Structural joints influence the design strength, material requirement of a structure. Structural joints experience damping dissipation due to friction damping or hysteresis damping. Damping is often used for reducing the vibrations in a structure. However, large amount of energy dissipation leads to deterioration of the material used for constructing the joint. Hence it is important to identify the system parameters like stiffness, viscous damping, friction force as well as the hysteretic restoring force that cause the energy dissipation in the structure. For identifying the uncertain system parameters like stiffness, viscous damping and magnitude of friction force, the SINDy algorithm is extended by using stick and slip temporal constraints. This is done by segregating the data of external forcing and response of SDoF system, applying the existing SINDy algorithm and applying the sticking and slipping conditions in the time domain. The proposed Extended SINDy approach estimates the system parameters more accurately compared to the existing SINDy algorithm. For studying the hysteresis in the structural joints, a pinned column base-plate was considered in an elastic region. Further, the Dahl model with different slope parameter for each branch of moment-rotation hysteresis is employed. The correct values of parameters are estimated using the Bayesian Optimization technique. This procedure yields a functional form representing a resisting hysteretic moment-rotation behaviour in a structural joint with good accuracy.

In recent years, there has been a lot of focus on system identification using vibration data instead of building mathematical models based on domain knowledge. The Sparse Identification of Nonlinear Dynamical System (SINDy) is a method that has been a great tool to identify the nonlinear dynamics. Therefore, in this report, the nonlinear systems such as duffing oscillator, Single Degree of Freedom (SDoF) with friction are identified using SINDy algorithm. An impact of noise in the measurement data is studied briefly. The components used in the process of identification are smooth finite difference-based differentiator, Sequential Threshold Least Squares (STLSq) optimizer and custom candidate library. Further, a comparison is made between the numerical models and the models obtained from PySINDy. The Root Mean Squares Errors are calculated for all the cases. It is seen that SINDy is capable of identifying these nonlinearities with good accuracy.