Subset Simulation Based Operational Risk Assessment of Procedures for Go-Around Handling Enabled by a Predictive Decision Support

Abstract

This paper presents a method to assess a novel procedure for Air Traffic Controllers, enabled by predictions of a machine learning-based go-around prediction model, regarding the operational risk of separation infringements and traffic alarms. In a previous work, potentially novel procedures were elaborated in human-in-the-loop simulations with Air Traffic Controllers. However, only a very limited number of simulations were possible due to the limited availability of Air Traffic Controllers, especially at the early stage of development of the decision support concept. Therefore, the evaluation of the decision support tool covered only a limited part of the operational domain. To tackle these shortcomings, this paper presents a subset simulation-based approach, a Monte Carlo variant to efficiently estimate small probabilities, which allows for assessing the concept over a wider operational spectrum and quantifying the risk of separation infringement and traffic alarms. The subset simulation-based method confirms that if the go-around prediction model predicts a go-around, the novel procedure could increase separation distances and thereby avoid separation infringements compared to the state-of-the-art procedure.

Full text

Subset Simulation Based Operational Risk Assessment of
Procedures for Go-Around Handling Enabled by a Predictive
Decision Support
Lukas Beller∗, Gökay Özer†, Florian Schwaiger‡and Florian Holzapfel§
Institute of Flight System Dynamics, Technical University of Munich, Garching, Bavaria, 85748, Germany
This paper presents a method to assess a novel procedure for Air Traffic Controllers,
enabled by predictions of a machine learning-based go-around prediction model, regarding
the operational risk of separation infringements and traffic alarms. In a previous work,
potentially novel procedures were elaborated in human-in-the-loop simulations with Air Traffic
Controllers. However, only a very limited number of simulations were possible due to the limited
availability of Air Traffic Controllers, especially at the early stage of development of the decision
support concept. Therefore, the evaluation of the decision support tool covered only a limited
part of the operational domain. To tackle these shortcomings, this paper presents a subset
simulation-based approach, a Monte Carlo variant to efficiently estimate small probabilities,
which allows for assessing the concept over a wider operational spectrum and quantifying
the risk of separation infringement and traffic alarms. The subset simulation-based method
confirms that if the go-around prediction model predicts a go-around, the novel procedure
could increase separation distances and thereby avoid separation infringements compared to
the state-of-the-art procedure.
I. Introduction
Machine learning (ML) tools have been discussed in the aviation-related research community for a while now. So
far, however, with a mostly isolated perspective on ML performance. One discussed use case is decision support
based on go-around predictions [
1
, p. 63]. Various different algorithm performances have been studied for various
airports [2–6].
The recent releases of EASA’s AI Roadmap, Guidance Material, and Machine Learning Application Approval steer
the scientific discussion toward certifiability aspects of ML tools in aviation. Defining a Concept of Operations (ConOps)
and performing a safety assessment of the ML-based tools and the changes resulting from their integration in the system
are tasks requested in EASA’s guidance material [
7
]. The demand for a safety assessment for Air Navigation Services
(ANS) originates from [
8
, §2.29] which, transferred into European legislation, requires Air Navigation Service Providers
(ANSPs) to perform a: "safety assessment and assurance of changes to the functional system" [9, ATS.OR.205].
For the use case of decision support tools based on go-around prediction algorithms, potential ConOPS and safety
assessments are less discussed in the literature so far. Developing operational scenarios are a key aspect of a ConOPS
[
10
, p. 14]. These operational scenarios include procedures that Air Traffic Controllers (ATCOs) could apply to handle
go-arounds, based on ML-based go-around predictions. As a first step, [
11
] performed a human-in-the-loop (HIL)
simulation exercise to identify potential new procedures following a positive go-around prediction. The results of
the HIL simulation identified procedures that, for true predictions, can improve safety regarding separation distances
and workload of ATCOs. In contrast, false predictions adversely affect the workload of ATCOs and the capacity of
the airport operation. However, since ATCOs are an expensive workforce and their availability is limited, especially
for research at this exploratory stage, the simulation exercises could not be performed in large numbers. The results
regarding the operational safety of these procedures can thus not be generalized over a wider spectrum of the operational
domain of the decision support tool.
Eurocontrol provides an Expanded Safety Reference Material to support safety assessments for ANS. This material
includes Accident Incident Models (AIM) that are intended to be used to identify the impact of changes on the safety
∗Research Engineer, Institute of Flight System Dynamics, Boltzmannstrasse 15, 85748 Garching b. München
†Master Student, Institute of Flight System Dynamics, Boltzmannstrasse 15, 85748 Garching b. München
‡Research Engineer, Institute of Flight System Dynamics, Boltzmannstrasse 15, 85748 Garching b. München
§Professor, Institute of Flight System Dynamics, Boltzmannstrasse 15, 85748 Garching b. München, AIAA Associate Fellow
1

