An Efficient Monthly Load Forecasting Model Using Gaussian Process Regression

Gaussian process regression‐based load forecasting model

“…in general is the covariance matrix which is updated using K kernel, here N is number of data sample [22].…”

“…A training set D is considered, D = {( x i , f i ), i = 1: N }, where f i = f ( x i ) (Initialization of function with respect to x i ) to predict f * for test data set x * of size N * ×D here K = ĸ ( X , X ) is N × N , K * = ĸ ( X , X *) is N × N * and K ** = ĸ ( X *, X *) is N *× N *. K in general is the covariance matrix which is updated using K kernel, here N is number of data sample [22]. $$$$\begin{equation}\left( { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} f\\ {f*} \end{array} } \right)\sim \mathcal{N}\left( {\left( { \def\eqcellsep{&}\begin{array}{@{}*{1}{c}@{}} {\mu 1}\\ {\mu 2} \end{array} } \right),\left( { \def\eqcellsep{&}\begin{array}{@{}*{2}{c}@{}} K&{K{\mathrm{*}}}\\ {Transpose\left( {K{\mathrm{*}}} \right)}&{K{\mathrm{**}}} \end{array} } \right)} \right)\end{equation}$$$$$$\mathcal{N}:Normal\ Distribution$$ $$$$\begin{equation}k\ \left( {{x}_i,{x}_j} \right) = \ \sigma _f^2exp\left( { - \frac{{{{\left( {{x}_i - {x}_j} \right)}}^2}}{{2{l}^2}}} \right) + {\delta }_{ij}\sigma _{noise}^2\end{equation}$$$$…”

“…Here $$\theta $$ is a set of hyperparameters. To tune the hyper‐parameters, maximize the log marginal probability [22].…”

“…A model using the combination of SVMs and social spider optimization was proposed for the STLF in [21]. In [22], a monthly LF model was proposed for Australian data measured during 2006 to 2010 at Sydney/NSW. In [23], monthly LF of Southeast Asia country was represented by using Seasonal auto regressiveintegrated moving average (ARIMA) and GPR.…”