4.3.2 Linear 2D Interpolation Error Reduction
In numerical analysis, a multivariate interpolation is interpolation on a function of more than one variable. The function to be interpolated is known at given points and the interpolation problem consists of yielding values at arbitrary points. Multivariate interpolation could be useful for flow meter self-calibration, where it is used to create a digital model from a set of error information (such as flow coefficient \(C\)) based on flowmeter measurements. It can be used to improve meter output at points where the error information is unknown.
Python coded 2D grid data algorithm has been used to fix a surface of the form z = f(x,y) from the training data (\(x,y,z\)). For example, (\(x,y,z\)) can be information extracted from flow meter outputs such as x as flow meter readings, y as Reynolds number and z as flow coefficient\(C\) . (\(x_{q},y_{q}\)). The grid-data function is then used to interpolate the surface at the query points or test points (\(x_{q},y_{q}\)) and returns the interpolated values (\(z_{i}\)). As illustrated in Fig. 9, the returned interpolated values can be visualized by using 2D Delaunay Triangulation method.