A closer look at sum-based embeddings for knowledge graphs containing procedural knowledge

While knowledge graphs and their embedding into low dimensional vectors are established fields of research, they mostly cover factual knowledge. However, to improve downstream models, e. g. for predictive quality in real-world industrial use cases, embeddings of procedural knowledge, available in the form of rules, could be utilized. As such, we investigate which properties of embedding algorithms could prove beneficial in this scenario and evaluate which established embedding methodologies are suited to form the basis of sum-based embeddings of different representations of procedural knowledge

PDPK: A Framework to Synthesise Process Data and Corresponding Procedural Knowledge for Manufacturing

Procedural knowledge describes how to accomplish tasks and mitigate problems. Such knowledge is commonly held by domain experts, e.g. operators in manufacturing who adjust parameters to achieve quality targets. To the best of our knowledge, no real-world datasets containing process data and corresponding procedural knowledge are publicly available, possibly due to corporate apprehensions regarding the loss of knowledge advances. Therefore, we provide a framework to generate synthetic datasets that can be adapted to different domains. The design choices are inspired by two real-world datasets of procedural knowledge we have access to. Apart from containing representations of procedural knowledge in Resource Description Framework (RDF)-compliant knowledge graphs, the framework simulates parametrisation processes and provides consistent process data. We compare established embedding methods on the resulting knowledge graphs, detailing which out-of-the-box methods have the potential to represent procedural knowledge. This provides a baseline which can be used to increase the comparability of future work. Furthermore, we validate the overall characteristics of a synthesised dataset by comparing the results to those achievable on a real-world dataset. The framework and evaluation code, as well as the dataset used in the evaluation, are available open source

Towards models of conceptual and procedural operator knowledge

To increase the utility of semantic industrial information models we propose a methodology to incorporate extracted operator knowledge, which we assume to be present in the form of rules, in knowledge graphs. To this end, we present multiple modelling patterns that can be combined depending on the required complexity. Aiming to combine information models with learning systems we contemplate desired behaviours of embeddings from a predictive quality perspective and provide a suited embedding methodology. This methodology is evaluated on a real world dataset of a fused deposition modelling process

The Hanle Effect as a Diagnostic of Magnetic Fields in Stellar Envelopes IV. Application to Polarized P Cygni Wind Lines

The Hanle effect has been proposed as a new diagnostic of circumstellar magnetic fields for early-type stars, for which it is sensitive to field strengths in the 1-300 G range. In this paper we compute the polarized P-Cygni line profiles that result from the Hanle effect. For modeling the polarization, we employ a variant of the ``last scattering approximation''. For cases in which the Sobolev optical depths are greater than unity, the emergent line intensity is assumed to be unpolarized; while for smaller optical depths, the Stokes source functions for the Hanle effect with optically thin line scattering are used. For a typical P Cygni line, the polarized emission forms in the outer wind, because the Sobolev optical depth is large at the inner wind. For low surface field strengths, weak P Cygni lines are needed to measure the circumstellar field. For high values of the surface fields, both the Zeeman and Hanle diagnostics can be used, with the Zeeman effect probing the photospheric magnetic fields, and the Hanle effect measuring the magnetic field in the wind flow. Polarized line profiles are calculated for a self-consistent structure of the flow and the magnetic geometry based on the WCFields model, which is applicable to slowly rotating stellar winds with magnetic fields drawn out by the gas flow. For surface fields of a few hundred Gauss, we find that the Hanle effect can produce line polarizations in the range of a few tenths of a percent up to about 2 percent.Comment: accepted to the Astrophysical Journa