Abstract

A digital twin based on rigorous statistical principles is motivated for simulation-based product verification and validation as well as condition-based maintenance. Two examples from the railway industry are presented to illustrate the application of the method: • Digital twin of the longitudinal kinematics of a train combined with incomplete, noisy field data, • Integration of test and analysis for fatigue validation of mechanical components, including multilevel modeling. Modeling and numerical solution of the examples is accomplished by Bayesian Inference using the statistical modeling language and open source software Stan. Bayesian Inference has only become popular and feasible over the last couple of decades with the development of more and more powerful simulation hardware. Our simulations were partly performed on standard workstations and partly on a numerical simulation cluster. Bayesian Inference has several nice properties: • In effect, we can fuse data and information from many different sources – simulation, test, field data, engineering knowledge, prior experience – in a statistically rigorous way. • We can flexibly create arbitrary, physically motivated statistical models. • Modeling assumptions are clearly stated, and not implicit as with many traditional statistical techniques. Thus, they can be discussed and improved and contribute to our engineering understanding of the results. • Uncertainty and predictive accuracy can be quantified and analyzed. • The amount of data required is much smaller than for physics-agnostic, data centric methods such as neural networks. • We can easily deal with partially missing data. Some challenges also need to be mentioned: Statistical modeling and simulation require combined in-depth expertise in engineering, statistics, and computational science, as well as sufficient computational resources. As with any other simulation method, convergence and correct results cannot be assured unless you are working with a well-posed model and know what you are doing. Overall, we highly recommend Bayesian Inference and Statistical Simulation for Uncertainty Quantification.