# Model Calibration Methodology to Assess the Actual Lighting Conditions of a Road Infrastructure

^{1}

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## Abstract

**:**

## 1. Introduction

_{2}emission reductions can be achieved by also including energy performance indicators in the decision tools used in lighting studies [19] as well as considering traffic intensity data in the design of intelligent outdoor lighting [20]. The implementation of optimization techniques by simulation tools is also useful to improve the safety of the citizens as well as to manage the operation and the costs of the street lighting facilities. The most accepted lighting simulation tools and their combined use have been investigated by Baloch et al. [21], deducing that MATLAB is the most popular software adopted by researchers for lighting simulation and EnergyPlus for energy consumption. MATLAB was used by Shaikh et al. [11] to develop an intelligent multi-objective system for the management of the energy efficiency in buildings and the users’ comfort. However, other tools such as Radiance, Daysim, BuildOpt, DIALux, Relux, or Oxytech have also been used by other authors in their works. Zhang et al. [12] optimized the design of a school building using genetic algorithms and combining thermal and daylight simulations with EnergyPlus and Radiance. Manzan [22] carried out a genetic optimization approach to design the optimal externally shading device using Daysim to compute lighting loads. Yoomak et al. [23] analyzed by means of an optimization and a simulation in Dialux the influence of the pole spacing and the mounting height of the luminaires in the lighting quality comparing high pressure sodium (HPS) and light emitting diode (LED) luminaires. These authors considered different road conditions (wet and dry) and street lamps arrangements (staggered, opposite and single-sided) for their work, concluding that HPS luminaires can provide better average luminance whereas LED luminaires can achieve better visual and comfort performance. Vera et al. [8] implemented the hybrid particle swarm optimization/Hooke–Jeeves (PSO/HJ) algorithm combining a variety of tools for lighting and thermal simulation. They applied an efficient and robust process using Radiance, GenOpt and EnergyPlus.

_{0}) of a road in order to scale the standard r-tables with their particular value. Gidlund et al. [30] analyzed the impact on energy saving by comparing between taking into account the standard r-tables or laboratory measurements of a pavement sample in the design conditions of the installation, evidencing that the use of flux control systems are necessary to compensate the data discrepancies. Additionally, new asphalts such as cool pavements are being developed to mitigate the heat island phenomenon and reduce the temperature of cities [31] and due to the use of white high reflective paints they have very different properties from conventional materials. All these studies revealed the need to develop methodologies to characterize new asphalts at reduced costs and obtain new r-tables.

## 2. Materials and Methods

_{0}parameter, related to the type of pavement considered in the modeling stage, according to the luminance of the road; and (iii) adaptation of the reflection properties of said asphalt also using experimental luminance data.

#### 2.1. Maintenance Factor Identification

#### 2.2. Average Luminance Coefficient Calibration

_{0}, and the specular factor, S1, respectively. It should be noted that higher values of Q

_{0}correspond to darker surfaces, whereas a low S1 value represents a more diffuse and less specular surface.

_{0}and S1, but the table can be rescaled if the real Q

_{0}of the considered road is known.

_{0}is calibrated to adapt the lightness of the road, as its real value may be far from the default due to the deterioration of the pavement or simply for design reasons. Moreover, the four types of surfaces of the R-classification are studied, bearing in mind that it is difficult to reliably determine the properties of a given asphalt after deterioration. For all four cases, the calibration methodology is applied considering the standard Q

_{0}as the design value for the process and the luminance as the variable used for the error calculation. As a result of the method, the Q

_{0}that reduces the model errors for each kind of surface is obtained. Then, according to the CV(RMSE) and RMSE, it is possible to evaluate and decide which type of surface is more representative and, therefore, better fits the analyzed surface.

#### 2.3. Adaptation of the Closest r-Table

## 3. Experimental System

_{0}factor and the adaptation of the r-table.

## 4. Results and Discussion

#### 4.1. Maintenance Factor Identification

#### 4.2. Average Luminance Coefficient Calibration

_{0}is greater than the design value for all the alternatives taken into consideration. This suggests that the road surface studied is less dark than the standard asphalt models adopted. Moreover, if the CV(RMSE) and the RMSE of the four tests are compared, it is verified that the R1 type of asphalt is the one that represents the measured surface with greater precision. Both the CV(RMSE) and the RMSE are lower for this alternative than for the rest, so it will be used to model the road in the following steps of the method. The fact that the surface approaches a type R1 pavement implies that the road is mainly diffuse. The table also shows that with this stage of the method it is possible to reduce the RMSE by 66%.

