Aerospace and Electronic Systems Magazine July 2018 - 10

EGT Prediction

Figure 6.

RMSE calculated based on predicted values of EGT with α, β, and γ
neural network topologies.

Cross-validation was implemented in order to avoid over-fitting
problems. Also inputs and their associated outputs were normalized
before performing training procedures to improve generalization of
the network's capability and provide a faster learning speed. Normalization process of the data was carried out in [0, 1] interval by
suitable characteristic values, for both engine parameters.
Three types of neural networks with different architectures
were employed. Neural network type α is a perceptron neural network and it consists of one hidden layer with 10 neurons. Neural
network type β is a multilayer perceptron neural network and it
consists of two hidden layers with 10 neurons in each layer. Neural
network type γ is a radial basis function neural network with maximum number of 50 neurons in its hidden layer. Sigmoid transfer
function was examined for each hidden layer, in both ANN types
of α and β, whereas linear transfer function was considered for
their output layers. On the other hand, for neural network type γ,
newrb transfer function was examined for its hidden layer, whereas
linear transfer function was considered for its output layer. Number
of neurons in hidden layers and also employed transfer function's
type in different hidden layers of neural networks, obtained by try
and error. Four to 16 number of neurons were used and for each
case RMSE were calculated to obtain optimum number of neurons
for ANN types of α and β. Finally, by comparing the RMSE values for different number of neurons, 10 neurons selected for ANN
types of α and β as optimum number of neurons in their hidden
layers. Same procedure performed for ANN type γ and 50 neurons
obtained as optimum number of neurons in its hidden layer. Transfer functions were selected by try and error and finally sigmoid and
newrb functions were selected as the best transfer functions in hidden layers of perceptron and RBF neural networks, respectively.
Linear transfer function is the best one and used for all types of the
employed neural networks in this research.
Using all α, β, and γ ANN topologies the degree of agreement
between predicted and measured values for EGT was quantified
by calculating RMSE between predictions and measured values.
RMSE which is a measure of α, β, and γ networks ability to predict
EGT is shown in Figure 6. As shown in Figure 6, the RMSE has
lower values for network type β, indicating that this network topology with two hidden layers has a better capability for prediction of
EGT. Network type β with two hidden layers, has more process10

Figure 7.

Predicted and measured values of EGT using ANN type α, β, and γ.

ing elements (neurons) compared with networks type α and γ, and
it could increase its computational ability in predicting nonlinear
functional relationships between parameters of the experimental
gas turbine engine.
Estimation performance of networks type α, β, and γ is shown
in Figure 7. This figure compares measured values of EGT (which
is normalized by proper characteristic values) with their associated predicted values using ANN type α, β, and γ. ANN's ability to
predict EGT can be evaluated from vertical distance between presented data and straight diagonal line in Figure 7. In other words,
vertical distance of presented data with diagonal lines could be
considered as an indication of error in prediction, whereas the data
with negligible error of prediction would fall on these lines.
To evaluate the degree of agreement between predicted and
measured values of EGT, coefficients of determination (R2) were
also calculated [24], as displayed in Figure 7. Higher values for R2
(i.e., when coefficient of determination gets closer to 1 in the range
of 0 to 1), demonstrates that the predicted data have adequate accuracy in matching measured experimental data [24]. Higher values
of R2 for EGT, along with the fact that presented data, in Figure 7,
are close to the diagonal line exhibit accuracy of predictions of networks type α, β, and γ and demonstrate their capability of estimating EGT in the whole range of studied operating conditions. Using
Figures 6 and 7, it can be concluded that network type β has better
prediction capability of predicting EGT values than networks type
α and γ. In addition, coefficient of determination (i.e., R2) for network type β is 0.868 which indicates this type of network (i.e., β)
has a good accuracy in predicting EGT. For as much as in the present work all the dynamic processes of the engine (from starting-up
to shutting down) have been considered, the value of 0.868 for
coefficient of determination is acceptable for predicting the EGT
by using the neural network type β.
Table 2 shows calculated RMSE which is a measure of agreement between experimental and predicted values of EGT using
networks type α, β, and γ.

