Catching Critical Transition in Engineered Systems

Figure 3

Critical transition analysis of the engineered systems when running into failures with various methods. (a) The original time series of the vibration signal collected from the bearing system approaching failure, with the dashed line segmenting the signals into three sections for succeeding analysis. (b–e) Critical transition analysis for (a). (b) The Gaussian kernel-based probability density estimates for the three sections of the vibration signal. The density of the third section significantly differs from the first two. (c) The results of Student's t-test of the vibration amplitude signal with the true value of the mean are the mean of a normally functioning section. The tested value shows an evident decrease to below 0.01, which significantly denies the null hypothesis, indicating that the system evolves into a different state when getting into system failure. (d) Forecasting with a 95% confidence interval (enclosed in the red bars) derived from the AIC-based ARIMA model for the third section of the vibration signal. The failure in encompassing the vibration signal in the section suggests a phase transient. (e) Logistic map for phase space analysis of the vibration signal. The first two sections are rather concentrated while the third section diverges to unstable. (b–e) A critical transition in the bearing system when it is arriving a system failure. (f) A time series of the turbofan engine system during the degradation simulation process with the dashed line separating the signals into two sections at a departure point. (g) The phase portrait of the two sections of the time series signal of the turbofan engine system. A governing dynamical equation, , is learned from the left section and a system equation, , for the right section [36]. It shows that the left section has only one stable equilibrium point, while the right section has two, of which the one at the negative axis potentially drives the system to unstable (i.e., the corresponding system failure). h(1–3) and j(1–3), two snippets of the three selected signals of the IGBT system at the normal functioning stage and the close-to-failure stage. (i, k) The phase portraits of the signals in h(1–3) and j(1–3). The phase portrait of the normal functioning stage has a clear limit cycle serving as the basin of attractor, while the portrait of the close-to-failure stage reveals divergent behaviors indicating the occurrence of critical transition. More analysis of critical transition can be found in the supplemental material. The above analysis of the engineered systems suggests that the systems undergo certain critical transitions when running into system failures.

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