Monitoring systems in sheet metal forming cannot rely on direct measurements of the physical condition of interest because the space between the die component and the material is inaccessible. Therefore, in order to gain further insight into the forming or stamping process, sensors must be used to detect auxiliary quantities such as acoustic emission and force that relate to the physical quantities of interest. While it is known that changes in force data are related to physical parameters of the process material, lubricant used, and geometry, the changes in data over large stroke series and their relationship to wear are the subject of this paper. Previously, force data from different wear conditions (artificially introduced into the system and not occurring in an industry-like environment) were used as input for clustering and classifying high and low wear force data. This paper contributes to fill the current research gap by isolating structural properties of data as indicators of wear growth to quantify the wear evolution during ongoing production in industry-like scenarios. The selected methods represent either established methods in sheet metal forming force data analysis, dimensionality reduction for local structure separation or generic feature extraction. The study is conducted on a set of four experiments with each containing about 3000 strokes.

The asymptotic posterior normality (APN) of the latent variable vector in an item response theory (IRT) model is a crucial argument in IRT modeling approaches. In case of a single latent trait and under general assumptions, Chang and Stout (Psychometrika, 58(1):37–52, 1993) proved the APN for a broad class of latent trait models for binary items. Under the same setup, they also showed the consistency of the latent trait’s maximum likelihood estimator (MLE). Since then, several modeling approaches have been developed that consider multivariate latent traits and assume their APN, a conjecture which has not been proved so far. We fill this theoretical gap by extending the results of Chang and Stout for multivariate latent traits. Further, we discuss the existence and consistency of MLEs, maximum a-posteriori and expected a-posteriori estimators for the latent traits under the same broad class of latent trait models.