynamic force of the horizontal tail, the model 331 is built only for the horizontal tail, so we can consider the 332 aircraft as the model shown in Figure. 7. To be conservative, 333 we assume the horizontal tail is a cuboid, which will generate 334 more moment, and the cylinder is the fuselage.  The VAAM [23] of the aircraft is:

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As the pilot's operation is only related to the current air-362 craft state (glide deviation), the process is Markovian. Thus, 363 we build a pilot operation model based on the concept of the 364 Markov process.

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The flight state set of the aircraft is S = {s 1 , s 2 , · · · , s n }, 366 the pilot action set is D = {d 1 , d 2 , · · · , d m }, and the proba-367 bility that the pilot will take action d m under the condition of 368 the aircraft s n is P nm = P ( d m | s n ). The state-action matrix P 369 [24] is then defined as: For any i ∈ (1, n) , m k=1 P ik = 1. The state at a certain time t 372 of the paired approach is S t , and then the state at time t + 1 is 373 s t+1 = s t + s. Among them, where δ j is the glide-path angle set by the flight procedure. 377 When calculating ω z , the control column angle is d ∈ D. 378 The POM and the whole approach process are described in 379 Figure. 8.

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Obviously, when the pilot takes an action in any state, the 381 probability is different and the matrix P will change, affecting 382 the whole approach process. Here, we introduce operational 383 accuracy P Correct , which is defined as the probability of the 384 VOLUME 10, 2022 pilot taking the correct action when the aircraft is in a certain 385 state.
where C Correct is the number of times the pilot has taken the 388 correct action, and C A is the total number of actions taken for 389 the pilot. The criteria for judging the correct action are:  (16).  In the case of the paired approach, vertical overlap is con-432 sidered to have occurred when the IM aircraft enters the wake 433 of the target aircraft in the vertical dimension or overlaps with 434 the fuselage of the target aircraft. The probability of vertical 435 overlap P z is shown in Equation (17): In the formula, T L z1 (t)>h(t)>L z2 (t) represents the time that the 438 IM aircraft is in the vertical overlap area during the approach 439 segment, and T is the total time required for the flight in the 440 final approach segment.

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The vertical overlap frequency N z is represented as:  same aircraft landing at the same airport. The direct corre-465 spondence law of the control column is: In the simulation results. Each line represents the glide 485 slope error in each simulation. Some lines have sudden 486 upward increase, which is due to the increase of glide slope 487 error caused by the pilot's wrong operation. The black thick 488 line in the figure is the average value, representing the overall 489 trend. The amplitude and frequency of the glide deviations 490 that are greater than 0 are larger than those less than 0. This 491 same rule is reflected in Figure. 15. This phenomenon occurs 492 because the pilots often draw the control column in the final 493 approach segment to avoid unsafe incidents caused by a low 494 descending height. 495 Figure 15 shows the glide deviation data recorded by the 496 QAR of a certain aircraft at the Tianjin airport when cut-497 ting into the final approach segment. We find the average 498 deviation value, which is indicated by the thick black line. 499 With the same method, the glide slope deviation data of 500 Shanghai Hongqiao Airport is obtained. And compared with 501 the simulation results with 73% accuracy and the actual data 502 of Tianjin Binhai Airport, shown as Figure.16. The simula-503 tion results are basically consistent with the actual opera-504 tion results. The initial glide deviation is set to 7 m due to 505 VOLUME 10, 2022 FIGURE 11. Simulation result when the operation accuracy is 64%. simulation results show that the correction accuracy of the 526 glide path error is positively correlated with the speed and the 527 pilot's operation accuracy during the approach. The paired 528 approach procedure stipulates that the height and the glide-529 path angle of the IM aircraft at the beginning of the pairing 530 are greater than that of the target aircraft 3 , and the landing 531 time of the two aircraft is similar, which makes the speed and 532 acceleration of the IM aircraft greater than those of the target 533 aircraft in numerical value. According to the statistical QAR 534 data results, the speed of the aircraft at the final approach fix 535 point is usually 80 m/s. Here, the initial speed of the target 536 aircraft is 78 m/s, the initial longitudinal interval between the 537 IM aircraft and the target aircraft is 2000 m, and the time 538 interval is 25 s. The calculated operating parameters of the 539 two machines are shown in Table 5. 540 Taking the simulation results as an example, the vertical 541 overlap situation is shown in Figure. 17. It can be seen that 542 due to the large vertical distance between two aircraft in the 543 early stage, both aircraft are still far from the overlap area 544 and stay within safe limits even though the IM aircraft is 545

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As a result, the probability of vertical overlap is 0.068481.

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The simulation results with 55% accuracy, and the other 559 five groups of common accuracies are shown in Figure. 18.

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From the figure, it can be seen that when the accuracy is in 561 the range of 61%-73%, the probability of vertical overlap 562 of the paired approach is kept around 0.052, overlapping 563 frequencies are stable at around 20 flights/hour, with no 564 significant deviation. When the operation accuracy is 55%, 565 the overlap frequency and probability increase dramatically. 566

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The simulation results show that when the pilot operation 568 accuracy is lower than the normal value, the glide deviation 569 will be affected first, and then the vertical overlap probability 570 and frequency will be influenced. The increase in accuracy 571 can not only shorten the time to correct the aircraft to the 572 glide path but also stabilizes the aircraft near the glide path. 573 When the accuracy is obviously lower than 61%, the prob-574 ability of vertical overlap will increase significantly. When 575 the accuracy is within the constant range, the probability and 576 the frequency of vertical overlap have little fluctuation and 577 almost no difference.   is about 10 −9 -10 −8 . However, the difference in the order of 581 magnitude between the simulation results in this paper and 582 the results of previous studies is due to the different concepts 583 of overlap probability and collision risk. The collision risk 584 CR is calculated as follows: 585 CR = N x P y P z + N y P x P z + N z P x P y (20) 586 In the formula, x, y, and z represent longitudinal, lateral, 587 and vertical dimensions, respectively; P i (i = x, y, z) repre-588 sents the overlap probability; N i (i = x, y, z) represents the 589 overlap frequency. If the collision risk needs to be calculated, 590 subsequent calculations of the probability and frequency of 591 the overlap of the lateral and longitudinal dimensions are also 592 required.

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Because the paired approach program has not been used 594 formally and there are few data available, calculation of the 595 paired approach vertical overlap probability and frequency 596 has been avoided. Compared with the evaluation results of 597 parallel routes in the same altitude layer, the probability of 598 vertical overlap of the paired approach in this paper is about 599 1/10 of that in parallel routes, which is due to the difference 600

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(2) Compared with the actual operating data, the simulation 612 results showed similar trends, and VAAM and POM could 613 simulate the approach process well. In the simulation process, 614 because of the requirement of the paired approach proce-615 dure, the two aircraft had an initial vertical interval, and the 616 time difference between the two aircraft entering the runway 617 entrance was short. This caused the vertical overlap to occur 618 in the last 10 seconds of the whole process.

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(3) The accuracy of pilot operation affected the time to 620 correct the aircraft to the glide path, where the higher the 621 accuracy, the shorter the time. And the whole adjustment 622 process has more stable process. A lower accuracy kept the 623 aircraft on the wrong glide path and increased the proba-624 bility and frequency of vertical overlap. When the pilot's 625 operational accuracy was between 61% and 73%, the vertical 626 overlap probability and frequency were almost constant.