A novel, finite-element-based framework for sparse data solution reconstruction and multiple choices
Digital twinning is gaining widespread popularity across various areas of engineering, and indeed it offers a capability of effective real-time monitoring and control, which are vital for cost-intensive experimental facilities, particularly the ones where extreme conditions exist. Sparse experimental measurements collected by various diagnostic sensors are usually the only source of information available during the course of a physical experiment. Consequently, in order to enable monitoring and control of the experiment (digital twinning), the ability to perform inverse analysis, facilitating the full field solution reconstruction from the sparse experimental data in real time, is crucial. Such solution reconstruction might be necessary to control a system, if a parameter to be controlled cannot be directly derived from the sparse measurements alone, as oftentimes is the case, for instance maximum temperature within a test piece. This paper shows for the first time that it is possible to directly solve inverse problems, such as solution reconstruction, where some or all boundary conditions (BCs) are unknown, by purely using a finite-element (FE) approach, without needing to employ any traditional inverse analysis techniques or any machine learning models, as is normally done in the field. The proposed novel and efficient FE-based inverse analysis framework employs a conventional FE discretisation, splits the loading vector into two parts corresponding to the known and unknown BCs, and then defines a loss function based on that split. In spite of the loading vector split, the loss function preserves the element connectivity. This function is minimised using a gradient-based optimisation; and the near real-time operation for heat conduction in a stainless-steel plate is achieved. Furthermore, this paper proposes a novel modification of the aforementioned approach, which allows it to generate a range of different solutions satisfying given requirements in a controlled manner. Controlled multiple solution generation in the context of inverse problems and their intrinsic ill-posedness is a novel notion, which has not been explored before. This is done in order to potentially introduce the capability of semi-autonomous system control with intermittent human intervention to the workflow. Having access to a variety of feasible alternatives during the experiment can augment the human decision-making process and assist the operator in evaluating and selecting the most suitable course of action.