Catching Critical Transition in Engineered Systems

Figure 4

The potential catastrophic bifurcation and critical transition in engineered systems. (a) The abrupt state change in the vibration signal of the bearing system while running into failure. (b) The abrupt state change in the fluctuation of the IGBT collector current extracted with FM. (c) The hypothesized catastrophic bifurcation at the system failure. The catastrophic bifurcation can be mapped to the sudden regime shifts in (a) and (b). Considering the nonlinear phenomenon like hysteresis, the above hypothesis is likely to hold. (d) The proposed three phases, a nominally designed working phase that is equivalent to the basin of attractions, a predefined safety-oriented phase when the system initializes the self-protection after certain failures happened, and an unstable failure phase exhibiting out-of-control performance, in engineered systems with dynamical behaviors. The catastrophic bifurcation, i.e., critical transition, occurs when the system departs from the basin of attraction and loses its resilience as the system fails.