of service provisions [
12
]. However, the cited release does not contain the relevant AIM for evaluating separation
infringement risks during go-arounds. An AIM release of 2020, for which no open-source publication is known to the
authors, includes a Mid-Air Collision Risk on Final Approach (MAC-FAP) model in a pre-release version v0.4 [
13
].
However, this MAC-FAP model does not quantify the probability of an aircraft following a published missed approach
procedure to conflict with other traffic, nor does it quantify the failure probability of the conflict management barrier. A
remark in the model states that these figures must be estimated based on local conditions for these model parts.
In research related to aviation safety, Monte Carlo (MC) simulations are an established method for quantitative
safety assessments. For a runway incursion, [
14
] presents a risk assessment using an MC approach based on a Petri Net
model. To assess the safety of a next-generation ATM system, [
15
] proposes an MC simulation approach that evaluates
near-mid-air collision risks. Both studies highlight the importance of accelerating MC simulations. They propose
decomposing the overall risk assessment in conditional MC simulations and recombining those based on a tree model.
Subset Simulation (SuS), another method of accelerating MC simulations, is an MC variant that quantifies failure
probabilities using products of conditional, intermediate failure probabilities [
16
]. Based on a runway overrun scenario,
[
17
] provides a risk assessment framework using the SuS algorithm, while [
18
] uses SuS to estimate probabilities of
conflict between air traffic.
To quantify some of the missing figures in the MAC-FAP AIM for a decision support tool using ML-based go-around
predictions, this paper proposes a SuS-based risk assessment approach. The goal is to verify the procedure design
regarding MAC risks. Thus, we aim to assess if the proposed procedure, as defined in [
11
], is conceptually safe regarding
MAC risks if applied under the investigated uncertainties.
The paper first introduces the SuS method in section II. Thereafter, section III describes two simulation scenarios.
The first one, referred to as the reference scenario, includes state-of-the-art procedures of ATCOs to handle go-arounds.
The second one, referred to as the solution scenario, features a proposed procedure enabled by a decision support tool
to handle go-arounds. Section IV describes the implementation of the simulation scenarios in a SuS environment.
Section V describes the obtained SuS results. Finally, section VI concludes the paper by discussing the results.
II. Subset Simulation
Subset
Simulation is an MC variant capable of efficiently estimating the failure probabilities of a system. Failure
domains for reliable systems correspond to remote regions of the systems’ input domain, typically in the tail (low
likelihood) regions of the input domains’ probability distributions. Ordinary MC methods, sampling predominantly
from the high likelihood regions of the input domain, thus fail to estimate failure probabilities efficiently. In recent
years, SuS was applied for risk assessment in a broad spectrum of engineering domains like civil engineering [
19
] or
aerospace engineering [20] [21] [22].
SuS, as defined in [
16
], assumes a system with
𝑛
parameters
𝚯=[𝜃1, 𝜃2, ..., 𝜃𝑛]
, for which a probability density
function (PDF)
𝑝(𝚯)
defines the joint distribution over the parameters
𝚯
. Furthermore, an indicator function
𝐼𝑓 𝑎𝑖𝑙 (𝚯)
evaluates to
1
, if the system is inside the failure domain
𝐹𝑓 𝑎𝑖𝑙
and
0
otherwise. Integrating the indicator function
𝐼𝑓 𝑎𝑖𝑙 (𝚯)
weighted with the PDF of the parameters
𝑝(𝚯)
over the parameters
𝚯
yields the failure probability of the
system
𝑃𝑓 𝑎𝑖𝑙 =∫𝐼𝑓 𝑎𝑖𝑙 (𝚯)𝑝(𝚯)𝑑𝚯.(1)
Instead of solving Eq.
(1)
directly, SuS iteratively computes the failure probability
𝑃𝑓 𝑎𝑖𝑙
. Therefore, SuS sequentially
defines intermediate failure probabilities
𝑃𝑖
, corresponding to intermediate failure domains
𝐹𝑖
, using intermediate
indicator functions 𝐼𝑖(𝚯). The intermediate failure domain in each sequential step
𝐹1⊂𝐹2⊂... 𝐹𝑚=𝐹𝑓 𝑎𝑖𝑙 (2)
is a subset of the previous intermediate failure domain. SuS repeats the intermediate steps until generating values for
𝚯
that lie in the actual failure domain
𝐹𝑓 𝑎𝑖𝑙
and for which
𝐼𝑖(𝚯)
equates to
1
. When reaching the actual failure domain,
the failure probability
𝑃𝑓 𝑎𝑖𝑙 =𝑃1
𝑚
Ö
𝑖=2
𝑃(𝐹𝑖|𝐹𝑖−1)(3)
equates from the product of the intermediate failure probabilities and the failure probability of the final subset.
The process uses a naive Monte Carlo method to generate the first intermediate failure domain
𝐹1
. Therefore, SuS
selects a subset of all generated samples closest to the actual failure domain
𝐹𝑓 𝑎𝑖𝑙
. SuS then uses these samples from
2

