NA SAffP-2 0 12-216018 

Comparison of Predictive Modeling Methods of Aircraft 

Landing Speed 

Ousmane N Diallo, Ph.D 

Ames Research Center 

Moffett Field, California 

June 2012 
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NASAffP-2012-216018 

Comparison of Predictive Modeling Methods of Aircraft 

Landing Speed 

Ousmane N Diallo, Ph.D 

Ames Research Center 

Moffett Field, California 

National Aeronautics and 

Space Administration 

Ames Research Center 

Moffett Field, California 94035-1000 

June 2012 
Available from: 

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7115 Standard Drive 

Hanover, MD 21076-1320 

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iii

TABLE OF CONTENTS

List of Figures ..................................................................................................................................v

List of Tables ................................................................................................................................ vii

Nomenclature ............................................................................................................................... viii

Summary ..........................................................................................................................................1

1 Introduction ............................................................................................................................. 1

2 Background and Motivation .................................................................................................... 2

2.1 Background ...................................................................................................................... 2

2.2 Motivation ........................................................................................................................ 3

3 Modeling Methodologies ......................................................................................................... 4

3.1 Data Selection and Processing ......................................................................................... 4

3.1.1 Data Collection ......................................................................................................... 4

3.1.2 Screening................................................................................................................... 4

3.1.3 Physically Relevant Parameters ................................................................................ 4

3.2 Mathematical Modeling: Multi-variable Regression Modeling ....................................... 5

3.2.1 Response Surface Equation....................................................................................... 5

3.2.2 Neural Network Modeling ........................................................................................ 5

4 Baselining: Flight Operating Manual Recommendation ........................................................ 7

4.1 Baselining ......................................................................................................................... 7

4.1.1 Landing with Low-and-No-Gust Condition.............................................................. 7

4.1.2 Landing with High-Gust Condition .......................................................................... 7

4.2 Model Evaluation ............................................................................................................. 8

5 Proof of Concept ..................................................................................................................... 9

5.1 RSE Application to Thirteen Input Variables .................................................................. 9

5.1.1 Low-and-No-Gust RSE Model ............................................................................... 11

5.1.2 High-Gust RSE Model ............................................................................................ 13

5.1.3 Summary and Discussion of Results for RSE Models with Thirteen

 Input Variables ........................................................................................................ 15

5.2 Application to Reduced Number of Input Variables: Five Inputs ................................. 17

5.2.1 RSE Modeling ......................................................................................................... 18

5.2.2 Neural Network Modeling ...................................................................................... 20

5.2.3 Models Evaluation for Five Input Variables ........................................................... 23

5.2.4 Results and Discussions for Five Input Variables .................................................. 26

6 Conclusions ........................................................................................................................... 29

7 References ............................................................................................................................. 31
iv

TABLE OF CONTENTS (cont.)

Appendix A. RSE Coefficients for Thirteen Variables ...............................................................33

Appendix B. RSE Models For Five Input Variables ...................................................................35

Appendix C. Neural Network Characteristics ............................................................................37

Appendix D. Models Comparison for Five Input Variables .......................................................41
v

LIST OF FIGURES

Figure 1. Feed-forward neural network illustration. ................................................................. 6

Figure 2. Example of correlated variables matrix. .................................................................. 10

Figure 3. Truncated Pareto chart for low-and-no-gust condition. ........................................... 11

Figure 4. Predicted vs. Actual speed for low-and-no-gust condition. ..................................... 12

Figure 5. Model error vs. Target speed error for low-and-no-gust condition. ....................... 13

Figure 6. Truncated Pareto chart for high-gust condition. ...................................................... 14

Figure 7. Predicted vs. Actual speed for high-gust condition. ................................................ 14

Figure 8. Model error vs. Recommended landing speed error for high-gust condition. ........ 15

Figure 9. Low-and-no-gust error comparison. ........................................................................ 16

Figure 10. High-gust error distribution. .................................................................................... 17

Figure 11. Pareto chart for low-and-no-gust condition for the reduced number of

variables (5). ............................................................................................................ 19

Figure 12. Pareto chart for high-gust for reduced number of variables (5). .............................. 19

Figure 13. Network for five input variables. ............................................................................. 20

Figure 14. Mean square error for low-and-no-gust condition. .................................................. 20

Figure 15. Output vs. Target for training, validation and testing for low-and-no-gust

dataset. ..................................................................................................................... 21

Figure 16. Error distribution of training, validation and testing for low-and-no-gust

condition. ................................................................................................................. 22

Figure 17. Mean square error for high-gust condition. ............................................................. 23

Figure 18. Output vs. Target for training, validation and testing for high-gust dataset. ........... 24

Figure 19. Error distributions of training, validation and testing for high-gust condition. ....... 25

Figure 20. Absolute value of percentage error for neural network, RSE, and baseline for

low-and-no-gust condition. ...................................................................................... 25

Figure 21. Absolute values of percentage error for neural network, RSE, and baseline for

high-gust condition. ................................................................................................. 26

Figure 22. Percentage error distributions for low-and-no-gust condition. ................................ 27

Figure 23. Percentage error distributions for high-gust condition. ........................................... 28

Figure A-1. Absolute values of percentage error distribution for low-and-no-gust condition

for thirteen input variables ....................................................................................... 34

Figure A-2. Absolute values of percentage error distribution for high-gust condition for

thirteen input variables ............................................................................................. 34

Figure C-1. Training characteristics for low-and-no-gust condition. .......................................... 37

Figure C-2. Regression plot for all the values (training, validation, and testing) together. ........ 37
vi

LIST OF FIGURES (cont.)

Figure C-3. Error distribution for 1387 data points. .................................................................... 38

Figure C-4. Training characteristics for high-gust condition. ..................................................... 38

Figure C-5. Regression plot for data together. ............................................................................ 39

Figure C-6. Error histogram for all 426 data points together. ..................................................... 39

Figure C-7. Absolute values of percentage error distribution for high-gust neural network

model for five input variables. ................................................................................. 40

Figure C-8. Regression plots comparison of neural network model error versus the

recommendation error for high-gust condition. ....................................................... 40

Figure D-1. Absolute values of percentage error for low-and-no-gust condition for five

 input variables. ........................................................................................................ 41

Figure D-2. Percentage of error distribution for low-and-no-gust condition for five input

variables. .................................................................................................................. 41

Figure D-3. Absolute values of percentage error for high-gust condition for five input

variables. .................................................................................................................. 42

Figure D-4. Percentages of error distribution for high-gust condition for five input variables. . 42
vii

LIST OF TABLES

Table 1. Variables Used for Modeling ................................................................................... 10

Table 2. Summary of Recommended Error vs. RSE Model Error for Landing Speed .......... 16

Table 3. Five Input Variables ................................................................................................. 18

Table 4. Summary Landing Speed Models Error vs. Baseline Error for Five Input

Variables .................................................................................................................. 26

Table A-1. RSE Coefficients for Thirteen Input Variables ........................................................ 33

Table B-1. RSE Coefficients for Five Input Variables .............................................................. 35

Table B-2. RSE Terms Contribution for Low-and-No-Gust Case for Five Input Variables ..... 36

Table B-3. RSE Terms Contribution for High-Gust Case for Five Input Variables .................. 36
viii

NOMENCLATURE

ADS-B Automatic Dependent Surveillance ± Broadcast

ATC Air traffic control

ATM Air traffic management

ATPA Automated Terminal Proximity Alert

DFW Dallas\Forth Worth International Airport

FAA Federal Aviation Administration

FAST Final Approach Spacing Tool

FFBF Feed-forward Back Propagation

GW Gust wind

IAS Indicated Airspeed

MD80 McDonnell Douglas 80

MSE Mean Square Error

NAS National airspace system

NextGen Next-Generation Air Transportation System

TAPSS Terminal Area Precision Scheduling and Spacing System

TMA Traffic Management Advisor

TRACON Terminal Radar Approach Control

R

2 Coefficient of determination

RMS Root Mean Square

RMSE Root Mean Square Error

RSE Response Surface Equation

RSM Response Surface Methodology

SW Steady wind

w weight of neural network neuron

b bias of neural network neuron
1

COMPARISON OF PREDICTIVE MODELING METHODS OF AIRCRAFT

LANDING SPEED

Ousmane N. Diallo, Ph.D

Ames Research Center

SUMMARY

Expected increases in air traffic demand have stimulated the development of air traffic control

tools intended to assist the air traffic controller in accurately and precisely spacing aircraft

landing at congested airports. Such tools will require an accurate landing-speed prediction to

increase throughput while decreasing necessary controller interventions for avoiding separation

violations. There are many practical challenges to developing an accurate landing-speed model

that has acceptable prediction errors. This paper discusses the development of a near-term

implementation, using readily available information, to estimate/model final approach speed

from the top of the descent phase of flight to the landing runway. As a first approach, all

variables found to contribute directly to the landing-speed prediction model are used to build a

multi-regression technique of the response surface equation (RSE). Data obtained from

operations of a major airlines for a passenger transport aircraft type to the Dallas/Fort Worth

International Airport are used to predict the landing speed. The approach was promising because

it decreased the standard deviation of the landing-speed error prediction by at least 18% from the

standard deviation of the baseline error, depending on the gust condition at the airport. However,

when the number of variables is reduced to the most likely obtainable at other major airports, the

RSE model shows little improvement over the existing methods. Consequently, a neural network

that relies on a nonlinear regression technique is utilized as an alternative modeling approach.

