A trigonometric approach to quaternary code designs with application to one-eighth and one-sixteenth fractions
The study of good nonregular fractional factorial designs has received significant attention over the last two decades. Recent research indicates that designs constructed from quaternary codes (QC) are very promising in this regard. The present paper shows how a trigonometric approach can facilitate a systematic understanding of such QC designs and lead to new theoretical results covering hitherto unexplored situations. We focus attention on one-eighth and one-sixteenth fractions of two-level factorials and show that optimal QC designs often have larger generalized resolution and projectivity than comparable regular designs. Moreover, some of these designs are found to have maximum projectivity among all designs.
A search of maximum generalized resolution quaternary-code designs via integer linear programming
Quaternary-code (QC) designs, an attractive class of nonregular fractional factorial designs, have received much attention due to their theoretical elegance and practical applicability. Some recent works of QC designs revealed their good properties over their regular counterparts under commonly used criteria. We develop an optimization tool that can maximize the generalized resolution of a QC design of a given size. The problem can be recast as an integer linear programming (ILP) problem through a linear simplification that combines the $$k$$k- and $$a$$a-equations, even though the generalized resolution does not linearly depend on the aliasing indexes. The ILP surprisingly improves a class of $$(1/16)$$(1/16)th-fraction QC designs with higher generalized resolutions. It also applies to obtain some $$(1/64)$$(1/64)th-fraction QC designs with maximum generalized resolutions, and these QC designs generally have higher generalized resolutions than the regular designs of the same size.
Frequency distributions of the mixing height over an urban area from SODAR data
The height of the mixing-layer (MLH) is an important parameter in the assessment of the dilution of primarily emitted or secondarily formed air pollutants in the atmospheric boundary-layer. A continuous measurement of MLH is possible only by remote sensing. Here, 17 months of SODAR data have been analysed automatically to derive the MLH over the city of Hannover in Northern Germany. In contrast to earlier studies the MLH has been determined from vertical profiles of the acoustic backscatter intensity and from the variance of the vertical velocity component. The results are presented in form of monthly frequency distributions and mean daily courses of MLH. These statistical evaluations of MLH show a clear annual course and interannual variability. The study shows the possibility to derive meaningful climatological information from long-term SODAR measurements for air quality issues.