Catching Critical Transition in Engineered Systems

Figure 1

The presence of early warning signals in terms of the CSD (i.e., increasing variance and autocorrelation) and deviating skewness in four engineered systems: the airbrake system of a locomotive, the bearing, the turbofan engine, and the IGBT. a(1), the air pressure signal in the brake pipe of a locomotive in the period of two days before the failure of unrecoverable pressure loss. The signal was collected by the Train Control/Management System (TCMS) of the locomotive every second. It was preprocessed by eliminating the data corresponding to the parking states. b(1), the vibration signal from a bearing test platform collected by NASA PCoE while the bearing is operating until breaking down. c(1), an unspecified signal in the turbofan engine degradation simulation collected by NASA PCoE while the engine runs to failure. d(1), the collector current signal of a power IGBT during accelerated aging tests collected by NASA PCoE. a(2–4), b(2–4), c(2–4), and d(2–4), the early warning signal indicators. a(2), b(2), c(2), and d(2), the variance of the respective signal. a(3), b(3), c(3), and d(3), the lag 1 autocorrelation of the respective signal. a(4), b(4), c(4), and d(4), the skewness of the respective signal. The sliding window to compute variance, autocorrelation, and skewness is chosen as 50% of the span of time series for all the four systems. There are strong evidences of CSD and deviating skewness in all the four systems when they approach system failures. An increasing trend in both variance and lag 1 autocorrelation (i.e., CSD) can be clearly recognized. Clear deviations are observed in the skewness indicator. For instance, the airbrake and the IGBT systems show a strong tendency of increase before the system failure. The skewness in the bearing system significantly oscillates when approaching failure, while the skewness in the case of the turbofan has a consistent tendency of decreasing from the original value at around 1.5. Despite the clear trend, strong fluctuations in the variance, autocorrelation, and skewness are observed in all the cases, suggesting systematic disturbances existing in the original time series. For example, the IGBT data were collected from the accelerated aging test by periodically switching on and off the device. It is the transient current after switching off that reflects the inherent resilience [32]. The times series of the collector current mainly be two components: the switch-on current signal (which is failure-insensitive) at around 8 A and the switch-off current signal (which is failure-sensitive) exponentially converging to zero (d(1)). We show how to derive a more evident tendency in the early warning signals by focusing on failure-sensitive components in Figure 2. (a) Pressure signal in a locomotive brake pipe before it fails. (b) The vibration signal in the bearing failure test (NASA PCoE Datasets) locomotive brake pipe before it fails. (c) A measured signal in the turbofan engine degradation simulation (NASA PCoE Datasets). (d) The collector current signal in IGBT accelerated aging test (NASA PCoE Datasets).

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