Research Papers

Online Sequential Learning of Neural Networks in Solar Radiation Modeling Using Hybrid Bayesian Hierarchical Approach

[+] Author and Article Information
Sajid Hussain

Department of Mechanical Engineering,
The Petroleum Institute,
P.O. Box 2533,
Abu Dhabi, The United Arab Emirates
e-mail: sahussain@pi.ac.ae

Ali AlAlili

Department of Mechanical Engineering,
The Petroleum Institute,
P.O. Box 2533,
Abu Dhabi, The United Arab Emirates
e-mail: alialalili@pi.ac.ae

1Corresponding author.

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING: INCLUDING WIND ENERGY AND BUILDING ENERGY CONSERVATION. Manuscript received January 28, 2016; final manuscript received September 6, 2016; published online October 18, 2016. Assoc. Editor: Philippe Blanc.

J. Sol. Energy Eng 138(6), 061012 (Oct 18, 2016) (10 pages) Paper No: SOL-16-1057; doi: 10.1115/1.4034907 History: Received January 28, 2016; Revised September 06, 2016

Traditional learning process in solar radiation modeling usually requires historical data to perform regularization using training and cross-validation approaches. However, in applications where no historical data are available, regularization cannot be performed using traditional techniques. This paper presents a hierarchical Bayesian framework with the extended Kalman filter (Bayesian-EKF) to perform regularization in sequential learning of the artificial neural network (ANN) for solar radiation modeling. A highly stochastic time series for daily solar radiation, the global horizontal irradiance (GHI), is modeled based on different meteorological variables including temperature (T), relative humidity (RH), wind speed (WS), and sunshine duration (SSD). A comparison is made with well-known methods including the ANN-based nonlinear autoregressive with exogenous inputs neural network (NARX-NN) and Wiener filter-based multivariate linear regression (MLR). The method is validated on test data using coefficient of determination (R2) and root mean squared error (RMSE). The proposed technique effectively estimates the noise components in the data and achieves superior performance as compared to the traditional learning processes of NARX-NN and MLR. Moreover, it is more robust to statistical outliers in the data and does not require prior history for training and cross-validation. In the presence of the outliers, the performance of the NARX-NN degrades from R2 = 94.73% to R2 = 85.85% but there is virtually no difference in the case of Bayesian-EKF. Over and above, MLR performs better than NARX-NN but worse than Bayesian-EKF.

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Fig. 1

Block diagram of the proposed method

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Fig. 3

Daily evolution of T, RH, WS, SSD, and GHI over Abu Dhabi, UAE

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Fig. 4

R2 boxplot versus hidden layer units for MLP (30 simulations each)

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Fig. 5

NARX-NN simulations without outliers: (a) GHI measured versus simulated and (b) regression analysis

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Fig. 6

NARX-NN simulations with outliers: (a) GHI measured versus simulated and (b) regression analysis

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Fig. 7

Bayesian-EKF without outliers: (a) GHI measured versus simulated, (b) regression analysis, and (c) q-parameter

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Fig. 8

Bayesian-EKF with outliers: (a) GHI measured versus simulated, (b) regression analysis, and (c) q-parameter

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Fig. 9

Boxplots for NARX and EKF comparisons




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