For the reduced number of variables cases, the standard deviation of the neural network models

errors represent over 5% reduction compared to the RSE model errors, and at least 10%

reduction over the baseline predicted landing-speed error standard deviation. Overall, the

constructed models predict the landing-speed more accurately and precisely than the current

state-of-the-art.

1 INTRODUCTION

One of the goals of our nation¶s Next-Generation Air Transportation System (NextGen) is the

accommodation of an expected traffic-demand increase in the already congested terminal

airspace (ref. 1). To meet that objective in the near term, there is a need to create tools to predict

separation violations in order to plan conflict-resolution strategies. Overall, there are two

categories of tools for the final approach: tools that maximize throughput such as the Traffic

Management Advisor (TMA) (ref. 2) or the Terminal Area Precision Scheduling and Spacing

System (TAPSS) (ref. 3) and those that predict separation violations such as the Automated
2

Terminal Proximity Alert (ATPA) (ref. 4) or the Final Approach Spacing Tool (FAST) (ref. 5).

Independent of the decision support tool used, accurate landing-speed estimates are needed to

provide accurate space between successive arriving aircraft because all the tools rely on

predictions of the flight-path of the aircraft. The air traffic controllers¶ practice and procedures

dictate aircraft speed throughout most of the airspace, but the flight crew (and aircraft

procedures) dictates the speed on approach in preparation for landing. Therefore, accurate

landing-speed prediction will be required for tools intended for use on final approach.

Uncertainty in landing speed is manifested as either an increase in separation violations or as

increased separation buffers (leading to reduced throughput).

There exist many different approaches to establish the landing speed of an aircraft to be used in

the decision support tools. However, most of the options would require an upgrade to avionics

equipment or a flight crew to verbally report landing speed, thereby increasing the workload for

both the flight crew and the controllers. Thus, to fulfill the goal of this work for near-term

implementation with no additional equipment requirement, the focus of this research is to

develop an accurate landing-speed model based on information that is readily available in

today¶s air traffic control system.

As a first choice, the multivariable regression technique based on the response surface equation

(RSE) is used to develop a statistical model of aircraft approach speed. The regression technique

employed data for descent and approach phases of flight, as well as environmental and airport

characteristics data. The MD80 (SP80) aircraft characteristics and the physical characteristics

data of the Dallas/Fort Worth International Airport (DFW) provide a test bed to implement the

proposed statistical modeling approach. There is a trade-off between the amount of information

needed to build the model and its accuracy. Then, as a need to expand the study to other major

airports arises, the modeling approach is restricted to input variables that are more likely to be

available (airlines internal data are usually difficult to obtain). However, because with the

reduced number of variables the RSE performs poorly, an alternative approach, the feed-forward

neural network, is developed.

The remainder of the paper is organized as follows: Section 2 sets the context, background, and

motivation for the problem addressed. Section 3 presents the modeling methodologies. Then

section 4 summarizes the current state-of-the-art or baseline for the landing-speed prediction. In

section 5 the modeling methodologies are applied to actual recorded data, and the results are

presented and discussed. Finally, section 6 summarizes the findings.

2 BACKGROUND AND MOTIVATION

2.1 Background

NextGen is the Federal Aviation Administration (FAA)¶s plan to modernize the National

Airspace System (NAS) in order to increase its capacity by 2025. While the plan projects an

increase in the traffic demand, which would exceed the current capacity of the NAS, there are

concerns about the increase in air traffic controllers¶ workload. The air traffic controllers¶

function is to guide aircraft from departure to destination safely and efficiently. There is a need
3

to create tools that can facilitate and strengthen the air traffic controllers¶ decision process, while

not compromising the safety requirement. This paper focuses on tools in the terminal

environment, specifically those that address separation between successive arrivals.

To maintain runway arrival throughput, controllers sequence aircraft as they approach the airport

for landing and try to ensure there are no separation violations between any pair of aircraft. The

task of separating aircraft becomes increasingly complex in highly congested terminal airspace

(ref. 6). Research in the field of air traffic management (ATM) investigates ways to automate

separation assurance, to predict potential future violations, and to develop procedures to avoid

such violations. Conflict prediction and resolution tools require the estimation of the landing

speed of an aircraft to construct an accurate trajectory from its current position to the runway

threshold. As a pair of successive arriving aircraft approaches the landing runway, there is a

natural process of compression of the distance between the pair when the leading aircraft is

slowed ahead of the trailing aircraft (ref. 7). Knowledge of the landing speed of the leading

aircraft is required for determination of the approach-speed profile of the trailing aircraft. Since

the air traffic controller does not prescribe a landing speed, those data must either come from the

aircraft or be estimated. Landing-speed estimation must be accurate to be used effectively by the

different air traffic control (ATC) tools.

2.2 Motivation

The main objective of this work is to build a landing-speed model based on variables readily

available in today¶s air traffic automation systems. A landing-speed model is necessary because

for a given pair of aircraft on final approach, the leading aircraft landing-speed must be predicted

with sufficient lead time to allow tools to prescribe trajectory changes to be communicated to the

trailing aircraft to avoid separation violations, with a potential risk of wake vortex hazards if too

little separation is prescribed. To mitigate the impact of inaccurate landing-speed estimates and

to account for uncertainty of trajectory prediction, it is common for air traffic controllers to add

excess separation between pairs of aircraft, leading directly to loss of runway throughput.

There are three viable options to consider when determining the landing speed of an aircraft:

1. The intended landing speed can be electronically communicated (e.g., via ADS-B

message data) to controllers by the flight crew. This approach would require special

avionics.

2. Controllers could verbally request the landing speed from the flight crew and input it in

an interactive tool. This approach could increase the controller¶s and/or flight crew¶s

workload.

3. A model can be built to estimate the landing speed of the aircraft.

The first two options require changes to the ground equipment and/or controller procedures:

significant undertakings that could face resistance in their implementation. This paper focuses on

the third option, which concentrates on near-term implementation, using readily available

information to estimate the landing speed.
4

3 MODELING METHODOLOGIES

While there are many data-driven modeling techniques that can be used to build predictive

models, all of them rely on the quality of the raw data and processing approach utilized. To be

useful, raw data typically need to go through a thorough cleaning-up process.

3.1 Data Selection and Processing

This paper proposes to predict a landing-speed estimate using regression of multi-variables to fit

contributing inputs to corresponding historical landing speed as output. The first step of any such

data-driven technique is data collection and processing. Although there are many different ways

to collect and process historical data, a methodical approach leveraging previous work (ref. 8) is

used and summarized as follows:

3.1.1 Data Collection

The first step of a model development consists of identifying and collecting as many variables as

possible to make sure no impactful variables are overlooked. Thus, for this landing-speed

modeling, a model is built for a specific aircraft type at a given airport because each airport has

its specific characteristics. The raw data are composed of all airline monitored flight parameters

(e.g., fuel consumption, aircraft weight, etc.), radar recorded data (e.g., ground speed, etc.) and

airport environmental conditions (e.g., wind, visibility, ceiling, etc.).

