Event hazard function learning and survival analysis for tearing mode onset characterization

Abstract

It is shown that concepts from survival analysis (branch of statistics dealing with various types of time-to-event data) are helpful when trying to quantify and understand the onset of tearing modes in tokamaks. It is argued that a probabilistic event prediction problem should be decomposed into (i) dynamical system evolution and (ii) event hazard function integration. Successful machine learning of a hazard (events per time) function from experimental data is demonstrated. The hazard function exhibits statistical properties that are consistent with expectation. A specific tearing delta-prime proxy is found to not contribute to the likelihood of the hazard function for the present case. Although in this paper the event is the onset of a tearing mode in a particular plasma scenario, these ideas should be equally applicable to disruption events.

An application of survival analysis to disruption prediction via Random Forests

“…This is essentially equation (7) in [29]. Applying the Kaplan-Meier formalism to disruption prediction is relatively straightforward: The event or failure is simply the disruption itself.…”

“…Here, it is prudent to distinguish the present application of survival analysis from that in [29,30]. In [29,30], a direct hazard model was used to calculate multivariable hazard functions from machine learning of experimental data, which could then be related to survival probabilities via (5).…”

“…Here, it is prudent to distinguish the present application of survival analysis from that in [29,30]. In [29,30], a direct hazard model was used to calculate multivariable hazard functions from machine learning of experimental data, which could then be related to survival probabilities via (5). This is, in a way, opposite to the approach adopted in this paper; nevertheless, their model has benefits including the incorporation of time-dependent covariates.…”

“…The present work is not the first application of survival analysis for event prediction in the realm of fusion. Only recently, "direct hazard modeling" was used to study and predict the onset of neoclassical tearing modes [29,30] which can often lead to disruptions of tokamak plasmas. The authors of [29] actually note the potential of the survival analysis approach for disruption prediction.…”

Progress in disruption prevention for ITER

“…Adaptive methods to train an algorithm "from scratch" have achieved satisfactory performance after only a few tens of disruptive shots [46], [47]. Probabilistic predictors express output in terms of a likelihood of disruption rather than a binary classification [47], [48], and the probabilistic approach has also been applied to forecasting the onset of a tearing mode [49]. Deep-learning algorithms have begun to incorporate timesequential data and higher-dimension data via advanced neural net methods with promising results, including accurate cross-machine predictions [50].…”