# An Artificial Neural Network for Analyzing Overall Uniformity in Outdoor Lighting Systems

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## Abstract

**:**

## 1. Introduction

## 2. Street Lighting/Experimental Context

#### The Simulation Software

## 3. Artificial Neural Networks

#### 3.1. ANN Application in Lighting Systems

- (1)
- Adaptive learning: An ability to learn how to do tasks based on the data given for training or initial experience.
- (2)
- Self-Organization: An ANN can create its own organization or representation of the information it receives during learning time.
- (3)
- Real Time Operation: ANN computations may be carried out in parallel, and special hardware devices are being designed and manufactured which take advantage of this capability.
- (4)
- Fault Tolerance via Redundant Information Coding: Partial destruction of a network leads to the corresponding degradation of performance. However, some network capabilities may be retained even with major network damage.

- (a)
- Determination of the effective reflectance of ceiling, room and floor cavities: This is a preliminary requirement for the determination of coefficient of utilization in the zonal cavity method.
- (b)
- Determination of the coefficient of utilization (CU): The CU table is provided for the discrete values of room cavity ratio (RCR), effective reflectance of ceiling cavity (ERCC) and room cavity wall reflectance (RWR) are calculated.
- (c)
- Other areas of application of ANN: In a similar way, the ANN may be used for the determination of correction factors for the coefficient of utilization, utilization factor in the room index method, glare index, correction factor for glare index, direct ratios, light output ratios from polar curves, selection of lighting fixtures. illuminance at any point using photometric data and upward and downward light output ratios.

#### 3.2. ANN Development

- Feed-forward networks: Feed-forward ANNs allow signals to travel one-way only; from input to output. There is no feedback (loops), i.e., the output of any layer does not affect that same layer. Feed-forward ANNs tend to be straightforward networks that associate inputs with outputs. They are extensively used in pattern recognition. This type of organization is also referred to as bottom-up or top-down.
- Feedback networks: Feedback networks can have signals traveling in both directions by introducing loops in the network. Feedback networks are very powerful and can get extremely complicated. Feedback networks are dynamic; their ‘state’ is changing continuously until they reach an equilibrium point. They remain at the equilibrium point until the input changes and a new equilibrium needs to be found. Feedback architectures are also referred to as interactive or recurrent, although the latter term is often used to denote feedback connections in single-layer organizations.
- Network layers: The commonest type of artificial neural network consists of three groups, or layers, of units. A layer of “input” units is connected to a layer of “hidden” units, which is connected to a layer of “output” units. The activity of the input units represents the raw information that is fed into the network. The activity of each hidden unit is determined by the activities of the input units and the weights on the connections between the input and the hidden units. The behavior of the output units depends on the activity of the hidden units and the weights between the hidden and output units. This simple type of network is interesting because the hidden units are free to construct their own representations of the input. The weights between the input and hidden units determine when each hidden unit is active, and so by modifying these weights, a hidden unit can choose what it represents. We also distinguish single-layer and multi-layer architectures. The single-layer organization, in which all units are connected to one another, constitutes the most general case and is of more potential computational power than hierarchically structured multi-layer organizations. In multi-layer networks, units are often numbered by layer, instead of following a global numbering.
- Perceptrons: The perceptron turns out to be a neuron with weighted inputs with some additional, fixed, pre-processing. Units are called association units and their task is to extract specific, localized featured from the input data. They were mainly used in pattern recognition even though their capabilities extended a lot more.

#### 3.3. Feedforward Neural Network (FNN)

- The number of layers
- The number of neurons in each layer
- The activation function
- The training algorithm (because this determines the final value of the weights and biases).