3.1.2 Screening

The screening step is important to center the analysis on variables that directly impact the

modeling task. Thus, the screening is necessary to get rid of duplicative and unnecessary

information for the model. This step serves to detect the parameters that contribute the most to

the landing-speed behavior. Also, during the screening step obvious parameters with no impact

(e.g., departure airport, etc.) on the model are eliminated.

3.1.3 Physically Relevant Parameters

It is common practice by airlines to track both the planned and actual variables for many key

parameters. However, in this work, only the actual values (as opposed to planned values) of the

variables are used. The use of actual variables would allow achieving more realistic models

because planned variables are typically based on the predicted actual variables augmented by a

margin value to account for the uncertainty of flight parameters (e.g., fuel burn, time, etc.). Also,

the variables irrelevant to these modeling methods such as city-pair, route information (domestic

or foreign), etc. are discarded.
5

3.2 Mathematical Modeling: Multi-variable Regression Modeling

The mathematical modeling is focused on two regression approaches. The first choice is the

linear regression technique because is easier to build and implement. However, when the linear

approach fails to provide an acceptable predictive model, the nonlinear feed-forward neural

network is used.

3.2.1 Response Surface Equation

The linear regression used in this study is the multivariate regression technique of the Response

Surface Methodology (RSM) (ref. 9). The RSM consists of building a response surface equation

(RSE), which constitutes simplified polynomial equations used to model behavior of complex

systems. RSE is used to relate the factors (or predictors) to the measured responses (landing

speed) over some specified region of interest. Use of the RSE can be justified by its ability to

combine parameters of different natures, and their cross-effects, in a single equation. The most

popularly used RSE is the second-order Taylor series approximation because it requires a

minimal computational investment:

 (1)

where:

R: the dependent parameter (response) of interest

: the intercept term

: regression coefficients for the first-order terms

: coefficients for the pure quadratic terms

: the coefficients for the cross-product terms

: the independent variables

: the number of factors

 : the error associated with neglecting higher-order effects

The RSE assumes that for any model the error, , should be normally distributed as N(0,1).

3.2.2 Neural Network Modeling

In general neural networks are an alternative to Response Surface Methods in the creation of

regression models for problems where the polynomial representation of the RSE does not

perform well (ref. 10). Among the neural network types, the feed-forward back propagation

(FFBP) is one of the easiest to build and implement. Usually, it is a good starting point to build a

model because a feed-forward neural network can theoretically fit any nonlinear relationship

between inputs and target.

R ! b0  bixi

i!1

k

 biixi

2

i!1

k

 bij xix j 

j!i1

k

i!1

kn1

bo

i

b

ii b

bij

i j

x ; x

k
6

Figure 1. Feed-forward neural network illustration.

3.2.2.1 Neural Network Background

Architecturally a neural network is composed of an input layer, hidden layers, and an output

layer as illustrated in Figure 1. The hidden layer is the data processing center of the network. The

output layer is the response to the simulation.

A layer is composed of neurons. In a layer, each input element is connected to each neuron

through a weight (w), and a bias (b) is added to the weighted input. Typically, there are three

main steps to build a neural network: training, validation and testing. Consequently, a dataset

composed of an input set and corresponding target output are divided into those three groups.

Usually there is a pre-processing step to get the data into a useful form. Then the training step

consists of tuning the values of weights and biases of the network to optimize network

performance (ref. 11). The validation step consists of using the second (validation) set of the data

to adjust the quality of the regression. Finally, the test set serves to check the network on a set

different from the one used for its construction.

Many training algorithms exist. The Levenberg-Marquardt is the most commonly used algorithm

for feed-forward networks when rapid training is desired. Based on the nature of this research to

model a regression of the input variables to predict the corresponding landing speed, the network

is trained for function approximation as opposed to the pattern recognition. A proper training

requires a training set based on known inputs and corresponding target outputs. It is also

customary for neural networks to undergo the training process (retraining) a couple of times to

improve the quality of the fit. Then, the performance function used as the stopping criteria is the

Mean Square Error (MSE) defined in equation (2) as:

 (2)
7

where:

: Mean Square Error, the average squared error between the network outputs and target

outputs

: ith error between the network outputs and target outputs

: ith target or actual output

: ith network predicted output

: number of inputs

4 BASELINING: FLIGHT OPERATING MANUAL RECOMMENDATION

Aircraft operating manuals provide landing-speed recommendations for each aircraft type based

on the landing-aircraft weight. In order to assess the quality of the proposed models, the current

aircraft operating manual recommendations are used as a baseline. As a case study, one of the

most common narrow-body air-transport aircraft is used.

4.1 Baselining

The MD80 super 80 version has two recommendations: one for low-and-no-gust condition

defined as gust wind below 10 knots and a high-gust condition for gust wind greater than

10 knots.

4.1.1 Landing with Low-and-No-Gust Condition

In the low-and-no-gust condition on the final approach, pilots are recommended to aim for a

target approach speed of:

(3)

where:

: Final approach target speed (knots indicated airspeed (IAS))

: Reference speed (knots IAS)

The reference speed is provided in the flight manual as a function of aircraft weight and aircraft

type.

4.1.2 Landing with High-Gust Condition

In the high-gust condition, it is recommended in the final approach that pilots use a target

approach speed of:

VT arg et ! Vref  5knots

VT arget

Vref
8

 (4)

where:

: Final approach target speed (knots IAS)

: Reference speed (knots IAS)

: Steady wind defined as the headwind component of the reported winds

: Gust wind defined as the headwind differential between the reported winds and the reported

gusts

However, for the high-gust condition there is also a restriction that the total wind additive to the

Vref should not exceed 20 knots.

4.2 Model Evaluation

After building the landing-speed model, there is a need to compare the model with the

recommended landing speed or target approach speed, which is the best available prediction of

landing speed. To compare the model against the target speed, two metrics are defined:

ErrorVtarget: calculated as the error between the VTarget (i.e. baseline speed) and the actual landing

speed as illustrated in equation (5):

 (5)

ErrorModel: calculated as the error between the model predicted landing speed and the actual

landing speed using the formula in equation (6):

 (6)

with:

VActual: Actual speed or true speed is defined as the sum ground speed (obtained from the

terminal radar approach control facilities (TRACON) radar data) and the reported wind at the

airport (from METAR),

VTarget: Target speed or flight manual-recommended landing speed is defined as the flight

manual-recommended approach speed based on aircraft type and aircraft weight. This speed is

used as the baseline landing speed for comparison.

VModel: Landing speed of the model is defined as the model predicted landing speed.

VT arget !Vref  1

2

SW GW

VT arget

Vref

SW

GW

ErrorVT arg et

!

VActual nVT arget

VT arg et

»100

ErrorVModel

!

VActual nVModel

VModel

»100
9

5 PROOF OF CONCEPT

Previous studies (refs. 7, 12) suggested that airport-specific parameters (airport elevation,

runway length, etc.) contribute to the final approach performance of a flight. More importantly, it

is clear that each aircraft type (e.g., B737-800 or MD80) has specific performance parameters

that would directly impact its landing speed. Consequently, to account for all these variations

that may affect the fidelity of any landing-speed model, an airport-specific and aircraft-specific

landing model was created using historical data.

As a proof of the concept, the proposed methodologies to predict aircraft landing speed are

applied to the MD80 aircraft type also referred to as the Super 80 (SP80) operations at the

Dallas/Fort Worth International Airport. DFW was chosen because data for detailed analysis

were available and the SP80 is highest number of a single aircraft type in service at this airport.

5.1 RSE Application to Thirteen Input Variables

The different steps of the proposed methodology are carried out using DFW and the SP80

aircraft type.

Step 1: Data collection

A dataset of over 300 variables is recorded over time. Collected data are composed of airport

topological (e.g., runway length and configuration), environmental information (e.g., visibility,

wind condition, ceiling), flight-specific parameters (e.g., city pair flown, fuel burn rate, landing

weight, etc.), and aircraft-specific parameters (e.g., empty gross weight, aircraft maximum

payload, etc.). For the remainder of this paper the collected data are considered as the true value

or actual value.

Step 2: Screening

The main goal of this section is the identification of the predictive values of the parameters. First,

variables that are known to be irrelevant are automatically eliminated (e.g., aircraft tail number,

city of departure, etc.). Also, if two or more variables provide the same information, only one of

them is used for the modeling. For example, as shown in Figure 2, the variables pax (number of

passengers) and LF_pax (load factor for passengers) have a correlation coefficient of 1. For

modeling purposes these two variables provide the same information, so one of them is sufficient.

