Model updating with a Modified Dual Kalman Filter acting on distributed strain measurements

Following the advances in measurement technology and its vast availability, mechanical systems and structures are increasingly equipped with sensors to obtain continuous information regarding the system state. Coupled with robust numerical models, this information can be used to build a numerical twin of the structure that is linked to its physical twin via a feedback loop. This results in the concept of Dynamic Data Driven Application Systems (DDDAS) that can predict and control the evolution of the physical phenomena at stake on the structure, as well as dynamically updating the numerical model with the help of real-time measurements [1, 2]. The physical evolution control is not addressed here, as the focus is mainly on the model updating part of the DDDAS process. This step requires data assimilation and sequentially solving a potentially ill-posed inverse problem. A robust approach towards solving inverse problems regarding numerical models with experimental inputs is the modified Constitutive Relation Error (mCRE) [3]. One of the critical features of this method is the distinction between reliable and unreliable information so that only reliable ones, such as equilibrium, known boundary conditions, and sensor positions, are strongly imposed in the definition of the functional. In contrast, unreliable information, namely constitutive relation, unknown boundary conditions, and sensor measurements, are dealt with in a more relaxed sense. This energy-based functional can be conceived as a least squares minimization problem on measurement error, regularized by a model error term, aka Constitutive Relation Error (