Linear and nonlinear time domain system identification at element level for structural systems with unknown excitation

Abstract

Three time domain system identification (SI) approaches, i.e., Modified Iterative Least Square with Unknown Input (ILS-UI), Localized Structural Identification, and Modified Iterative Least Square--Extended Kalman Filter with Unknown Input (ILS-EKF-UI), are proposed to identify defects at the element level of structures. In all these methods, structures are modeled using the finite element method (FEM) and the structural parameters (stiffness and damping) are identified using only output response measurements without using any information on input excitation. Excitations are identified as a byproduct of the SI procedures. If damping is considered to be proportional or Rayleigh-type, the time domain SI technique becomes nonlinear even though the dynamic system remains linear. The Modified ILS-UI approach is essentially a nonlinear SI algorithm. The Localized Structural Identification combines a time domain SI technique and FEM formulation representing a part of the structure. The time domain responses at each time instance represent an equilibrium status of the system which is reflected in the nodal equilibrium in the FEM. Using the Localized Structural Model, only dynamic responses at the local region closely connected to the part of the structure to be identified are required. This dramatically reduces the measurement requirements, and makes it possible to identify the parameters of the whole structure by identifying only part of it. This study discusses how to select elements of the local structure and how to determine the locations and number of the output measurements. The Modified ILS-EKF-UI approach was developed by combining the Modified ILS-UI and the Localized Structural Identification. Using the Modified ILS-EKF-UI approach, the system can be identified using responses at a reduced number of dynamic degrees of freedom. This method allows the finite element mesh to be refined further for more localized parameter identification without additional response information. All three methods are verified using numerical examples. They identify the structures very well. They are found to be more accurate than other methods currently reported in the literature even when input excitation information is used to identify structures. Various types of structures are examined, including shear buildings, plane frames, and plane trusses. The proposed methods are found to be robust even when the responses are contaminated with noise.