Consequently, after dropping the linear dependent parameters, LF_pax, FBR (fuel burn rate), and

ESAD_nm (equivalent still air distance) are among the retained variables for modeling.

Step 3: Physically irrelevant parameters to the model are eliminated.

The result of the screening and physical relevance steps, based on the principle of using the

minimum possible number of variables, yields a reduced set of thirteen parameters as the most

relevant to aircraft landing speed (shown in Table 1). Only the selected thirteen variables are
10

used as inputs to fit the multivariable regression model defined in equation (1), where the

response is the landing speed. It should be noted, however, that not all of these parameters have

equal importance.

Figure 2. Example of correlated variables matrix.

TABLE 1. VARIABLES USED FOR MODELING

Parameter Description

Head wind Head Wind

Gust wind Gust Wind

Ceiling_ft Forecast Ceiling

Vis_ft Forecast Visibility

asms Available Seat Miles

APAY Actual Payload

Act_Land_Wgt Actual Landing Weight

FUEL_LOAD Fuel Load

AFUBO Actual fuel burn

FBR Fuel burn rate

RSV Reserve fuel

ESAD_nm Equivalent still air distance

LF_pax Load factor for passenger
11

The MD80 flight manual provides a set of recommendations for low-and-no-gust condition and

another set for high-gust condition (ref. 13). Under the normal operating conditions, the MD80

flight manual defines the low-and-no-gust condition for reported wind between 0 and 10 knots,

whereas it defines the high-gust condition for reported wind over 10 knots.

A landing-speed model will be constructed for each of the two scenarios set forth by the MD80

flight manual. The model that predicted landing speed will be compared to the one recommended

by the airlines¶ flight manual to highlight the benefits of the proposed modeling approach.

5.1.1 Low-and-No-Gust RSE Model

Using the 13 retained parameters shown in Table 1, the coefficients of the first-order terms, the

second-order terms, the cross-term, and the intercept are all calculated by fitting the variables

into the response. The statistical package JMP is used to compute the different RSE coefficients

(see appendix A). The equation obtained is the multivariable model. To illustrate the contribution

of each variable and cross-term to the landing speed model for the low-and-no-gust condition, a

Pareto chart shown in Figure 3 is generated.

The Pareto chart provides much information to the system modelers. It shows the orthogonal

estimate, which is the orthogonal projection of the model along the RSE terms. For example, the

model projection along the APAY axis has a value of 3.62, which represents the norm (or

weight) of the model vector along the APAY axis. Furthermore, it can be inferred from the

Pareto chart that the variable APAY contributes the greatest variability to the landing-speed

model with about 13.5% contribution, followed in decreasing order by the headwind (~8.2%

contribution), the actual landing weight (~5.2% contribution), the ceiling (~4.3%), the cross-term

of headwind-landing weight (~3% contribution), and so on. Also, the Pareto chart allows us to

assess the relative importance of each term in the RSE; for example, the relative contribution of

Figure 3. Truncated Pareto chart for low-and-no-gust condition.

! "# $ %"# $ &" # $ ' "#$ (""# $

) *+ *,- . /0$

1*2/0$

20% 40% 60% 80% 100%

Cumulative

curve
12

the headwind variable (with a value of 2.23) weights about 1.6 times the relative contribution of

the actual landing weight (Act_Land_Wgt) variable (with a value of 1.42) to the landing-speed

model for the low-and-no-gust condition. Other important information gained from the Pareto

chart is the visualization of the cumulative effect of the RSE terms. Using the cumulative

contribution curve, systems modelers can make a decision about the appropriate level of fidelity

necessary. As illustrated in Figure 3, the cumulative contribution of the truncated Pareto chart

showing the first 19 out of 104 terms represent 57% of the 13-variables RSE model for the lowand-no-gust condition.

Other information obtained from the Pareto chart is that even though the flight manual proposes

that headwind and gust wind play important roles in predicting the landing speed (see equations

(2) and (3)), their significance is not as important as suggested, weighting only 8.2% and 2%,

respectively, of the landing-speed model.

After the model is obtained, the quality of the model is assessed using several goodness-of-fit

metrics. Figure 4 illustrates the predicted landing-speed model compared to the recorded actual

landing speed. The coefficient of determination R2 and the root-mean-square (RMS) error are

computed to be 0.43 and 6.16, respectively. The blue line represents the actual landing speed

(also called the 45-degree line); a perfect predictor would have values along the blue line. As

Figure 4 shows, there still is some sizable landing-speed prediction error for the low-and-no-gust

condition despite the use of the same dataset modeling and testing.

Figure 4. Predicted vs. Actual speed for low-and-no-gust condition.
13

Figure 5. Model error vs. Target speed error for low-and-no-gust condition.

The error on baseline speed and the error on the model are calculated for the low-and-no-gust

condition using equations (5) and (6), respectively. Figure 5 represents a visual representation of

the calculated error metrics for the low-and-no-gust condition. The red stars represent the

absolute value of the model error, and the blue open circles, the absolute value of the targetspeed error. The error metric clearly shows that the baseline error is larger than the RSE model

error for the low-and-no-gust condition.

5.1.2 High-Gust RSE Model

For the high-gust condition, the same thirteen input variables in Table 1 are used to construct a

RSE model. A new set of RSE coefficients are calculated (see appendix A) and the Pareto chart

is obtained and shown on Figure 6.

Similar to the low-and-no-gust condition, the APAY variable is the biggest contributor to the

landing speed for the high-gust condition, with 11%. However, the second contributor is the

visibility (~8% contribution), contrary to the low-and-no-gust condition. Also, the relative

contribution parameters are different from the low-and-no-gust case; thus, the Pareto chart for

the high-gust condition is different from the low-and-no-gust one.

Figure 7 shows the predicted versus actual landing speed. The goodness of fit of the model is

assessed with the calculation of the coefficient of determination R2 of 0.62 and the RMS error of

5.79. The blue line on Figure 7 represents the actual landing speed (also called the 45-degree

line). It also corresponds to the ideal fit of a coefficient of determination R2 of 1. The goodnessof-fit metrics for the high-gust wind condition shows that overall the model for the high-gust

condition is a better than the model obtained for the low-and-no-gust wind condition. It is worth
14

mentioning that the values of the goodness-of-fit shown in the figure represent only the dataset

used in this study.

Figure 6. Truncated Pareto chart for high-gust condition.

Figure 7. Predicted vs. Actual speed for high-gust condition.
15

Figure 8. Model error vs. Recommended landing speed error for high-gust condition.

Correspondingly, the error on baseline speed and the error on the model are calculated for the

high-gust condition using the same equations, (5) and (6), respectively. Figure 8 illustrates the

calculated error metrics for high-gust conditions. The red stars represent the absolute value of the

model error, and the blue open circles, the absolute value of the target-speed error.

As is evidence in Figure 5 (low-and-no-gust condition) and Figure 8 (high-gust condition), the

value of the model error is consistently smaller than that of the target speed error. Although the

model error is better than the target-speed error for both wind conditions, Figure 8 shows that

model error values for the high-gust case are relatively smaller than the error values of the lowand-no-gust case, while Figure 5 shows larger errors for the low-and-no-gust case.

5.1.3 Summary and Discussion of Results for RSE Models with Thirteen Input

Variables

Table 2 summarizes the statistical characteristics of the RSE model versus the baseline landingspeed error. It appears that the RSE model with thirteen input variables is better than the airline¶s

flight manual-recommended target landing speed based on the statistical parameters metrics. The

mean value of the error of both the low-and-no-gust and high-gust wind conditions is very close

to 0 (i.e., -1.80e-4 and 5.07e-5, respectively), whereas the mean values for the target error

landing speed are 4.25 for the low-and-no-gust wind condition and -6.92 for the high-gust wind

condition. The fact that the mean of the model error is nearly 0 illustrates the closeness of the

model to the actual landing speed. The standard deviations of the model error are also smaller

(4.36 and 3.65, respectively, for low-and-no-gust and high-gust conditions) compared to the

standard deviations of the target landing-speed error (5.18 and 4.38, respectively, for low-andno-gust and high-gust conditions), illustrating less dispersion of the model-predicted landing

speed from the actual landing speed than the target landing speed.
16

TABLE 2. SUMMARY OF RECOMMENDED ERROR VS. RSE MODEL ERROR FOR

LANDING SPEED

Overall, the standard deviation of the RSE model error reduced the standard deviation of the

baseline error by 18% for the low-and-no-gust condition and 22% for the high-gust case.

