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Figure 2.1 (a) Graph of the singular values of the Hankel matrices of the impulse response for different orders  of the state space model. (b) Zoom of Figure 2.1a.

Figure 2.2 Matrix A of the estimated state space model for order number 16.

Figure 2.3 Eigenvalues of the state space matrix A for the models of order 16 (x) and 20 (0).

Figure 2.4 Eigenvalues of the state space matrix A from the first two replications, for the models

Figure 2.5 Model selection graph when the no-disturbance option is set.

Figure 2.6 Eigenvalues of the state space matrix A from the first three replications, with the no-  disturbance option and for the models of order (a) 16 and (b) 20.

Figure 2.7 Eigenvalues of the undamaged system (largest circles), and comparison with those  calculated for the three different replications of the previously considered damaged system

Figure 2.1 (a) Graph of the singular values of the Hankel matrices of the impulse response for different orders  of the state space model. (b) Zoom of Figure 2.1a.

Figure 2.2 Matrix A of the estimated state space model for order number 16.

Figure 2.3 Eigenvalues of the state space matrix A for the models of order 16 (x) and 20 (0).

Figure 2.4 Eigenvalues of the state space matrix A from the first two replications, for the models

Figure 2.5 Model selection graph when the no-disturbance option is set.

Figure 2.6 Eigenvalues of the state space matrix A from the first three replications, with the no-  disturbance option and for the models of order (a) 16 and (b) 20.

Figure 2.7 Eigenvalues of the undamaged system (largest circles), and comparison with those  calculated for the three different replications of the previously considered damaged system

Figure 3.1 Construction-cost versus maintenance-estimate and monitoring- impact.

(a) A hydralic shaker: larger force capacity than electro-dynamic shaker but limited high frequency capability  Figure 3.2 Different types of forced excitation methods.

Figure 3.3 An embedded network of distributed piezoelectric actuators/sensors: this thin film of  sensor/actuator network can be either surface mounted or embedded into composite structures.

Figure 3.4 Examples of ambient excitations.

Figure 4.1 Today’s conventional wired monitoring system.

Figure 4.2 Two layers wireless architecture.

Figure 4.5 Units with wireless communication.

Figure 5.2 Sections of the Poincaré maps drawn for the two sets of signals introduced in Chapter

Figure 5.3 Classification of a dynamic system based on Kolmogorov entropy: a) regular, b stochastic or chaotic, and c) fully random.

Figure 5.4 Entropy evolution from the central cell for the 12 pulses: set of damaged case signals.

Figure 5.5 Entropy evolution from the central cell for the 12 pulses: set of undamaged case

be synthesized into Equation (6.6) with

are assembled in a 78x78 global stiffness matrix K gicp, following the standar  finite element procedures.  The 4x4 element stiffness matrices of the form

Figure 6.2 F- histogram for the undamaged state of the structure under different load conditions.

Figure 6.3 SSE-histograms for the undamaged state of the structure under different load conditions. Response at 20 m, and k = 20 predictors.

Figure 6.4 F-histograms for the undamaged state of the structure under different load conditions  and for three levels of random noises in the measurements. Response at 20 m, and k = 20

Figure 6.5 SSE-histograms for the undamaged state of the structure under different load

Figure 6.6 F-histograms for the undamaged state of the structure under different load conditions  and for three levels of random noises in the measurements. Response at 20 m, and k = 10

Figure 6.7 SSE-histograms for the undamaged state of the structure under different load

Figure 6.9 F-histograms for the damaged and undamaged states of the structure under different

Figure 6.10 SSE-histograms for the damaged and undamaged states of the structure under

Figure 6.11 F-histograms for the damaged and undamaged states of the structure under different  load conditions and for three levels of random noises in the measurements.

Figure 6.13 Flow chart of the proposed SHM scheme.

Figure 7.1 The ASCE benchmark structural system: (a) real structure at UBC; and (b) analytical model. From [Johnson et al., 2000].

Figure 7.3 Sensor locations and id numbers.

Figure 7-5: Histograms comparison at different sensor locations for CASE 2, damage pattern 1.

Figure 7-4: Histograms comparison at different sensor locations for CASE 2, damage pattern 2.

Figure 8.2 (a) Plant view and (b) Elevation of the BABY FRAME specimen.

Figure 8.3 Details of the welded beam-column connections. (a) Exterior joint. (b) Interior joint. (c) Internal view of an exterior joint.

Figure 8.4 Cross-section of the reinforced concrete slab on the beam flange

Damage Detection and Localization in the Space of the Observed Variables  Figure 8.6 (a) Shaker installed on the top of the structure. (b) Technical description of the electro-

Figure 8.9 Acceleration-time histories measured by sensor 3 during (a) the damaged and (b) the

Figure 8.7 (a) Damaged state and (b) undamaged state of the structure. Note that the sensors

Figure 8.8 Force-time histories measured by sensor 1 during (a) the damaged and (b) the  located close to the damage are the accelerometers 17, 14, 16, and 18.

Figure 8.10 SSE comparison for the accelerometers 17, 14, 18, and 16.

Figure 9.1 Front prospect (top) and plant (bottom) of Palazzo Geraci: (a) in the nineteenth  building presented itself as documented by Figure 9.1a.

Figure 9.2 (a) The central part of the facade of Palazzo Geraci nowadays, and  on the left side they are less evident than on the right side.

Figure 9.3 (a) The reduced model in its present location outside of the laboratory (the structure on

Figure 9.4 Cracks at different locations of the reduced model: (a) left openings; (b) right  ee er A , Ch Oh On oF ir 9 Pr 2h i ch er cr oS i 2 a ee ew

Figure 9.5 Sensors locations and id numbers. Note that the main cracks in the structure are

Figure 9.7 Forced excitation methods. (a) Instrumented hammer. (b) Shaker at the top of the  structure, in central position.

Figure 9.8 Undamaged state of the structure.  side (r.h.s.) of the structure, and of sensor 2 on the left hand side (1.h.s).

Figure 9.9 Accelerations recorded by sensor 11 during the tests performed with different

These equations are called the least squares normal equations. Note that there

scalar form. Writing out Equation (A.10) in detail, we obtain

baa A  Figure B.1 (a) The original 1:2 scale model of the Palazzo Geraci facade built at the ELSA Laboratory, in Ispra. (b) Front prospect and sections of the original model.

Figure B.3 Structural details of the columns.

Figure B.4 Structural details of the anchorage of the steel element to the top of the column capital.

Figure B.6 Reference earthquake used for the pseudo-dynamic tests.

Figure B.5 Pseudo-dynamic tests of the specimen.