Prediction of Annual Daylighting Performance Using Inverse Models

This paper presents the results of a study that developed improved inverse models to accurately predict the annual daylighting performance (sDA and lighting energy use) of various window configurations. This inverse model is an improvement over previous inverse models because it can be applied to variable room geometries at different weather locations in the US. The room geometries can be varied from 3 m × 3 m × 2.5 m to 15 m × 15 m × 10 m (length × width × height). The other variables used in the model include orientation (N, E, S, W), window-to-floor ratio, window location in the exterior wall, glazing visible transmittance, ceiling visible reflectance, wall visible reflectance, shade type (overhangs, fins), shade visible reflectance, lighting power density (LPD) (W/m2), and lighting dimming setpoint (lux). Such models can quickly advise architects during the preliminary design phase about which daylighting design options provide useful daylighting, while minimizing the annual auxiliary lighting energy use. The inverse models tested and developed were multi-linear regression (MLR) models, which were trained and tested against Radiance-based annual daylighting simulation results. In the analysis, 482 cases with different model conditions were simulated, to develop and validate the inverse models. This study used 75% of the data to train the model and 25% of the data to validate the model. The results showed that the new inverse models had a high accuracy in the annual daylighting performance predictions, with an R2 of 0.99 and an CV(RMSE) of 15.19% (RMSE of 58.91) for the lighting energy (LE) prediction, and an R2 of 0.95 and an CV(RMSE) of 14.38% (RMSE of 8.02) for the sDA prediction. In addition, the validation results showed that the LE MLR model and sDA MLR model had an R2 of 0.96 and 0.85, and RASE of 121.89 and 8.54, respectively, which indicate that the inverse models could accurately predict daylighting results for sDA and lighting energy use.