Department of Mathematical and Computational Sciences
Permanent URI for this community
Browse
Browsing Department of Mathematical and Computational Sciences by Author "Bere, Alphonce"
Now showing 1 - 6 of 6
Results Per Page
Sort Options
Item Open Access A comparison of some methods of modeling baseline hazard function in discrete survival models(2019-09-20) Mashabela, Mahlageng Retang; Bere, Alphonce; Sigauke, CastonThe baseline parameter vector in a discrete-time survival model is determined by the number of time points. The larger the number of the time points, the higher the dimension of the baseline parameter vector which often leads to biased maximum likelihood estimates. One of the ways to overcome this problem is to use a simpler parametrization that contains fewer parameters. A simulation approach was used to compare the accuracy of three variants of penalised regression spline methods in smoothing the baseline hazard function. Root mean squared error (RMSE) analysis suggests that generally all the smoothing methods performed better than the model with a discrete baseline hazard function. No single smoothing method outperformed the other smoothing methods. These methods were also applied to data on age at rst alcohol intake in Thohoyandou. The results from real data application suggest that there were no signi cant di erences amongst the estimated models. Consumption of other drugs, having a parent who drinks, being a male and having been abused in life are associated with high chances of drinking alcohol very early in life.Item Open Access Forecasting hourly electricity demand in South Africa using machine learning models(2020-08-12) Thanyani, Maduvhahafani; Sigauke, Caston; Bere, AlphonceShort-term load forecasting in South Africa using machine learning and statistical models is discussed in this study. The research is focused on carrying out a comparative analysis in forecasting hourly electricity demand. This study was carried out using South Africa’s aggregated hourly load data from Eskom. The comparison is carried out in this study using support vector regression (SVR), stochastic gradient boosting (SGB), artificial neural networks (NN) with generalized additive model (GAM) as a benchmark model in forecasting hourly electricity demand. In both modelling frameworks, variable selection is done using least absolute shrinkage and selection operator (Lasso). The SGB model yielded the least root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE) on testing data. SGB model also yielded the least RMSE, MAE and MAPE on training data. Forecast combination of the models’ forecasts is done using convex combination and quantile regres- sion averaging (QRA). The QRA was found to be the best forecast combination model ibased on the RMSE, MAE and MAPE.Item Open Access Hierarchical forecasting of electricity demand in South Africa(2020-08-11) Netshiomvani, Rofhiwa; Sigauke, Caston; Bere, AlphonceThe study focuses on the application of hierarchical time series in forecasting electricity demand using South African data. The methods used are top-down, bottom-up and optimal combination. The top-down method is based on the disaggregation of the forecasts of the total series and distribute these down the hierarchy based on the historical proportions of the data. The bottom-up approach aggregates the individual forecasts at the lower levels, while the optimal combination technique optimally combines the bottom forecasts. Out-of-sample forecast performance evaluation was conducted to get some indication of the forecasting performance of the models. MAPE was used to determine the best model. Bottom–up approach is found to be the best approach compared to optimal combination and top–down approaches. In order to combine forecasts and compute the prediction intervals for the developed models the quantile regression averaging (QRA) and linear regression (LR) is used. The best set of forecasts is selected based on the prediction interval normalised average width (PINAW) and pinball loss. The best model based on pinball loss is QRA and the best model based on PINAW at 95 % is QRA.Item Open Access Medium term load forecasting in South Africa using Generalized Additive models with tensor product interactions(2018-09-21) Ravele, Thakhani; Siguake, Caston; Bere, AlphonceForecasting of electricity peak demand levels is important for decision makers in Eskom. The overall objective of this study was to develop medium term load forecasting models which will help decision makers in Eskom for planning of the operations of the utility company. The frequency table of hourly daily demands was carried out and the results show that most peak loads occur at hours 19:00 and 20:00, over the period 2009 to 2013. The study used generalised additive models with and without tensor product interactions to forecast electricity demand at 19:00 and 20:00 including daily peak electricity demand. Least absolute shrinkage and selection operator (Lasso) and Lasso via hierarchical interactions were used for variable selection to increase the model interpretability by eliminating irrelevant variables that are not associated with the response variable, this way also over tting is reduced. The parameters of the developed models were estimated using restricted maximum likelihood and penalized regression. The