Efficient long-term degradation profiling in time series for complex physical systems

The long term operation of physical systems inevitably leads to their wearing out, and may cause degradations in performance or the unexpected failure of the entire system. To reduce the possibility of such unanticipated failures, the system must be monitored for tell-tale symptoms of degradation that are suggestive of imminent failure. In this work, we introduce a novel time series analysis technique that allows the decomposition of the time series into trend and fluctuation components, providing the monitoring software with actionable information about the changes of the system's behavior over time. We analyze the underlying problem and formulate it to a Quadratic Programming (QP) problem that can be solved with existing QP-solvers. However, when the profiling resolution is high, as generally required by real-world applications, such a decomposition becomes intractable to general QP-solvers. To speed up the problem solving, we further transform the problem and present a novel QP formulation, Non-negative QP, for the problem and demonstrate a tractable solution that bypasses the use of slow general QP-solvers. We demonstrate our ideas on both synthetic and real datasets, showing that our method allows us to accurately extract the degradation phenomenon of time series. We further demonstrate the generality of our ideas by applying them beyond classic machine prognostics to problems in identifying the influence of news events on currency exchange rates and stock prices. We fully implement our profiling system and deploy it into several physical systems, such as chemical plants and nuclear power plants, and it greatly helps detect the degradation phenomenon, and diagnose the corresponding components.