State prediction of MR system by VMD-GRNN based on fractal dimension

Taking the test signals of magneto-rheological vibration system under different states as research objects, four Generalized Regression Neural Network (GRNN) prediction algorithms, based on time series, time series Auto-Regressive (AR) model coefficients, time series box dimensions, and Variational Modal Decomposition (VMD) box dimensions, are designed. Moreover, four Back Propagation Neural Network (BPNN)comparative prediction algorithms, based on the four previous parameters, are also designed. These eight algorithms are applied to predict vibration damping efficiency of the system. The prediction results show that, compared to the BPNN prediction algorithm, the corresponding four GRNN prediction algorithms have the advantages of strong self-learning ability, fast convergence speed, high prediction accuracy, and stable prediction results. Among the eight prediction algorithms, the GRNN prediction algorithm, based on VMD box dimension, forecasts the results with good stability, better self-learning ability, and higher computing speed, which can maximize the prediction accuracy of the system, the minimum prediction error can reach 1.9049% when the parameters K =  4, N = 33, and Spread = 0.601. To sum up, through parameter optimization, the optimal parameter combination scheme of GRNN prediction algorithm, based on VMD box dimension, is obtained, and the best prediction effect is achieved.