Closed-form symbolic computation of the global efficiency of complex systems by means of digraphs

Efficiency represents an important parameter that characterizes a mechanism or a machine. This value gives fundamental information about the energy that is lost during the process. Machines or mechanisms can be combined in order to build a more complex system. For example, they can be arranged as a series or as a parallel layout. For these cases, the efficiency can be easily evaluated. However, in general, the configuration is more complicated and a true evaluation of the efficiency becomes rather difficult. For this reason, this paper suggests a possible algorithm, based on graph theory, for the closed form symbolic computation of the efficiency of complex systems. One interesting feature of the algorithm consists in the possibility of applying the method to those systems which embeds one or more power circulation loops. As a requirement, it is assumed that the system to be analyzed can be represented by a group of blocks and a group of flows between the blocks.