Applications of Bayesian temperature profile reconstruction to automated comparison with heat transport models and uncertainty quantification of current diffusion

Abstract

Please cite this article in press as: M. Irishkin, et al., Applications of Bayesian temperature profile reconstruction to automated comparison with heat transport models and uncertainty quantification of current diffusion, Fusion Eng. Des. (2015), http://dx.h i g h l i g h t s• We developed a method for automated comparison of experimental data with models.• A unique platform implements Bayesian analysis and integrated modelling tools.• The method is tokamak-generic and is applied to Tore Supra and JET pulses.• Validation of a heat transport model is carried out.• We quantified the uncertainties due to Te profiles in current diffusion simulations. a b s t r a c tIn the context of present and future long pulse tokamak experiments yielding a growing size of measured data per pulse, automating data consistency analysis and comparisons of measurements with models is a critical matter. To address these issues, the present work describes an expert system that carries out in an integrated and fully automated way (i) a reconstruction of plasma profiles from the measurements, using Bayesian analysis (ii) a prediction of the reconstructed quantities, according to some models and (iii) a comparison of the first two steps. The first application shown is devoted to the development of an automated comparison method between the experimental plasma profiles reconstructed using Bayesian methods and time dependent solutions of the transport equations. The method was applied to model validation of a simple heat transport model with three radial shape options. It has been tested on a database of 21 Tore Supra and 14 JET shots. The second application aims at quantifying uncertainties due to the electron temperature profile in current diffusion simulations. A systematic reconstruction of the Ne, Te, Ti profiles was first carried out for all time slices of the pulse. The Bayesian 95% highest probability intervals on the Te profile reconstruction were then used for (i) data consistency check of the flux consumption and (ii) defining a confidence interval for the current profile simulation. The method has been applied to one Tore Supra pulse and one JET pulse.

Application of Gaussian process regression to plasma turbulent transport model validation via integrated modelling

“…As a final note, both the proposed figures-of-merit discussed in this paper for evaluating the agreement and trustworthiness between simulation inputs and outputs, found in Equations (9) and 10, should not be confused with other statistically meaningful quantities, ie. probability, likelihood, etc.…”

“…The sensitivity of density peaking to the rotational shear is consistent with previous works [22, 31], although a more detailed transport analysis of this effect is recommended and left for future work. Figure 15 shows the analysis of these sensitivities according to the FOM given in Equation (9). The negative impact of the removal of the rotation contributions within QuaLiKiz on the n e and T i agreement can be seen.…”

“…This is further supported by the level of agreement between the input profiles from the GPR technique and the output profiles from the converged JETTO + QuaLiKiz execution, as shown by the blue line in Figure 8. From these base case settings, a wide variety of additional sensitivity studies were performed, as further discussed in Sections 4.3 Figure 9 shows the results of applying Equation (9) to the profiles shown in Figures 8. As shown in this figure, the level of agreement between the experimental fit and the simulation output profiles is quantitatively captured by the proposed metric, with a value of S ≥ 0.5 indicating that the profile lies within the ±2σ boundary of the experimental fit distribution.…”

“…The application of the point-distribution metric described in Equation (9) to the data presented in Figure 16 were omitted from this paper as they did not reveal additional insights.…”

“…Figure9shows the results of applying Equation(9) to the profiles shown in Figures 8. As shown in this figure, the level of agreement between the experimental fit and the simulation output profiles is quantitatively captured by the proposed metric, with a value of S ≥ 0.5 indicating that the profile lies within the ±2σ boundary of the experimental fit distribution.…”