Abstract: Structural nonlinear restoring force or hysteretic behavior provides a direct description of the initiation and development of structural damage and can be used for the quantitative evaluation of structural energy consumption under dynamic loading. In this study, an approach for identifying nonlinear restoring force and mass distribution using limited acceleration measurements under incomplete excitation condition is proposed. A multi-degree-of-freedom (MDOF) structural equipped with a Magnetorheological (MR) damper mimicking a nonlinear member is established to numerically validate the approach. Based on an Unscented Kalman Filter (UKF) and a Chebyshev polynomial model, without the use of any parametric models of the nonlinear restoring force, or assumption on the stiffness, damping and mass distribution, the nonlinear restoring force and mass distribution are identified successfully. The results show that the proposed time domain nonlinear restoring force identification approach is general and capable of identifying structural nonlinearity and mass distribution with limited acceleration measurements under incomplete excitation cases, which can be used for the damage detection and energy consumption evaluation of engineering structures under strong dynamic loading.