The concept of diagonal approximated signature: new surrogate modeling approach for continuous-state systems in the context of resilience optimization

Abstract

The increasing size and complexity of modern systems presents engineers with the inevitable challenge of developing more efficient yet comprehensive computational tools that enable sound analyses and ensure stable system operation. The previously introduced resilience framework for complex and sub-structured systems provides a solid foundation for comprehensive stakeholder decision-making, taking into account limited resources. In their work, a survival function approach based on the concept of survival signature models the reliability of system components and subsystems. However, it is limited to a binary component and system state consideration. This limitation needs to be overcome to ensure comprehensive resilience analyses of real world systems. An extension is needed that guarantees both maintaining the existing advantages of the original resilience framework, yet enables continuous performance consideration. This work introduces the continuous-state survival function and concept of the Diagonal Approximated Signature (DAS) 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. A stochastic process models the time-dependent degradation of the continuous-state components. The proposed approach enables direct computation of the continuous-state survival function by means of an explicit formula and a stored DAS, avoiding costly online Monte Carlos Simulation (MCS) and overcoming the limitation of a binary component and system state consideration during resilience optimization for sub-structured systems. A proof of concept is provided for multi-dimensional systems and an arbitrary infrastructure system.