Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers

Computational framework for real-time diagnostics and prognostics of aircraft actuation systems

Prognostics and health management (PHM) are emerging approaches to product life cycle that will maintain system safety and improve reliability, while reducing operating and maintenance costs. This is particularly relevant for aerospace systems, where high levels of integrity and high performances are required at the same time. We propose a novel strategy for the nearly real-time fault detection and identification (FDI) of a dynamical assembly, and for the estimation of remaining useful life (RUL) of the system. The availability of a timely estimate of the health status of the system will allow for an informed adaptive planning of maintenance and a dynamical reconfiguration of the mission profile, reducing operating costs and improving reliability. This work addresses the three phases of the prognostic flow – namely (1) signal acquisition, (2) fault detection and identification, and (3) remaining useful life estimation – and introduces a computationally efficient procedure suitable for real-time, on-board execution. To achieve this goal, we propose to combine information from physical models of different fidelity with machine learning techniques to obtain efficient representations (surrogate models) suitable for nearly real-time applications. Additionally, we propose an importance sampling strategy and a novel approach to model damage propagation for dynamical systems. The methodology is assessed for the FDI and RUL estimation of an aircraft electromechanical actuator (EMA) for secondary flight controls. The results show that the proposed method allows for a high precision in the evaluation of the system RUL, while outperforming common model-based techniques in terms of computational time