Honey Yield Forecast Using Radial Basis Functions

Honey yields are difficult to predict and have been usually associated with weather conditions. Although some specific meteorological variables have been associated with honey yields, the reported relationships concern a specific geographical region of the globe for a given time frame and cannot be used for different regions, where climate may behave differently. In this study, Radial Basis Function (RBF) interpolation models were used to explore the relationships between weather variables and honey yields. RBF interpolation models can produce excellent interpolants, even for poorly distributed data points, capable of mimicking well unknown responses providing reliable surrogates that can be used either for prediction or to extract relationships between variables. The selection of the predictors is of the utmost importance and an automated forward-backward variable screening procedure was tailored for selecting variables with good predicting ability. Honey forecasts for Andalusia, the first Spanish autonomous community in honey production, were obtained using RBF models considering subsets of variables calculated by the variable screening procedure

Adaptive Sampling for Nonlinear Dimensionality Reduction Based on Manifold Learning

We make use of the non-intrusive dimensionality reduction method Isomap in order to emulate nonlinear parametric flow problems that are governed by the Reynolds-averaged Navier-Stokes equations. Isomap is a manifold learning approach that provides a low-dimensional embedding space that is approximately isometric to the manifold that is assumed to be formed by the high-fidelity Navier-Stokes flow solutions under smooth variations of the inflow conditions. The focus of the work at hand is the adaptive construction and refinement of the Isomap emulator: We exploit the non-Euclidean Isomap metric to detect and fill up gaps in the sampling in the embedding space. The performance of the proposed manifold filling method will be illustrated by numerical experiments, where we consider nonlinear parameter-dependent steady-state Navier-Stokes flows in the transonic regime

On the use of second-order derivatives and metamodel-based Monte-Carlo for uncertainty estimation in aerodynamics

International audienceThis article adresses the delicate issue of estimating physical uncertainties in aerodynamics. Usually, flow simulations are performed in a fully deterministic approach, although in real life operational uncertainty arises due to unpredictable factors that alter the flow conditions. In this article, we present and compare two methods to account for uncertainty in aerodynamic simulation. Firstly, automatic differentiation tools are used to estimate first- and second-order derivatives of aerodynamic coefficients with respect to uncertain variables, yielding an estimate of expectation and variance values (Method of Moments). Secondly, metamodelling techniques (radial basis functions, kriging) are employed in conjunction with Monte-Carlo simulations to derive statistical information. These methods are demonstrated for 3D Eulerian flows around the wing of a business aircraft at different regimes subject to uncertain Mach number and angle of attack

Uncertainty Quantification for Robust Design

The objective of this chapter is to present, analyze and compare some practical methods that could be used in engineering to quantify uncertainty, for mechanical systems governed by partial differential equations. Most applications refer to aerodynamics, but the methods described in this chapter can be applied easily to other disciplines, such as structural mechanics

On the use of second-order derivatives and metamodel-based Monte-Carlo for uncertainty estimation in aerodynamics

International audienceThis article adresses the delicate issue of estimating physical uncertainties in aerodynamics. Usually, flow simulations are performed in a fully deterministic approach, although in real life operational uncertainty arises due to unpredictable factors that alter the flow conditions. In this article, we present and compare two methods to account for uncertainty in aerodynamic simulation. Firstly, automatic differentiation tools are used to estimate first- and second-order derivatives of aerodynamic coefficients with respect to uncertain variables, yielding an estimate of expectation and variance values (Method of Moments). Secondly, metamodelling techniques (radial basis functions, kriging) are employed in conjunction with Monte-Carlo simulations to derive statistical information. These methods are demonstrated for 3D Eulerian flows around the wing of a business aircraft at different regimes subject to uncertain Mach number and angle of attack

Radial Basis Function Methods for Interpolation to Functions of Many Variables

A review of interpolation to values of a function f(x), x 2 R , by radial basis function methods is given. It addresses the nonsingularity of the interpolation equations, the inclusion of polynomial terms, and the accuracy of the approximation sf , where s is the interpolant. Then some numerical experiments investigate the situation when the data points are on a low dimensional nonlinear manifold in R . They suggest that the number of data points that are necessary for good accuracy on the manifold is independent of d, even if d is very large. The experiments employ linear and multiquadric radial functions, because an iterative algorithm for these cases was developed at Cambridge recently. The algorithm is described briefly. Fortunately, the number of iterations is small when the data points are on a low dimensional manifold. We expect these findings to be useful, because the manifold setting for large d is similar to typical distributions of interpolation points in data mining applications