Resilience Performance Modelling using PT Delay Elements

Resilience is mostly represented using a curve of performance. There are multiple mathematical resilience performance representations. When subjected to external forces or disturbances, infrastructure systems often exhibit a delayed response, the characteristic of what is already mentioned in the cited works. If resilience is understood as a dampening factor to some disturbance, it is suitable to model it phenomenologically using delay elements. A delay element basically is the functional description (transfer function) between an input and output relation. The input describes the presence of a disturbance, which is mostly a step function, and following that the delay element could be used to describe the delayed system response. It is important to mention that the decay and recovery in performance are generally not able to be modelled using the same transfer function, because in most real cases the decay happens much faster than the repair process. Therefore, the behaviour needs to be either directional, or time dependent. We apply the concept of modelling a resilience process using delay elements to the use-case of a power outage in a factory. The availability of electricity serves as the input step function for this scenario. The output of the model describes the system performance, such as the number of parts produced or sold by the factory. After a sudden power outage, depending on the circumstances, the factory may be able to continue producing or selling for a shorter or longer period. This represents the system's response to the power failure. Once the disruption is resolved, production and sales can resume, albeit with a delay.

Keywords: Resilience management, infrastructure, modelling.