#### 3.4. Number of Layers

#### 3.5. Number of Neurons in Each Layer

#### 3.6. Activation Function of Each Layer

#### 3.7. Training Algorithm

#### 3.7.1. Levenberg-Marquadt Back-Propagation

#### 3.7.2. Scaled Conjugated Gradient Back-Propagation

#### 3.7.3. Gradient Descent with Momentum

#### 3.7.4. Gradient Descent with Adaptive Learning Rate Back-Propagation

#### 3.7.5. Gradient Descent with Momentum and Adaptive Learning Rate Back-Propagation

#### 3.7.6. Gradient Descent Back-Propagation

#### 3.8. Validation Process

- (1)
- Select the two algorithms with the highest regression parameters (R) for the training step
- (2)
- Select the two algorithms with the highest regression parameters (R) for the validation step
- (3)
- Select the algorithm with the lowest values (MSE) in all the processes.

## 4. Experimental Results and Discussion

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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Variable Name | Variable Description |
---|---|

Type of lamp | Mercury Vapor |

High Pressure Sodium Vapor | |

Low Pressure Sodium Vapor | |

Metal Halide | |

LED | |

Luminaire arrangement | Unilateral |

Paired | |

Quincunx | |

Power of the lamp | Power consumed divided by the time it takes to consume [w] |

Width of the lamp | Physical dimension of the lamp [cm] |

Interdistance | Distance between two luminaires [m] |

Spacing between luminaire and road | Distance between the lights and the road [m] |

Mounting height | Data Lamp height [m] |

Arm length | Length of the arm supporting the lamp [m] |

Tilt arm | Tilt arm supporting the lamp [degrees] |

System flux | Measure of perceived light output [lumen] |

Lamp flux | Power emitted by a light source as visible radiation [lumen] |

Colour temperature | Temperature of an ideal black-body radiator that radiates light of comparable hue to the light source [°K] |

Luminaire power | Power of the complete lighting unit [w] |

Training Methods | Step | MSE | R |
---|---|---|---|

Levenberg-Marquardt back-propagation | Training | 0.0123 | 0.6644 |

Validation | 0.0095 | 0.8997 | |

Testing | 0.0516 | −0.0531 | |

Scaled conjugate gradient back-propagation | Training | 1.6627 | 0.1063 |

Validation | 0.3712 | 0.8983 | |

Testing | 0.0146 | 0.6128 | |

Gradient descent with momentum | Training | 0.5760 | −0.3032 |

Validation | 0.0503 | −0.8773 | |

Testing | 0.0535 | −0.0212 | |

Gradient descent with adaptive lr back-propagation | Training | 4.3641 | 0.3517 |

Validation | 4.0630 | 0.1115 | |

Testing | 0.1268 | 0.3491 | |

Gradient descent w/momentum & adaptive lr back-propagation | Training | 6.0454 | −0.0046 |

Validation | 0.0305 | 0.3640 | |

Testing | 0.2339 | −0.3598 | |

Gradient descent back-propagation | Training | 0.0155 | 0.6747 |

Validation | 0.0054 | 0.8820 | |

Testing | 0.3753 | 0.8123 |

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## Share and Cite

**MDPI and ACS Style**

Corte-Valiente, A.D.; Castillo-Sequera, J.L.; Castillo-Martinez, A.; Gómez-Pulido, J.M.; Gutierrez-Martinez, J.-M.
An Artificial Neural Network for Analyzing Overall Uniformity in Outdoor Lighting Systems. *Energies* **2017**, *10*, 175.
https://doi.org/10.3390/en10020175

**AMA Style**

Corte-Valiente AD, Castillo-Sequera JL, Castillo-Martinez A, Gómez-Pulido JM, Gutierrez-Martinez J-M.
An Artificial Neural Network for Analyzing Overall Uniformity in Outdoor Lighting Systems. *Energies*. 2017; 10(2):175.
https://doi.org/10.3390/en10020175

**Chicago/Turabian Style**

Corte-Valiente, Antonio Del, José Luis Castillo-Sequera, Ana Castillo-Martinez, José Manuel Gómez-Pulido, and Jose-Maria Gutierrez-Martinez.
2017. "An Artificial Neural Network for Analyzing Overall Uniformity in Outdoor Lighting Systems" *Energies* 10, no. 2: 175.
https://doi.org/10.3390/en10020175