System Identification in Time Domain
for Structural Damage Assessment
Using L1-Regularization and Time Windowing Technique
Seung Keun Park
This paper presents a system identification scheme in time domain to estimate stiffness and damping parameters of a structure using measured acceleration. An error function is defined as the time integral of the least-squared error between measured accelerations and calculated accelerations by a numerical model of a structure. Damping parameters as well as stiffness properties of a structure are considered as system parameters. To alleviate the ill-posedness of SI problems two regularization techniques are employed. L2-Regularization function defined by the L2-norm of the first derivative of system parameters with respect to time and L1-Regularization function defined by the L1-norm of the first derivative of system parameters with respect to time are proposed to alleviate the ill-posed characteristics of inverse problems and to accommodate discontinuities of system parameters in time. In L2-Regularization scheme, the regularization factor is determined by the geometric mean scheme. In L1-Regularization scheme, regularization effect is determined by a truncation number of TSVD(Truncated Singular Value Decomposition). The time window concept is proposed to trace variation of system parameters in time. To represent discontinuity of system parameters in time, L1-Regularization scheme is employed in time windowing technique. The validity of the proposed method is demonstrated by a numerical simulation study on a two-span truss bridge.
Time-domain system identification, Regularization, Time Windowing Technique, Rayleigh damping