𝐹1
as seeds, generating new samples to define the subsequent failure domain. The ratio of samples that make up the
intermediate failure domain
𝐹𝑖
from all generated samples in one step, referred to as conditional failure probability, is a
design parameter of SuS. In our simulations, we selected the conditional failure probabilities
𝑃1=𝑃(𝐹𝑖|𝐹𝑖−1)=0.1,∀𝑖=2, . . . , 𝑚 −1.(4)
From the second step onward, samples are generated using a modified Metropolis-Hastings algorithm [16].
For the work presented in this paper, we use a SuS toolbox [
23
] implemented in MATLAB
®
. The toolbox
provides several Markov Chain Monte Carlo (MCMC) algorithm options. For this work, we chose the element-wise
Metropolis-Hastings algorithm. The toolbox takes as input a model describing the system under investigation, the
simulation’s initial states, and the distributions of the parameters
𝚯
. If no failure is at or above a failure probability of
10−9
, the default setting is to abort the SuS. We stick to this default setting for this paper. The following sections define
the simulation scenario and the simulation implementation, providing the toolbox’s input for the studies presented in
this paper.
III. Simulation Scenarios
The simulation exercise in [
11
] investigates procedures to handle go-around situations enabled by a go-around
prediction tool. The tool, specified in [
6
], provides predictions for three points during an aircraft’s approach at
6NM
,
4NM
, and
2NM
from the runway threshold. According to [
11
], the prediction at
4NM
yields the best overall results and
will therefore be examined closer regarding safety risks in this study.
The separation-related knock-on effects of go-arounds investigated in this paper do not occur for all go-arounds.
The probabilities computed by this SuS approach have to be interpreted as conditional probabilities, given the initial
conditions of the described scenario arise. The scenario assumes conflicting departure and missed approach procedures,
as well as high traffic volumes. One real-world example with such conditions, illustrated in Figure 1, is Munich airport’s
runway 26L, where the Southern Standard Instrument Departure Routes, labeled S-SIDs in [
24
, AD 2 EDDM 5-7-31]
conflict with missed approach procedures defined in the Instrument Approach Chart (IAC) [24, AD 2 EDDM 4-2-3].
Fig. 1 The S-SIDs on the left, highlighted in red, and the missed approach procedure, indicated by the dashed
line, on the right conflict towards the OTT Very High Frequency Omnidirectional Range Station in the bottom of
each chart. [24]
Figure 2 illustrates the initial conditions of this scenario recorded with ADS-B data, with the important difference
that we assume the arrival aircraft to perform a missed approach, whereas the figure illustrates a successful landing.
The scenario as implemented in the simulation for this study consists of two aircraft, one that intends to depart on
3

the S-SID and one that performs an ILS approach according to the IAC. In high-traffic situations, the gap between
two consecutively landing aircraft, highlighted by the yellow and blue circles, is between
4−5NM
. The departing,
blue-circled aircraft waits at the holding point with a conditional line-up clearance. The condition for the line-up is the
passing of the yellow-circled aircraft that lands on the same runway previous to the simulated, red-circled arrival aircraft.
The yellow-circled aircraft is important for the sequence of events in the simulation. However, it is not relevant when
computing separation distances between the two modeled red- and blue-circled aircraft. Thus, it was not simulated and
is explained only for contextual coherence. For the analysis, we simulate two scenarios that start with the described
Fig. 2 A series of screenshots from 5 June 2024 at 09:32:54, 09:34:25, and 09:34:53 UTC+2, illustrate the
simulated scenario. The pictures are generated using ADS-B data from Bratwurst ADS-B Network and tar1090
software, which uses map data from Open Street Map. In the top picture, the departure aircraft, indicated with
the blue circle, has a conditional line-up clearance, given the aircraft in the yellow circle passes the holding point.
The arrival aircraft, indicated with the red circle, performs an ILS approach, as described in the IAC, with a 4-5
NM gap to the yellow-circled A/C on the same approach. The middle picture illustrates the moment the arriving
aircraft passes the runway threshold. The bottom picture illustrates the departure aircraft on the S-SID. The
simulation described in this section shall explore the separation-related risks between the departure and arrival
aircraft if the arrival aircraft performs a go-around instead of the landing, as illustrated in the bottom picture.
initial conditions. A reference scenario using state-of-the-art procedures to handle go-arounds and a solution scenario
that includes a prediction when the arriving aircraft is
4NM
from the runway threshold. Both scenarios start identically.
However, they evolve differently due to the differing procedures. Both aircraft are given a set of commands during
a scenario, modeling the interaction of the flight crews and the ATCO. All commands and their activation order are
predefined in the simulation environment and defined in the sequence diagrams in Figure 3 and Figure 4. Variables
that influence the separation of aircraft are defined as parameters of the SuS. The following subsections explain the
procedures used in the reference and solution scenarios.
A. Reference Scenario
In the Reference Scenario, the arrival aircraft’s pilot initiates the go-around during the final approach. Once the
ATCO recognizes the go-around, the ATCO vectors the arrival aircraft to a heading that establishes separation from
the departing aircraft as soon as possible. The sequence diagram in Figure 3 illustrates the sequence of actions in
the reference scenario, as defined in [
11
]. The diagram expresses the pilot actions inside the blocks. The actions and
communication arrows are ordered chronologically from top to bottom. In the reference scenario, multiple parameters
can impact the separation distance between both simulated aircraft. Based on feedback from ATCOs and pilots, we select
seven of them, referred to as
Θ𝑅=[𝜃𝑅1, ..., 𝜃𝑅 𝑘 , ..., 𝜃 𝑅7]
as variable parameters for the SuS analysis of the reference
scenario. The PDFs defining the reference scenario parameters
Θ𝑅
are based on inputs from ATCOs and academic
resources focused on statistical aircraft trajectory studies. The SuS parameters and the respective PDFs are defined in
Table 1. Pilots perform go-arounds for various reasons. The point of the go-around initialization has an impact on the
separation distances between the missed approach and departure trajectory. Thus, based on ATCO feedback,
𝑝(𝜃𝑅1)
4