Another way to show the accuracy and precision of the RSE models compared to the baseline is

by examining the error distributions. Figure 9 shows the absolute value of the model error (blue

bar) and the baseline error (red bar) distributions for the low-and-no-gust condition. Figure 9

shows that out of the 1387 data points considered, around 950 of them have predicted landingspeed error within 0 to 4%, while there are only about 600 data points within the same error

interval for the baseline error. On the opposite side, for a larger percentage error range of 8 to

12%, there are about 340 data points for the model error and about 500 data points for the

baseline error.

Figure 9. Low-and-no-gust error comparison.

Baseline Model Baseline Model

Mean 4.2 -1.80E-04 -6.9 5.10E-05

std 5.2 4.4 4.4 3.6

Min -14.5 -12.6 -19.2 -11.7

Median 4.3 -0.1 -7.3 -0.1

Max 40.9 27.3 7.6 10.6

25% quartile 0.8 -2.9 -9.9 -2.8

75% quartile 7.5 2.5 -4.2 2.5

Statistical

Parameters

Low-and-no gust Error High gust Error
17

Figure 10. High-gust error distribution.

Figure 10 represents the error distributions of the absolute value of the RSE model (blue bar) and

the baseline (red bar) for the high-gust condition. A similar tendency is observed for the highgust case as well. For the lower error percentage range (0 to 4%), there are about 310 out of 426

data points for the model compared to only about 90 data points or so for the baseline error. At

the higher error range (8% to 12%) there are only 15 data points for the model versus 140

instances of baseline errors.

In summary, for the thirteen input variables case, the comparison metrics used all show that the

RSE model is better than the current state-of-the-art (baseline). That is, for both the low-and-nogust and high-gust conditions, there is 18% less dispersion for the low-and-no-gust case and 22%

less dispersion for the model error compared to the baseline error. This finding implies the model

is more precise in predicting the landing speed. Also, for both gust conditions, there are more

instances of data-point percentage error concentrated within the 0% to 4% range for the model

than the baseline, indicating that the model is more accurate. However, the coefficients of

determination R2 (0.43 and 0.62, respectively) are smaller relative to the ideal value of 1. That

lack of fit of the model may be explained in part by the model uncertainty and the lack of

knowledge of the pilots¶ decision-making process to achieve landing.

5.2 Application to Reduced Number of Input Variables: Five Inputs

It is important to note that the thirteen variables used in the previous example would not be

available at most airports because airlines typically do not provide the data to the public.

Therefore, the study is repeated for the more realistically obtainable variables composed of the
18

TABLE 3. FIVE INPUT VARIABLES

Parameter Description

Head wind Head Wind

Gust wind Gust Wind

Ceiling_ft Forecast Ceiling

Vis_ft Forecast Visibility

Act_Land_Wgt Actual Landing Weight

five parameters listed in Table 3. These data are typically available to individuals through normal

acquisition means (e.g., Federal Aviation Administration (FAA) websites).

In a similar approach, the data are divided into two groups: low-and-no-gust condition in one

group and high-gust condition in another. As a first attempt, the multivariable linear regression

modeling method of RSE is reproduced.

5.2.1 RSE Modeling

The RSE is built following the steps underlined in the modeling methodologies section using the

same data points as in the case of thirteen input variables. However, only the five input

parameters listed in Table 3 are fitted into a RSE with the recorded actual landing speed as target

output for each of the gust conditions.

5.2.1.1 RSE Model for Landing with Low-and-No-Gust Condition

Figure 11 shows that for a study with only five variables, the main contributor is the aircraft

landing weight, representing about 32% toward the model, followed by the headwind (18%),

ceiling (9.5%), and visibility (5%), respectively. The computed coefficients of the second-order

regression equation can be seen in appendix B for the low-and-no-gust condition. Then the crossterms of headwind-visibility, ceiling-landing weight, and the gust wind followed. In other words,

the gust wind contributes to the model the least.

The quality of the fit is assessed by calculating the values of the coefficient of determination R2

of 0.37 and the RMS error (RMSE) is 6.29. These values show that the RSE approach performs

worse for the five input variables case than the thirteen.

5.2.1.2 RSE Model for High-Gust Condition

Like in the low-and-no-gust case, as illustrated in Figure 12, the aircraft weight is main

contributor to the landing speed for the reduced number of variables (five), representing over

28% of the high-gust model. The computed coefficients of the second-order regression equation

can be seen in appendix B for the high-gust case. Contrary to the low-and-no-gust condition, the

visibility is the second-highest contributor with a negative impact representing around 19%,

followed by headwind, which contributes around 9%. The ceiling (2.5%) and the gust wind

(0.4%) contribute marginally to the overall model.
19

Figure 11. Pareto chart for low-and-no-gust condition for the reduced number of variables (5).

Figure 12. Pareto chart for high-gust for reduced number of variables (5).

The quality of the fit is assessed by calculating the values of the coefficient of determination R2

of 0.50, and the RMS error is 5.95. Similar to the low-and-no-gust case, it is clear that the RSE

approach performs worse for the five input variables than for the thirteen. Because of the poor fit,

other options such as the neural network are investigated.
20

5.2.2 Neural Network Modeling

The neural network model handles nonlinear relationships between inputs and target better than

linear regression techniques. Because the linear regression technique of RSE did not provide

high enough quality of fit, it is worth exploring a nonlinear technique such as the neural network.

Like in the RSE modeling approach, a neural network model is built for the low-and-no-gust

condition and another one for the high-gust condition.

5.2.2.1 Neural Network Model for Low-and-No-Gust Condition

The five variables from Table 3 are used as inputs to build a feed-forward network with a

schematic shown in Figure 13 for the low-and-no-gust condition.

The dataset is randomly divided into three groups as follows: 70% used for training, 20% for

validation, and the remaining 10% for testing. Then, the training process consists of tuning the

weights and biases until the validation dataset converges as illustrated in Figure 14.

Figure 13. Network for five input variables.

Figure 14. Mean square error for low-and-no-gust condition.
21

After the training, validation, and testing steps, the model output is plotted versus the target for

the dataset as shown in Figure 15. The graphs of all three datasets are shown for the sake of

transparency. Also from the Figure 15, the regression values of the network output versus the

target are 0.62, 0.58, and 0.56 for the training set, the validation, and the testing set, respectively.

The fact that the correlation values of all three datasets are within the same range shows a

consistency between the training sets and the testing set.

The error distribution in Figure 16 shows the dispersion of the training, validation, and testing set

errors between the network prediction and the target. The error distributions approximate a

normal distribution for each dataset. The reduced standard deviation of the testing set may be

explained by the smaller number of its data points. Additionally, Figure 16 stresses the fact that

all three datasets have similar statistical characteristics.

The remaining neural network model characteristics can be found in appendix C for both the

low-and-no-gust and high-gust conditions.

Figure 15. Output vs. Target for training, validation and testing for low-and-no-gust dataset.
22

Figure 16. Error distribution of training, validation and testing for low-and-no-gust condition.

5.2.2.2 Neural Network Model for Landing with High-Gust Condition

In a similar fashion, a neural network model is built for the high-gust condition as illustrated in

Figure 13. For the sake of consistency, the high-gust dataset is randomly divided into three

groups: 70% used for training, 20% for validation and 10% for testing. Figure 17 illustrates the

convergence of the network after twelve iterations, with the best validation performance reached

at the sixth iteration.

Figure 18 shows how well the model output for the training, validation, and testing datasets did

versus the target values after 6 iterations. Also, it shows the regression fit in each case. The

regression values of the network output versus the target are better for the high-gust condition

than for the low-and-no-gust condition with 0.70, 0.65, and 0.62 for the training set, the

validation, and the testing set, respectively. Similar to the low-and-no-gust condition, the

correlation values of the three datasets are within the same range, showing a consistency among

the datasets used to model the high-gust case.
23

Figure 17. Mean square error for high-gust condition.

