Upgrades of Genetic Programming for Data-Driven Modeling of Time Series.

In many engineering fields and scientific disciplines, the results of experiments are in the form of time series, which can be quite problematic to interpret and model. Genetic programming tools are quite powerful in extracting knowledge from data. In this work, several upgrades and refinements are proposed and tested to improve the explorative capabilities of symbolic regression (SR) via genetic programming (GP) for the investigation of time series, with the objective of extracting mathematical models directly from the available signals. The main task is not simply prediction but consists of identifying interpretable equations, reflecting the nature of the mechanisms generating the signals. The implemented improvements involve almost all aspects of GP, from the knowledge representation and the genetic operators to the fitness function. The unique capabilities of genetic programming, to accommodate prior information and knowledge, are also leveraged effectively. The proposed upgrades cover the most important applications of empirical modeling of time series, ranging from the identification of autoregressive systems and partial differential equations to the search of models in terms of dimensionless quantities and appropriate physical units. Particularly delicate systems to identify, such as those showing hysteretic behavior or governed by delayed differential equations, are also addressed. The potential of the developed tools is substantiated with both a battery of systematic numerical tests with synthetic signals and with applications to experimental data.

Data driven theory for knowledge discovery in the exact sciences with applications to thermonuclear fusion.

In recent years, the techniques of the exact sciences have been applied to the analysis of increasingly complex and non-linear systems. The related uncertainties and the large amounts of data available have progressively shown the limits of the traditional hypothesis driven methods, based on first principle theories. Therefore, a new approach of data driven theory formulation has been developed. It is based on the manipulation of symbols with genetic computing and it is meant to complement traditional procedures, by exploring large datasets to find the most suitable mathematical models to interpret them. The paper reports on the vast amounts of numerical tests that have shown the potential of the new techniques to provide very useful insights in various studies, ranging from the formulation of scaling laws to the original identification of the most appropriate dimensionless variables to investigate a given system. The application to some of the most complex experiments in physics, in particular thermonuclear plasmas, has proved the capability of the methodology to address real problems, even highly nonlinear and practically important ones such as catastrophic instabilities. The proposed tools are therefore being increasingly used in various fields of science and they constitute a very good set of techniques to bridge the gap between experiments, traditional data analysis and theory formulation.

A comprehensive study of the uncertainties in bolometric tomography on JET using the maximum likelihood method.

Essential physical quantities of magnetically confined plasmas are derived on a routine basis from bolometric reconstructions. In the last few years at the Joint European Torus (JET), the Maximum Likelihood method has demonstrated the capability of providing reliable reconstructions for this class of ill-posed problems. The article is focused on quantifying the effects of important sources of errors, usually underestimated, that can influence both the reconstructions and the derived quantities. A complete set of phantoms has been used to test the robustness of the technique. The main sources of uncertainties investigated in this contribution are random noise, presence of outliers in the measurements, uncertainty of the position of the magnetic topology, and missing measurements from damaged or unreliable bolometers. The study provides a comprehensive quantification of the uncertainties to associate with most typical emissivities encountered in practice and constitutes a good basis for a more accurate evaluation of the power balances on the JET.

Image computing techniques to extrapolate data for dust tracking in case of an experimental accident simulation in a nuclear fusion plant.

In this paper, a preliminary shadowgraph-based analysis of dust particles re-suspension due to loss of vacuum accident (LOVA) in ITER-like nuclear fusion reactors has been presented. Dust particles are produced through different mechanisms in nuclear fusion devices, one of the main issues is that dust particles are capable of being re-suspended in case of events such as LOVA. Shadowgraph is based on an expanded collimated beam of light emitted by a laser or a lamp that emits light transversely compared to the flow field direction. In the STARDUST facility, the dust moves in the flow, and it causes variations of refractive index that can be detected by using a CCD camera. The STARDUST fast camera setup allows to detect and to track dust particles moving in the vessel and then to obtain information about the velocity field of dust mobilized. In particular, the acquired images are processed such that per each frame the moving dust particles are detected by applying a background subtraction technique based on the mixture of Gaussian algorithm. The obtained foreground masks are eventually filtered with morphological operations. Finally, a multi-object tracking algorithm is used to track the detected particles along the experiment. For each particle, a Kalman filter-based tracker is applied; the particles dynamic is described by taking into account position, velocity, and acceleration as state variable. The results demonstrate that it is possible to obtain dust particles' velocity field during LOVA by automatically processing the data obtained with the shadowgraph approach.

UMEL: a new regression tool to identify measurement peaks in LIDAR/DIAL systems for environmental physics applications.

Recently, surveying large areas in an automatic way, for early detection of both harmful chemical agents and forest fires, has become a strategic objective of defence and public health organisations. The Lidar and Dial techniques are widely recognized as a cost-effective alternative to monitor large portions of the atmosphere. To maximize the effectiveness of the measurements and to guarantee reliable monitoring of large areas, new data analysis techniques are required. In this paper, an original tool, the Universal Multi Event Locator, is applied to the problem of automatically identifying the time location of peaks in Lidar and Dial measurements for environmental physics applications. This analysis technique improves various aspects of the measurements, ranging from the resilience to drift in the laser sources to the increase of the system sensitivity. The method is also fully general, purely software, and can therefore be applied to a large variety of problems without any additional cost. The potential of the proposed technique is exemplified with the help of data of various instruments acquired during several experimental campaigns in the field.