Fig. 3 The sequence and action diagram of both the pilots and the ATCO in the reference scenario.
models the go-around initialization point as a uniform distribution from
2.5NM
to
0.1NM
from the runway threshold.
We did not model touch-and-go maneuvers in the simulation. Thus, we limited the lower end of the distribution to
0.1NM
. The time point of the departure’s take-off is a second important parameter. Since the line-up process is not
included in the simulation model, we model the take-off initialization dependent on the arrival aircraft’s position relative
to the runway threshold and based on ATCO feedback. The distribution
𝑝(𝜃𝑅2)
is limited by two constraints. First is
the conditional line-up clearance, which is described above. Second, the latest time point ATCOs are not retrieving a
take-off clearance, in case the take-off has not started when the arrival aircraft is
2.3NM
from the runway threshold. In
this case, a new scenario occurs, which is not considered in this simulation since the runway is blocked and the arrival
aircraft is commanded to go around. The weight distributions for the arrival and departure aircraft are estimated based
on a statistical, commercial operation analysis report done in the USA [
25
]. For
𝑝(𝜃𝑅3)
and
𝑝(𝜃𝑅4)
, the cumulative
distribution functions stated in the report were transformed into a piecewise linear distribution (PLD) function and used
in the simulations to generate samples. The time that passes between the initiation of the go-around and the vectoring of
the aircraft by the ATCO, defined by
𝑝(𝜃𝑅5)
was approximated based on ATCO experience and truncated at
0
at the
lower end. The distributions for the approach speed
𝑝(𝜃𝑅6)
and climb speed
𝑝(𝜃𝑅7)
are modeled based on A320 data
from an open-source kinematic aircraft performance database [
26
]. We truncated
𝑝(𝜃𝑅7)
at the lower end, so it is at
least the rotation speed 𝑉𝑅=150𝑘𝑡 𝑠
B. Solution Scenario
The solution scenario assumes that an algorithm, as presented in [
6
], predicts a go-around when the arrival aircraft
is
4NM
from the runway threshold. The sequence diagram in Figure 4 illustrates the procedure used by the ATCOs to
handle the go-around described [
11
]. After observing the prediction at
4𝑁 𝑀
from the runway threshold, the ATCO does
not provide a take-off clearance to the departure aircraft, given the potential conflict of the departure and missed-approach
procedure.
The departure aircraft has a conditional line-up clearance, conditioned on the preceding arrival aircraft passing the
holding point. Therefore, the departing aircraft performs the lineup, blocking the runway. The ATCO cannot clear the
arrival aircraft for landing and instructs a go-around to the pilot. The resulting go-around initiation thus depends on
the ATCO’s and pilot’s reaction time to the prediction. Similar to the reference scenario described in section III.A,
5

Table 1 Reference Scenario Variable Descriptions
Var. Unit Explanation Probability Distribution
𝜃𝑅1NM The Euclidean distance between runway threshold
and the Arrival A/C when it’s pilot initiates a go-around. 𝑝(𝜃𝑅1) ∼ U (0.1,2.5)
𝜃𝑅2NM
The Euclidean distance between the runway threshold
and the Arrival A/C when the Departure A/C
initiates the take-off.
𝑝(𝜃𝑅2) ∼ N ( 2.85,0.83)
𝜃𝑅3kg Arrival A/C payload weight including fuel 𝑝(𝜃𝑅3) ∼ P.L.D.
from [25, p. A-1]
𝜃𝑅4kg Departure A/C payload weight including fuel 𝑝(𝜃𝑅4) ∼ P.L.D.
from [25, p. A-1]
𝜃𝑅5sec
The time that is required for ATCO to observe
the go-around, vector the Arrival A/C to a non-collusion
heading and the Arrival A/C pilot to start turning the A/C.
𝑝(𝑅5) ∼ N ( 6,1.33)
𝜃𝑅6m/s Arrival A/C Approach Speed (True Air Speed) 𝑝(𝜃𝑅6) ∼ N (72.43,3.49)
𝜃𝑅7m/s Departure A/C Climb Speed (True Air Speed) 𝑝(𝜃𝑅7) ∼ N (83.31,4.64)
Fig. 4 The sequence and action diagram of both the pilots and the ATCO in the solution scenario. The ATCO
withholds the take-off clearance when the prediction tool indicates a go-around. As a result, the runway is
blocked for the arrival aircraft, forcing the ATCO to command a go-around for the arrival aircraft.
6

