# Modeling Energy LED Light Consumption Based on an Artificial Intelligent Method Applied to Closed Plant Production System

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

^{−2}s

^{−1}) are the main components of light recipes. Light recipes are commonly configured in continuous mode, but can also be configured in pulsed mode to save energy. Reducing the energy costs of illumination systems in CPPS, and the fabrication of efficient light devices, are challenges for the near future [18].

_{2}were the inputs. The aim was the optimization of the greenhouse process, as well as reducing the disturbance and inadaptability of the system [34].

_{2}levels, among others, in a CPPS. Implemented approaches include computer systems, fluid dynamics, multi-objective evolutionary algorithms (MOEA), Neural Networks, and the predictive control model. However, predictions of energy consumption in artificial lighting systems based on light recipes considering the light operation modes (pulsed and continuous) have not been reported. Hence, it is essential to assume that a challenge for CPPS is to apply strategies to improve energy consumption without affecting crop yield and quality. Aiming to generate new alternatives that may contribute to forecasting CPPS energy consumption, we propose two nonlinear models based on artificial intelligence that support modeling of the energy requirements of the LED lighting. The models include a vector with seven inputs and an output represented by the energy consumption of the CPPS. In the literature, no proposal has yet considered the components of light (red, blue, green, and white) and its mode of operation, i.e., continuous or pulsed (i.e., intensity, pulse frequency, and duty cycle). The first model uses genetic programming (GP), and the second feedforward neural networks (FNNs). We applied and compared these techniques in the generation of nonlinear models because they have been used for this propose [35,36,37,38,39,40,41]. This research applies 10-fold cross-validation to select the training complexity parameters because this approach almost eliminates the bias of the estimated error [42,43,44,45,46]. Ten-fold cross-validation is the most widely used in the literature because, even with random sampling, it reflects the behavior in the original dataset. Furthermore, it has been shown that any increase in the number of folds beyond 10 only increases computational effort, while slightly reducing the variance in the results owing to the number of folds does not impact the dataset distributions [42,44,46].

^{2}), and One-Way Analysis of Variance (ANOVA). The GP and FNNs models generated in this proposal can be applied or programmed as part of a monitoring system for CPPS which prioritize energy efficiency.

## 2. Materials and Methods

#### 2.1. Lighting System Characteristics

#### 2.2. Experimental Setup

^{−2}s

^{−1}and the frequency was set at 100, 500, and 1000 Hz with duty cycles of 40%, 50%, 60%, 70%, 80%, 90% for each treatment (see Figure 1a). The second dataset was constructed with the design of four different light recipes (circles at the bottom of Figure 1a) at intensities of 60, 70, 85, 90, 100, 120, 130, 150, 160, 180 µmol m

^{−2}s

^{−1}, frequencies of 100, 500, and 1000 Hz, and with randomly selected duty cycles of 60%, 70%, and 80%, as shown in Table 2. The general configuration and control of the illumination system are shown in Figure 1b. We selected the inputs and output, splitting the dataset in 80% for training and 20% for testing. The training stage fixes the algorithm’s parameters with ten-folds cross-validation to obtain the best predictions of energy consumption through the light recipes shown in Figure 1c. Triplicate experiments for all conditions were carried out with both continuous and pulsed LED light modes.

#### 2.3. Energy Consumption

#### 2.4. Nonlinear Test of Energy Consumption in Irradiation LED Lighting System

^{−2}s

^{−1}from Dataset 1.

_{6}); then, if the model is lineal, the following equations should be satisfied: $f({x}_{6}=500\mathrm{Hz})=5f({x}_{6}=100\mathrm{Hz})$ and $f({x}_{6}=500\mathrm{Hz})=f({x}_{6}=100\mathrm{Hz})+f({x}_{6}=100\mathrm{Hz})+f({x}_{6}=100\mathrm{Hz})+f({x}_{6}=100\mathrm{Hz})+f({x}_{6}=100\mathrm{Hz})$. We tested linearity according to the method described in [47], with the light recipe 95R5B at 110 µmol m

^{−2}s

^{−1}and 80% duty cycle from the dataset 1 by considering these axioms that define a linear map.

#### 2.5. Genetic Programming

_{P}) chromosomes with (N

_{O}) operators. After that, the fitness function evaluates the quality of each chromosome (f(x

_{L})). Then, the tournament randomly selects (S

_{T}) chromosomes for the mating pool (M

_{P}), where those with the best fitness generate offspring (O) with crossover operation, as detailed by Poli et al. [36]. Then, the offspring with probability (P

_{M}) is mutated, and two mutation points select the mutated alleles [42,44]. The algorithm runs (N

_{G}) generations and returns the best individual in the population.

#### 2.6. Feedforward Artificial Neural Networks

^{m}

^{+1}is the activation function,

**W**

^{m}

^{+1}is the weight matrix, and

**b**

^{m}

^{+1}the bias matrix in the layer m+1,

**a**

^{m}as the previous neuron output in the layer m, and m = 0, 1…, M−1, where M represents the number of layers [52].

^{m}

^{+1}activation functions are hyperbolic tangent sigmoids (tanh) represented in Equation (3) for hidden layers. Moreover, the linear function indicated in Equation (4) provides approximations with finite discontinuities [52].

**W**

^{m}, corresponding with the $i$ neuron in the $m$ layer and its $j$ input; ${a}^{m-1}{}_{i}$ is the output of the neuron $i$ at layer $m-1$; and ${b}^{m}{}_{i}$ is the bias of the neuron $i$ at layer $m$.

#### 2.7. Spearman’s Correlation

_{value}represents the correlation reliability, i.e., the probability of presenting the correlation [55].

#### 2.8. Procedure for the Construction of the Nonlinear Models

_{value}are selected. Next, it is necessary to train the GP and FNNs models.

_{1}), red light component (x

_{2}), green light component (x

_{3}), blue light component (x

_{4}), white light component (x

_{5}), pulsed frequency (x

_{6}), and duty cycle (x

_{7}) as input variables. Finally, sines and cosines of each variable are used to build Fourier series with which to approximate any function with a finite number of discontinuities [56].

_{G}generations using $MAE(\widehat{y},y)$, and then the best candidate is returned.

^{2}statistic measure used in Equation (10); this is commonly used for scoring regression models, as in [60,61,62]. R

^{2}is in the range of [0,1] with 1 for a regression model that fully explains the variability of the output variable [63]. The second is a box plot that compares, in a graphical representation, the media and quartiles of the analyzed groups. In this case, we tested the GP and FNN errors in a single dimension. The third is one-way analysis of variance (ANOVA), which was used to examine equality between two categorical variables (GP or FNN model) of quantitative outcomes with two or more levels of treatments (with metrics of error including MAE, MSE, SEE, and MAPE) [64].

## 3. Results and Discussion

_{P}= 200, S

_{T}= 20, and P

_{M}= 8%, for a limit of N

_{G}= 5000 generations. We avoided overfitting by selecting the complexity parameters (number of operations per parentheses and the number of parentheses) with 10-fold cross-validation in the training set. The best parameters obtained were 16 operators and 2 parentheses, with a cross-validation MAE of 3.0649, after testing 1−20 operators and 1−2 parentheses.

#### 3.1. GP and FNNs Behavior in Test 1

^{2}). The MAE estimated for the GP model was 1.1239 and 3.0649 in the testing stage for the cross-validated MAE, i.e., a cross-validated error which was higher than the test error, which indicated a model without overfitting. In this context, the FNNs model obtained an accuracy or 1-MAPE, a MAPE, and the average errors between the real output value and a predicted one were 98.99%, 1.01%, and 0.4827 watts (SEE), respectively. The FNNs model effectively explains 99.34% of the variability of the output variable (R

^{2}). The MSE for the ANN model was 0.3007 and 0.8666 in the testing stage for the cross-validated MSE, i.e., a cross-validated error higher than the test error, which indicated a model without overfitting.

#### 3.2. GP and FNNs Models Behavior in Test 2

^{2}). The FNNs model achieved 98.21% accuracy (1-MAPE) and 1.79% error (MAPE); the average error (SEE) between a real output value and a predicted one was 0.6776 watts, which explains 97.79% of the output variability (R

^{2}).

^{2}was superior.

#### 3.3. GP and FNNs Models Statistic Comparison

## 4. Conclusions

^{2}, box plot, and one-way ANOVA with a risk probability of 1.55%. Additionally, FNNs trained faster (6.063 h), in terms of processing all the tested architectures, than GP, which required 169.274 h due to the high computational cost, as noted in the literature.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**General experimental design. (

**a**) Experimental setup for the two datasets. (

**b**) Measuring general scheme. (

**c**) Energy consumption nonlinear models construction.

**Figure 3.**Energy consumption behavior for 95R5B light recipe at 110 µmol m

^{−2}s

^{−1}with different pulsed frequencies and duty cycles.

