A new artificial multi-neural approach to estimate the hourly global solar radiation in a semi-arid climate site

Abstract

In this study, we propose a new hybrid machine-learning algorithm called artificial multi-neural approach, for developing a multi-input single-output (MISO) model to estimate the hourly global solar radiation (HGSR) time series in Agdal site (latitude 31° 37′ N, longitude 08° 01′ W, elevation 466 m), Marrakesh, Morocco. To achieve this goal, three training algorithms (scaled conjugate gradient, Levenberg-Marquardt, and resilient backpropagation) are selected to train the developed model, using some accessible hourly meteorological variables recorded during 7 years (from 2008 to 2014) as exogenous inputs. Furthermore, a pertinence determination test (PDT) is used to point out the most pertinent inputs for the accurate HGSR estimation. The best configuration of the multi-neural model includes five known input parameters as the best scenario, i.e., acquisition hour, air temperature, relative humidity, wind speed, and precipitation. Some statistical indicators are used to evaluate the performance of the developed model. The obtained results demonstrate the reliability and the precision of our proposed machine-learning algorithm, representing a good solution for estimating solar radiation time series needed to design and manage solar energy systems compared to the present standards.

Appendix

List of ANN parameters:

ω_ij:

Input-first hidden layer weights

ω_jl:

First hidden-second hidden layer weights

ω_lk:

Second hidden-output layer weights

θ_{1, j}:

First hidden layer biases

θ_{2, l}:

Second hidden layer biases

θ_{3, k}:

Output layer biases

x_i:

ANN inputs

y_{1, j}:

First hidden layer outputs

y_{2, l}:

Second hidden layer outputs

O_k:

ANN outputs