variables that influence the separation between the two aircraft are defined as parameters for the SuS of the solution
scenario. The PDF
𝑝(𝜃𝑆1)
models this variation in reaction time based on ATCO feedback. The PDS
𝑝(𝜃𝑆2)
, defined
based on pilot feedback, models the climb angle of the initiated go-around. The ATCO instructs the arriving aircraft to
turn heading 165, once passing the minimum sector altitude. Once the ATCO observes the heading change on the radar,
the ATCO clears the departing aircraft for take-off. The time of the take-off clearance thus depends on the climb angle
𝜃𝑆2
. The parameters
𝑝(𝜃𝑆3)=𝑝(𝜃𝑅3)
,
𝑝(𝜃𝑆4)=𝑝(𝜃𝑅4)
,
𝑝(𝜃𝑆5)=𝑝(𝜃𝑅6)
, and
𝑝(𝜃𝑆6)=𝑝(𝜃𝑅7)
are similar to the
respective reference scenario parameters with identical distributions. Also, if applicable, the same truncation logic
applies. Additionally, we truncated
𝑝(𝜃𝑆1)
at the lower end at
0s
. Table 2 summarizes the parameter distributions
𝑝(𝜃𝑆𝑘 ).
Table 2 Solution Scenario Variables
Var. Unit Explanation Probability Distribution
𝜃𝑆1sec
The time that is required for ATCO to
acknowledgego-around prediction and
communicate it to the arrival A/C pilot.
𝑝(𝜃𝑆1) ∼ N ( 12,1.33)
𝜃𝑆2deg Arrival A/C climb angle during go-around 𝑝(𝜃𝑆2) ∼ N ( 9,0.66)
𝜃𝑆3kg Arrival A/C payload weight including fuel 𝑝(𝜃𝑆3) ∼ P.L.D.
from [25, p. A-1]
𝜃𝑆4kg Departure A/C payload weight including fuel 𝑝(𝜃𝑆4) ∼ P.L.D.
from [25, p. A-1]
𝜃𝑆5m/s Arrival A/C Approach Speed (True Air Speed) 𝑝(𝜃𝑆5) ∼ N ( 72.43,3.49)
𝜃𝑆6m/s Departure A/C Climb Speed (True Air Speed) 𝑝(𝜃𝑆6) ∼ N (83.31,4.64)
IV. Simulation Implementation
As defined in section II, SuS quantifies the failure probability of a system, based on an indicator function
𝐼𝑓 𝑎𝑖𝑙 (Θ)
that evaluates if the system is inside the failure domain or not. According to the AIM for MAC-FAP [
13
], the barrier
after the ATC collision prevention barrier that we want to assess is the Traffic Alert and Collision Avoidance System
(TCAS). We, therefore, define a failure of the procedure to handle the missed approach if the TCAS system issues a
traffic advisory (TA). To compute the indicator function, the simulation model for the SuS consists of two aircraft models,
each containing flight dynamics and basic flight control models as well as state machines, modeling the sequence of
actions between the ATCO and the flight crew. Each simulation is simulated for
180𝑠
from the initial conditions, which
gives the simulation enough time to model the effects of the procedures defined in section III. The following subsections
describe the indicator function and the aircraft models.
A. Indicator Function
Given accurate aircraft state information, [
27
] provides a logic that models Traffic Alert and Collision Avoidance
System II (TCAS-II) advisories. The logic issues an advisory when both, a horizontal component
𝐻 𝐴𝑙=∥sh∥≤DMOD𝑙OR (sh·vh<0AND 𝜏𝑚𝑜𝑑,𝑙 (sh,vh) ≤ TAU𝑙),(5)
and a vertical component
𝑉 𝐴𝑙=|𝑠𝑧| ≤ ZTHR𝑙OR (𝑠𝑧·𝑣𝑧<0AND 𝑡𝑐𝑜 𝑎,𝑙 (𝑠𝑧, 𝑣 𝑧) ≤ TAU𝑙)(6)
are true. The parameters
DMOD𝑙
,
ZTHR𝑙
, and
TAU𝑙
are thresholds, depending on altitude-dependent severity levels,
indicated by the subscript 𝑙. The vectors
sh= 𝑥𝐶𝐺
𝑑𝑒 𝑝
𝑦𝐶𝐺
𝑑𝑒 𝑝 !𝑁
− 𝑥𝐶𝐺
𝑎𝑟𝑟
𝑦𝐶𝐺
𝑎𝑟𝑟 !𝑁
and vh= ¤𝑥𝐶𝐺
𝑑𝑒 𝑝
¤𝑦𝐶𝐺
𝑑𝑒 𝑝 !𝑁
− ¤𝑥𝐶𝐺
𝑎𝑟𝑟
¤𝑦𝐶𝐺
𝑎𝑟𝑟 !𝑁
(7)
describe the relative horizontal distance
sh
and relative horizontal velocity
vh
between the departure aircraft’s center
of gravity, indicated by subscript
𝑑𝑒 𝑝
and superscript
𝐶𝐺
, and the arrival aircraft’s CG, indicated by subscript
𝑎𝑟𝑟
.
7

