Enhancing Extreme Learning Machine Robustness via Residual-Variance-Aware Dynamic Weighting and Broyden–Fletcher–Goldfarb–Shanno Optimization: Application to Metro Crowd Flow Prediction

Aiming at the robustness problem of the extreme learning machine (ELM) in noisy and nonuniform data scenarios, this paper proposes an improved algorithm (BFGS-URWELM) that integrates uniform residual weighting and Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton optimization. This method introduces a sample weighting mechanism based on the target residual variance, dynamically adjusts the importance of training samples, and iteratively corrects the input weights and biases of the ELM in combination with the BFGS optimization strategy, effectively improving the prediction accuracy and stability of the model. The experiment is based on the passenger flow data of 80 subway stations and compares traditional machine learning algorithms, ensemble learning methods, and ELM variant models. The results show that BFGS-URWELM achieves 28.34, 0.3071, and 19.76 in the RMSE, MAPE, and MAE indicators, respectively, which are 19.9–33.5% higher than the baseline ELM. In addition, the residual distribution is more concentrated near the zero value, and the goodness of fit R2 is improved to 0.96. The algorithm significantly reduces the prediction error under high-noise data and provides a highly robust solution for traffic flow prediction tasks.