The error distribution in Figure 19 shows the dispersion of the training, validation, and testing set

errors between the network prediction and the target.

For the high-gust condition, the training and validation sets have similar error distributions, but

they are different from the testing set. This lack of well-defined error distributions may be

explained by the reduced number of data points for the high-gust condition at DFW.

5.2.3 Models Evaluation for Five Input Variables

The two different modeling methodologies are evaluated and compared to the baseline landing

speed using the two error metrics defined earlier in equations (5) and (6). Thus, the two models

(RSE and neural network) are evaluated for both the low-and-no-gust and high-gust conditions

using the error metrics defined earlier.

Figure 20 and Figure 21 are visual representations of the error metrics for the low-and-no-gust

and high-gust conditions, respectively. The blue open circles represent the absolute value of the

baseline error, the red stars represents the absolute value of the neural network model error, and

the black plus sign represent the absolute value of the RSE model error.

For the low-and-no-gust condition, Figure 20 shows that the absolute value of the predicted

landing-speed errors of the models are concentrated mostly between 0 and 6% for most of the

1387 data points used, while the flight-operating manual-predicted landing speed has most of the

absolute value error within the 8% to 20% range for the same dataset.
24

Figure 18. Output vs. Target for training, validation and testing for high-gust dataset.

As for the high-gust condition, a visual inspection of Figure 21 shows that the magnitude of the

absolute value of the predicted landing-speed errors of the model are mostly concentrated

between 0 and 6% for most of the 426 data points used. However, the most of the absolute values

of the flight-operating manual predicted landing-speed errors are within the 4% to 16% range for

the same dataset.

As illustrated in Figure 20 (low-and-no-gust condition) and Figure 21 (high-gust condition), the

absolute values of the predicted landing-speed errors of the model (neural network (red stars) and

RSE (black plus signs) are consistently lower than those of the current state-of-the-art landingspeed prediction (blue circles).
25

Figure 19. Error distributions of training, validation and testing for high-gust condition.

Figure 20. Absolute value of percentage error for neural network, RSE, and baseline for

low-and-no-gust condition.
26

Figure 21. Absolute values of percentage error for neural network, RSE, and baseline for

high-gust condition.

5.2.4 Results and Discussions for Five Input Variables

Because the RSE model with the reduced number of input parameters poorly predicts the landing

speed, the neural network models were built for both the low-and-no-gust and high-gust

conditions. Then, the neural network models were assessed and compared to the RSE model and

to the recommended landing speed provided by the operating flight manual.

Despite the reduced number of input variables from thirteen to five, the neural network models

provide better landing-speed predictions for both low-and-no-gust and high-gust conditions than

the airlines¶ operating flight manual. Table 4 summarizes statistical parameters, comparing the

errors between the neural network models and the flight manual.

TABLE 4. SUMMARY LANDING SPEED MODELS ERROR VS. BASELINE ERROR FOR

FIVE INPUT VARIABLES

NN_Model RSE_Model Baseline NN_Model RSE_Model Baseline

Mean -5.9E-02 -1.4E-04 4.2 -1.6E-01 1.3E-06 -6.9

std Dev 4.4 4.6 5.2 4.0 4.2 4.4

Min -13.5 -14.9 -14.5 -12.5 -13.3 -19.2

Median -0.1 -0.1 4.3 -0.4 -0.4 -7.3

Max 29.5 32.8 40.9 13.4 15.0 7.6

25 Percentile -3.0 -3.1 0.8 -7.0 -2.7 -9.9

75 Percentile 2.4 2.7 7.5 2.3 2.6 -4.2

Statistical

Parameters

Low and No Gust Error High Gust Error
27

An analysis of Table 4 indicates that the mean values of the percentage error of the models are

about 0 for both low-and-no-gust and high-gust conditions (-0.1% and -0.2%, respectively)

compared to existing flight manual-recommended values (4.2% and -6.9%, respectively).

Furthermore, the standard deviation is smaller for the models than the existing flight operating

manual recommendations. These two statistical parameters demonstrate that the neural network

landing-speed prediction models are closer to the actual landing speed for both the low-and-nogust and high-gust conditions.

It is also worth comparing the neural network and the RSE models to see how each of them fared

compared to the baseline. Figure 22 and Figure 23 show the comparative error distributions of

the neural network model (blue bars), the RSE (light green bars) and the baseline (red bars) for

the low-and-no-gust and the high-gust conditions, respectively. For both gust conditions, the

error distributions of the models approximate a normal distribution, implying that the errors of

the models are random, with peak around 0% error. A direct comparison between the two types

of models shows that the neural network model performs better than the RSE model, because

there are more instances of 0% to 2% error for the neural network than for the RSE. The number

of instances of RSE error becomes larger for higher error values. There are also some important

differences between the individual distributions.

An analysis of the error distribution for the low-and-no-gust condition (Figure 22) shows that the

neural network has the highest number of cases around 0%. As the error value increases, the

number of instances of neural network model error decreases faster than the RSE, meaning there

are fewer data points with larger predicted landing-speed errors for the neural network model

than for the RSE. It is also clearly apparent in Figure 22 that both models (with peak value at

0%) perform better than the baseline (with peak at 5%).

Figure 22. Percentage error distributions for low-and-no-gust condition.
28

Figure 23. Percentage error distributions for high-gust condition.

An analytical analysis of the low-and-no-gust condition suggests that the neural network model

is a better landing-speed predictor than the RSE model: while both modeling methods have mean

error values of 0 (i.e., accuracy), the neural network model error has a standard deviation 5.6%

lower (less dispersion) than the RSE model. Compared to the baseline error, the neural network

model error reduces the baseline error standard deviation by 18.8% while the RSE model error

reduces the baseline error by 12.5%.

Another interesting observation from Figure 22 is that for the low-and-no-gust condition, the

flight operating manual tends to underestimate the landing speed; that is, it under-predicts the

landing speed (see equation (6)). In other words, at the low-and-no-gust condition, pilots

overshoot the landing speed compared to the flight manual recommendation.

Similarly, the error distribution of the high-gust condition shown in Figure 23 demonstrates that

both the neural network model and the RSE model having their highest number of cases of error

around 0% (with peak value at 0%) predict the landing speed with less error than the baseline

(with peak at -10%) does.

As the error value increases, the number of instances of neural network model error decreases

faster than the RSE, whereas the error values get larger in the negative direction, so it is not clear

which model performs better. However, an analytical analysis of the high-gust condition

statistics shows that the neural network model predicts landing speed more precisely than the

RSE model because while both models have mean values of error at 0 (i.e. similar accuracy), the

neural network model error has a standard deviation 5.5% lower (less dispersion) than the

RSE model.
29

Moreover, while the neural network model represents a sizeable 9.5% landing-speed prediction

precision improvement over the baseline prediction, the RSE is a mere 3.8% improvement over

the baseline.

Contrary to the low-and-no-gust condition, in the high-gust case shown in Figure 23 the flightoperating manual overestimates the landing speed. Thus, the predicted landing speed is over

predicted compared to pilots¶ achieved landing speed.

Overall, both models predict landing speed more accurately (e.g., 0 mean value) and more

precisely (e.g. lower error standard deviation) than baseline under both gust conditions. For the

normal landing-speed range, both models are capable of predicting the landing speed within a

few knots for most data points. However, for a reduced number of input variables, the neural

network models for both gust conditions yield a better landing-speed prediction than does the

RSE modeling approach. More illustrative figures showing the advantages of the neural network

model over the RSE model can be found in appendix D. The ability of neural networks to handle

the nonlinear regression better is to be credited for the improved precision capability. One of the

main disadvantages of using the neural network modeling approach for this type of study is that

it works like a black box for the end user, providing no insight on the impact or the variance of

each input variable on the landing speed. Therefore, valuable information provided to researchers

about the contribution of each parameter to the RSE model shown on Pareto chart types would

be lost in the neural network modeling approach.