Respectively, the values
𝑠𝑧=𝑧𝐶𝐺
𝑑𝑒 𝑝 ,𝑁 −𝑧𝐶𝐺
𝑎𝑟𝑟 , 𝑁 and 𝑣𝑧=¤𝑧𝐶 𝐺
𝑑𝑒 𝑝 ,𝑁 − ¤𝑧𝐶 𝐺
𝑎𝑟𝑟 , 𝑁 (8)
describe the relative vertical distance
𝑠𝑧
and velocity
𝑣𝑧
of the departure and arrival aircraft. The subscript
𝑁
denotes a
right-hand, local, flat-earth coordinate system with its origin in the runway threshold and the
𝑥
and
𝑦
axis aligned with
the north and east direction. The modified time to the closest point of approach
𝜏𝑚𝑜𝑑,𝑙 (sh,vh)=DMOD2
𝑙−∥sh∥2
sh·vh
(9)
and time of horizontal closest approach
𝑡𝑐𝑜𝑎 (𝑠𝑧, 𝑣 𝑧)=−𝑠𝑧
𝑣𝑧
.(10)
The parameter values for the TCAS II TA’s, depending on the height above ground level
ℎ𝑎𝑔𝑙
, are defined in [
28
, p.
126] and summarized in Table 3. The departure aircraft in the simulation is within all three listed altitude bands. For
simplicity and to avoid jumps in the indicator function, we decided to fix the 𝑙=3for the simulations.
Table 3 TCAS II Traffic Advisory Thresholds [28]
ℎ𝑎𝑔𝑙 (ft) 𝑙DMOD (NM) TAU TA (s) ZTHR TA (ft)
0-1000 2 - 20 850
1000-2350 3 0.2 25 850
2350-5000 4 0.35 30 850
SuS requires a one-dimensional indicator function. To include the constraints defined in Eq.
(5)
and
(6)
, we define
the indicator function as
𝐼𝑓 𝑎𝑖𝑙 =(1𝑖 𝑓 𝐽𝑚𝑖𝑛 <0
0𝑖 𝑓 𝐽𝑚𝑖𝑛 ≥0(11)
where
𝐽𝑚𝑖𝑛 =min 𝐽(𝑡)=min max[𝐽(𝑡)ℎ,−𝜖] + max[𝐽(𝑡)𝑧,−𝜖],
𝐽(𝑡)ℎ=min∥sh(t)∥−DMOD𝑙
DMOD𝑙
,𝜏𝑚𝑜𝑑,𝑙 (sh(t),vh(t) ) − TAU𝑙
TAU𝑙and
𝐽(𝑡)𝑧=min𝑠𝑧(𝑡) − 𝑍𝑇 𝐻 𝑅
𝑍𝑇 𝐻 𝑅 ,𝑡𝑐𝑜𝑎 (𝑠𝑧(𝑡), 𝑣 𝑧(𝑡)) − TAU𝑙
TAU𝑙,
(12)
by normalizing each constraint by its threshold. The variable
𝑡∈ [𝑡𝑡 𝑎 𝑘𝑒𝑜 𝑓 𝑓 , 𝑡𝑚 𝑎𝑥 ]
defines the time between the take-off
of the departing aircraft and the simulation end, and 𝜖is an arbitrarily small parameter, which we set 𝜖=0.1.
Simulating the aircraft trajectories for the indicator function requires a flight dynamics simulation model, an aircraft
control model, and a model for the ATCO, which are defined in the next subsection.
B. Flight Dynamics Model
We modeled both the arrival and departing aircraft using the same generic, medium wake turbulence category
aircraft. The model orients itself on an Airbus A320, a common aircraft operated at Munich airport. In the following,
we provide a short overview of the model, as a complete description of the model is beyond the scope of this paper. The
general parameters of the modeled aircraft can be seen in Table 4. The geometrical and weight properties are taken from
[29]. The following briefly outlines the kinematic, aerodynamic, propulsion, and ground interaction models.
8

Table 4 Generic Transport Aircraft Parameter Overview
Wing Area 120 𝑚2Mass Range 42 𝑡−73 𝑡
Wing Span 35 𝑚Ixx 1.14 ×106
Mean Aero. Chord (MAC) 4𝑚Iyy 2.4×106𝑘𝑔/𝑚2
Fuselage Length 60 𝑚Izz 3.35 ×106𝑘𝑔/𝑚2
Fuselage Width 8𝑚Ixz 1.04 ×106𝑘𝑔/𝑚2
Fuselage Width 4𝑚Engine Thrust@SL (x2) 2.2×102𝑘 𝑁
1. Kinematics
The model uses quaternion-based, six-degrees-of-freedom (6DOF) equations of motion in ECEF coordinates as
defined in [
30
, pp. 54] and implemented by Simulink in the Aerospace Toolbox. The moment of inertia, the center
of gravity, and the mass of each aircraft are assumed to be constant throughout the simulation. The model includes
aerodynamics, propulsion, and ground interactions to calculate the forces and moment inputs for the 6DOF equation of
motion. For each category, the modeling approach is briefly explained in the following.
2. Aerodynamics
To model the aerodynamic properties, 2D airfoil geometry data from AIRBUS operation manuals [
29
] was used in
XFLR5’s [
31
] XFOIL [
32
] analysis to generate a dataset of aerodynamic coefficients. Based thereon, a multi-point
model approach was utilized where the lifting surfaces are divided into multiple panels, and aerodynamic effects are
calculated at each panel separately. Additionally, effects from control surfaces, flaps, slats, and basic interactions
between the wings and the tail were calculated using the methods provided in [33], [34], [35] and [36].
3. Propulsion
The model and parameters for the propulsion model of the aircraft are from the Aircraft Noise and Performance
(ANP) Database [
37
, p.B-6]. The database provides a formula to calculate the thrust generated by a specified aircraft
engine as a function of the engine’s rotation speed in percent.
4. Ground Interactions
For ground interaction, a simple second-order mass-damper system was used to model the oleo displacement
dynamics [
38
]. The height of the ground is assumed constant, with the threshold elevation of Runway 26L. As for
friction, the ground model generates a static friction force that acts in the opposite direction of the landing gear’s
movement. Rather than implementing a detailed wheel model, a small friction coefficient was used to model the
behavior of a turning wheel. The friction coefficient used for all landing gears is
0.005
. The ground interactions model
is only designed to model departures and not landings of the aircraft. This is also why touch-and-go maneuvers are not
considered in this paper, requiring a more sophisticated ground interaction model.
C. Flight Controller
The aircraft model has a set of proportional-integral controllers with fixed gains to control pitch, roll, yaw, and
thrust. The gains were tuned to have stable dynamics at the altitudes between 1400 𝑓 𝑡 −5000 𝑓 𝑡 . Furthermore, several
autopilot modes were implemented. The controller modes used in the analysis are presented in Table 5. The glideslope
and localizer hold functions are implemented to mimic the approach method using the Instrument Landing System (ILS).
These modes allow an approaching aircraft to maintain the runway heading and descend with approximately 3 degrees of
flight path angle to the runway threshold. All departure routes on Runway 26L have a maximum speed limit in the initial
phase between 220 and 250 KIAS (Knots-Indicated Air Speed), depending on the route. Thus, unless otherwise stated,
a speed limit of 235 Knots-True Air Speed was used in both scenarios. In addition, climb angles are relevant for the
simulation outputs.
𝜃𝑆2
defines the go-around climb angle in the solution scenario. For the climb angles after take-off,
the autopilot commands a climb angle of 8 degrees, as obtained from [
26
]. One simplifying assumption of the model is
9

