Identifying Self-excited Vibrations with Evolutionary Computing

This study uses differential evolution to identify the coefficients of second-order differential equations of self-excited vibrations from a time signal. The motivation is found in the ample occurrence of this vibration type in engineering and physics, in particular in the real-life problem of vibrations of hydraulic structure gates. In the proposed method, an equation structure is assumed at the level of the ordinary differential equation and a population of candidate coefficient vectors undergoes evolutionary training. In this way the numerical constants of non-linear terms of various self-excited vibration types were recovered from the time signal and the velocity value only at the initial time. Comparisons are given regarding accuracy and computing time. Dependency of the test errors on the algorithm parameters is studied in a sensitivity analysis. The presented evolutionary method shows good promise for future application in engineering systems, in particular operational early-warning systems that recognise oscillations with negative damping before they can cause damage.