Multiple Regression and Big Data Analysis for Predictive Emission Monitoring Systems

Predictive Emission Monitoring Systems (PEMS) offer a cost-effective and environmentally friendly alternative to Continuous Emission Monitoring Systems (CEMS) for monitoring pollution from industrial sources. Multiple regression is one of the fundamental statistical techniques to describe the relationship between dependent and independent variables. This model can be effectively used to develop a PEMS, to estimate the amount of pollution emitted by industrial sources, where the fuel composition and other process-related parameters are available. It often makes them sufficient to predict the emission discharge with acceptable accuracy. In cases where PEMS are accepted as an alternative method to CEMS, which use gas analyzers, they can provide cost savings and substantial benefits for ongoing system support and maintenance. The described mathematical concept is based on the matrix algebra representation in multiple regression involving multiple precision arithmetic techniques. Challenging numerical examples for statistical big data analysis, are investigated. Numerical examples illustrate computational accuracy and efficiency of statistical analysis due to increasing the precision level. The programming language C++ is used for mathematical model implementation. The data for research and development, including the dependent fuel and independent NOx emissions data, were obtained from CEMS software installed on a petrochemical plant.

Degrees of freedom in low rank matrix estimation

The objective of this paper is to quantify the complexity of rank and nuclear norm constrained methods for low rank matrix estimation problems. Specifically, we derive analytic forms of the degrees of freedom for these types of estimators in several common settings. These results provide efficient ways of comparing different estimators and eliciting tuning parameters. Moreover, our analyses reveal new insights on the behavior of these low rank matrix estimators. These observations are of great theoretical and practical importance. In particular, they suggest that, contrary to conventional wisdom, for rank constrained estimators the total number of free parameters underestimates the degrees of freedom, whereas for nuclear norm penalization, it overestimates the degrees of freedom. In addition, when using most model selection criteria to choose the tuning parameter for nuclear norm penalization, it oftentimes suffices to entertain a finite number of candidates as opposed to a continuum of choices. Numerical examples are also presented to illustrate the practical implications of our results.

Source apportionment of PM_(2.5)light extinction in an urban atmosphere in China

Haze in China is primarily caused by high pollution of atmospheric fine particulates（PM2.5）.However, the detailed source structures of PM2.5 light extinction have not been well established, especially for the roles of various organic aerosols, which makes haze management lack specified targets. This study obtained the mass concentrations of the chemical compositions and the light extinction coefficients of fine particles in the winter in Dongguan, Guangdong Province, using high time resolution aerosol observation instruments. We combined the positive matrix factor（PMF） analysis model of organic aerosols and the multiple linear regression method to establish a quantitative relationship model between the main chemical components, in particular the different sources of organic aerosols and the extinction coefficients of fine particles with a high goodness of fit（R^2= 0.953）. The results show that the contribution rates of ammonium sulphate,ammonium nitrate, biomass burning organic aerosol（BBOA）, secondary organic aerosol（SOA） and black carbon（BC） were 48.1%, 20.7%, 15.0%, 10.6%, and 5.6%, respectively. It can be seen that the contribution of the secondary aerosols is much higher than that of the primary aerosols（79.4% versus 20.6%） and are a major factor in the visibility decline. BBOA is found to have a high visibility destroying potential, with a high mass extinction coefficient, and was the largest contributor during some high pollution periods. A more detailed analysis indicates that the contribution of the enhanced absorption caused by BC mixing state was approximately 37.7% of the total particle absorption and should not be neglected.