Table 5 Aircraft Flight Controller Modes
Channel Controller Mode
Pitch Climb Angle Hold, Altitude Hold, Glideslope Signal Hold
Heading Heading Hold, Localizer Signal Hold
Thrust Thrust Lever, True Air Speed Hold
that the arrival aircraft flies on the localizer and glideslpe, before initiating a go-around. Thus the only varying paramter
that influences the go-around initialization point is the distance from the runway threshold, determined by 𝜃𝑅1or 𝜃𝑆1.
D. Simulation Composition
The arrival aircraft is initialized on the glide slope and localizer at
7𝑁 𝑀
from the runway threshold with the
arrival speed
𝜃𝑅6
or
𝜃𝑆5
. The departure aircraft is initilized at the starting position of the runway. The sequence of
the scenario evolution and the procedures to resolve the simulated situation for both scenarios follow the sequence
diagrams in Figure 3 and Figure 4. The sequence of interactions between the ATCO and pilots were implemented using
the Simulink
®
Stateflow
®
environment. Figure 5 illustrates 300 simulations of the reference (Figure 5a) and solution
scenario (Figure 5b) generated by SuS. The red lines illustrate the arrival aircraft trajectories. The cyan lines illustrate
the departure aircraft trajectories. The black lines indicate the position of both aircraft at which 𝐽𝑚𝑖𝑛 arises.
Terrain source: GMTED2010 7.5 arc-second resolution (approximately 250 meters) for most of the globe. Data available from the U.S. Geological Survey.Terrain source: GMTED2010 7.5 arc-second resolution (approximately 250 meters) for most of the globe. Data available from the U.S. Geological Survey. • • Source: Esri, Maxar, Earthstar Geographics, and the GIS User CommunitySource: Esri, Maxar, Earthstar Geographics, and the GIS User Community
(a) Trajectories, generated in the Reference Scneario
Terrain source: GMTED2010 7.5 arc-second resolution (approximately 250 meters) for most of the globe. Data available from the U.S. Geological Survey.Terrain source: GMTED2010 7.5 arc-second resolution (approximately 250 meters) for most of the globe. Data available from the U.S. Geological Survey. • • Source: Esri, Maxar, Earthstar Geographics, and the GIS User CommunitySource: Esri, Maxar, Earthstar Geographics, and the GIS User Community
(b) Trajectories, generated in the Solution Scneario
Fig. 5 The Figure illustrates 300 simulated arrival and departure aircraft trajectories from the reference and
solution scenario, as generated by SuS.
Attribution for terrain data and satellite imagery used for the Figures: 1. Terrain source: GMTED2010. Data
available from the U.S. Geological Survey. 2. Source: Esri, Maxar, Earthstar Geographics, and the GIS User
Community
V. Results
With the model defined in Section IV, we conduct the proposed SuS-based risk assessment approach using the SuS
toolbox [
23
]. We performed a SuS with
3000
samples per subset for the reference and solution scenario, described in
Section III. We define the threshold failure probability to terminate SuS as
𝑃𝑓 𝑎𝑖𝑙 <10−9
, which will stop the simulation
if SuS does not find a failure with a probability of magnitude 10−9or higher.
Figure 6 illustrates all outputs of the SuSs for both scenarios. The figure shows the horizontal separation
sh
and
10

