Analysis and comparison between regression models for temperature estimation of solar collectors operating with nanofuids

Abstract

The objective of this work is to verify the application of polynomial regression methods, Ridge and Lasso regression in the nowcasting of the fluid temperature and energy gain of a solar collector operating with nanofluids. The collector has temperature and global/direct solar radiation sensors for data logging. In addition the R programming language was used for the statistical analysis of R2, MAE (Mean Absolute Error) and RMSE (Root Mean Squared Error). The models were applied in three different data sets, which regarded to the data for water temperature prediction and TiO2 nanofluids with a concentration of 25 ppm and 75 ppm, where each method applied seven predictors for the fluid temperature nowcasting. The best Root Mean Squared error found in the test sets was 2.281°C for a degree 3 polynomial regression, whereas the Ridge presented an RMSE of 3.190°C. The Ridge and the Lasso usually improve least squares methods but they did not perform well in this data set, the Ridge regression considered a model with all the predictors and got a high test error, as far as the Lasso excluded some predictors and got an improved result. A cross-validation was performed to know the degree of the most effective polynomial for the analysis of these data and the polynomial regression of degree 3 obtained the best result, confirming that the fluid temperature does not follow a linear trend mainly during the hours from 5:30 to 21:30.