Process Industries Soft Sensor Modeling Based on Semi-Supervised Growing Echo States Gaussian Process

The echo state Gaussian process (ESGP) is an efficient method for modeling dynamical systems and has been successfully employed in soft sensor modeling within the process industry. However, the ESGP operates as a supervised learner, necessitating manual configuration of the reservoir. In practical process industries, many industrial samples lack labels, resulting in incomplete data. To address these challenges, this article introduces a semi-supervised growing ESGP (SS-GESGP). First, we propose a growing ESGP (GESGP) for incremental automatic reservoir construction. Subsequently, to tackle soft-sensing modeling with incomplete data, we integrate a state resampling technique into the GESGP learning process. This technique resamples the echo state, incorporating both labeled and unlabeled spatiotemporal information. By leveraging the resampled states for Gaussian process (GP), we convert semi-supervised problems into supervised learning scenarios. Finally, the SS-GESGP is evaluated using both time-series benchmarks and real-world process industry data. Experimental results demonstrate that the proposed method exhibits superior soft-sensing performance compared with state-of-the-art approaches.