A Data Driven Black Box Approach for the Inverse Quantification of Set-Theoretical Uncertainty

Inverse uncertainty quantification commonly uses the well established Bayesian framework. Recently, alternative interval methodologies have been introduced. However, in their current state of the art implementation, both techniques suffer from a large and usually unpredictable computational effort. Thus, both techniques are not applicable in a real-time context. To achieve a low-cost, real-time solution to this inverse problem, we introduce a deep-learning framework consisting of unsupervised auto-encoders and a shallow neural network. This framework is trained by means of a numerically generated dataset that captures typical relations between the model parameters and selected measured system responses. The performance and efficacy of the technique is illustrated using two distinct case studies. The first case involves the DLR AIRMOD, a benchmark case that has served as reference case for the inverse uncertainty quantification problem. The results demonstrate that the achieved accuracy is on par with the existing interval method found in literature, while requiring only a fraction of its computational resources. The second case study examines a resistance pressure welding process, which is known to require extremely fast monitoring and control due to the high process throughput. Based on the proposed method, and with only a limited selection of simulated responses of the process, it is possible to identify the interval uncertainty of the crucial parameters of the process. The computational cost in this case makes it possible for an inverse uncertainty quantification in a real-time setting.