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Metaheuristic and Machine Learning Models for TFE-731-2, PW4056, and JT8D-9 Cruise Thrust

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Published/Copyright: February 18, 2016
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Abstract

The requirement for an accurate engine thrust model has a major antecedence in airline fuel saving programs, assessment of environmental effects of fuel consumption, emissions reduction studies, and air traffic management applications. In this study, utilizing engine manufacturers’ real data, a metaheuristic model based on genetic algorithms (GAs) and a machine learning model based on neural networks (NNs) trained with Levenberg-Marquardt (LM), delta-bar-delta (DBD), and conjugate gradient (CG) algorithms were accomplished to incorporate the effect of both flight altitude and Mach number in the estimation of thrust. For the GA model, the analysis of population size impact on the model’s accuracy and effect of number of data on model coefficients were also performed. For the NN model, design of optimum topology was searched for one- and two-hidden-layer networks. Predicted thrust values presented a close agreement with real thrust data for both models, among which LM trained NNs gave the best accuracies.

Nomenclature

Abbreviations
ATM

Air traffic management

BADA

Base of Aircraft Data

CG

Conjugate gradient

CV

Cross-validation

DBD

Delta-bar-delta

FNN

Feed-forward neural network

GA

Genetic algorithm

HL

Hidden layer

IP

Intellectual Property

LM

Levenberg-Marquardt

MAPE

Mean absolute percentage error

MSE

Mean squared error

NN

Neural network

PE

Processing elements

Symbols
ai, bi

Genetic algorithm thrust model coefficients (i=1–3)

ei

Output error for every input pattern of the network

E

Error function of the network

h

Flight altitude

I

Identity matrix

J

Jacobian matrix

M

Mach number

r

Linear correlation coefficient

t

Time

T

Engine cruise thrust

V

Sum of squared error function of the network

w

Weight vector of the neural network

α

Learning rate

αk

Variable learning rate

θ

Smoothing factor

κ

Additive constant

λ

Non-negative gain

ϕ

Multiplicative constant

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Received: 2016-1-10
Accepted: 2016-2-3
Published Online: 2016-2-18
Published in Print: 2017-8-28

© 2017 Walter de Gruyter GmbH, Berlin/Boston

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