**Figure 4.**GP model results in Test 1. (

**a**) Data estimated (red) versus energy consumption data measured (blue). (

**b**) Absolute error between estimated behavior and measured energy consumption (red).

**Figure 5.**FNNs model results in Test 1. (

**a**) Data estimated (red) versus energy consumption data measured (blue). (

**b**) Absolute error between estimated behavior and measured energy consumption (red).

**Figure 6.**GP model results in Test 2. (

**a**) Data estimated (red) versus energy consumption data measured (blue). (

**b**) Absolute error between estimated behavior and measured energy consumption (red).

**Figure 7.**FNNs model results in Test 2. (

**a**) Data estimated (red) versus energy consumption data measured (blue). (

**b**) Absolute error between estimated behavior and measured energy consumption (red).

Recipes | Red | Green | Blue | White |
---|---|---|---|---|

95R5B | 95% | 0% | 5% | 0% |

83R17B | 83% | 0% | 17% | 0% |

60R40B | 60% | 0% | 40% | 0% |

57W43B | 0% | 0% | 43% | 57% |

67R11B22G | 67% | 22% | 11% | 0% |

67R33G | 67% | 33% | 0% | 0% |

100W | 0% | 0% | 0% | 100% |

50R50B | 50% | 0% | 50% | 0% |

70R30B | 70% | 0% | 30% | 0% |

30R70B | 30% | 0% | 70% | 0% |

Recipes | Red | Green | Blue | White |
---|---|---|---|---|

60R20G20B | 60% | 20% | 20% | 0% |

40R50B10W | 40% | 0% | 50% | 10% |

40R60B | 40% | 0% | 60% | 0% |

30R10G60B | 30% | 10% | 60% | 0% |

Variables | ${\mathit{x}}_{1}$ | ${\mathit{x}}_{2}$ | ${\mathit{x}}_{3}$ | ${\mathit{x}}_{4}$ | ${\mathit{x}}_{5}$ | ${\mathit{x}}_{6}$ | ${\mathit{x}}_{7}$ | $\mathit{y}$ |
---|---|---|---|---|---|---|---|---|

Slopes | 135.0 | 175.75 | 61.05 | 129.5 | 185.0 | 1000.0 | 90.0 | 34.10 |

Offsets | 50.0 | 0 | 0 | 0 | 0 | 0 | 0.0 | 20.60 |

Variables | ${\mathit{x}}_{1}$ | ${\mathit{x}}_{2}$ | ${\mathit{x}}_{3}$ | ${\mathit{x}}_{4}$ | ${\mathit{x}}_{5}$ | ${\mathit{x}}_{6}$ | ${\mathit{x}}_{7}$ |
---|---|---|---|---|---|---|---|

$\rho $ | 0.9109 | 0.2039 | −0.0219 | 0.2908 | 0.3064 | 0.0891 | 0.0620 |

${p}_{value}$ | 0 | 0 | 0.0990 | 0 | 0 | 0 | 0 |

Technique | MAE | MSE | SEE | MAPE | R^{2} |
---|---|---|---|---|---|

GP | 1.1239 | 2.0691 | 1.4384 | 0.0390 | 0.9267 |

FNNs | 0.3007 | 0.2330 | 0.4827 | 0.0101 | 0.9934 |

Technique | MAE | MSE | SEE | MAPE | R^{2} |
---|---|---|---|---|---|

GP | 1.4508 | 3.3328 | 1.8256 | 0.0465 | 0.8399 |

FNNs | 0.5386 | 0.4591 | 0.6776 | 0.0179 | 0.9779 |

**Table 7.**ANOVA analysis of error metrics MAE, MSE, SEE and MAPE between GP and FNN models for PROB > F(${P}_{value}$ for testing null hypotesis).

Source of Variation | Sums of SQUARES | Degree of Freedom | Mean Square Error | F | PROB > F |
---|---|---|---|---|---|

Columns | 4.6294 | 1 | 4.62938 | 7.59 | 0.0155 |

Error | 8.5407 | 14 | 0.61005 | ||

Total | 13.1701 | 15 |

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**MDPI and ACS Style**

Olvera-Gonzalez, E.; Rivera, M.M.; Escalante-Garcia, N.; Flores-Gallegos, E.
Modeling Energy LED Light Consumption Based on an Artificial Intelligent Method Applied to Closed Plant Production System. *Appl. Sci.* **2021**, *11*, 2735.
https://doi.org/10.3390/app11062735

**AMA Style**

Olvera-Gonzalez E, Rivera MM, Escalante-Garcia N, Flores-Gallegos E.
Modeling Energy LED Light Consumption Based on an Artificial Intelligent Method Applied to Closed Plant Production System. *Applied Sciences*. 2021; 11(6):2735.
https://doi.org/10.3390/app11062735

**Chicago/Turabian Style**

Olvera-Gonzalez, Ernesto, Martín Montes Rivera, Nivia Escalante-Garcia, and Eduardo Flores-Gallegos.
2021. "Modeling Energy LED Light Consumption Based on an Artificial Intelligent Method Applied to Closed Plant Production System" *Applied Sciences* 11, no. 6: 2735.
https://doi.org/10.3390/app11062735