6 CONCLUSIONS

The principal goal of this study is to create aircraft landing-speed models that are unbiased

(accurate) with minimum variance (precise), and demonstrate potential for near-term

implementation. An accurate predicted landing-speed is required for the achievement of

NextGen goals, so that a trailing aircraft trajectory (speed and altitude) can be adjusted to avoid

any predicted separation violations. Among the immediate potential benefits to having an

accurate landing speed model are: an increase in airport throughput by decreasing the excess

separation buffer between successive arrival aircraft, a potential increase in overall safety in lowvisibility conditions, and a possible decrease in fuel burn as a consequence of decreased travel

time and landing procedures. It is worth noting that the inability to reduce or eliminate the excess

separation buffer due to trajectory uncertainty at the nation¶s busiest airports is one of the key

hurdles to meeting the anticipated demand of the NextGen NAS.

As a proof of concept to the proposed multivariable regression technique of RSE, the thirteen

most impactful variables for MD80 landing speed at DFW for the case of thirteen input variables

are used. The qualities of fit of the models are assessed with a coefficient of determination R2 of

0.43 for the low-and-no-gust model and R2 of 0.62 for the high-gust RSE model. In order to

expand the landing-speed prediction modeling approach to other major airports, the RSE

modeling is repeated with the five likely readily available variables. The quality of fit for the

RSE model deteriorates with coefficients of determination R2of 0.37 and 0.5 for low-and-nogust and high-gust conditions respectively. These results reveal that more work on the model is

required to enhance its predictive ability.
30

In an attempt to improve on the predictive performance of the RSE model with five input

variables, feed-forward neural network models are developed for each gust condition. While both

models have similar accuracy, the neural network models approximate the actual landing speed

much better than the RSE models because the error standard deviations of the neural network

models were reduced by 5.6% and 5.5% (better precision) for the low-and-no-gust and high-gust

conditions, respectively. More importantly, the prediction of the landing speed of the neural

network is an 18.8% and 9.5% precision improvement over the existing state-of-the-art that is the

flight manual recommendation for low-and-no-gust and high-gust conditions respectively.

Comparatively, the RSE models are 12.5% and a mere 3.8% improvement of the landing-speed

prediction precision over the flight operating manual recommendation for low-and-no-gust and

high-gust conditions, respectively.

Ultimately, the proposed data-based modeling approach shows great potential for predicting

actual landing speed far better than the existing operating flight manual recommendation for

final approach speed commonly prescribed in commercial aircraft flight manuals. The two

different regression techniques presented in this paper begin to address the research challenges in

the prediction of final approach speed modeling. The models achieved a more accurate (mean

value of error of 0) and precise (less dispersion) prediction of the landing speed for the narrowbody air transport used as a test-bed than the current flight operating procedure recommendation

can. Thus under normal landing conditions, each of the constructed models predicted the landing

speed within a couple of knots of the actual achieved speed.

The next steps of this research should be applying these modeling approaches to other airports

and aircraft types. Finally, the proposed modeling approach can be improved by identifying more

relevant parameters and finding a way to quantify pilots¶ decision-making processes for the

landing procedure. In the meantime, the study allows us to conclude that pilots tend to

overcompensate landing speed in the low-and-no-gust condition and under-shoot landing speed

under high-gust conditions. This finding is very important in trying to model pilots¶ behavior to

improve existing and future terminal area tools.
31

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Virginia, Sept. 2011.

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Methodology: Process and Product Optimization Using Designed Experiments. Vol. 705.

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(BRAINN) Documentation. Version 2.3, Jan. 2009.

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13. MD-80 Flight Manual, TR 02-01, 2002.
32
33

APPENDIX A. RSE COEFFICIENTS FOR THIRTEEN VARIABLES

Table A-1 list the RSE coefficients for thirteen input variables.

