# GRADUATE SEMINAR - "Interrogation of the Fundamental Subspaces of the change in Flexibility Regarding Damage", by Professor Dionisio P. Bernal, Department of Civil and Environmental Engineering, Northeastern University, Boston, MA

Education - Colloquium - WPI Only

Wednesday, November 7, 2012

2:00 PM-3:00 PM

Higgins Laboratories

HL116

Theorems connecting the kernel and the image of changes in flexibility resulting from structural

damage are discussed. The first theorem relates the kernel to the location of damage by showing that

this null space is a basis for vectors that, when treated as loads on the undamaged domain, lead to

stress fields that are zero over closed regions that contain the damage. The kernel theorem dates back

to 2002 and its implementation is known as the Damage Locating Vector (DLV) Approach. The image related

theorem has been designated as the Influence Line Damage Locating (ILDL) theorem and it states that the

image of the change in flexibility is a basis for the influence lines of the stress resultants at the

damaged locations. Implementation of ILDL, which has been recently formulated, is done by inspecting

subspace angles between a matrix whose columns are influence lines sampled at sensor locations and the

column space of the flexibility change. The final piece of information in the singular value decomposition

of the change in flexibility, namely, the non-zero singular values, is shown to contain the information

needed to evaluate the damage severity. Application of the localization theorems and the quantification

of the damage, which proves to be the solution of an attractive fixed point, are illustrated in simulations

and in a laboratory experiment.

Suggested Audiences:
College

E-mail:
mdemetri@wpi.edu

Phone: 508-831-5459

Last Modified: October 24, 2012 at 10:54 AM

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## GRADUATE SEMINAR - "Interrogation of the Fundamental Subspaces of the change in Flexibility Regarding Damage", by Professor Dionisio P. Bernal, Department of Civil and Environmental Engineering, Northeastern University, Boston, MA

Education - Colloquium - WPI Only

Wednesday, November 7, 2012

2:00 PM-3:00 PM

Higgins Laboratories

HL116

Theorems connecting the kernel and the image of changes in flexibility resulting from structural

damage are discussed. The first theorem relates the kernel to the location of damage by showing that

this null space is a basis for vectors that, when treated as loads on the undamaged domain, lead to

stress fields that are zero over closed regions that contain the damage. The kernel theorem dates back

to 2002 and its implementation is known as the Damage Locating Vector (DLV) Approach. The image related

theorem has been designated as the Influence Line Damage Locating (ILDL) theorem and it states that the

image of the change in flexibility is a basis for the influence lines of the stress resultants at the

damaged locations. Implementation of ILDL, which has been recently formulated, is done by inspecting

subspace angles between a matrix whose columns are influence lines sampled at sensor locations and the

column space of the flexibility change. The final piece of information in the singular value decomposition

of the change in flexibility, namely, the non-zero singular values, is shown to contain the information

needed to evaluate the damage severity. Application of the localization theorems and the quantification

of the damage, which proves to be the solution of an attractive fixed point, are illustrated in simulations

and in a laboratory experiment.

Suggested Audiences: College

E-mail: mdemetri@wpi.edu

Phone: 508-831-5459

Last Modified: October 24, 2012 at 10:54 AM

Powered by the Social Web - Bringing people together through Events, Places, & Common Interests