The Concept of Diagonal Approximated Signature: New Surrogate Modeling Approach for Continuous-State Systems

The increasing size and complexity of modern systems present engineers with the inevitable challenge of developing more efficient, yet comprehensive computational tools that enable sound analyses and ensure stable system operation. This work proposes the continuous-state survival function (CSSF), and the concept of the diagonal approximated signature (DAS) is introduced as a corresponding surrogate model. The proposed concept is based on combinatorial decomposition adapted from the concept of survival signature. This allows for the advantageous property of separating topological and probabilistic information. Potentially high-dimensional coherent structure functions are the foundation. The proposed approach enables direct computation of the CSSF by means of an explicit formula and a stored DAS, avoiding costly online Monte Carlo simulation (MCS) and overcoming the limitation of binary component and system state consideration during resilience optimization for sub-structured systems. A proof of concept is provided for multidimensional systems and an arbitrary infrastructure system.