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International audience; It is sometimes desirable to delve further into how the inputs affect the output in design optimization and uncertainty analysis. Surrogate models such as Gaussian Process Regression and support vector regression are useful for such tasks and can be further enhanced by introducing advanced post-processing methods. This paper investigates Shapley Additive Explanation (SHAP) as a tool to aid surrogate-assisted data-driven analysis. In particular, surrogate-enabled SHAP analysis allows visualization of the input-output relationship in a meaningful way using summary SHAP plots and SHAP dependence plots. Some importantinformation that can be extracted and visualized from SHAP includes the importance of input variables (i.e., global sensitivity analysis), nonlinearity level, and level of interactions. The benefits of Shapley values for engineering analysis using surrogate models are demonstrated in three engineering test problems.

International audience; Many engineering problems are governed by complex governing equations that are difficult and typically require high computational costs to solve. Machine learning and surrogate modelling aid such an endeavour by providing a cheap-to-evaluate prediction model that acts as a replacement of the original model. While most research focuses on predicting scalar values (e.g., lift and drag), predicting the solution field is also of interest in many practical engineering and scientific applications. This paper proposes a Physics-Informed Proper Orthogonal Decomposition (POD) technique that improves the solution field prediction by enforcing governing equations as a loss penalty. The proposed idea utilizes a reduced-order modeling technique based on POD to decompose solution snapshots into singular vectors and values. A Gaussian Process Regression is then utilized to predict the singular values from variable parameters. The predicted singular values from the data of the problem are then adjusted via optimization to minimize the physics-informed loss and achieve better prediction. In this paper, we illustrate the efficacy of the proposed method on simple two-dimensional partial differential equations. The result clearly shows that the proposed physics-informed POD outperforms the conventional POD in terms of approximation error.

The search for a more efficient method to destroy aircraft trailing vortices requires a good understanding of the early development of the vortices. For that purpose, an experimental investigation has been conducted to study the formation and near-field dynamics of a wing tip vortex. Two versions of the Digital Particle Image Velocimetry (DPIV) technique were used in the studies. Planar DPIV was used to obtain velocity fields adjacent to the wing surface. Stereoscopic DPIV, which allows instantaneous measurements of all three components of velocity within a planar slice, was used to measure velocity fields behind the wing. The trailing vortex was produced by a rectangular half-wing model with an NACA 0012 profile. All measurements were made at Reynolds number, based on chord length, of 9040. The present study has found that the wing sheds multiple vortices. A structure that closely resembles a wing tip vortex is first observed on the suction side of the wing near the tip at the mid-chord section of the wing. At the trailing edge of the wing, a smaller vortex with an opposite sense of rotation is observed next to the tip vortex. In addition to the two vortices, two vortex layers with opposite sense of rotation, one on the pressure side and one on the suction side, are apparent at the trailing edge. Farther downstream, most of the vorticity in the vortex layer, with the same sense of rotation as the tip vortex, rolls up into the wing tip vortex. The vortices, with opposite sense of rotation, break up into smaller vortices which orbit around the tip vortex. At least one relatively strong satellite vortex appears in some of the instantaneous fields. The studies found that the interaction of the tip vortex and satellite vortices give rise to the unsteady motion of the wing tip vortex. In addition, the studies also examined the effects of the boundary layer and the tip geometry to the strength and motion of the trailing vortex.