Modeling and assessment of intrinsic resilience kernel based on convolution model considering multi-disruption: A disruption-response perspective

Quantitative resilience assessment of engineered systems predominantly relies on performance-over-time metrics, which cannot decouple the system’s intrinsic resilience from external disruption influences, leading to disruption-dependent and non-comparable assessments. To overcome this, this paper introduces the concept of an intrinsic resilience kernel, defined as the system’s performance response to a unit impulse disruption, which represents its inherent recovery mechanisms. A convolution model-based framework is proposed to assess this kernel under multi-disruption conditions, modeling cumulative performance loss as the convolution of the disruption profile and the intrinsic resilience kernel. Relative to performance-centric models, the novelty lies in adopting a disruption-response perspective that formally separates external disruptions from the intrinsic system property, with convolution providing a principled mathematical tool for evaluation in dynamic environments. Simulation experiments on a networked unmanned system-of-systems demonstrate that the derived intrinsic resilience kernel is invariant to different disruption patterns and determined solely by internal resilience mechanisms, providing a consistent metric for resilience design.