Health Assessment of Engineering Structures Using Graphical Models - Structural Seismic Design Optimization and Earthquake Engineering - page 363

s l × s s l ×

graph damage detection, diagnosis and identifica-
tion algorithm is executed using Matlab.

ˆ ]

∑ ∑ ∑

[ A R A = p A ; q = 1 2 , , ... ,s

ji i jq j jq

j = 1 i = 1 j = 1

(25)

9.1 Health Assessment of a
Fifteen-Story Shear Building
under Earthquake Load

Eq. (25) gives s (4 or 6) simultaneous algebraic
equations which when solved provide the system
parameters including the stiffness and damping
coefficient of the damaged columns.
Thus, the quantitative damage identification
is performed for the substructure that contains
the damaged component by minimizing the er-
ror in the identified structural parameters. This
offers tremendous savings in the computations.
Damage quantification of continuous systems
follows the same procedures and is discussed in
the next section.

This example studies dynamic analysis and health
assessment of a 15-story shear building under the
first horizontal acceleration of the 1995 Kobe
earthquake (Takatori station) scaled to 0.30 g
PGA (PEER, 2005). We investigate the dynamic
analysis of the structure first. The numerical
values of floor masses, columns stiffnesses and
damping used in the BG simulation analyses are
given in Table 5. This structure was modeled using
a fifteen degree-of-freedom mechanical system
with linear behavior.

9. NUMERICAL ILLUSTRATIONS

9.1.1 Health Assessment of the
Structure

Two numerical examples are considered to
demonstrate the use of bond graphs for dynamic
analysis and health assessment of discrete and
continuous systems. The first example considers
a 15-story building under earthquake load. The
second example demonstrates the health assess-
ment of a high-rise building subjected to simulated
Kanai-Tajimi acceleration using the finite-mode
bond graphs.
The bond graph models of both structures are
created using the Fault Adaptive Control Technol-
ogy (FACT) software (Mosterman & Biswas,
1999) in the Generic Modeling Environment
(GME-6, 2006) to generate a simulation model
(Matlab Simulink model) (Mathworks, 1999) that
is used to simulate the structural response. FACT
contains a library of bond graph elements (i.e., I-,
C-, R-, S e -, S f -, TF- and GY-elements and con-
necting bonds) that are used to assemble the bond
graph model in GME. The displacement, velocity,
and acceleration responses for the building are
computed using the simulation model. The bond

Damage in structural components is simulated
as reduction of 20% in the stiffness parameters
of the fourteenth floor (case 1) and the first floor
(case 2). Damage in the sensors is modeled as
bias or drift in the fourteenth floor or first floor
sensors. The procedures described in Sections
3 and 5 are used to generate the BG and TCG
models of the structure. The BG and TCG mod-
els are constructed from those shown in Figure
4 by duplicating the blocks of the third floor and
third sensor. The damage signatures are derived
as described in Section 7.

9.1.1.1 Damage in Structural Components\
We first study damage in the structural compo-
nents. For noise-free measurements, a reduction
of 20% is introduced to the stiffness of the four-
teenth floor. The damage criterion is taken as
deviation in response measurements by more than
5% from corresponding values of healthy structure.
The damage was successfully detected to be in