_{0}factor can be seen in Figure 10, in which the luminance levels in different longitudinal sections of the road have been represented. The luminance before the calibration, ${L}_{uncal\left(R1\right)}$, and the experimental luminance, ${L}_{exp}$, can be compared in the image. The data indicate that the simulation of the uncalibrated model is not an accurate method to determine the luminance on the road since the experimental luminance levels are much higher than those simulated. As mentioned, this is due to the fact that the road is not as dark as the standard parameters establish. By increasing the Q

_{0}factor the results of the calibrated simulation, ${L}_{cal}$, are closer to the experimental ones. Figure 10 also depicts the luminance calculated using reflection properties of R3 class, ${L}_{uncal\left(R3\right)}$, the typically pavement class used in lighting design.

#### 4.3. Adaptation of the Closest r-Table

^{2}to 0.37 cd/m

^{2}. Furthermore, Table 8 also shows that the CV(RMSE) is reduced by 34%, achieving a value lower than 13% for the calibrated simulation.

## 5. Conclusions

_{0}factor is calibrated in order to evaluate the lightness of the road asphalt using experimental luminance data. This is useful to improve the model by reducing the errors induced by not considering the deterioration of the road. Taking into account that the state of the road is not the same throughout its useful life, it is interesting to re-evaluate the properties of the asphalt every so often, especially before addressing modifications in the lighting system. Results corroborate that it is possible to achieve a CV(RMSE) reduction of 86% for the case study.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Stages of the calibration methodology: calibration variables and external data used for the error calculation.

**Figure 4.**Measurement equipment used to collect luminance and illuminance data: (

**a**) CX-2B imaging luminance meter; (

**b**) Mobilux luxmeter.

**Figure 5.**Position of the luminaires on the roadway and experimental illuminance. Black dots show the distribution of the points at which measurements were taken.

**Figure 7.**Road lighting installation considered to verify the methodology: (

**a**) picture of the real scenario; and (

**b**) luminance image photographed with the luminance meter.

**Figure 8.**Location of the luminaires on the roadway and experimental luminance collected. Black dots show the distribution of the points at which measurements were taken.

**Figure 9.**Illuminance in longitudinal sections of the road. ${E}_{exp}$: illuminance collected experimentally; ${E}_{cal}$ and ${E}_{uncal\left(old\right)}$: simulated illuminance from the calibrated and uncalibrated model; and ${E}_{uncal\left(new\right)}$: simulated illuminance considering recently installed lamps without losses.

**Figure 10.**Luminance in longitudinal sections of the road. ${L}_{exp}$: luminance collected experimentally; ${L}_{uncal\left(R1\right)}$: simulated luminance using the lightness established by default for a R1 road surface; ${L}_{uncal\left(R3\right)}$: simulated luminance using the lightness established by default for a R3 road surface; and ${L}_{cal}$: simulated luminance after the calibration of the Q

_{0}factor.

**Figure 11.**Depiction of the r-table for the standard R1 road surface (

**a**) and the calibrated surface (

**b**).

**Figure 12.**Luminance in longitudinal sections of the road. ${L}_{exp}$: luminance collected experimentally; ${L}_{uncal}$: simulated luminance using the r-table established by default for a R1 road surface after calibration of the Q

_{0}factor; and ${L}_{cal}$: simulated luminance after the calibration of the reduced luminance coefficients of the r-table.

