An Optimal Sensor Placement Method For Nonlinear Dynamic Systems

Nonlinear dynamic system identification is an effective means of understanding structural dynamic characteristics during its service period, especially when suffered from severe damage. Optimal sensor placement is one of the key issues in study on nonlinear dynamic system identification. However, traditional method of optimal sensor placement is limited to linear system. The methods of time-variant mode of nonlinear structure developed in recent years provide the effective potential for optimal sensor placement of nonlinear dynamic system.This thesis mainly consists of three parts as follows:Discrete wavelet transform and Lipschitz index, continuous wavelet transform ridge line and the instantaneous frequency of nonlinear system are investigated. The yielding and unloading moment of bilinear structures under seismic waves are identified and the instantaneous frequency of nonlinear system with piecewise linear stiffness or cubic hardening stiffness are also identified.The nonlinear normal modes of certain special nonlinear structures are analyzed. The combination of nonlinear modal matrix and effective independence method of optimal sensor location is proposed. The nonlinear average modal matrix and the most disadvantaged modal matrix are defined for nonlinear system. The most disadvantaged modal matrix together with EI method are implemented for the optimal sensor placement of nonlinear structure with inter-story softening stiffness.Effective independence method is used in the optimal sensor placement of nonlinear structure with weak layer which is actualized by reducing the stiffness of that layer. The EI contribution value of the sensor in the weak layer is calculated based on time-variant relative and inter-story displacement modal matrix.