Vol.:(0123456789) 1 3
Irrigation Science
https://doi.org/10.1007/s00271-019-00647-1
ORIGINAL PAPER
Hydraulic performance of labyrinth‑channel emitters: experimental
study, ANN, and GEP modeling
Mohamed A. Mattar
1,3
· Ahmed I. Alamoud
1
· Ahmed A. Al‑Othman
1
· Hosam O. Elansary
2
· Abdel‑Halim H. Farah
1
Received: 24 March 2019 / Accepted: 20 August 2019
© Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract
Laboratory experiments were used to estimate the hydraulic performance of emitters, i.e., the emitter fow variation (q
var
)
and manufacturer’s coefcient of variation (CV
m
), by measuring the discharge of diferent labyrinth-channel emitters at
diferent operating pressures (P) and water temperatures (T). Considering the importance of the structural parameters of
the labyrinth-channel emitters in drip irrigation design, which has been experimentally confrmed, artifcial neural network
(ANN) and gene expression programming (GEP) models were developed to predict q
var
and CV
m
. The ANN and GEP mod-
els were trained and tested using structural parameters (including the number, height (H), and spacing of trapezoidal units
and the fow path width and length) of diferent labyrinth-channel emitters, P and T as the input variables, and q
var
and CV
m
as the outputs. Statistical criteria, including the coefcients of correlation (r), relative root-mean-square error (RRMSE),
and mean absolute error (MAE), were used to examine the accuracy of the developed models. The ANN models exhibited
good correlation with experimental values, with high r values 0.995 and 0.969 for q
var
and 0.997 and 0.947 for CV
m
in the
training and testing processes, respectively. The ANN models had lower RRMSE and MAE values than the GEP models.
Furthermore, H was the dominant variable for obtaining the most accurate prediction model. The results confrm that the
ANN models are superior to the GEP models for the prediction of the hydraulic performance of emitters.
List of symbols
ANN Artifcial neural network
(
B
1
)
j
Biases in the hidden layer
(
B
2
)
k
Biases in the output layer
C
sx
Skewness coefcient
CV
m
Manufacturer’s coefcient of variation
f Activation function
GEP Gene expression programming
H Trapezoidal unit height (mm)
k
x
Kurtosis coefcient
L Path length (mm)
m Number of data
MAE Mean absolute error
N Trapezoidal unit number
n
i
Number of input neurons
n
j
Number of hidden neurons
n
Total number of emitters along the drip line
P Operating pressure (kPa)
q
i
Discharge rate of emitter i (L h
−1
)
q
max
Maximum emitter discharge rate (L h
−1
)
q
min
Minimum emitter discharge rate (L h
−1
)
q
var
Emitter fow variation (%)
q Average emitter discharge rate (L h
−1
)
r Coefcient of correlation
RMSE Root-mean-square error
RRMSE Relative root-mean-square error
S Trapezoidal unit spacing (mm)
S
x
Standard deviation
T Water temperature (°C)
W Path width (mm)
(
W
1
)
ji
Weights from the input layer to the hidden layer
(
W
2
)
kj
Weights from the hidden layer to the output
layer
x Value of either the hidden-layer neuron or the
output-layer neuron
X
Ei
Experimental value
Communicated by Yunkai Li.
* Mohamed A. Mattar
mmattar@ksu.edu.sa
1
Agricultural Engineering Department, College of Food
and Agriculture Sciences, King Saud University, Riyadh,
Saudi Arabia
2
Plant Production Department, College of Food
and Agriculture Sciences, King Saud University, Riyadh,
Saudi Arabia
3
Agricultural Engineering Research Institute (AEnRI),
Agricultural Research Centre, Giza, Egypt