Fig. 1 Schematic representation of the sparsity-based optimization framework for determining nonlinear structural system equations of motion More about this image found in Schematic representation of the sparsity-based optimization framework for d...

Fig. 2 Schematic representation of a stochastically excited TMDI nonlinear system with a fractional derivative element More about this image found in Schematic representation of a stochastically excited TMDI nonlinear system ...

Fig. 3 Determining the equations of motion of a TMDI nonlinear structural system by employing various sparsity-based optimization approaches; comparisons between the original and the estimated coefficients of the model representation of Eq. (3) More about this image found in Determining the equations of motion of a TMDI nonlinear structural system b...

Fig. 4 Bayesian CS-based prediction and uncertainty quantification of the mean displacement ( x 1 ) time-history ± 1 standard deviation More about this image found in Bayesian CS-based prediction and uncertainty quantification of the mean dis...

Fig. 5 Bayesian CS-based prediction and uncertainty quantification of the mean velocity ( x ˙ 1 ) time-history ± 1 standard deviation More about this image found in Bayesian CS-based prediction and uncertainty quantification of the mean vel...

Fig. 6 Schematic representation of the stochastically excited nonlinear electromechanical energy harvester with a fractional derivative element More about this image found in Schematic representation of the stochastically excited nonlinear electromec...

Fig. 7 Determining the equations of motion of a nonlinear electromechanical energy harvesting system based on various sparsity-based optimization approaches; comparisons between the original and the estimated coefficients of the model representation of Eq. (3) More about this image found in Determining the equations of motion of a nonlinear electromechanical energy...

Fig. 8 Bayesian CS-based prediction and uncertainty quantification of the response of a nonlinear energy harvesting system: mean response voltage time-history in conjunction with ±1 standard deviation More about this image found in Bayesian CS-based prediction and uncertainty quantification of the response...

Fig. 1 High-level representation of a monitored dynamical system. S represents a physical engineering system subjected to an input u ( t ), while being exposed to disturbances d ( t ) and deterioration processes h ( t ). The system produces an output y ( t ), a subset of which is usually mon... More about this image found in High-level representation of a monitored dynamical system. S represents a...

Fig. 2 Illustration of the infiltration of the classes or our defined uncertainty taxonomy in the essential representation of a monitored dynamical system, as portrayed in Fig. 5 . The defined classes include input uncertainty, model form uncertainty, model parameter/variable uncertainty, measure... More about this image found in Illustration of the infiltration of the classes or our defined uncertainty ...

Fig. 3 Categorization of purely data-driven system methods for damage identification, organized according to the domain the method operates in, the method class, and the specific feature that is produced to serve for damage identification. This figure is adapted from Ref. [ 64 ]. This table overvi... More about this image found in Categorization of purely data-driven system methods for damage identificati...

Fig. 4 Graphical representation of the two-story frame with annotation of the hysteretic (nonlinear) link positions, as well as the positions of acceleration sensors that are assumed to be deployed for the state estimation/virtual sensing task of Sec. 4.4 More about this image found in Graphical representation of the two-story frame with annotation of the hyst...