Differential evolution for system identification of self-excited vibrations

• A competitive version of the differential evolution algorithm is applied to regression on second-order ordinary differential equations from only the original time signal.
• Specific attention is devoted to application aspects of self-excited vibrations in physics and engineering.
• Extensive numerical experiments reveal the factors that influence test errors in free optimization.
• Two novel approaches for a constrained optimization treatment of this inverse problem are proposed. This enables accurate identification of the target coefficients of the dynamical system.

This study uses a differential evolution method to identify the coefficients of second-order differential equations of self-excited vibrations from a time signal. The motivation is found in the frequent occurrence of this vibration type in physics and engineering. In the proposed method, an equation structure is assumed at the level of the differential equation and a population of candidate coefficient vectors undergo evolutionary training. In this way the numerical constants of non-linear terms of various self-excited vibration types were recovered, requiring only the original signal. The method is validated by comparison with regression of the analytical solution of a linear vibration. Comparisons are given regarding accuracy and computation time. A sensitivity analysis reveals the influence of the problem stiffness and the settings of the integration algorithm for evaluating the candidate models. The algorithm is extended to allow for stability constraints based on classification of candidates by comparing with data from Monte Carlo simulations. This boosts accuracy tremendously and yields accurate coefficient values. The presented method shows promise for future applications in engineering, such as early-warning systems.