An L2,1-regularized cascaded broad learning framework for robust anomaly detection in complex industrial metrology

To address the complexity, high dimensionality, and severe data imbalance in industrial metrology, we propose an L2,1-Regularized Cascaded Broad Learning Framework (L21RCBLS) for robust anomaly detection. Our study makes three key contributions: (i) a cascaded feature structure with residual connections is designed to enhance sequential representation while mitigating gradient instability and parameter forgetting; (ii) a sparsity-inducing L2,1-norm optimization strategy is introduced to improve robustness against ubiquitous industrial noise and scattered outliers; and (iii) the mathematical convergence of the proposed iterative optimization algorithm is theoretically established. Extensive experiments on real-world industrial datasets (over 16,600 samples) demonstrate that L21RCBLS consistently outperforms eight baseline models, including CNN, BiGRU, and pNBEBLS. For three critical product dimensions (Size 1 to 3), the model achieves optimal performance with Mean Squared Error (MSE) as low as (0.000152, 0.000152, 0.000098) and R2 scores exceeding (0.914520, 0.943989, 0.921815). Ablation studies further confirm that the synergy of residual cascading and L2,1-regularization is vital for maintaining high precision under limited and skewed data conditions, offering a computationally efficient solution for real-time quality control.