Robust scaling in fusion science: case study for the L-H power threshold

In regression analysis for deriving scaling laws in the context of fusion studies, standard regression methods are usually applied, of which ordinary least squares (OLS) is the most popular. However, concerns have been raised with respect to several assumptions underlying OLS in its application to fusion data. More sophisticated statistical techniques are available, but they are not widely used in the fusion community and, moreover, the predictions by scaling laws may vary significantly depending on the particular regression technique. Therefore we have developed a new regression method, which we call geodesic least squares regression (GLS), that is robust in the presence of significant uncertainty on both the data and the regression model. The method is based on probabilistic modeling of all variables involved in the scaling expression, using adequate probability distributions and a natural similarity measure between them (geodesic distance). In this work we revisit the scaling law for the power threshold for the L-to-H transition in tokamaks, using data from the multi-machine ITPA databases. Depending on model assumptions, OLS can yield different predictions of the power threshold for ITER. In contrast, GLS regression delivers consistent results. Consequently, given the ubiquity and importance of scaling laws and parametric dependence studies in fusion research, GLS regression is proposed as a robust and easily implemented alternative to classic regression techniques

A New Robust Regression Method Based on Minimization of Geodesic Distances on a Probabilistic Manifold: Application to Power Laws

In regression analysis for deriving scaling laws that occur in various scientific disciplines, usually standard regression methods have been applied, of which ordinary least squares (OLS) is the most popular. In many situations, the assumptions underlying OLS are not fulfilled, and several other approaches have been proposed. However, most techniques address only part of the shortcomings of OLS. We here discuss a new and more general regression method, which we call geodesic least squares regression (GLS). The method is based on minimization of the Rao geodesic distance on a probabilistic manifold. For the case of a power law, we demonstrate the robustness of the method on synthetic data in the presence of significant uncertainty on both the data and the regression model. We then show good performance of the method in an application to a scaling law in magnetic confinement fusion.Comment: Published in Entropy. This is an extended version of our paper at the 34th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2014), 21-26 September 2014, Amboise, Franc

A knowledge-based geometry repair system for robust parametric CAD models

In modern multi-objective design optimization (MDO) an effective geometry engine is becoming an essential tool and its performance has a significant impact on the entire MDO process. Building a parametric geometry requires difficult compromises between the conflicting goals of robustness and flexibility. This article presents a method of improving the robustness of parametric geometry models by capturing and modeling engineering knowledge with a support vector regression surrogate, and deploying it automatically for the search of a more robust design alternative while trying to maintain the original design intent. Design engineers are given the opportunity to choose from a range of optimized designs that balance the ‘health’ of the repaired geometry and the original design intent. The prototype system is tested on a 2D intake design repair example and shows the potential to reduce the reliance on human design experts in the conceptual design phase and improve the stability of the optimization cycle. It also helps speed up the design process by reducing the time and computational power that could be wasted on flawed geometries or frequent human intervention