Review of the mathematical foundations of data fusion techniques in surface metrology

The recent proliferation of engineered surfaces, including freeform and structured surfaces, is challenging current metrology techniques. Measurement using multiple sensors has been proposed to achieve enhanced benefits, mainly in terms of spatial frequency bandwidth, which a single sensor cannot provide. When using data from different sensors, a process of data fusion is required and there is much active research in this area. In this paper, current data fusion methods and applications are reviewed, with a focus on the mathematical foundations of the subject. Common research questions in the fusion of surface metrology data are raised and potential fusion algorithms are discussed

A new creep model directly using tabulated test data and implemented in ansys

Nowadays plastics are increasingly used in highly stressed structures in all kinds of constructions. The time dependency, the so-called viscosity, is a crucial part of the material behavior of plastics. A typical form of viscosity is creep. Creep is the increase of deformation under constant load. In the FE-simulation creep behavior is usually described by creep law functions. The commercial software provide many creep law functions depending on time, stress, strain, temperature and multiple material parameters. To run a creep simulation, the user must define all the parameters which requires a certain effort. Curve-fitting procedures might be of help, the results, however, often are not precise enough. For these reasons, we introduce our new creep model doing the similar job as the creep law functions but being able to directly use the tabulated data of the creep tests without curve-fitting procedures. In this paper, we use the model to create a 3D stress-creep strain-time surface based on the tabulated data like isochronous curves, which is represented by bicubically blended Coons patches to provide a good convergence due to their differentiability. This creep model supports strain hardening, which shows more realistic behavior when the load changes significantly during the simulated proces

The Panchromatic High-Resolution Spectroscopic Survey of Local Group Star Clusters - I. General Data Reduction Procedures for the VLT/X-shooter UVB and VIS arm

Our dataset contains spectroscopic observations of 29 globular clusters in the Magellanic Clouds and the Milky Way performed with VLT/X-shooter. Here we present detailed data reduction procedures for the VLT/X-shooter UVB and VIS arm. These are not restricted to our particular dataset, but are generally applicable to different kinds of X-shooter data without major limitation on the astronomical object of interest. ESO's X-shooter pipeline (v1.5.0) performs well and reliably for the wavelength calibration and the associated rectification procedure, yet we find several weaknesses in the reduction cascade that are addressed with additional calibration steps, such as bad pixel interpolation, flat fielding, and slit illumination corrections. Furthermore, the instrumental PSF is analytically modeled and used to reconstruct flux losses at slit transit and for optimally extracting point sources. Regular observations of spectrophotometric standard stars allow us to detect instrumental variability, which needs to be understood if a reliable absolute flux calibration is desired. A cascade of additional custom calibration steps is presented that allows for an absolute flux calibration uncertainty of less than ten percent under virtually every observational setup provided that the signal-to-noise ratio is sufficiently high. The optimal extraction increases the signal-to-noise ratio typically by a factor of 1.5, while simultaneously correcting for resulting flux losses. The wavelength calibration is found to be accurate to an uncertainty level of approximately 0.02 Angstrom. We find that most of the X-shooter systematics can be reliably modeled and corrected for. This offers the possibility of comparing observations on different nights and with different telescope pointings and instrumental setups, thereby facilitating a robust statistical analysis of large datasets.Comment: 22 pages, 18 figures, Accepted for publication in Astronomy & Astrophysics; V2 contains a minor change in the abstract. We note that we did not test X-shooter pipeline versions 2.0 or later. V3 contains an updated referenc

A Comparison of Interpolation Methods for Sparse Data: Application to Wind and Concentration Fields

In order to produce gridded fields of pollutant concentration data and surface wind data for use in an air quality model, a number of techniques for interpolating sparse data values are compared. The techniques are compared using three data sets. One is an idealized concentration distribution to which the exact solution is known, the second is a potential flow field, while the third consists of surface ozone concentrations measured in the Los Angeles Basin on a particular day. The results of the study indicate that fitting a second-degree polynomial to each subregion (triangle) in the plane with each data point weighted according to its distance from the subregion provides a good compromise between accuracy and computational cost