Development of data-based model-free representation of non-conservative dissipative systems

A general procedure is presented for developing data-based, non-parametric models of non-linear multi-degree-of-freedom, non-conservative, dissipative systems. Two broad classes of methods are discussed: one relying on the representation of the system restoring forces in a polynomial-basis format, and the other using artificial neural networks to map the complex transformations relating the system state variables to the needed system outputs. A non-linear two-degree-of-freedom system is used to formulate the approach under discussion and to generate synthetic data for calibrating the efficiency of the two methods in capturing complex non-linear phenomena (such as dry friction, hysteresis, dead-space non-linearities, and polynomial-type non-linearities) that are widely encountered in the applied mechanics field. Subsequently, a reconfigurable test apparatus was used to generate experimental measurements from a physical non-linear “joint” involving two-dimensional motion (translation and rotation) and complicated interaction forces between the different motion axes, among its internal elements. Both the polynomial-basis approach and the neural network method were used to develop high-fidelity, non-parametric models of the physical test article. The ability of the identified models to accurately “generalize” the essential features of the non-linear system was verified by comparing the predictions of the models with experimental measurements from data sets corresponding to different excitations than those used for identification purposes. It is shown that the identification techniques under discussion can be useful tools for developing accurate simulation models of complex multi-dimensional non-linear systems under broadband excitation.