The research in this Ph.D. study is divided into main segments. First, uncertainty quantification of incident solar radiation on building facades, and second, reliability assessments of proposed shading strategies. The strength and novelty of this research are derived from both segments, however, the first part merits a more in-depth focus since a detailed approach  to uncertainty quantification of incident solar radiation has been less  noticed in the topic of building energy simulation. Most of the current  literature on solar availability over building surfaces have been performed on an urban scale. This study tends to merge urban and building scales and provide a more detailed model of solar radiation diffraction from the urban canyon. The  sensitive role of incident radiation in different aspects of building energy performance calls for more accurate approximations of this measure. Quantifying the incident solar radiation on the building surfaces can help to reduce the  performance gap between simulation and reality, as this analysis provide a  better vision on the long-term performance of different building component (e.g. memberings, external venetions, paint/coatings and etc). Consequently, it will facilitate decision-making for designers as they face various options. Incident solar radiation on the building envelope has an important role on the temperature of the exterior layer of the wall, and  consequently, affects the hygro-thermal performance of the building. Considering  that the hygro-thermal performance of the wall is among the parameters which  affect microbiological growth risk, uncertainty quantification of the incident radiation on the facade, and the resulting envelope temperature merit careful considerations\cite{paolini2016application}. The outcome of the first part of this study could be combined with the occupant  behavioral models, concerning the importance of interaction between building users  and visual/thermal comfort. A better estimation of the amount of incident  radiation over the building facade will result in more accurate estimations of  solar heat gains as well as internal daylight.  
In this paper, uncertainty quantification of ground reflected irradiance is demonstrated, which marks the starting point of this Ph.D. research. The paper tends to propose a methodology through which,  evaluation of the reliability of shading devices during the cooling season is facilitated.

Data description

Since the typical weather data present a long time average of climate parameters, therefore it is possible that some critical weather changes are ignored.  For instance, Europe experienced two heat waves in during the last decades. An extreme one in 2003 and another in 2015. Studies show that unqualified building design had a significant role in the amount of damages. The required values of solar irradiation are extracted from the 5 years of weather data in Milano. Global, direct normal and diffuse irradiance from 2012 till 2016 are the main source of data used in the simulations.

Methodology

\label{methodology}
Until a decade ago, uncertainties were divided into two major categories based on the natures of their source: epistemic and aleatory. Epistemic uncertainty concerns phenomenon, on which we have imperfect knowledge. This type of  uncertainty is reducible through repeated measurements of the uncertain  phenomena. Meanwhile, aleatory uncertainty is related to lack of knowledge and cannot be explained by a distribution as scarce data are available regarding the pattern of their occurrence \cite{Kiureghian_2009}. However, the concept of uncertainty has been recently approached by three main perspectives i.e. randomness (probabilistic), fuzziness (Possibilistic), and uncertain (neither probabilistic nor possibilistic) theory \cite{Dubois_2001}
Uncertain parameters of related to solar radiation in street canyon