A State-Space Approach to Optimal Level-Crossing Prediction for Linear Gaussian Processes

Extreme value analysis of optimal level‐crossing prediction for linear Gaussian processes

“…Instead of designing an alarm system for each time step, a single alarm system can be designed for all time steps. The approximation is based on the limiting statistics that are reached at steady‐state, which greatly reduces the computational burden, as previously identified (Martin, 2010). As such, the solution of the steady‐state Lyapunov function, , suffices for evolution of the unconditional state covariance matrix.…”

“…In earlier work (Martin, 2010), a novel state‐space approach to the optimal alarm systems literature was introduced, which contributed to the Kalman filter‐based fault detection literature from a different theoretical angle. Originally, it was shown by Svensson (1998) and Svensson et al.…”

“…This becomes important when considering the numerous applications that might benefit from an intelligent tradeoff between false alarms and missed detections. An extreme value analysis using the critical threshold that enables definition of the level‐crossing event will be investigated, to secure limiting conditions related to certain approximations to the optimal level‐crossing predictor and baseline methods for comparison that were also previously introduced (Martin, 2010).…”

“…This case is more practically relevant when monitoring residuals that may be derived from the output of other machine learning algorithms or transformed parameters that relate to critical performance of a system or process. The two‐sided case was also investigated in the earlier work (Martin, 2010) and serves as a precursor to this article. As such, it will be investigated here as well.…”

“…Optimal alarm regions cannot be expressed in closed form, and thus ROC curve analysis must be performed either empirically or with a computationally prohibitive generic Monte Carlo numerical integration routine where the integration region is given by storing precomputed points along the boundary of the alarm region (Svensson, 1998). As such, one of the aims of the previous study (Martin, 2010) was to investigate approximations for the design of an optimal alarm system. The resulting false alarm and missed detection probabilities that can be derived from ROC curve analysis were also compared to competing baseline methods and may provide some level of predictive capability, but have no provision for minimizing false alarms for the prediction of level‐crossing events.…”