Industrial Process Soft Sensing Based on Nonlinear Sparse Generalized Method of Moments Estimation Model and Relevance Vector Regression

In industrial processes, soft sensing is widely used to predict key quality variables. Selecting appropriate auxiliary variables is crucial for establishing an accurate soft sensing model. However, current research still faces challenges in balancing accuracy and efficiency in auxiliary variable selection, which affects predictive performance. Therefore, this paper proposes a variable selection method based on the Nonlinear Sparse Generalized Method of Moments (NS-GMM) and integrates it with Relevance Vector Regression (RVR) for soft sensing modeling to achieve precise prediction of key variables. Considering the nonlinear relationships among actual variables, and traditional GMM models are designed for linear problems, the kernel technique is first incorporated into the GMM model to form a nonlinear GMM model. Second, regularization terms are introduced into the nonlinear GMM model to sparsify the model parameters, thereby alleviating the “contamination effect” in variable selection. Furthermore, the parameters of the NS-GMM are used to construct a variable selection criterion to filter out auxiliary variables that have a significant impact on the target variable. Then, the selected auxiliary variables are used to train an RVR model for soft sensing modeling and prediction. Finally, numerical simulations validate the effectiveness of the improved GMM approach. The performance of the proposed method is verified using the penicillin fermentation process. Experimental results demonstrate that the proposed method outperforms traditional methods in both variable selection and prediction performance. This method provides new insights and tools for precise measurement and control in industrial processes.