Conditional POD for predicting extreme events in turbulent flow time signals.

Extreme events in turbulent flows are rare, fast excursions from typical behavior that can significantly impact systems performance and reliability. Predicting such events is challenging due to their intermittent nature and rare occurrence, which limits the effectiveness of data-intensive methods. This paper, therefore, introduces a novel data-driven approach for on-the-fly early-stage prediction of extreme events in time signals. The method identifies the most energetic time-only POD mode of an ensemble of time segments leading to extreme events in a signal. High similarity between incoming signals and the computed mode serves as an indicator of an approaching extreme event. A support vector machine is employed to classify the signals as preceding an extreme event or not. This approach is fully data-driven and requires minimal training data, making it particularly suitable for significantly rare events. The method is applied to predict extreme dissipation events in a wall-bounded shear flow at different Reynolds numbers and wall distances, demonstrating robust performance across a range of intermittency levels. Even with limited training data, leading to an imperfect representation of the extreme event statistics, the method provides predictions at lead times that match and usually exceed the timeframe for which the Hankel-DMD method remains accurate. This opens up the possibility of using the conditional POD method to flag incoming extreme events so that potentially unreliable forecasts from signal prediction methods, such as Hankel-DMD, can be discarded or their forecasting horizon shortened.