Class | S1 Limit | Table | S1 Standard | Q_{0} Standard |
---|---|---|---|---|

RI | S1 < 0.42 | R1 | 0.25 | 0.10 |

RII | 0.42 ≤ S1 < 0.85 | R2 | 0.58 | 0.07 |

RIII | 0.85 ≤ S1 <1.35 | R3 | 1.11 | 0.07 |

RIV | 1.35 ≤ S1 | R4 | 1.55 | 0.08 |

Mobilux Luxmeter | |

Light intensity range | From 0 to 120 klx |

Light sensor | Silicon photo diode with V(λ) filter |

Light sensitive surface of the diffuser | 8 mm |

Measuring rate | 2 measurements per second |

CX-2B Imaging Luminance Meter | |

Resolution | 1360 × 1024 |

Focal length | 56 mm |

Luminance accuracy | ±5% |

CCD working temperature | 5 °C |

Field of view | 9.1° (horizontal) × 6.7° (vertical) |

**Table 3.**Discrepancies between measuring the position of the luminance meter manually or using the PnP method.

Variable | Measured Value | PnP Value |
---|---|---|

x | 72.000 | 72.002 |

y | 3.500 | 3.568 |

z | 1.000 | 1.083 |

Variable | Design Value | Calibrated Value |
---|---|---|

Maintenance Factor for Lamp 1 | 0.67 | 0.3201 |

Maintenance Factor for Lamp 2 | 0.67 | 0.8481 |

Maintenance Factor for Lamp 3 | 0.67 | 0.7307 |

Statistical Error | Initial Simulation | Calibrated Simulation | Reduction (%) |
---|---|---|---|

CV(RMSE) (%) | 29.73 | 13.11 | 55.90 |

RMSE [lx] | 6.88 | 3.02 | 56.10 |

**Table 6.**Results of the calibration of the reduced luminance coefficient for the four pavement classes of the R-classification.

r-Table | Design Value | Calibrated Value | Statistical Error | Initial Simulation | Calibrated Simulation | Reduction (%) |
---|---|---|---|---|---|---|

R1 | 0.10 | 0.2288 | CV(RMSE) (%) | 130.96 | 19.06 | 85.45 |

R1 | 0.10 | 0.2288 | RMSE (cd/m^{2}) | 1.73 | 0.58 | 66.47 |

R2 | 0.07 | 0.2048 | CV(RMSE) (%) | 191.52 | 25.73 | 86.57 |

R2 | 0.07 | 0.2048 | RMSE (cd/m^{2}) | 2.02 | 0.79 | 60.89 |

R3 | 0.07 | 0.2018 | CV(RMSE) (%) | 185.30 | 39.41 | 78.73 |

R3 | 0.07 | 0.2018 | RMSE (cd/m^{2}) | 2.03 | 1.25 | 38.42 |

R4 | 0.08 | 0.2122 | CV(RMSE) (%) | 162.32 | 47.88 | 70.50 |

R4 | 0.08 | 0.2122 | RMSE (cd/m^{2}) | 1.98 | 1.55 | 21.72 |

Variable | Design Value | Calibrated Value | Variable | Design Value | Calibrated Value |
---|---|---|---|---|---|

$a\left(\mathsf{\gamma}=0.00\right)$ | 1.000 | 1.286 | $b\left(\mathsf{\beta}=0\right)$ | 1 | 1.188 |

$a\left(\mathsf{\gamma}=14.04\right)$ | 0.800 | 0.947 | $b\left(\mathsf{\beta}=2\right)$ | 1 | 1.188 |

$a\left(\mathsf{\gamma}=26.57\right)$ | 0.667 | 0.717 | $b\left(\mathsf{\beta}=5\right)$ | 1 | 0.937 |

$a\left(\mathsf{\gamma}=36.87\right)$ | 0.571 | 0.663 | $b\left(\mathsf{\beta}=10\right)$ | 1 | 0.607 |

$a\left(\mathsf{\gamma}=45.00\right)$ | 0.500 | 0.618 | $b\left(\mathsf{\beta}=15\right)$ | 1 | 0.506 |

$a\left(\mathsf{\gamma}=51.34\right)$ | 0.444 | 0.655 | $b\left(\mathsf{\beta}=20\right)$ | 1 | 0.500 |

$a\left(\mathsf{\gamma}=56.31\right)$ | 0.400 | 0.582 | $b\left(\mathsf{\beta}=25\right)$ | 1 | 0.500 |

$a\left(\mathsf{\gamma}=60.26\right)$ | 0.364 | 0.541 | $b\left(\mathsf{\beta}=30\right)$ | 1 | 0.500 |

$a\left(\mathsf{\gamma}=63.43\right)$ | 0.333 | 0.448 | $b\left(\mathsf{\beta}=35\right)$ | 1 | 0.500 |

$a\left(\mathsf{\gamma}=68.20\right)$ | 0.286 | 0.294 | $b\left(\mathsf{\beta}=40\right)$ | 1 | 0.500 |

