Statistical Methods for Estimation of Paint Thickness and its Variance
Examensarbete för masterexamen
Engineering mathematics and computational science (MPENM), MSc
IPS Virtual Paint at Fraunhofer Chalmers Centre (FCC) is a software for simulating electrostatic spray painting of objects. Simulating the painting process is extremely computationally demanding and hence very time consuming. It is therefore desirable to be able to obtain results based on as few number of simulations as possible. This, and the random behavior of the simulations, give rise to randomness in the estimated paint thickness that is not easily quantified by means of ordinary methods. The purpose of this thesis is to further develop methods for estimating the resulting paint thickness and its variance. Different varieties of models based on nonparametric kernel density estimation for estimating of paint thickness were evaluated. This was done using synthetic data, along with data generated via IPS Virtual Paint. Variations of anisotropic kernel estimations for reducing bias in the estimates were also investigated. Also, methods for enhancing existing methods when performing paint thickness estimations along the edges of an object were developed. Both the anisotropic methods together with the edge compensation algorithms showed to improve the quality of the estimates. Previous work at FCC have used regression models for estimating the variance of the estimated paint thickness. This method is however not applicable for the entire object. In this report an alternative method, based on bootstrap, for estimating the variance is analyzed. The results show that bootstrap performs well for the different scenarios investigated, with results consistent with regression models and more exact estimates produced through numerous painting simulations.
Matematik , Grundläggande vetenskaper , Mathematics , Basic Sciences