Improved equilibrium reconstructions by advanced statistical weighting of the internal magnetic measurements.

In a Tokamak the configuration of the magnetic fields remains the key element to improve performance and to maximise the scientific exploitation of the device. On the other hand, the quality of the reconstructed fields depends crucially on the measurements available. Traditionally in the least square minimisation phase of the algorithms, used to obtain the magnetic field topology, all the diagnostics are given the same weights, a part from a corrective factor taking into account the error bars. This assumption unduly penalises complex diagnostics, such as polarimetry, which have a limited number of highly significant measurements. A completely new method to choose the weights, to be given to the internal measurements of the magnetic fields for improved equilibrium reconstructions, is presented in this paper. The approach is based on various statistical indicators applied to the residuals, the difference between the actual measurements and their estimates from the reconstructed equilibrium. The potential of the method is exemplified using the measurements of the Faraday rotation derived from JET polarimeter. The results indicate quite clearly that the weights have to be determined carefully, since the inappropriate choice can have significant repercussions on the quality of the magnetic reconstruction both in the edge and in the core. These results confirm the limitations of the assumption that all the diagnostics have to be given the same weight, irrespective of the number of measurements they provide and the region of the plasma they probe.

Influence of plasma diagnostics and constraints on the quality of equilibrium reconstructions on Joint European Torus.

One of the main approaches to thermonuclear fusion relies on confining high temperature plasmas with properly shaped magnetic fields. The determination of the magnetic topology is, therefore, essential for controlling the experiments and for achieving the required performance. In Tokamaks, the reconstruction of the fields is typically formulated as a free boundary equilibrium problem, described by the Grad-Shafranov equation in toroidal geometry and axisymmetric configurations. Unfortunately, this results in mathematically very ill posed problems and, therefore, the quality of the equilibrium reconstructions depends sensitively on the measurements used as inputs and on the imposed constraints. In this paper, it is shown how the different diagnostics (Magnetics Measurements, Polarimetry and Motional Stark Effect), together with the edge current density and plasma pressure constraints, can have a significant impact on the quality of the equilibrium on JET. Results show that both the Polarimetry and Motional Stark Effect internal diagnostics are crucial in order to obtain reasonable safety factor profiles. The impact of the edge current density constraint is significant when the plasma is in the H-mode of confinement. In this plasma scenario the strike point positions and the plasma last closed flux surface can change even by centimetres, depending on the edge constraints, with a significant impact on the remapping of the equilibrium-dependent diagnostics and of pedestal physics studies. On the other hand and quite counter intuitively, the pressure constraint can severely affect the quality of the magnetic reconstructions in the core. These trends have been verified with several JET discharges and consistent results have been found. An interpretation of these results, as interplay between degrees of freedom and available measurements, is provided. The systematic analysis described in the paper emphasizes the importance of having sufficient diagnostic inputs and of properly validating the results of the codes with independent measurements.

Mutual interaction of Faraday rotation and Cotton­Mouton phase shift in JET polarimetric measurements.

The paper presents a study of Faraday rotation (FR) angle and Cotton­Mouton (CM) phase shift measurements to determine their mutual interaction and the validity of the linear models presently used in equilibrium codes. Comparison between time traces of measurements and model calculations leads to the result that only an exact numerical solution of Stokes equations can reproduce in all the experimental data. As a consequence, approximated linear models can be applied only in a limited range of plasma parameters. In general, the nonlinear coupling between FR and CM is important for the evaluation of polarimetry parameters.

Recent developments of the JET far-infrared interferometer-polarimeter diagnostic.

The far-infrared diagnostic provides essential internal measurements of the plasma density and magnetic field topology (q-profile via Faraday rotation angle) in real-time. The diagnostic capabilities have recently been extended in a number of key areas. Fast interferometer data, with 10 µs time resolution, and a new MATLAB code have allowed improved analysis of the evolution of density profiles during fast events such as vertical plasma displacements, edge localized mode, pellet fuelling, and disruptions. Using the polarimeter measurements in real-time, a new calibration procedure has been developed based on a propagation code using the Mueller matrix formalism. A further major upgrade of the system is presently underway: adding a second color laser to the vertical channels and implementing a new phase counter based on analog zero crossing and field-programmable gate array boards.

A new calibration code for the JET polarimeter.

An equivalent model of JET polarimeter is presented, which overcomes the drawbacks of previous versions of the fitting procedures used to provide calibrated results. First of all the signal processing electronics has been simulated, to confirm that it is still working within the original specifications. Then the effective optical path of both the vertical and lateral chords has been implemented to produce the calibration curves. The principle approach to the model has allowed obtaining a unique procedure which can be applied to any manual calibration and remains constant until the following one. The optical model of the chords is then applied to derive the plasma measurements. The results are in good agreement with the estimates of the most advanced full wave propagation code available and have been benchmarked with other diagnostics. The devised procedure has proved to work properly also for the most recent campaigns and high current experiments.