Lithium-ion batteries are widely used in the automobile industry (electric vehicles and hybrid electric vehicles) due to their high energy and power density. However, this raises new safety and reliability challenges which require development of novel sophisticated Battery Management Systems (BMS). A BMS ensures the safe and reliable operation of a battery pack and to realize it a model must be solved. However, current BMSs are not adapted to the specifications of the automotive industry, as they are unable to give accurate results at real-time rates and during a wide operation range. For this reason, the main focus of this work is to develop a Hybrid Twin, as introduced in Chinesta et al. (Arch Comput Methods Eng (in press), 2018. so as to meet the requirements of the new generation of BMS. To achieve this, three reduced order model techniques are applied to the most commonly used physics-based models, each one for a different range of application. First, a POD model is used to greatly reduce the simulation time and the computational effort for the pseudo-2D model, while maintaining its accuracy. In this way, cell design, optimization of parameters, and simulation of battery packs can be done while saving time and computational resources. In addition, its real-time performance has been studied. Next, a regression model is constructed from data by using the sparse-Proper Generalized Decomposition (s-PGD). It is shown that it achieves realtime performance for the whole electric vehicle (EV) system with a battery pack. In addition, this regression model can be used in a BMS without issues because of the simple algebraic expression obtained. A simulation of the EV with the proposed approach is demonstrated using the system simulation tool SimulationX (ESI ITI GmbH. Dresden, Germany). Furthermore, the Digital Twin created using the s-PGD does not only allow for real-time simulations, but it can also adapt its predictions taking into consideration the real driving conditions and the real driving cycle to change the planning in real-time. Finally, a data-driven model based on the employment of Dynamic Mode Decomposition techniques is developed to extract an on-line model that corrects the gap between prediction and measurement, thus constructing the first (to our knowledge) hybrid twin of a Li-ion battery able to self-correct from data. In addition, thanks to this model, the above gap is corrected during the driving process, taking into consideration real-time restrictions.

The concept of “hybrid twin” (HT) has recently received a growing interest thanks to the availability of powerful machine learning techniques. This twin concept combines physics-based models within a model order reduction framework—to obtain real-time feedback rates—and data science. Thus, the main idea of the HT is to develop on-the-fly data-driven models to correct possible deviations between measurements and physics-based model predictions. This paper is focused on the computation of stable, fast, and accurate corrections in the HT framework. Furthermore, regarding the delicate and important problem of stability, a new approach is proposed, introducing several subvariants and guaranteeing a low computational cost as well as the achievement of a stable time-integration.