Nonlinear Restoring Force Identification Of Structures With Dynamic Response Measurements

Due to the rapid increase in the number of deteriorating structures and damagedstructures under strong dynamic loadings such as earthquakes, it is crucial to evaluatetheir current reliability, performance, and condition for the prevention of potentiallycatastrophic events, as well as for remaining life estimation, retrofitting andstrengthening. The development of vibration-based structural damage detectionapproach has been one of the most active research areas in civil and infrastructuralengineering for life-cycle performance evaluation and maintenance.The initiation and development of damage such as cracks in an engineeringstructure under dynamic loadings is a typical nonlinear process. Strictly speaking, theconventional vibration and eigenvalues extraction based damage identificationapproaches are suitable for linear systems only. Due to the uniqueness of nonlinearityof different engineering structures, it is usually difficult to express the nonlinearrestoring force (NRF) of an engineering structure such as a reinforced concrete (RC)structure in a parametric form. Consequently, it is highly desirable to develop ageneral structural nonlinearity identification approach for damage detection inquantitative way.Based on the above background, a double-Chebyshev polynomial modelinginvolving the instantaneous values of the state variables of a MDOF structural systemis proposed to represent the system nonlinearities is developed.For theoretical method, based on second central difference method, a techniquethat can obtain displacement and velocity from acceleration response is employed inthis paper. Based on the complete and incomplete excitations applied to the structureand the corresponding acceleration response and excitation measurement time series,each coefficient of the double Chebyshev polynomial is identified by means ofstandard least-square techniques and Newton’s third law, without any assumptions onthe parametric model of the nonlinear restoring force, and of prior knowledge of themass distribution of the system.In the numerical simulation, the feasibility and robustness of the proposedapproach is validated via numerical simulation with a4-DOF model incorporating MRdamper or VANDERPOL damper, which was employed to induce nonlinear behaviorin the system. The nonlinear restoring force is identified under two different cases, in which the system was under complete and incomplete excitations, were investigated.Moreover, the effect of noise level was also taken into consideration. Based on theextend Kalman filter method with a weighted global iteration(EKF-WGI),Numericalsimulations of several different types of nonlinear systems are used to demonstrate thevalidity of the EKF-WGI.In the dynamic test, an experimental4-story steel shear building structureequipped with two MR dampers which were used to mimic structural nonlinearperformance. The damper force is first identified by the proposeddouble-Chebyshev-polynomial-based approach and then compared with thecorresponding measurements which are obtained from the force transducer. Theresults show that though the constitutive model of the structural members and thestructural mass distribution are both assumed to be unknown, the proposed methodcould still identify NRF with acceptable accuracy only by the correspondingacceleration response and excitation measurement time series, and it provides apromising approach for damage detection where structural nonlinearity needs to beconsidered.