A data-driven uncertainty quantification method for scarce data and rare events

Abstract

The efficient integration of manufacturing, experimental or operational data into physical simulations using uncertainty quantification techniques is becoming increasingly important for the engineering industry. There is a genuine interest to use uncertainty quantification methods to improve product efficiency, reliability, and safety. However, temporary methods still have various limitations, which have prevented a wider industrial application. This thesis analyses existing problems in industry and contributes new solutions in five areas: data scarcity, the curse of dimensionality, rare events, discontinuous models and epistemic model-form uncertainty. The major novelty of this work is a new data-driven Polynomial Chaos framework called SAMBA that can be used to improve engineering designs by accounting for uncertainties in simulations more efficiently and accurately. SAMBA provides a single solution to many industrial problems. It is particularly useful for applications where only scarce statistical data is available and to efficiently quantify the likelihood of rare events with disastrous consequences, the so-called Black Swan. Other benefits are the simple reconstruction of adaptive and anisotropic sparse grid quadrature rules to alleviate the curse of dimensionality, a simpler combination of arbitrary distributions and random data within a single method, and higher accuracy for data sets that do not follow a definable distribution. To deal with special cases, two extensions have been added to SAMBA's framework: first, a modification that allows the use of arbitrary points within Pad\'e approximations for models containing discontinuities and second, a general multi-fidelity framework to counteract model-form uncertainty in simulations. The thesis concludes with the application of SAMBA to various state-of-the-art models in Formula 1, turbomachinery, and space flight (one example analyses structural dynamics uncertainty of NASA's Space Launch System). Particularly innovative are two applications: one showing how to account for Black Swans in gas turbine simulations and one how to deal with scarce data in Formula 1.