## 3 Results and Discussion
### DIALux(r) Analysis Results

Table 2: Average and maximum illuminance on the desks (\(E_{\text{an},dk}\) and \(E_{\text{max},dk}\)) and blackboards (\(E_{\text{an},b}\) and \(E_{\text{max},b}\)) in the classrooms studied in the following cases: current (measured by lux meter), current case simulation by DIALux®, case 1, case 2, and case 3. The average and maximum UGR glare values obtained in the simulations have been also included. Figure 8: Illuminances calculated by DIALux®, \(E_{dl}\), on each of the desks in classrooms A-005, A-016, A-038, and B-306, compared to the measurements taken in each case, \(E_{m}\): A line indicating the ideal simulation is included on each graph. The Root Mean Square Error (RMSE) of \(E_{dl}\) in relation to \(E_{m}\) is included in each graph. This correlation can also be quantified by means of the Root Mean Square Error (RMSE). For each classroom, assuming data is reasonably distributed according a Gaussian process (data from the A005, A016, and B036 classrooms are Gaussian according to the Shapiro-Wilk test with 0.05 significance level; data from A038 do not; however, this last result changes if the two points--from a 42-point sample--representing the larger difference between simulated and testing data are not taken into account), the RMSE represents the limit encompassing 66% of the differences between the simulated and measured illuminances (i.e., the limit marking 66% of the desks displaying a minor difference between those illuminances. This difference is reflected by the vertical distance between the points and the unit slope line on the graphs in Figure 8). The RMSE values obtained from the simulations are as follows: 16.0 lx (A-005), 26.3 lx (A-016), 18.7 lx (A-038), and 33.7 lx (B-306). Bearing in mind that the above data show a difference between the simulated and measured data of 3.2% to 6.7% of the reference value of the recommended illuminance level, 500 lx [43], the accuracy of the simulation performed with DIALux(r) was assumed to be reasonable. After studying the reasonable suitability of DIALux(r) simulations, 3 different case studies were proposed in order to improve the current situation:  
* Case 1: The proposal consists of painting the walls of the classrooms white. In this case, the luminaires (and lamps) and their distribution are maintained. * Case 2: Installation of new lamps (in the luminaires), using the same model as before, should increase their luminous flux. This improvement was programmed in DIALux(r) by applying a 0% attenuation value to all simulated control groups. * Case 3: Replacement of the current luminaires with a different model employing LED technology, PHILIPS SM134V PSD W20L120 1 xLED37S/840 OC, was chosen to maintain the current arrangement of the luminaires in order to simplify the installation process. Because of the project size, it was decided to choose a single luminaire model in order to achieve two fundamental advantages: to simplify maintenance and to reduce the investment by increasing the purchase volume and by possibly obtaining additional discounts. The following numbers of luminaires were used in each of the classrooms studied: 18 (A-005), 8 (A-016), 19 (A-038), and 17 (B-306). Most of the lamps currently installed (PHILIPS) have a luminous flux of 3350 lm. Since the aim is also to increase the current average illuminance value, it was decided to choose lamps with a higher luminous flux: 3700 lm. Because the ceilings in the building A classrooms are very high, it was advantageous to choose luminaires that can be hung (or installed directly on the ceiling, which is necessary in the building B classrooms due to their lower ceiling height). In addition, an \"OC\" diffuser was chosen. Regarding the color temperature of the luminaires, 4000 K was selected (current situation and recommended by the regulations). On the technical data sheet provided by the manufacturer, it should be emphasized that the color reproduction index is greater than or equal to 80, thus complying with European standards.