Use of LU decomposition of modal flexibility in structural damage detection: Numerical validation

The flexibility can be approximately synthesized with the first several measured modal parameters, i.e. the so called modal flexibility. The modal flexibility matrix will change with damage in a structure, and the change of modal flexibility should contain the information of damage. It is important to find a damage index that can pick up damage from the change of modal flexibility. To address this issue, the mathematical tool LU decomposition is introduced to deal with the modal flexibility matrix in order to find damage clearly. After decomposition, the modal flexibility is decomposed into a lower triangular matrix L and an upper triangular matrix U. Numerical results of both single and multiple damage cases under white noise excitation indicate that the matrix U has enough information of damage; and the proposed new technique can be utilized to locate the damage accurately. The present numerical study will lay a foundation for the application of real-time structural health monitoring in experiments and engineering.