In binary Gaussian process classification the prior class membership probabilities are obtained by transforming a Gaussian process to the unit interval, typically either with the logistic likelihood function or the cumulative Gaussian likelihood function. Multiclass classification problems can be handled by any binary classifier by means of so-called binarization techniques, which reduces the multiclass problem into a number of binary problems. Other than introducing the mathematics behind the theory and methods behind Gaussian process classification, we compare the binarization techniques one-against-all and one-against-one in the context of Gaussian process classification, and we also compare the performance of the logistic likelihood and the cumulative Gaussian likelihood. This is done by means of two experiments: one general experiment where the methods are tested on several publicly available datasets, and one more specific experiment where the methods are compared with respect to class imbalance and class overlap on several artificially generated datasets. The results indicate that there is no significant difference in the choices of binarization technique and likelihood function for typical datasets, although the one-against-one technique showed slightly more consistent performance. However the second experiment revealed some differences in how the methods react to varying degrees of class imbalance and class overlap. Most notably the logistic likelihood was a dominant factor and the one-against-one technique performed better than one-against-all.

<div>In contrast to traditional steel and aluminum, short fiber reinforced polymer composites (SFRCs) provide promising alternatives in material selection for automotive and aerospace applications due to their potential to decrease weight while maintaining excellent mechanical properties. However, uncertainties about the influence of complex microstructures and defects on mechanical response have prevented widespread adoption of material models for</div><div>SFRCs. In order to build confidence in models’ predictions requires deepened insight into the heterogenous damage mechanisms. Therefore, this research takes a micro-mechanics standpoint of assessing the damage behavior of SFRCs, particularly micro-void nucleation at the fiber tips, by passing information of microstructural attributes within neighborhoods of incipient damage and non-damage sites, into a framework that establishes correlations between the microstructural information and damage. To achieve this, in-situ x-ray tomography of the gauge sections of two cylindrical injection molded dog-bone specimens, composed of E-glass fibers in a polypropylene matrix, was conducted while the specimens were monotonically loaded until failure. This was followed by (i) the development of microstructural characterization frameworks for segmenting fiber and porosity features in 3D images, (ii) the development of a digital volume correlation informed damage detection framework that confines search spaces of potential damage sites, and (iii) the use of a Gaussian process classification framework to explore the dependency of micro-void nucleation on neighboring microstructural defects by ranking each of their contributions. Specifically, the analysis considered microstructural metrics related to the closest fiber, the closest pore, and the local stiffness, and the results demonstrated that less stiff resin rich areas were more relevant for micro-void nucleation than clustered fiber tips, T-intersections of fibers, or varying porosity volumes. This analysis provides a ranking of microstructural metrics that induce microvoid nucleation, which can be helpful for modelers to validate their predictions on proclivity of damage initiation in the presence of wide distributions of microstructural features and</div><div>manufacturing defects. </div>