Modelling of measuring systems -- From white box models to cognitive approaches

Mathematical models of measuring systems and processes play an essential role in metrology and practical measurements. They form the basis for understanding and evaluating measurements, their results and their trustworthiness. Classic analytical parametric modelling is based on largely complete knowledge of measurement technology and the measurement process. But due to digital transformation towards the Internet of Things (IIoT) with an increasing number of intensively and flexibly networked measurement systems and consequently ever larger amounts of data to be processed, data-based modelling approaches have gained enormous importance. This has led to new approaches in measurement technology and industry like Digital Twins, Self-X Approaches, Soft Sensor Technology and Data and Information Fusion. In the future, data-based modelling will be increasingly dominated by intelligent, cognitive systems. Evaluating of the accuracy, trustworthiness and the functional uncertainty of the corresponding models is required. This paper provides a concise overview of modelling in metrology from classical white box models to intelligent, cognitive data-driven solutions identifying advantages and limitations. Additionally, the approaches to merge trustworthiness and metrological uncertainty will be discussed.