Research on a semi-supervised soft sensor modelling method for complex chemical processes based on INGO-VMD-ESN

Abstract The dynamic and non-linear nature of complex chemical processes often leads to low prediction accuracy of key quality variables by traditional soft sensors, thus affecting the overall system control accuracy and operational efficiency. Therefore, this paper proposes a semi-supervised soft sensor modelling method based on improved the northern goshawk optimization (INGO)-variable mode decomposition (VMD)-echo state network (ESN). Firstly, a new semi-supervised fusion method is proposed to address the problem of model training difficulty due to the scarcity of labelled samples and process dynamics, which reconstructs the sample dataset by fusing labelled and unlabelled samples into more representative new samples, improving the model’s generalization ability. Secondly, for the noise interference present in the reconstructed data, the input data is denoised using the VMD method to improve the quality of data. Then, a soft sensor model is built based on ESN. Additionally, the denoising and prediction performance of VMD and ESN is significantly affected by parameters, therefore the paper utilizes the INGO algorithm to achieve parameter rectification for VMD and ESN. Finally, the method is validated based on actual sulphur recovery data from a refinery. The results demonstrate that the method effectively mitigates the impact of dynamics and nonlinearity in the complex chemical process which enhances prediction accuracy.