The existing quantitative (such as fractal dimension) methods for the dynamic performance of magnetorheological (MR) damping systems have problems in predicting damping efficiency due to the small sample size, overfitting risk, poor generalization and robustness, and difficulty in meeting industrial reliability requirements. In order to improve the prediction accuracy of damping efficiency in MR damping systems, ensure the reliability of prediction results for small sample datasets, this study first calculates five entropy indices – Approximate Entropy (ApEn), Sample Entropy (SampEn), Permutation Entropy (PermEn), Fuzzy Entropy (FuzzyEn), and Shannon Entropy (ShannonEn) – of the system’s time series under different operating states. These indicators are used to accurately evaluate the dynamic performance of the system and determine parameters that quantify its dynamic quality. Taking damping efficiency as the prediction objective, each entropy index is treated as a single input parameter, and a cross validation generalized regression neural network (GRNN) model is adopted to select the optimal entropy calculation parameter from the comprehensive score evaluation prediction results. On this basis, the entropy feature vector was reconstructed, and a reconstruction entropy feature prediction algorithm based on GRNN and balance criterion was established. The performance of the model was compared with existing prediction algorithms, and the performance of the optimal combination was verified. The industrial environment was simulated, and the industrial application prospects of the model were evaluated. Key findings indicate that: The preferred single entropy parameter using GRNN can achieve a prediction accuracy of 99 %, which is suitable for quantifying the dynamic quality of the system. Among all single entropy parameters, approximate entropy(ApEn) exhibits the highest prediction accuracy; The comprehensive scoring method based on GRNN Gaussian kernel selects the optimal parameter scheme for single entropy calculation; The reconstructed entropy feature vector was used to select the optimal entropy feature combination scheme for damping efficiency prediction based on GRNN inverse multiple quadratic (IMQ)-kernel and balance criterion; The combination of “ApEn+FuzzyEn” GRNN IMQ-kernel and balance criterion not only achieves better prediction accuracy than existing VMD-box dimension-GRNN, Long Short-Term Memory (LSTM), Random Forest (RF), and Support Vector Machine (SVM), but also demonstrates good generalization, robustness and reliability, as well as stable performance under different SNR noises. The relevant algorithms have also achieved good prediction accuracy and generalization in other datasets. This research model algorithm breaks through the accuracy bottleneck of traditional fractal dimension methods and provides an efficient, stable, and reliable prediction solution for small sample datasets. Its industrial application prospects are broad.
Chen et al. (Sun,) studied this question.