Use of information theory with discrete models of continuous systems
Bobby D. Middleton, M.W. Golay · International Journal of General Systems · 2008
A technique is presented whereby the Shannon entropy can be used to define two parameters—the effective range and the uncertainty index—which can be used to quantify consistently the uncertainty in realistic continuous systems by comparing the probability distribution associated with the actual system to a uniform distribution having the same entropy value. Knowing the entropy value of a distribution which describes a system can allow decision-makers to choose more easily between systems in order to achieve a given objective. It also provides a metric for ranking the importance of input parameters for a given system based upon their relative impact upon the total uncertainty of the output of the system. Since the data collected from most engineering systems are actually a set of discrete samples, a method is introduced to calculate the Shannon entropy using spreadsheet software and then calculate the effective range and uncertainty index. The technique is used to choose between two policies for an example construction project and to rank input variables in order of decreasing effect upon the output uncertainty of the project.