Lognormal Fitting of Particle Size Distribution Data Monitored in Animal Buildings: Linear versus Nonlinear Regression Approach

Abstract

Lognormal distribution is the most frequently used particle size distribution (PSD) model in agricultural air quality research, and a proper determination of volume median diameter (VMD) and geometric standard deviation (GSD) is crucial for model applications. In this study, the prevalent linear regression approach was compared to the nonlinear regression approach with PSD data monitored in 15 animal buildings using four particle size analyzers: Horiba, DSP, Coulter, and Malvern. Results showed that the linear regression approach significantly underestimated VMD values, and the resulting relative errors were higher overall than those yielded by the nonlinear regression approach. As a measure of model approximation, the values of the sum of absolute differences (SAD) derived from linear regression were considerably larger than those offered by nonlinear regression. The relative errors and SAD values both suggested a poorer performance of the linear regression approach. The SAD values and the relative errors in estimated VMD and GSD decreased as R2 approached 1. However, even at R2 = 0.98, the linear regression approach misestimated VMD values by up to 30% (or 14.6 µm) and yielded SAD values of around 20% to 40%. A strong interference of minor PSD peaks on the linear regression results was identified, which partly explains the inferior performance of the linear regression approach as compared to the nonlinear regression approach. For future relevant studies, the limitations of the linear regression approach should be recognized, and a preliminary comparison between different PSD parameter estimation approaches is recommended.