Draft: Resilient Design of Complex Engineered Systems

This paper presents a general methodology to calculate the resiliency of complex engineered systems based on complex network theory. Graph spectral theory has been used simultaneously with complex network theory for years. Resiliency is a key driver in how systems are developed to operate in an expected operating environment, and how systems change and respond to the environments in which they operate. This paper uses a popular method for mathematically identifying features in complex networks based on the adjacency matrix; commonly used to represent edge connections between nodes in complex networks. A similar approach can also be used to define the physical connections within complex engineered systems. In conjunction with the adjacency matrix, the degree and Laplacian matrices have eigenvalue and eigenspectrum properties that can be used with complex engineered systems to calculate their design resiliency. One such property of the Laplacian matrix is called the algebraic connectivity. The algebraic connectivity is defined as the second smallest eigenvalue of the Laplacian matrix and is proven to be directly related to the resiliency of a complex network. Our motivation in the present work is to calculate the algebraic connectivity and other graph metrics to predict the resiliency of the system under design.