A well established approach for the performance prediction of engineering systems involves the application of physical laws to derive mathematical models which are then solved in order to study their nonlinear behavior. The advances in mathematical and numerical tools have made the analysis, prediction and control of engineering systems increasingly more accurate. Various solutions and control strategies have been developed too numerous to mention here.
Invariably, all engineering systems are nonlinear and exhibit phenomena that can only be predicted by nonlinear models. Traditionally however, analysis and design of engineering systems has employed linear models simply because the mathematics is well developed, and the analysis procedures are straight-forward for linear systems. More recently, partly because of advances in nonlinear mathematical analysis, and partly because of increase in the availability of high performance computing, nonlinear analysis has begun to make its way into the engineering world. Still, the prevailing assumption is that the nonlinear regime of operation is potentially harmful and should be avoided. However, although operating in the nonlinear region could indeed be catastrophic if one did not have sufficient knowledge, it is quite probable that optimal operations could well be in the nonlinear regime and should be explored
The principal thesis of this research is that the nonlinear dynamic response of practical systems contains valuable information about the system including knowledge that could be used for diagnostics. We wish to explore this idea starting with simple models and extending gradually to more complex ones.
The following specific projects are investigated: