A spectrum-driven damage identification by minimum constitutive relation error and sparse regularization. (February 2020) - Guo, Jia; Jiao, Jian; Fujita, Kohei; Takewaki, Izuru
Highlights: Guidance for the application of power spectrum density data based on minimum constitutive relation error principle has been provided. Only measurement power spectrum density data from few limited sensors are needed for damage identification. Sparse regularization has demonstrated a pronounced effect on the accuracy and robustness for the identification results. Abstract: This paper proposes a novel model-based damage identification strategy based on minimum constitutive relation error and sparse regularization using the power spectrum density data. Firstly, the stationary random vibration problem is transformed into a series of harmonic vibrations by the pseudo excitation method and the error in constitutive relation is established by the admissible stress field and admissible displacement field. A much more general and simpler strategy so as to build the admissible stress field is addressed by requiring only an extra decomposition of the stiffness matrix. Then, the sparse regularization is added to the original constitutive relation error objective function to circumvent the ill-posedness of the inverse problem. Finally, the solution of this nonlinear optimization problem is solved by the alternating minimization method. The proposed method has the advantage that only measurement power spectrum density data from few limited sensors are needed in the inverse analysis. Numerical and experimental results show the effectiveness and robustness of this approach.