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This work addresses the problem of determining the number of components from sequential spectroscopic data analyzed by non-negative matrix factorization without separability assumption (SepFree NMF). These data are stored in a matrix M of dimension “measured times” versus “measured wavenumbers” and can be decomposed to obtain the spectral fingerprints of the states and their evolution over time. SepFree NMF assumes a memoryless (Markovian) process to underline the dynamics and decomposes M so that M = WH, with W representing the components’ fingerprints and H their kinetics. However, the rank of this decomposition (i.e., the number of physical states in the process) has to be guessed from pre-existing knowledge on the observed process. We propose a measure for determining the number of components with the computation of the minimal memory effect resulting from the decomposition; by quantifying how much the obtained factorization is deviating from the Markovian property, we are able to score factorizations of a different number of components. In this way, we estimate the number of different entities which contribute to the observed system, and we can extract kinetic information without knowing the characteristic spectra of the single components. This manuscript provides the mathematical background as well as an analysis of computer generated and experimental sequentially measured Raman spectra.
To accelerate the growth of Industry 4.0 technologies, the digitalization of mechanical testing laboratories as one of the main data-driven units of materials processing industries is introduced in this paper. The digital lab infrastructure consists of highly detailed and standard-compliant materials testing knowledge graphs for a wide range of mechanical testing processes, as well as some tools that enable the efficient ontology development and conversion of heterogeneous materials’ mechanical testing data to the machine-readable data of uniform and standardized structures. As a basis for designing such a digital lab, the mechanical testing ontology (MTO) was developed based on the ISO 23718 and ISO/IEC 21838-2 standards for the semantic representation of the mechanical testing experiments, quantities, artifacts, and report data. The trial digitalization of materials mechanical testing lab was successfully performed by utilizing the developed tools and knowledge graph of processes for converting the various experimental test data of heterogeneous structures, languages, and formats to standardized Resource Description Framework (RDF) data formats. The concepts of data storage and data sharing in data spaces were also introduced and SPARQL queries were utilized to evaluate how the introduced approach can result in the data retrieval and response to the competency questions. The proposed digital materials mechanical testing lab approach allows the industries to access lots of trustworthy and traceable mechanical testing data of other academic and industrial organizations, and subsequently organize various data-driven research for their faster and cheaper product development leading to a higher performance of products in engineering and ecological aspects.