IEEE A&E SYSTEMS MAGAZINE

JULY 2018



Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine July 2018

No label
Aerospace and Electronic Systems Magazine July 2018 - No label
Aerospace and Electronic Systems Magazine July 2018 - Cover2
Aerospace and Electronic Systems Magazine July 2018 - 1
Aerospace and Electronic Systems Magazine July 2018 - 2
Aerospace and Electronic Systems Magazine July 2018 - 3
Aerospace and Electronic Systems Magazine July 2018 - 4
Aerospace and Electronic Systems Magazine July 2018 - 5
Aerospace and Electronic Systems Magazine July 2018 - 6
Aerospace and Electronic Systems Magazine July 2018 - 7
Aerospace and Electronic Systems Magazine July 2018 - 8
Aerospace and Electronic Systems Magazine July 2018 - 9
Aerospace and Electronic Systems Magazine July 2018 - 10
Aerospace and Electronic Systems Magazine July 2018 - 11
Aerospace and Electronic Systems Magazine July 2018 - 12
Aerospace and Electronic Systems Magazine July 2018 - 13
Aerospace and Electronic Systems Magazine July 2018 - 14
Aerospace and Electronic Systems Magazine July 2018 - 15
Aerospace and Electronic Systems Magazine July 2018 - 16
Aerospace and Electronic Systems Magazine July 2018 - 17
Aerospace and Electronic Systems Magazine July 2018 - 18
Aerospace and Electronic Systems Magazine July 2018 - 19
Aerospace and Electronic Systems Magazine July 2018 - 20
Aerospace and Electronic Systems Magazine July 2018 - 21
Aerospace and Electronic Systems Magazine July 2018 - 22
Aerospace and Electronic Systems Magazine July 2018 - 23
Aerospace and Electronic Systems Magazine July 2018 - 24
Aerospace and Electronic Systems Magazine July 2018 - 25
Aerospace and Electronic Systems Magazine July 2018 - 26
Aerospace and Electronic Systems Magazine July 2018 - 27
Aerospace and Electronic Systems Magazine July 2018 - 28
Aerospace and Electronic Systems Magazine July 2018 - 29
Aerospace and Electronic Systems Magazine July 2018 - 30
Aerospace and Electronic Systems Magazine July 2018 - 31
Aerospace and Electronic Systems Magazine July 2018 - 32
Aerospace and Electronic Systems Magazine July 2018 - 33
Aerospace and Electronic Systems Magazine July 2018 - 34
Aerospace and Electronic Systems Magazine July 2018 - 35
Aerospace and Electronic Systems Magazine July 2018 - 36
Aerospace and Electronic Systems Magazine July 2018 - 37
Aerospace and Electronic Systems Magazine July 2018 - 38
Aerospace and Electronic Systems Magazine July 2018 - 39
Aerospace and Electronic Systems Magazine July 2018 - 40
Aerospace and Electronic Systems Magazine July 2018 - 41
Aerospace and Electronic Systems Magazine July 2018 - 42
Aerospace and Electronic Systems Magazine July 2018 - 43
Aerospace and Electronic Systems Magazine July 2018 - 44
Aerospace and Electronic Systems Magazine July 2018 - 45
Aerospace and Electronic Systems Magazine July 2018 - 46
Aerospace and Electronic Systems Magazine July 2018 - 47
Aerospace and Electronic Systems Magazine July 2018 - 48
Aerospace and Electronic Systems Magazine July 2018 - 49
Aerospace and Electronic Systems Magazine July 2018 - 50
Aerospace and Electronic Systems Magazine July 2018 - 51
Aerospace and Electronic Systems Magazine July 2018 - 52
Aerospace and Electronic Systems Magazine July 2018 - 53
Aerospace and Electronic Systems Magazine July 2018 - 54
Aerospace and Electronic Systems Magazine July 2018 - 55
Aerospace and Electronic Systems Magazine July 2018 - 56
Aerospace and Electronic Systems Magazine July 2018 - 57
Aerospace and Electronic Systems Magazine July 2018 - 58
Aerospace and Electronic Systems Magazine July 2018 - 59
Aerospace and Electronic Systems Magazine July 2018 - 60
Aerospace and Electronic Systems Magazine July 2018 - 61
Aerospace and Electronic Systems Magazine July 2018 - 62
Aerospace and Electronic Systems Magazine July 2018 - 63
Aerospace and Electronic Systems Magazine July 2018 - 64
Aerospace and Electronic Systems Magazine July 2018 - 65
Aerospace and Electronic Systems Magazine July 2018 - 66
Aerospace and Electronic Systems Magazine July 2018 - 67
Aerospace and Electronic Systems Magazine July 2018 - 68
Aerospace and Electronic Systems Magazine July 2018 - 69
Aerospace and Electronic Systems Magazine July 2018 - 70
Aerospace and Electronic Systems Magazine July 2018 - 71
Aerospace and Electronic Systems Magazine July 2018 - 72
Aerospace and Electronic Systems Magazine July 2018 - Cover3
Aerospace and Electronic Systems Magazine July 2018 - Cover4
http://www.brightcopy.net/allen/aesm/34-2s
http://www.brightcopy.net/allen/aesm/34-2
http://www.brightcopy.net/allen/aesm/34-1
http://www.brightcopy.net/allen/aesm/33-12
http://www.brightcopy.net/allen/aesm/33-11
http://www.brightcopy.net/allen/aesm/33-10
http://www.brightcopy.net/allen/aesm/33-09
http://www.brightcopy.net/allen/aesm/33-8
http://www.brightcopy.net/allen/aesm/33-7
http://www.brightcopy.net/allen/aesm/33-5
http://www.brightcopy.net/allen/aesm/33-4
http://www.brightcopy.net/allen/aesm/33-3
http://www.brightcopy.net/allen/aesm/33-2
http://www.brightcopy.net/allen/aesm/33-1
http://www.brightcopy.net/allen/aesm/32-10
http://www.brightcopy.net/allen/aesm/32-12
http://www.brightcopy.net/allen/aesm/32-9
http://www.brightcopy.net/allen/aesm/32-11
http://www.brightcopy.net/allen/aesm/32-8
http://www.brightcopy.net/allen/aesm/32-7s
http://www.brightcopy.net/allen/aesm/32-7
http://www.brightcopy.net/allen/aesm/32-6
http://www.brightcopy.net/allen/aesm/32-5
http://www.brightcopy.net/allen/aesm/32-4
http://www.brightcopy.net/allen/aesm/32-3
http://www.brightcopy.net/allen/aesm/32-2
http://www.brightcopy.net/allen/aesm/32-1
http://www.brightcopy.net/allen/aesm/31-12
http://www.brightcopy.net/allen/aesm/31-11s
http://www.brightcopy.net/allen/aesm/31-11
http://www.brightcopy.net/allen/aesm/31-10
http://www.brightcopy.net/allen/aesm/31-9
http://www.brightcopy.net/allen/aesm/31-8
http://www.brightcopy.net/allen/aesm/31-7
https://www.nxtbookmedia.com