The uncertainty and sensitivity analyses for multivariables of the optimal system based on deterministic parameters are necessary, as multivariables are full of uncertainties in the real operation. However, the generic methodology for multi-dimensional uncertainties quantification is rare, and the energy performance simulation is normally at high computational cost, especially considering a huge amount of parameters uncertainties. In this study, the on-site renewable electricity generation of an optimal hybrid renewable system based on deterministic parameters, was investigated, under high-level parameters' uncertainties. A generic uncertainty quantification methodology was proposed using the two-dimensional Markov Chain Monte Carlo to quantify multi-dimensional uncertainties. A machine-learning based data-driven model, using the supervised machine learning with high computational efficiency, was developed to predict the on-site renewable electricity generation, and thereafter used for the uncertainty and sensitivity analyses. Compared with the deterministic scenario parameters, the cases with the scenario uncertainties can increase the peak power and the total amount of the on-site renewable electricity generation. This study proposes a novel generic uncertainty quantification methodology, together with a machine-learning based data-driven model for conducting the uncertainty analysis of an optimal renewable system based on deterministic parameters, which are important for the promotion of renewable and sustainable buildings. (C) 2019 Elsevier Ltd. All rights reserved.