Manifold semi-supervised learning for aluminum electrolysis temperature identification based on regularized hierarchical extreme learning machine

The aim of this article is to develop a soft approach for a real-time cell temperature prediction in the aluminum electrolysis reduction. Under the limited labeled data constraint, Laplacian semi-supervised learning methods, which can fully utilize the underlying structure of the data distribution and further extract information contained in all available data, has recently received extensive attention in the field of soft sensor modeling. Since the Laplacian underlying manifold is a constant, it remains a challenging task to improve the extrapolating ability for the case that only a few labeled samples are available. This study presents a soft modeling method based on a semi-supervised deep learning structure, which was developed from the hierarchical autoencoders with extreme learning machine. Furthermore, a Laplacian–Hessian semi-supervised extreme learning machine is built to learn all the geometric distribution information. The Laplacian–Hessian semi-supervised extreme learning machine method is applied to estimate the cell temperature in an aluminum reduction process. The experimental results demonstrate the performance and robustness of the proposed algorithm are superior to those of the existing state-of-the-art methods.