A LOCAL RESTORING FORCE SURFACE METHoD

The Restoring Force method and equivalent Force-State Mapping Trchmque were proposed to identify nonlinear mechanical systems [l-S]. The 6md result of the methods was a modelling of the nonlinear force in function of the displacement and the velocity. The 6rst method proposed a polynomial series while the secand expressed the model by its values on a grid. In this paper a generalised and combined approach of both methods is presented. The new method identities the nonlinear force using a local nonparametric representation, while the mass is identified globally from the same data. This results in a set of quasi uncoupled equations which reduces the calculation effort significantly. The uncertainty due to stochastic errors (noise) and systematic model errors are studied. The benefit of a uniform phase plane covermg is demonstrated and by means of simulations, it is shawn how close a well chosen multlslne displacement 161 appmaches these properties. Nomenclature Overdats denote differentiation with respect to time. Caret brackets denote mean values and circumflexes denote estimators. A supn accent stands for the transpose operation. Cell indices indicate a belonging to a grid element. Capital letters indicate w&ices and vectors. The Greek capital operator A expresses the