vertical separation
𝑠𝑧
, at the time of
𝐽𝑚𝑖𝑛
. The
”◦”
markers illustrate the reference scenario’s output, and the
”+”
markers illustrate the solution scenario’s output. Furthermore, the different colors indicate the different subsets in which
the outputs are generated. Additionally, the grey box illustrates the limits of minimum radar separation, and the red box
illustrates the limits of a TCAS TA, which we defined as the failure domain of the investigated procedures in section
IV.A.
SuS generates, next to the initial MC samples in blue, nine further subsets for both scenarios. With increasing
subsets,
𝐽𝑚𝑖𝑛
decreases for both scenarios. For the reference scenario, the smallest value of the indicator function,
found by SuS, is
𝐽𝑚𝑖𝑛, 𝑅 =2.9
. For the solution scenario, the smallest value of the indicator function is
𝐽𝑚𝑖𝑛, 𝑆 =11.2
.
Therefore, SuS could not detect a failure with a probability higher than
10−9
for the reference and solution scenario,
conditioned on the input parameter distributions defined in section III. Additionally,
78%
of the simulations from the
Fig. 6 This figure illustrates the resulting horizontal separation
sh
and vertical distance
𝑠𝑧
of the SuSs at
𝐽𝑚𝑖𝑛
for
the reference and solution scenario. The different colors of the samples indicate the different subsets generated by
SuS. Additionally the Minimum Radar Separation Limits as well as the Traffic Advisory Limits are illustrated.
direct MC layer of the reference scenario are below radar separation limits at least one time during the simulation. On
the contrary, no simulation in the solution scenario in all subsets is below these limits. The solution scenario manages to
establish minimum radar separation by ensuring vertical separation above 1000ft.
VI. Conclusion
Defining procedures for an ML-based tool in ATM is part of a ConOPS, which is a requirement in EASA’s guidance
on ML applications [
7
]. Additionally, [
7
] requires performing a safety assessment of the envisioned change of the ATM
system. One part thereof, the change of operational procedures, is investigated in this paper. Therefore, we propose
an approach to assess the operational safety of procedures to handle go-arounds regarding aircraft separation. The
approach is applied to a specific scenario of conflicting departure and missed approach procedures, as well as high
traffic volume. This scenario is of interest for decision support tools based on go-around prediction algorithms since
go-arounds in these scenarios produce knock-on effects of separation challenges that require immediate action from
ATCOs. Go-around predictions could, in these scenarios, enable procedures to handle go-arounds with less coordinative
actions and more time in advance [
11
]. Thus, a state-of-the-art procedure is compared to such a proposed procedure
following a positive go-around prediction regarding separation risks. Based on the MAC-FAP AIM model from [
13
],
we define the procedure as failing if a TA is triggered within a simulation run.
First, the overall conclusion is that both procedures do not fail conceptually. The SuSs indicates that a TA does not
occur with a probability above
10−9
if ATCOs use either procedure defined in section III to handle go-arounds in the
described scenario. The SuS approach accounts for uncertainties in the aircraft weights, speeds, and delay times in the
11

ATCO and pilot reactions, as defined in Table 1 and Table 2. Therefore, the SuS manages to cover a wider spectrum
operational domain, compared to the initial HIL approach in [
11
], generalizing the findings for the defined uncertainties
in the parameters of SuS. Furthermore, the SuSs show that over the investigated operational domain, specified through
PDFs of the SuS parameters, the procedure enabled by go-around prediction provides a higher buffer of the indicator
𝐽𝑚𝑖𝑛
towards failure, compared to the reference procedure. Also, the SuS of the solution scenario does not find any
radar separation infringements, unlike in the reference scenario. This indicates that the procedure enabled by go-around
predictions could provide an additional barrier in the MAC-FAP AIM, preventing a conflict between missed approach
and departure aircraft. However, the SuS approach assumes that work is done as imagined and defined in the sequence
diagrams in Figure 3 and Figure 4. The results only hold if the procedures are applied within the defined limits of
uncertainty over the SuS parameters. This approach does not consider human errors or technical failures.
The presented approach still has several limitations. The first limitation is the selection of the SuS parameters and
the estimation of their PDFs. In contrast to estimating the parameter PDFs from literature, a more targeted approach
would be to estimate the PDFs from operational data at the investigated airport, e.g., from Automatic Dependent
Surveillance-Broadcast or Quick Access Recorder data. This would enable the proposed approach to model the actual
operational domain at the investigated airport even closer to reality. A second limitation is the limited selection of aircraft
models. Only similar, medium-type, two-engine aircraft models were used for this approach. While this is a likely
combination of arrival and departure aircraft, it would be interesting to perform the same simulations with combinations
of different wake turbulence category aircraft. Another limitation is the detail of the modeling. By enhancing the
aircraft controls, approaches not following the glide slope and localizer signal perfectly could, e.g., be included in the
investigation of the procedures, thereby considering more degrees of freedom in the go-around trajectories.
The question arising from these results is whether the potential additional safety margin and potential reduction
of separation challenges are worth the development and implementation costs. Also, the reference scenario can be
considered safe under the assumptions tested with this SuS. The potential improvements will not affect every go-around,
as the ML-based go-around prediction underlying this investigation shows recall values of around 20% and precision
values of 90% [
6
]. Based on these results, the proposed procedure will statistically only affect 20% of go-arounds, while
80% still have to be handled according to the reference procedure. To answer this question, probabilities of human
errors and technical errors have to be investigated to complete the missing figures for the AIM MAC-FAP model.
In summary, the presented work can yield one missing part of the required safety assessment for changes to the
ATM system based on the AIM models. In the future, the approach should be refined to include uncertainties based
on operational data recorded at the airport under investigation. The model depth and the combination of different
wake turbulence category aircraft can also contribute to the complete picture. Furthermore, the ML-based prediction
accuracies and human as well as technical failure probabilities have to be investigated and combined to complete the
AIM model for a complete safety assessment of the go-around prediction-based decision support concept.
Acknowledgments
The definition of the case study and the development of the simulation model was carried out within SafeOPS,
a project that received funding from the SESAR Joint Undertaking (JU) under grant agreement No 892919. The
JU receives support from the European Union’s Horizon 2020 research and innovation program and the SESAR JU
members other than the Union.
The development and implementation of the methodology to evaluate the operational safety of a machine learning-
based decision support tool was carried out within SafeTEAM, a project that received funding from the European Union
under grant agreement No 101069877.
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