A non-linear inverse vibration problem of estimating the external forces for a system with displacement-dependent parameters

The conjugate gradient method, i.e., the iterative regularization method, is used in an inverse non-linear force vibration problem of estimating the unknown time-dependent external forces in a damped system with the displacement-dependent spring constant and damping coefficients. The accuracy of the inverse analysis is examined by using the simulated exact and inexact measurements. Since the system parameters are functions of displacement, the present study, from a purely mathematical viewpoint, is thus a genuine non-linear inverse vibration problem. The numerical simulations are performed to test the validity of the present algorithm by using different types of system parameters, external forces and measurement errors. Results show thatan excellent estimation on the external forces can be obtained with any arbitrary initial guesses with a couple of second's CPU time at Pentium III-500 MHz PC.