A multi-model fusion soft measurement method for cement clinker f-CaO content based on K-means ++ and EMD-MKRVM

Abstract

The content of free calcium oxide (f-CaO) in cement clinker is a key indicator for testing the quality of cement clinker. To address the problem that the content of f-CaO cannot be detected online, a multi-model fusion soft measurement method based on K-means++ clustering, empirical modal decomposition combined with multi-kernel relevance vector machines (EMD-MKRVM) is proposed to predict f-CaO content under different operating conditions. First, time-series analysis and matching of input variables with f-CaO content were performed, based on which a combination of empirical modal decomposition (EMD) and sample entropy (SE) denoising method was used to filter out high- frequency noise from the original data and extract effective signal information for reconstruction. Second, the K-means++ algorithm was used to cluster the processed training sample data, and multi-kernel relevance vector machine (MKRVM) sub-models were established by training the sample data of each sub-class and then the affiliation between the test samples and each sub-class was calculated as the weights of the sub-model output values, and the final model prediction output was obtained by multi-model fusion. Finally, the real data from cement plants were used for validation. The results show that compared with the single MKRVM model, multi–relevance vector machine (RVM) model, multi–support vector machine (SVM) model, and multi-MKRVM model using only EMD denoising method, the mean absolute error (MAE) of the multi-MKRVM model proposed in this paper was reduced by 42%, 7%, 14%, and 35%; root mean square error (RMSE) is reduced by 28%, 10%, 12%, and 21%; squares due to error (SSE) is reduced by 51%, 24%, 27%, and 41%; Theils inequality coefficient (TIC) is reduced by 27%, 17%, 21%, and 19%; $R^2$ is improved by 64%, 18%, 39%, and 91%; and Index of agreement (IA) is improved by 28%, 9%, 22%, and 13%. The multi-MKRVM model proposed in this paper has higher accuracy, better generalization ability and stability, and provides an effective method for f-CaO content prediction under complex multiple working conditions.