A comparison between multivariate linear model and maximum likelihood estimation for the prediction of elemental composition of coal using proximate analysis

The elemental composition of coal is essential for analysing the overall process of energy conversion systems. Simultaneous information regarding the elemental composition of coal fed into a boiler is of increasing interest for plant operation. In this study, methods of estimating the elemental composition of coal using proximate analysis and a higher heating value were developed to meet requirements in boiler operation. A novel method was developed to formulate the multivariate linear model (MLM) for predicting the elemental composition of coal by solving a set of simultaneous equations with extensive correlations between coal components and an elemental composition constraint. The maximum likelihood estimation (MLE) approach for predicting carbon, hydrogen, oxygen, nitrogen, and sulphur contents was also developed based on a series of extensive correlations among coal components. The maximum likelihood estimator employs more correlations and considers the performance of prediction residuals for each correlation, offering a better prediction accuracy than the MLM, which is based on fewer correlations and neglects prediction residuals. A total of 743 data points was used to derive the MLM and MLE models, which were validated and verified by another set of data that included the same variety of coal types. The proposed methods can estimate the complete elemental composition of coal (C, H, O, N, and S) with acceptable prediction accuracy for engineering purposes. Another important finding is that average absolute error corresponding to the measured values of nitrogen is only 14.14%, although the predicted nitrogen contents did not follow the trends of the measured values.