AbstractThis study uses differential evolution to identify the coeffic ients of second-order differentia l equations of self-e xc ited vibrations fro m a time signal. The motivation is found in the ample occurrence of this vibration type in engineering and physics, in particu lar in the real -life proble m of v ibrations of hydraulic structure gates. In the proposed method, an equation structure is assumed at the level of the ordinary differentia l equation and a population of candidate coefficient vectors undergoes evolutionary training. In this way the numerical constants of non-linear terms of various self-e xc ited vibration types were recovered fro m the time signal and the velocity value only at the initial t ime. Co mparisons are given regarding accuracy and computing time. Dependency of the test errors on the algorith m para meters is studied in a sensitivity analysis. The presented evolutionary method shows good promise for future applicat ion in engineering systems, in particular operational early -wa rning systems that recognise oscillations with negative damping before they can cause damage.