TKS-BLS: Temporal Kernel Stationary Broad Learning System for Enhanced Modeling, Anomaly Detection, and Incremental Learning With Application to Ironmaking Processes
针对宽度学习系统在非线性映射、输入输出时间错配、非平稳场景和增量学习理论优化方面的不足，提出时间核平稳宽度学习系统，通过核技术、时间对齐参数和KL散度目标函数实现稳健建模与异常检测，在七个真实炼铁数据集上验证了优越性。
Broad learning system (BLS), a tri-layer feedforward neural network, has gained widespread recognition for its exceptional scalability and computational efficiency. However, BLS and its derivatives encounter several challenges: 1) overlooking the uncertainty introduced by numerous nonlinear random mappings; 2) failing to cope with the misalignment of model inputs with the output sampling rate; 3) lack of attention to nonstationary scenarios; and 4) absence of theoretical optimization for incremental learning. To overcome these obstacles, we propose a regression modeling and anomaly detection scheme rooted in a temporal kernel stationary BLS (TKS-BLS). We first create a nonlinear kernel broad representation (NKBR) extraction strategy, providing a robust nonlinear foundation for random feature mapping via kernel technology. Following this, we probe the mechanism of temporal matching between model inputs and outputs through a temporal alignment parameter, interpretable under a latent variable relationship. In the integration phase, we establish a Kullback-Leibler divergence objective function to facilitate the capture of stationary relationships within time-series data, in conjunction with the regression error. Subsequently, a double-loop parameter optimization algorithm and an independent incremental learning mechanism are put forth, both backed by comprehensive theoretical analyses. Our method’s superiority is thoroughly confirmed by experimental outcomes from extensive case studies across seven real ironmaking process datasets.