Markov chain montecarlo method applied to rounding zeros of compositional data: first approach

As stated in Aitchison (1986), a proper study of relative variation in a compositional data set should be based on logratios, and dealing with logratios excludes dealing with zeros. Nevertheless, it is clear that zero observations might be present in real data sets, either because the corresponding part is completely absent –essential zeros– or because it is below detection limit –rounded zeros. Because the second kind of zeros is usually understood as “a trace too small to measure”, it seems reasonable to replace them by a suitable small value, and this has been the traditional approach. As stated, e.g. by Tauber (1999) and by Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000), the principal problem in compositional data analysis is related to rounded zeros. One should be careful to use a replacement strategy that does not seriously distort the general structure of the data. In particular, the covariance structure of the involved parts –and thus the metric properties– should be preserved, as otherwise further analysis on subpopulations could be misleading. Following this point of view, a non-parametric imputation method is introduced in Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000). This method is analyzed in depth by Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2003) where it is shown that the theoretical drawbacks of the additive zero replacement method proposed in Aitchison (1986) can be overcome using a new multiplicative approach on the non-zero parts of a composition. The new approach has reasonable properties from a compositional point of view. In particular, it is “natural” in the sense that it recovers the “true” composition if replacement values are identical to the missing values, and it is coherent with the basic operations on the simplex. This coherence implies that the covariance structure of subcompositions with no zeros is preserved. As a generalization of the multiplicative replacement, in the same paper a substitution method for missing values on compositional data sets is introduced

Stability lobes diagram identification and surface roughness monitoring in milling processes

La millora de la productivitat i la qualitat són indubtablement dues de les principals exigències del sector productiu modern i factors clau per la competitivitat i la supervivència. Dins aquest sector,la fabricació per arrancada de material juga encara avui en dia un paper protagonista tot i l'aparició de noves tècniques de conformat per addició.Indústries com l'aeronàutica, l'automobilística,la del motlle o l'energètica, depenen en bona part de les prestacions de les màquines-eina. Aquesta Tesi aborda dos aspectes rellevants quan es tracta de millorar de la productivitat i la qualitat del sector productiu: el problema del fimbrament, més conegut per la denominació anglosaxona chatter,i la monitorització de la rugositat superficial en el mecanitzat a alta velocitat.