$a\left(\mathsf{\gamma}=71.57\right)$ | 0.250 | 0.228 | $b\left(\mathsf{\beta}=45\right)$ | 1 | 0.500 |

$a\left(\mathsf{\gamma}=74.05\right)$ | 0.222 | 0.137 | $b\left(\mathsf{\beta}=60\right)$ | 1 | 0.500 |

$a\left(\mathsf{\gamma}=75.96\right)$ | 0.200 | 0.100 | $b\left(\mathsf{\beta}=75\right)$ | 1 | 0.500 |

$a\left(\mathsf{\gamma}=77.47\right)$ | 0.182 | 0.091 | $b\left(\mathsf{\beta}=90\right)$ | 1 | 0.500 |

$a\left(\mathsf{\gamma}=78.69\right)$ | 0.167 | 0.083 | $b\left(\mathsf{\beta}=105\right)$ | 1 | 0.500 |

$a\left(\mathsf{\gamma}=79.70\right)$ | 0.154 | 0.077 | $b\left(\mathsf{\beta}=120\right)$ | 1 | 0.500 |

$a\left(\mathsf{\gamma}=80.54\right)$ | 0.143 | 0.072 | $b\left(\mathsf{\beta}=135\right)$ | 1 | 0.500 |

$a\left(\mathsf{\gamma}=81.25\right)$ | 0.133 | 0.133 | $b\left(\mathsf{\beta}=150\right)$ | 1 | 1.029 |

$a\left(\mathsf{\gamma}=81.87\right)$ | 0.125 | 0.125 | $b\left(\mathsf{\beta}=165\right)$ | 1 | 0.890 |

$a\left(\mathsf{\gamma}=82.41\right)$ | 0.118 | 0.118 | $b\left(\mathsf{\beta}=180\right)$ | 1 | 0.500 |

$a\left(\mathsf{\gamma}=82.87\right)$ | 0.111 | 0.111 | |||

$a\left(\mathsf{\gamma}=83.29\right)$ | 0.105 | 0.105 | |||

$a\left(\mathsf{\gamma}=83.66\right)$ | 0.100 | 0.100 | |||

$a\left(\mathsf{\gamma}=83.99\right)$ | 0.095 | 0.095 | |||

$a\left(\mathsf{\gamma}=84.29\right)$ | 0.091 | 0.091 | |||

$a\left(\mathsf{\gamma}=84.56\right)$ | 0.087 | 0.087 | |||

$a\left(\mathsf{\gamma}=84.81\right)$ | 0.083 | 0.083 | |||

$a\left(\mathsf{\gamma}=85.03\right)$ | 0.080 | 0.080 | |||

$a\left(\mathsf{\gamma}=85.24\right)$ | 0.077 | 0.077 |

**Table 8.**CV(RMSE) and RMSE calculated for the initial simulation and the simulation of the calibrated model.

Statistical Error | Initial Simulation | Calibrated Simulation | Reduction (%) |
---|---|---|---|

CV(RMSE) (%) | 19.06 | 12.57 | 34.05 |

RMSE (cd/m^{2}) | 0.57 | 0.37 | 35.09 |

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**MDPI and ACS Style**

Ogando-Martínez, A.; Troncoso-Pastoriza, F.; Eguía-Oller, P.; Granada-Álvarez, E.; Erkoreka, A.
Model Calibration Methodology to Assess the Actual Lighting Conditions of a Road Infrastructure. *Infrastructures* **2020**, *5*, 2.
https://doi.org/10.3390/infrastructures5010002

**AMA Style**

Ogando-Martínez A, Troncoso-Pastoriza F, Eguía-Oller P, Granada-Álvarez E, Erkoreka A.
Model Calibration Methodology to Assess the Actual Lighting Conditions of a Road Infrastructure. *Infrastructures*. 2020; 5(1):2.
https://doi.org/10.3390/infrastructures5010002

**Chicago/Turabian Style**

Ogando-Martínez, Ana, Francisco Troncoso-Pastoriza, Pablo Eguía-Oller, Enrique Granada-Álvarez, and Aitor Erkoreka.
2020. "Model Calibration Methodology to Assess the Actual Lighting Conditions of a Road Infrastructure" *Infrastructures* 5, no. 1: 2.
https://doi.org/10.3390/infrastructures5010002