The Nonlinear Mechanical Vibration Response Prediction Model Based on Multi‐Domain Feature Fusion and Improved Back Propagation Neural Network

ABSTRACT Nonlinear systems exhibit strong coupling and time‐varying parameters; these characteristics make it difficult for traditional mechanism‐based modeling methods to adapt to uncertain loads and complex working conditions. The prediction accuracy of vibration responses is thus limited. In order to handle these issues, this study proposes a big data‐driven improved back propagation neural network (BPNN) method for high‐precision prediction of vibration responses in nonlinear systems. This method first collects full‐condition vibration data through multi‐source sensors; it extracts multi‐domain (MD) features from the Time Domain (TD), Frequency Domain (FD), and Time‐Frequency Domain (TFD) to construct a high‐dimensional input dataset. Second, a three‐layer BPNN structure with input, hidden, and output layers is designed; meanwhile, the Rectified Linear Unit (ReLU) activation function is adopted to solve the vanishing gradient problem. Finally, adaptive learning rate and momentum terms are introduced to optimize the model training mechanism; this modification improves training speed and stability. Based on the public Nonlinear Mechanical Vibration Dataset (NMVD), a three‐level comparison system (a benchmark model, an improved model, and mainstream methods) is established. Experimental results show that the improved BP model converges in 1373 iterations; its convergence speed is increased by 50% compared with the traditional BP model. The Mean Squared Error (MSE) is reduced to 0.0032, the Coefficient of Determination ( R 2 ) reaches 0.9745, and the residual standard deviation is reduced by 39.87%. Thus, the proposed model shows remarkable advantages in both prediction accuracy and training stability. This study solves the technical limitations of traditional methods in predicting vibration responses of nonlinear systems via MD feature fusion and optimization of the BP algorithm training mechanism. This provides an efficient engineering approach for vibration analysis of complex nonlinear systems; it also offers data‐driven technical support for equipment vibration control and fault early warning.