TABLE A-1. RSE COEFFICIENTS FOR THIRTEEN INPUT VARIABLES

Term Low Gust

Coefficient Estimate

High Gust

Coefficient Estimate

Intercept -575.35 1078.88

headWind -8.76 -6.74

gustWind -560.98 2.18

Ceiling_ft -4.94E-03 5.48E -03

Vis_ft 5.06E -03 4.59E -03

asms 1.57E -03 0.03

APAY 6.53E -03 0.02

Act_Land_Wgt 0.02 -0.03

FUEL_LOAD 0.01 0.01

AFUBO -0.01 -0.01

FBR 1.19 1.66

RSV -0.23 0.08

ESAD_nm -0.02 -4.83

LF_pax -5.27 6.66

headWind*headWind 0.01 3.50E -03

headWind*gustWind -0.29 4.23E -03

gustWind*gustWind 0.22 -0.01

headWind*Ceiling_ft 8.16E -06 1.02E -05

gustWind*Ceiling_ft 1.56E -05 -2.60E-06

Ceiling_ft*Ceiling_ft 7.55E -09 2.87E -08

headWind*Vis_ft -5.98E-06 4.36E -05

gustWind*Vis_ft 0.02 2.38E -05

Ceiling_ft*Vis_ft 1.08E -07 -2.99E-08

Vis_ft*Vis_ft -2.65E-08 -5.69E-10

headWind*asms -5.42E-06 3.28E -05

gustWind*asms -4.98E-05 -4.30E-05

Ceiling_ft*asms -6.83E-09 -2.25E-08

Vis_ft*asms -4.13E-09 -6.76E-08

asms*asms -6.82E-09 2.36E -08

headWind*APAY 6.10E -06 -4.92E-04

gustWind*APAY -6.79E-05 3.77E -04

Ceiling_ft*APAY -2.34E-08 -2.83E-08

Vis_ft*APAY 6.07E -09 3.73E -07

asms*APAY -6.08E-08 4.25E -07

APAY*APAY 8.68E -08 -1.40E-07

headWind*Act_Land_Wgt 1.17E -04 -1.89E-05

gustWind*Act_Land_Wgt -6.66E-05 2.85E -05

Ceiling_ft*Act_ Land_Wgt -3.33E-09 -8.34E-08

Vis_ft*Act_Land_Wgt -2.82E-08 9.67E -08

asms*Act_Land_Wgt -2.62E-08 -3.15E-07

APAY*Act_Land_Wgt 9.33E -09 -5.88E-07

Act_Land_Wgt*Act_Land_Wgt -1.08E-07 1.43E -07

headWind*FUEL_LOAD -1.30E-04 3.87E -04

gustWind*FUEL_LOAD -3.10E-05 -2.92E-04

Ceiling_ft*FUEL_LOAD 3.38E -08 -7.07E-09

Vis_ft*FUEL_LOAD -1.02E-07 -6.87E-08

asms*FUEL_LOAD 9.76E -08 3.30E -07

APAY*FUE L_LOAD 1.49E -06 1.54E -06

Act_Land_Wgt*FUEL_LOAD -5.65E-08 2.62E -09

FUEL_LOAD*FUE L_LOAD -7.91E-08 2.20E -08

headWind*AFUBO 7.40E -06 -2.80E-04

gustWind*AFUBO -1.50E-05 1.85E -04

Ceiling_ft*AFUBO 8.37E -09 2.76E -08

Vis_ft*AFUBO 1.24E -08 5.09E -08

asms*AFUBO 7.16E -09 -1.59E-08

APAY*AFUBO -3.37E-07 -5.91E-07

Act_Land_Wgt*AFUBO 8.27E -08 -6.98E-08

FUEL_LOAD*AFUBO -6.13E-07 7.54E -07

AFUBO *AFUBO 9.40E -09 -4.59E-07

headWind*FBR -7.51E-03 0.05

gustWind*FBR -5.27E-03 -0.02

Ceiling_ft*FBR 2.14E -06 6.13E -06

Vis_ft*FBR -6.32E-06 -2.87E-05

asms*FBR 1.37E -05 -9.66E-06

APAY*FBR -1.84E-05 2.29E -04

Act_Land_Wgt*FBR -1.63E-05 3.37E -05

FUEL_LOAD*FBR 8.74E -05 5.08E -05

AFUBO *FBR 6.71E -06 1.38E -05

FBR *FBR -2.95E-03 -1.39E-03

headWind*RSV -2.57E-04 1.08E -03

gustWind*RSV 1.26E -04 -1.13E-03

Ceiling_ft*RSV 3.56E -07 3.68E -07

Vis_ft*RSV -2.64E-07 -3.20E-06

asms*RSV -1.62E-07 5.25E -07

APAY*RSV -2.19E-06 -3.05E-07

Act_Land_Wgt*RSV 1.10E -06 -7.24E-07

FUEL_LOAD*R SV -2.86E-06 -4.71E-06

AFUBO *RSV 1.36E -06 5.10E -06

FBR *RSV 3.27E -04 -1.22E-03

RSV*RSV 1.53E -05 3.52E -05

headWind*ESAD_nm 9.60E -04 -1.51E-03

gustWind*ESAD_nm 7.04E -03 4.58E -03

Ceiling_ft*ESAD_nm 9.29E -07 3.19E -06

Vis_ft*ESAD_nm 7.07E -07 1.02E -05

asms*ESAD_nm 1.88E -06 -7.89E-06

APAY*ESAD_nm 1.26E -05 -6.05E-05

Act_Land_Wgt*ESAD_nm 2.84E -06 5.24E -05

FUEL_LOAD*ESAD_nm -4.31E-06 -6.40E-05

AFUBO *ESAD_nm -2.31E-07 1.35E -05

FBR*ESAD_nm -2.42E-03 1.47E -03

RSV*ESAD_nm 4.03E -06 -1.47E-04

ESAD_nm*ESAD_nm -1.49E-04 5.98E -04

headWind*LF_pax -0.03 0.13

gustWind*LF_pax 0.05 -0.11

Ceiling_ft*LF_pax 4.84E -06 3.11E -05

Vis_ft*LF_pax 1.39E -05 -1.20E-04

asms*LF_pax 2.43E -05 -3.18E-05

APAY*LF_pax -2.33E-05 2.81E -04

Act_Land_Wgt*LF_pax 4.87E -05 7.18E -05

FUEL_LOAD*LF_pax -4.01E-04 -4.35E-04

AFUBO*LF_pax 6.73E -05 1.69E -04

FBR*LF_pax 0.01 -0.07

RSV*LF_pax -5.87E-05 -5.86E-04

ESAD_nm*LF_pax 0.00 2.46E -03

LF_pax*LF_pax -0.01 -0.05
34

Figure A-1 and Figure A-2 show the absolute values of the percentage error distributions for the

low-and-no-gust and high-gust conditions, respectively, for thirteen input variables example.

Figure A-2. Absolute values of percentage error distribution for high-gust condition for

thirteen input variables.

Figure A-1. Absolute values of percentage error distribution for low-and-no-gust

condition for thirteen input variables.
35

APPENDIX B. RSE MODELS FOR FIVE INPUT VARIABLES

Table B-1 gives the response surface equation (RSE) coefficients for the low-and-no-gust and

high-gust conditions for the five input variables.

Table B-2 and Table B-3 give their contribution for the low-and-no-gust and high-gust

conditions, respectively.

TABLE B-1. RSE COEFFICIENTS FOR FIVE INPUT VARIABLES

Term

Low Gust

Coefficient

Estimate

High Gust

Coefficient

Estimate

Intercept 37.543892 301.49002

headWind 0.1533788 6.1802607

gustWind -613.7826 -4.735832

Ceiling_ft -0.001962 -0.001217

Vis_ft 0.0006099 -0.00105

Act_Land_Wgt 0.0011325 -0.003061

headWind*headWind 0.0025122 0.0379639

headWind*gustWind -0.280288 -0.069674

gustWind*gustWind 0.2022918 0.0209201

headWind*Ceiling_ft 9.08E-06 2.57E-05

gustWind*Ceiling_ft 8.01E-06 -1.59E-05

Ceiling_ft*Ceiling_ft 9.36E-09 2.19E-08

headWind*Vis_ft -1.72E-05 -7.32E-05

gustWind*Vis_ft 0.0193626 0.0001126

Ceiling_ft*Vis_ft 2.99E-08 9.66E-10

Vis_ft*Vis_ft -1.90E-08 -1.86E-08

headWind*Act_Land_Wgt 5.12E-06 -3.13E-05

gustWind*Act_Land_Wgt 1.93E-06 1.45E-05

Ceiling_ft*Act_Land_Wgt 5.40E-09 4.84E-09

Vis_ft*Act_Land_Wgt 2.28E-09 4.22E-09

Act_Land_Wgt*Act_Land_Wgt -3.12E-09 1.61E-08
36

TABLE B-2. RSE TERMS CONTRIBUTION FOR LOW-AND-NO-GUST CASE FOR

FIVE INPUT VARIABLES

TABLE B-3. RSE TERMS CONTRIBUTION FOR HIGH-GUST CASE FOR FIVE

INPUT VARIABLES

Terms in decreasing

Contribution

Contribution

to Model (%)

Act_land_Wgt 31.40

headWind 18.11

Ceiling_ft 9.49

Vis_ft 4.62

HeadWind*Vis_ft 4.43

Ceiling_ft*Act_land_Wgt 4.39

gustWind 4.32

Vis_ft*Vis_ft 3.55

gustWind*gustWind 3.30

Ceiling_ft*Ceiling_ft 3.18

Ceiling_ft*Vis_ft 2.27

headWind*Ceiling_ft 2.16

gustWind*Vis_ft 1.96

headWind*Act_land_Wgt 1.76

Act_land_Wgt*Act_land_Wgt 1.31

gustWind*Ceiling_ft 1.28

headWind*gustWind 1.24

Vis_ft*Act_land_Wgt 0.95

gustWind*Act_land_Wgt 0.28

headWind*headWind 0.02

Terms in decreasing

Contribution

Contribution

to Model (%)

Act_land_Wgt 28.12

Vis_ft 18.22

headWind 8.83

Ceiling_ft*Ceiling_ft 6.77

HeadWind*Vis_ft 5.37

Act_land_Wgt*Act_land_Wgt 4.99

gustWind*Vis_ft 3.65

gustWind*Ceiling_ft 3.36

Vis_ft*Vis_ft 3.30

headWind*Act_land_Wgt 2.86

Ceiling_ft 2.50

gustWind*Act_land_Wgt 2.47

headWind*Ceiling_ft 2.04

Ceiling_ft*Act_land_Wgt 1.71

Vis_ft*Act_land_Wgt 1.60

headWind*gustWind 1.41

headWind*headWind 1.26

Ceiling_ft*Vis_ft 0.60

gustWind*gustWind 0.53

gustWind 0.42
37

APPENDIX C. NEURAL NETWORK CHARACTERISTICS

Figure C-1 shows the neural network model characteristics for the low-and-no-gust condition.

Figure C-2 shows the regression plot for all the values (training validation, and testing) together

for the low-and-no-gust condition.

Figure C-1. Training characteristics for low-and-no-gust condition.

Figure C-2. Regression plot for all the values (training, validation, and testing) together.
38

Figure C-3 shows the error distribution for the 1387 (training, validation, and testing) data points.

Figure C-4 shows the neural network model characteristics for high-gust condition

Figure C-3. Error distribution for 1387 data points.

Figure C-4. Training characteristics for high-gust condition.
39

Figure C-5 shows the regression plot for all the data (training, validation, and testing) together

for the high-gust condition.

Figure C-6 shows the error distribution for all 426 (training, validation, and testing) data point

used to model the high-gust condition together.

Figure C-5. Regression plot for data together.

Figure C-6. Error histogram for all 426 data points together.
40

Figure C-7 shows the absolute values of percentage error distribution for the high-gust neural

network model for five input variables. It is clear that the error is more spread for the

recommended (baseline) value for the high±gust case. As the error values increase, there are

fewer instances of the model and more of the recommended.

Figure C-8 also illustrates a larger spread of the recommended (baseline) error compared to the

model for high-gust case.

Figure C-7. Absolute values of percentage error distribution for high-gust neural network

model for five input variables.

Figure C-8. Regression plots comparison of neural network model error versus the

recommendation error for high-gust condition.
41

APPENDIX D. MODELS COMPARISON FOR FIVE INPUT VARIABLES

Figure D-1 gives the absolute values of percentage errors, and Figure D-2 shows the percentages

of error distribution for the low-and-no-gust condition for five input variables.

Figure D-1. Absolute values of percentage error for low-and-no-gust condition for five

input variables.

Figure D-2. Percentage of error distribution for low-and-no-gust condition for five input variables.
42

Figure D-3 gives the absolute values of percentage error, and Figure D-4 gives the percentages of

error distribution for the high-gust condition for five input variables.

Figure D-3. Absolute values of percentage error for high-gust condition for five input variables.

Figure D-4. Percentages of error distribution for high-gust condition for five input variables.