A discontinuous ”D” variant for identification of non-smooth systems

significant source of uncertainty in modern societies is linked to the assessment of the current state of infrastructure. Namely, the ability to identify damage in structures, such as transportation networks and buildings hosting power and health facilities, is critical for decision making in terms of their rehabilitation or even decommissioning. Structural damage often manifests in the form of brittle or ductile failure, with the development of cracks or yielding of members respectively. These phenomena are associated with substantially differentiated structural behavior depending on the existence and amount of damage. Mathematically this may be attributed to the non-smooth nature of these systems. In an attempt to ensure robust diagnostics, feedback from the system by means of structural health monitoring, allows to identify and quantify damage and to assess the underlying system properties. Toward this end, Bayesian identification algorithms have proven robust in tackling increased modelling complexity, and may even achieve so in an online manner. A basic requirement of the algorithms however, is that the models to be identified involve continuously observable states and identifiable parameters. This assumption is nonetheless violated for non-smooth systems, which involve parameter subsets that are not continuously identifiable. The identifiability of some of the involved parameters may switch during the evaluation, depending on the realization of the state vector. While on an “unidentifiability mode”, it is beneficial to avoid updating the estimate of those parameters. This is termed by the authors as the Discontinuous ‘D-’ modification. This work will present the D- modification to different Bayesian identification algorithms. The robustness of the ‘D-’ algorithms over their standard counterparts will be discussed in terms of the converging properties. A suitable example illustrates the performance of the methods in problems involving detection and quantification of damage