Journal
ADVANCES IN ENGINEERING SOFTWARE
Volume 149, Issue -, Pages -Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.advengsoft.2020.102900
Keywords
Numerical integration; Design of experiments; Space-filling designs; Latin hypercube sampling; Voronoi tessellation; Periodic space
Categories
Funding
- Czech Science Foundation [GA19-12197S, GC19-06684J]
Ask authors/readers for more resources
The selection of points for numerical integration of the Monte Carlo type, largely used in analysis of engineering problems, is developed. It is achieved by modification of the metric in the minimax optimality criterion. The standard minimax criterion ensures the design exhibits good space-filling property and therefore reduces the variance of the estimator of the integral. We, however, show that the points are not selected with the same probability over the space of sampling probabilities: some regions are over- or under-sampled when designs are generated repetitively. This violation of statistical uniformity may lead to systematically biased integral estimators. We propose that periodic metric be considered for calculation of the minimax distance. Such periodic minimax criterion provides statistically uniform designs leading to unbiased integration results and also low estimator variance due to retained space-filling property. These conclusions are demonstrated by examples integrating analytical functions. The designs are constructed by two different algorithms: (i) a new time-stepping algorithm resembling a damped system of attracted particles developed here, and (ii) the heuristic swapping of coordinates. The designs constructed by the time-stepping algorithm are attached to the paper as a supplementary material. The computer code for construction of the designs is attached too.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available