A Multi-State Model of the Aging Process of Cyber-Physical Systems

Abstract

Cyber-Physical Systems (CPSs) are systems with tight integration and dependence between software and hardware parts, typically used as control systems and supervised by human operators. In this paper, we propose a multi-state model (commonly used to model the hardware degradation) to describe the aging of the cyber part of a CPS, where memory leakage is considered as the degradation process that leads to a service rate decrease, resulting in data jamming in the mission queue which, in turns, increases the memory request. The CPS is blocked and significantly increases the control delay when the amount of memory available cannot satisfy the demand of the mission queue. With control delay, the CPS may fail to control the system during transients: as an example, a typical Nuclear Power Plant (NPP) control rod system is taken as the CPS and its cyber degradation process modelled with the proposed multi-state degradation model. The unreliability of control rod system is quantified with respect to a transient of power step change, considering cyber degradation and hardware stochastic failure.

Multi-State Reliability Assessment Model of Base-Load Cyber-Physical Energy Systems (CPES) during Flexible Operation Considering the Aging of Cyber Components

“…In this Section, the multi-state model of the aging process of a CPS originally presented in [15] is briefly recalled and customized for application to the CRS of Section 2.…”

“…Calculate system-blocking transition rate λ B with the model described in [15] and the procedure summarized in Section 3.3; 2.…”

“…Assuming the functionalities of cyber components of a CPES is quite important given the long operation time of CPESs, and their reliability is threatened by aging processes typical of cyber systems. Then, to assess the reliability of CPESs accounting for the aging and degradation of cyber systems, in [15] we proposed a multi-state model for describing the aging process driven by memory leakage [16,17], which leads to service rate decrease and, eventually, data-jamming in the mission queue [18,19], which, in turn, increases the memory request; in such conditions, the cyber system blocks its function, significantly increasing the control delay [20,21], deteriorating the system stability and controllability during transients, when the amount of memory available cannot satisfy the demand of the mission queue. In this paper, we elaborate on this modelling approach to propose a framework of analysis for complete support to the reliability assessment of CPES for load-following.…”

“…To demonstrate the use of the reliability assessment framework, we consider the Control Rod System (CRS) of a typical NPP. We apply the multi-state model [15] that integrates the hardware components' stochastic failures with the aging of cyber components, and quantify the unreliability of the CPS with respect to transients during load-following operations under normal/emergency conditions.…”