comprehensive identification of nonlinear structural systems with the low number and non-homogeneous sensing using modern bayesian methods

In this paper, a general framework is presented to estimate the unknown parameters of structures. the unknown parameters can consist of a vast range of variables, such as the dynamical parameters of structure, the motivation inputs, the responses of other degree of freedoms (dofs) except un-sensed ones, etc. engineering problems can be widely classified into four general areas: 1. direct problem: the system matrices, the initial conditions, and the external forces are the inputs of problem and the output variables should be calculated. 2. inverse problem: the system matrices as well as some measurements related to the dofs are the inputs of problem and the external forces and initial conditions should be determined.3. system identification problems: the external forces and initial conditions together with some measurements related to the dofs are the inputs of problem and the system matrices or some components of them should be determined. 4. research problems: some measurements related to the dofs are taken as the inputs of problem and the system matrices, external forces, initial conditions, and remaining dofs are the outputs.