best models were selected based on smallest values of the Akaike information criterion (AIC), Bayesian information criterion (BIC) and Generalized cross validation (GCV) along with the highest Adjusted R2. Forecasts from best models with and without tensor product interactions were evaluated using mean absolute percentage error (MAPE), mean absolute error (MAE) and root mean square error (RMSE). Operational forecasting was proposed to forecast the demand at hour 19:00 with unknown predictor variables. Empirical results from this study show that modelling hours individually during the peak period results in more accurate peak forecasts compared to forecasting daily peak electricity demand. The performance of the proposed models for hour 19:00 were compared and the generalized additive model with tensor product interactions was found to be the best tting model.Item Open Access Modelling flood heights of the Limpopo River at Beitbridge Border Post using extreme value distributions(2016) Kajambeu, Robert; Sigauke, Caston; Bere, AlphonceHaulage trucks and cross border traders cross through Beitbridge border post from landlocked countries such as Zimbabwe and Zambia for the sake of trading. Because of global warming, South Africa has lately been experiencing extreme weather patterns in the form of very high temperatures and heavy rainfall. Evidently, in 2013 tra c could not cross the Limpopo River because water was owing above the bridge. For planning, its important to predict the likelihood of such events occurring in future. Extreme value models o er one way in which this can be achieved. This study identi es suitable distributions to model the annual maximum heights of Limpopo river at Beitbridge border post. Maximum likelihood method and the Bayesian approach are used for parameter estimation. The r -largest order statistics was also used in this dissertation. For goodness of t, the probability and quantile- quantile plots are used. Finally return levels are calculated from these distributions. The dissertation has revealed that the 100 year return level is 6.759 metres using the maximum likelihood and Bayesian approaches to estimate parameters. Empirical results show that the Fr echet class of distributions ts well the ood heights data at Beitbridge border post. The dissertation contributes positively by informing stakeholders about the socio- economic impacts that are brought by extreme flood heights for Limpopo river at Beitbridge border postItem Open Access Solar power forecasting using Gaussian process regression(2023-10-05) Chandiwana, Edina; Sigauke, Caston; Bere, AlphonceSolar power forecasting has become an important aspect affecting crucial day-to-day activities in people's lives. Many African countries are now facing blackouts due to a shortage of energy. This has caused the urge to encourage people to use other energy sources to rise, resulting in different energy inputs into the main electricity grid. When the number of power sources being fed into the main grid increases, so does the need for efficient methods of forecasting these inputs. Thus, there is a need to come up with efficient prediction techniques inorder to facilitate proper grid management. The main goal of this thesis is to explore how Gaussian process predicting frameworks can be developed and used to predict global horiz0ontal irra- diance. Data on Global horizontal irrandiance and some weather variables collected from various meterological stations were made available through SAURAN (Southern African Universities Radiometric Network). The length of the dataset ranged from 496 to 17325 datapoints. Ve proposed using Gaussian process regression (GPR) to predict solar power generation. In South Africa, studies based on GPR regarding forecasting solar power are still very few, and more needs to be done in this area. At first, we explored covariance function selection, and a GPR was developed using Core vector regression (CVR). The predictions produced through this method were more accurate than the benchmark models used: Gradient Boosting Regression (GBR) and Support Vector Regression then, we explored interval estimation, Quantile re- gression and GPR were coupled in order to develop the modelling framework. This was also done to improve the accuracy of the GPR models. The results proved that the model performed better than the Bayesian Structural Time Series Regression. Ve also explored spatial dependence; spatio-temporal regression was incorporated into the modelling framework coupled with GPR. This was done to incorporate various weather stations' conditions into the modelling process. The spatial analysis results proved that GPR coupled with spatial analysis produced results that were superior to the Autoregressive Spatial analysis and benchmark model used: Linear Spatial analysis. The GPR results had accuracy measures that proved superior to the benchmark models. Various other tools were used to improve the accuracy of i the GPR results. This includes the use of combining forecasts and standardisation of predictions. The superior results indicate a vast benefit economic-wise because it allows those who manage the power grid to do so effectively and efficiently. Effective power grid management reduces power blackouts, thus benefitting the nation eco- nomically and socially.