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...

Fig. 5 Illustration of the nonlinear hysteretic mechanism that is applied for each link element, according to its DOF. The link elements are noticeable through the additional nodes (white circles) near the end of each beam/column element. The arrows indicate the local coordinate system assumed for... More about this image found in Illustration of the nonlinear hysteretic mechanism that is applied for each...

Fig. 6 Welch-based coherence function estimates (Monte Carlo experiments; LTI frame, point O2): ( a ) along x -axis and ( b ) along y -axis More about this image found in Welch-based coherence function estimates (Monte Carlo experiments; LTI fram...

Fig. 7 Welch-based FRF estimates (Monte Carlo experiments; LTI frame, point O2): ( a ) magnitude along x -axis, ( b ) phase along x -axis, ( c ) magnitude along y -axis, and ( d ) phase along y -axis More about this image found in Welch-based FRF estimates (Monte Carlo experiments; LTI frame, point O2): (...

Fig. 8 ARX model order estimation (Monte Carlo experiments; LTI frame, point O2. The squares indicate mean value and the vertical bars standard deviation): ( a ) along x -axis and ( b ) along y -axis. More about this image found in ARX model order estimation (Monte Carlo experiments; LTI frame, point O2. T...

Fig. 9 ARX model parameter vectors (Monte Carlo experiments; LTI frame, point O2. The squares indicate mean value and the vertical bars standard deviation): ( a ) ARX x ( 30 , 30 , 0 ) models and ( b ) ARX y ( 42 , 42 , 0 ) models. More about this image found in ARX model parameter vectors (Monte Carlo experiments; LTI frame, point O2. ...

Fig. 10 ARX-estimated vibration modes (Monte Carlo experiments; LTI frame, point O2): ( a ) natural frequency along x -axis, ( b )modal damping ratio along x -axis, ( c ) natural frequency along y -axis, and ( d ) modal damping ratio along y -axis More about this image found in ARX-estimated vibration modes (Monte Carlo experiments; LTI frame, point O2...

Fig. 11 AR-estimated vibration modes (Monte Carlo experiments; LTI frame, point O2): ( a ) natural frequency along x -axis and ( b ) modal damping ratio along x -axis More about this image found in AR-estimated vibration modes (Monte Carlo experiments; LTI frame, point O2)...

Fig. 12 Temperature and modulus data for the lineat time variant (LTV) frame: ( a ) temperature time-series over the long temporal scale, ( b ) sample (bars) and associated kernel-based (continuous line) PDF estimates, and ( c ) elastic modulus versus temperature More about this image found in Temperature and modulus data for the lineat time variant (LTV) frame: ( a )...

Fig. 13 Behavior of the first three natural frequencies of the LTV frame: ( a ) versus temperature and ( b ) versus long time-scale More about this image found in Behavior of the first three natural frequencies of the LTV frame: ( a ) ver...