Manifold learning techniques and statistical approaches applied to the disruption prediction in tokamaks

The nuclear fusion arises as the unique clean energy source capable to meet the energy needs of the entire world in the future. On present days, several experimental fusion devices are operating to optimize the fusion process, confining the plasma by means of magnetic fields. The goal of plasma confined in a magnetic field can be achieved by linear cylindrical configurations or toroidal configurations, e.g., stellarator, reverse field pinch, or tokamak. Among the explored magnetic confinement techniques, the tokamak configuration is to date considered the most reliable. Unfortunately, the tokamak is vulnerable to instabilities that, in the most severe cases, can lead to lose the magnetic confinement; this phenomenon is called disruption. Disruptions are dangerous and irreversible events for the device during which the plasma energy is suddenly released on the first wall components and vacuum vessel causing runaway electrons, large mechanical forces and intense thermal loads, which may cause severe damage to the vessel wall and the plasma face components. Present devices are designed to resist the disruptive events; for this reason, today, the disruptions are generally tolerable. Furthermore, one of their aims is the investigation of disruptive boundaries in the operational space. However, on future devices, such as ITER, which must operate at high density and at high plasma current, only a limited number of disruptions will be tolerable. For these reasons, disruptions in tokamaks must be avoided, but, when a disruption is unavoidable, minimizing its severity is mandatory. Therefore, finding appropriate mitigating actions to reduce the damage of the reactor components is accepted as fundamental objective in the fusion community. The physical phenomena that lead plasma to disrupt are non-linear and very complex. The present understanding of disruption physics has not gone so far as to provide an analytical model describing the onset of these instabilities and the main effort has been devoted to develop data-based methods. In the present thesis the development of a reliable disruption prediction system has been investigated using several data-based approaches, starting from the strengths and the drawbacks of the methods proposed in the literature. In fact, literature reports numerous studies for disruption prediction using data-based models, such as neural networks. Even if the results are encouraging, they are not sufficient to explain the intrinsic structure of the data used to describe the complex behavior of the plasma. Recent studies demonstrated the urgency of developing sophisticated control schemes that allow exploring the operating limits of tokamak in order to increase the reactor performance. For this reason, one of the goal of the present thesis is to identify and to develop tools for visualization and analysis of multidimensional data from numerous plasma diagnostics available in the database of the machine. The identification of the boundaries of the disruption free plasma parameter space would lead to an increase in the knowledge of disruptions. A viable approach to understand disruptive events consists of identifying the intrinsic structure of the data used to describe the plasma operational space. Manifold learning algorithms attempt to identify these structures in order to find a low-dimensional representation of the data. Data for this thesis comes from ASDEX Upgrade (AUG). ASDEX Upgrade is a medium size tokamak experiment located at IPP Max-Planck-Institut für Plasmaphysik, Garching bei München (Germany). At present it is the largest tokamak in Germany. Among the available methods the attention has been mainly devoted to data clustering techniques. Data clustering consists on grouping a set of data in such a way that data in the same group (cluster) are more similar to each other than those in other groups. Due to the inherent predisposition for visualization, the most popular and widely used clustering technique, the Self-Organizing Map (SOM), has been firstly investigated. The SOM allows to extract information from the multidimensional operational space of AUG using 7 plasma parameters coming from successfully terminated (safe) and disruption terminated (disrupted) pulses. Data to train and test the SOM have been extracted from AUG experiments performed between July 2002 and November 2009. The SOM allowed to display the AUG operational space and to identify regions with high risk of disruption (disruptive regions) and those with low risk of disruption (safe regions). In addition to space visualization purposes, the SOM can be used also to monitor the time evolution of the discharges during an experiment. Thus, the SOM has been used as disruption predictor by introducing a suitable criterion, based on the trend of the trajectories on the map throughout the different regions. When a plasma configuration with a high risk of disruption is recognized, a disruption alarm is triggered allowing to perform disruption avoidance or mitigation actions. The data-based models, such as the SOM, are affected by the so-called "ageing effect". The ageing effect consists in the degradation of the predictor performance during the time. It is due to the fact that, during the operation of the predictor, new data may come from experiments different from those used for the training. In order to reduce such effect, a retraining of the predictor has been proposed. The retraining procedure consists of a new training procedure performed adding to the training set the new plasma configurations coming from more recent experimental campaigns. This aims to supply the novel information to the model to increase the prediction performances of the predictor. Another drawback of the SOM, common to all the proposed data-based models in literature, is the need of a dedicated set of experiments terminated with a disruption to implement the predictive model. Indeed, future fusion devices, like ITER, will tolerate only a limited number of disruptive events and hence the disruption database won't be available. In order to overcome this shortcoming, a disruption prediction system for AUG built using only input signals from safe pulses has been implemented. The predictor model is based on a Fault Detection and Isolation (FDI) approach. FDI is an important and active research field which allows to monitor a system and to determine when a fault happens. The majority of model-based FDI procedures are based on a statistical analysis of residuals. Given an empirical model identified on a reference dataset, obtained under Normal Operating Conditions (NOC), the discrepancies between the new observations and those estimated by the NOCs (residuals) are calculated. The residuals are considered as a random process with known statistical properties. If a fault happens, a change of these properties is detected. In this thesis, the safe pulses are assumed as the normal operation conditions of the process and the disruptions are assumed as status of fault. Thus, only safe pulses are used to train the NOC model. In order to have a graphical representation of the trajectory of the pulses, only three plasma parameters have been used to build the NOC model. Monitoring the time evolution of the residuals by introducing an alarm criterion based on a suitable threshold on the residual values, the NOC model properly identifies an incoming disruption. Data for the training and the tests of the NOC model have been extracted from AUG experiments executed between July 2002 and November 2009. The assessment of a specific disruptive phase for each disruptive discharge represents a relevant issue in understanding the disruptive events. Up to now at AUG disruption precursors have been assumed appearing into a prefixed time window, the last 45ms for all disrupted discharges. The choice of such a fixed temporal window could limit the prediction performance. In fact, it generates ambiguous information in cases of disruptions with disruptive phase different from 45ms. In this thesis, the Mahalanobis distance is applied to define a specific disruptive phase for each disruption. In particular, a different length of the disruptive phase has been selected for each disrupted pulse in the training set by labeling each sample as safe or disruptive depending on its own Mahalanobis distance from the set of the safe discharges. Then, with this new training set, the operational space of AUG has been mapped using the Generative Topography Mapping (GTM). The GTM is inspired by the SOM algorithm, with the aim to overcome its limitations. The GTM has been investigated in order to identify regions with high risk of disruption and those with low risk of disruption. For comparison purposes a second SOM has been built. Hence, GTM and SOM have been tested as disruption predictors. Data for the training and the tests of the SOM and the GTM have been extracted from AUG experiments executed from May 2007 to November 2012. The last method studied and applied in this thesis has been the Logistic regression model (Logit). The logistic regression is a well-known statistic method to analyze problems with dichotomous dependent variables. In this study the Logit models the probability that a generic sample belongs to the non-disruptive or the disruptive phase. The time evolution of the Logit Model output (LMO) has been used as disruption proximity index by introducing a suitable threshold. Data for the training and the tests of the Logit models have been extracted from AUG experiments executed from May 2007 to November 2012. Disruptive samples have been selected through the Mahalanobis distance criterion. Finally, in order to interpret the behavior of data-based predictors, a manual classification of disruptions has been performed for experiments occurred from May 2007 to November 2012. The manual classification has been performed by means of a visual analysis of several plasma parameters for each disruption. Moreover, the specific chains of events have been detected and used to classify disruptions and when possible, the same classes introduced for JET are adopted