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Hydraulic performance of labyrinth-channel emitters: experimental study, ANN, and GEP modeling

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Abstract

Laboratory experiments were used to estimate the hydraulic performance of emitters, i.e., the emitter flow variation (qvar) and manufacturer’s coefficient of variation (CVm), by measuring the discharge of different labyrinth-channel emitters at different 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 confirmed, artificial neural network (ANN) and gene expression programming (GEP) models were developed to predict qvar and CVm. The ANN and GEP models were trained and tested using structural parameters (including the number, height (H), and spacing of trapezoidal units and the flow path width and length) of different labyrinth-channel emitters, P and T as the input variables, and qvar and CVm as the outputs. Statistical criteria, including the coefficients 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 qvar and 0.997 and 0.947 for CVm 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 confirm that the ANN models are superior to the GEP models for the prediction of the hydraulic performance of emitters.

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Abbreviations

ANN:

Artificial neural network

\(\left( {B_{ 1} } \right)_{j}\) :

Biases in the hidden layer

\(\left( {B_{ 2} } \right)_{k}\) :

Biases in the output layer

C sx :

Skewness coefficient

\({\text{CV}}_{\text{m}}\) :

Manufacturer’s coefficient of variation

f :

Activation function

GEP:

Gene expression programming

H:

Trapezoidal unit height (mm)

k x :

Kurtosis coefficient

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

\(n^{\prime}\) :

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)

\(q_{\text{var}}\) :

Emitter flow variation (%)

\(\bar{q}\) :

Average emitter discharge rate (L h−1)

r :

Coefficient 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)

\(\left( {W_{ 1} } \right)_{ji}\) :

Weights from the input layer to the hidden layer

\(\left( {W_{2} } \right)_{kj}\) :

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

\(X_{i}\) :

Normalized inputs

\(x_{\max}\) :

Maximum value

\(x_{\text{mean}}\) :

Mean value

\(x_{\min}\) :

Minimum value

\(X_{Pi}\) :

Predicted value

\(\overline{{X_{\text{E}} }}\) :

Average value of the experimental data

\(Y_{k}\) :

Outputs

i :

Number of input neuron

j :

Number of hidden neuron

k :

Number of output neuron

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at King Saud University for funding this work through research group No. RG-1440-022.

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Authors and Affiliations

  1. Agricultural Engineering Department, College of Food and Agriculture Sciences, King Saud University, Riyadh, Saudi Arabia

    Mohamed A. Mattar, Ahmed I. Alamoud, Ahmed A. Al-Othman & Abdel-Halim H. Farah

  2. Plant Production Department, College of Food and Agriculture Sciences, King Saud University, Riyadh, Saudi Arabia

    Hosam O. Elansary

  3. Agricultural Engineering Research Institute (AEnRI), Agricultural Research Centre, Giza, Egypt

    Mohamed A. Mattar

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  1. Mohamed A. Mattar
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  2. Ahmed I. Alamoud
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Correspondence to Mohamed A. Mattar.

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Mattar, M.A., Alamoud, A.I., Al-Othman, A.A. et al. Hydraulic performance of labyrinth-channel emitters: experimental study, ANN, and GEP modeling. Irrig Sci 38, 1–16 (2020). https://doi.org/10.1007/s00271-019-00647-1

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