Rapid Noise Prediction of a Three-Stage Helical Gear Reducer Using a BOA-ISSA-BPNN Surrogate Model

To reduce the time and computational cost of vibro-acoustic simulations in gear reducer noise evaluation, this study develops a simulation-driven surrogate modeling framework for a three-stage helical gear reducer. A high-fidelity “vibration–acoustic radiation” simulation chain is established, where the housing vibration responses computed in Romax Designer are mapped into ACTRAN to obtain the radiated noise. Using Optimal Latin Hypercube Sampling, 300 designs are generated by varying the first-stage pinion micro-modification parameters (tooth drum, tooth slope, and tooth profile), and the average RMS sound pressure level over six field points is adopted as the noise metric. A BP neural network (BPNN) surrogate is then constructed, in which Bayesian Optimization (BOA) is used to tune hidden layer nodes and learning rate, and an improved Sparrow Search Algorithm (ISSA) is employed to optimize the initial weights and biases, forming the proposed BOA-ISSA-BPNN model. On the test set, the proposed model achieves R² = 0.97499, RMSE = 0.91385, and MAE = 0.6547, with an average prediction time of 32.35s. Meanwhile, comparisons with SVM, BPNN, BOA-BPNN, SSA-BPNN, and ISSA-BPNN demonstrate superior prediction accuracy; moreover, relative to the hour-level computational cost of high-fidelity simulations, the proposed surrogate enables rapid noise evaluation on the order of tens of seconds, enabling fast micro-modification design iteration and practical engineering decision-making.