The method of the independent components for sustainable building design

The probabilistic framework of the Multi-Attribute Utility Theory (MAUT) is a powerful tool to determine the optimal decision under uncertainty. In this case, the goal of the decision problem is to find the probability that an option is better than another. The authors have previously developed MAUT in conjunction with the Performance-Based Engineering (PBE) approach, giving rise to the extended framework PBE-MAUT. It has been previously applied for sustainable building design, where analyses involving energy expenditures and sustainability are considered in addition to safety of the building. The main challenge of PBE-MAUT is the evaluation of the distribution of the uncertain parameters; these typically are not independent, and do not follow known parametric distributions. In this paper, we present a novel method for the evaluation of the joint distributions of the uncertain random variables, starting from their sample data. The proposed approach is based on the Independent Components Analysis and the Maximum Entropy (MaxEnt) principle, giving rise to the Independent Component Maximum Entropy Method (IC-MEM). In IC-MEM, at first the method of the Independent Component (IC) is applied to sample data. In this way, a coordinate transformation from the original space toward the space of the ICs is developed. Second, the Probability Density Function (PDF) of the ICs are determined through the Multi Gaussian Maximum Entropy Method (MGMEM), which is a method based on the MaxEnt principle. The knowledge of the PDF of the ICs allows their simulation. Through the inverse coordinate transformation, from space of the ICs toward the original space, samples of the joint random variables are determined. As a result, PBE-MAUT can be effectively adopted as a powerful Decision Support Tool (DST) for the decision-maker.