EACS 2016 Paper No. 167

There has long been interest in the concept of causality in systems theory and structural dynamics. In the context of nonlinear system identification, the Hilbert transform method of detecting nonlinear behaviour depends crucially on the concept of causality. One might argue that there are actually two interrelated definitions, or principles, of causality current and important in structural dynamics, and more widely in general time series analysis. The first ‘definition’ of causality, one might call the responsibility definition, is based on the idea that an event B (the effect) only occurs if an event A (the cause) occurs. The second definition – the priority – definition, asserts that cause must precede effect (in time) in any classical dynamic situation. The responsibility concept of causality is already embedded in structural dynamics, as it largely maps onto the idea of correlation; the coherence function associated with a Frequency Response Function (FRF) is essentially a representation of the idea. The priority concept is the crucial ingredient in the Hilbert transform test mentioned earlier. The objective of the current paper is to discuss where causality can illuminate processes in linear and structural dynamics and to provide illustrations based on transmissibilities and FRFs for Multi-Degree-of-Freedom (MDOF) systems.