Structural System Identification and Damage Detection
through Regularization Technique
Using Frequency Response Function
Tin Tin Win
A new damage detection algorithm based on a system identification scheme with regularization technique is developed using a frequency response function (FRF) in the frequency domain. The algorithm is applicable to for a time invariant model of a structure with recorded earthquake response or measured acceleration data from a dynamic test. The error function is defined as the frequency integral of the least squared error between the measured and calculated FRF. The FRF is obtained by a non-smooth, complex-valued fi-nite Fourier transform of acceleration.
In most pervious studies on frequency domain in SI modal stiffness and modal damping properties are used as system parameters. In this work, stiffness properties of a structure and the coefficient of Rayleigh damping are selected as system parameters. Since it is impossible to measure acceleration at all of the degrees of freedom in structural modal. Sparseness of the measurements occurred due to incomplete data. Furthermore, the meas-ured response included noise. Due to sparseness and completeness in measurement, SI problems are usually illposed.
Tikhonov regularization technique is applied to overcome the ill-posedness of system identification problems. The regularization function is defined as on the norm of the difference between estimated system parameter vector and the baseline system parameters. The singular value decomposition is utilized to investigate the role of the regularization and the characteristic of the non-linear inverse problem. The first order sensitivity of a finite Fourier transform is obtained by direct differentiation to develop the mathematical model. For an optimal regularization factor, a geometric mean scheme (GMS) method was used. This method was a geometric mean between the maximum singular value and the mini-mum singular value of the sensitivity matrix of the response transform. A recursive quadratic programming (RQP) was used to solve a constrained nonlinear optimization problem. The Gauss-Newton approximation of the Hessian was used for a simple compu-tation. The validity of the proposed method was demonstrated by numerical examples on shear buildings.
system identification (SI), regularization technique, damage assessment, ill-posedness, Frequency Response Function (FRF), geometric mean scheme (GMS), recursive quadratic programming (RQP)