To recover external forces of nonlinear systems using weak-form numerical differentiators
Date Issued
2016
Date
2016
Author(s)
Lin, Jheng-Jhang
Abstract
The second-order differential of a noisy signal is written as a second-order ordinary differential equation, being a special case of the recovery of unknown external force in a second-order linear system, which is transformed into a linear parabolic type partial differential equation. Then the Green second identity is employed to derive a boundary integral equation in terms of the adjoint Trefftz spectral functions. We find a weak-form method to recover the external force and then a weak-form second-order differentiator(WFSOD) is developed to compute the second-order differential from a given noisy signal, of which only the signal itself is specified, without needing of its first-order differential. Finally, the weak-form method is used to recover the external forces of nonlinear systems within a large time interval and under a large noise.
Subjects
weak-form second-order differentiator
Nonlinear inverse vibration problem
Adjoint Trefftz test functions
Green’s second identity
weak-form method
spectral functions
Type
thesis