Smart manufacturing implies creating virtual replicas of the processing operations, taking into account the material dimension and its multi-physics transformation when forming processes operate. Performing efficient, that is, online accurate predictions of the induced properties (including potential defects) of the formed part (to optimally control the process parameters) needs moving beyond usual offline simulation based on nominal models, and proceeds by assimilating data. This will serve, from one side, to keep the model calibrated, and from the other, to enrich the model and its associated predictions, to avoid bias, to improve accuracy or for performing online diagnosis, by advertising on preventive maintenance. For all these purposes, a new alliance between physics-based and data-driven modelling approaches seems a very valuable route for empowering engineering in general, and smart manufacturing in particular. The present paper revisits the main methodologies involved in the construction of the component or system Hybrid Twins.

Data-driven modeling provides an efficient approach to compute approximate solutions for complex multiphysics parametrized problems such as induction hardening (IH) process. Basically, some physical quantities of interest (QoI) related to the IH process will be evaluated under real-time constraint, without any explicit knowledge of the physical behavior of the system. Hence, computationally expensive finite element models will be replaced by a parametric solution, called metamodel. Two data-driven models for temporal evolution of temperature and austenite phase transformation, during induction heating, were first developed by using the proper orthogonal decomposition based reduced-order model followed by a nonlinear regression method for temperature field and a classification combined with regression for austenite evolution. Then, data-driven and hybrid models were created to predict hardness, after quenching. It is shown that the results of artificial intelligence models are promising and provide good approximations in the low-data limit case.

Many models assumed to be able to predict the response of structural systems fail to efficiently accomplish that purpose because of two main reasons. First, some structures in operation undergo localized damage that degrades their mechanical performances. To reflect this local loss of performance, the stiffness matrix associated with the structure should be locally corrected. Second, the nominal model is sometimes too coarse grained for reflecting all structural details, and consequently, the predictions are expected to deviate from the measurements. In that case, there is no small region of the model that needs to be repaired, but the entire domain needs to be repaired; therefore, the entire structure-stiffness matrix should be corrected. In the present work, we propose a methodology for locally correcting or globally enriching the models from collected data, which is, upon its turn, completed beyond the sensor’s location. The proposed techniques consist in the first case of an L1-minimization procedure that, with the support of data, aims at the same time period to detect the damaged zone in the structure and to predict the correct solution. For the global enrichment, instead, the methodology consists of an L2-minimization procedure with the support of measurements. The results obtained showed, for the local problem, a correction up to 90% with respect to the initially incorrectly predicted displacement of the structure, and for the global one, a correction up to 60% was observed (this results concern the problems considered in the present study, but they depend on different factors, such as the number of data used, the geometry or the intensity of the damage). The benefits and potential of such techniques are illustrated on four different problems, showing the large generality and adaptability of the methodology.

Many engineering systems can be described by using differential models whose solutions, generally obtained after discretization, can exhibit a noticeable deviation with respect to the response of the physical systems that those models are expected to represent. In those circumstances, one possibility consists of enriching the model in order to reproduce the physical system behavior. The present paper considers a dynamical system and proposes enriching the model solution by learning the dynamical model of the gap between the system response and the model-based prediction while ensuring that the time integration of the learned model remains stable. The proposed methodology was applied in the simulation of the top-oil temperature evolution of a power transformer, for which experimental data provided by the RTE, the French electricity transmission system operator, were used to construct the model enrichment with the hybrid rationale, ensuring more accurate predictions.

Trajectory optimization is a complex process that includes an infinite number of possibilities and combinations. This work focuses on a particular aspect of the trajectory optimization, related to the optimization of a velocity along a predefined path, with the aim of minimizing power consumption. To tackle the problem, a functional formulation and minimization strategy is developed, by means of the Euler-Lagrange equation. The minimization is later performed using a neural network approach. The strategy is deemed Lagrange-Net, as it is based on the minimization of the energy functional, by the means of Lagrange's equation and neural network approximations.