# Application of Artificial Neural Networks for Noise Barrier Optimization

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Environmental Noise Impact Assessment

#### Parameters for Measuring Traffic Noise

#### 2.2. The Urban Stretch of Highway BR-476 as the Object of Study

#### 2.3. In Situ Modeling

#### 2.4. Design of Experiments

^{k}full factorial design, i.e., with two controllable variables and with k = 2 levels. The levels were raised from the minimum (−1) to the maximum (1). The area of acoustic shadow, with an average level of 55 dB(A), and the sound attenuation calculated from the Transmission Loss (TL) [39] were considered responses and were defined as:

^{2}factorial DoE, Table 5 shows the relationship between natural and coded levels, indicating the factors that are controllable during the design phase. The simulated responses were therefore based on combinations of these two controllable factors.

#### 2.5. Artificial Neural Networks

_{1}and y

_{2}responses listed in Table 6, a specialized neural network was trained with only 1 neuron in the output layer. Table 7 shows the configuration of the ANNs that were trained.

^{2}. This is the most important metric to be evaluated when comparing the performance of the ANNs and the DoE.

_{eq})

_{mean}, was calculated for each topology. The following steps were carried out:

- (i)
- 50 independent training sessions were performed for each topology shown in Table 7. The spatial weights matrix was reset to zero in each new training session. The normalized mean square error (MSE) training performance indicator of each training session was stored as MSE(i), with i = 1 up to 50.
- (ii)
- The simple average of the set of 50 MSE values corresponding to the training session of the previous step was calculated for each of the 5 topologies shown in Table 6. This average value was calculated as: ${\mathrm{MSE}}_{\mathrm{mean}}=(1/50){\sum}_{\mathrm{i}=1}^{50}\mathrm{MSE}(\mathrm{i}).$
- (ii)
- It was checked whether the MSE(i) of each of the 50 trained neural networks was greater than the MSE
_{mean}value. If the MSE(i) < MSE_{mean}, then this MSE(i) network was added to the new optimized MSE_{opt}set. - (iv)
- The simple average of this new MSE
_{opt}set was calculated, thus generating the (ANN_{eq})_{mean}.

_{eq})

_{mean}, was derived. In contrast, the original PM calculates the significance based only on the maximum value of the profile curve for each input variable.

## 3. Results and Discussion

#### 3.1. Assessment Results

^{2}, according to Curitiba Municipal Law No. 10625 [35] and the Brazilian standard NBR-10151 [34] Noise Assessment in Communities, in terms of acceptable percentages: from 0% to 20%—clearly polluted; from 21% to 50%—partially polluted, from 51% to 70%—slightly polluted, and from 71% to 100%—ideal.

#### Current Situation

#### 3.2. Implementation Phase

#### 3.3. Operationalization Phase

#### 3.4. Environmental Impact Matrix

#### 3.5. Significance Analysis of the Design of Noise Barriers–A Qualitative Approach

^{2}= 0.928. It should also be noted that the greatest absolute difference between the measured and simulated noise levels was 3.3 dB(A), which is in line with the condition that the difference should not exceed ±4.6 dB(A).

#### 3.6. Significance Analysis of the Design of Noise Barriers—Quantitative Approach

#### 3.6.1. Significance Analysis Using DoE

^{2}= 0.7454 and R

^{2}= 0.9621 were obtained for TL and AS, respectively.

#### 3.6.2. Significance Analysis Using ANNs

_{eq})

_{mean}values after optimization than those of the networks without MSE optimization. Moreover, after optimization, the Pearson R

^{2}correlation levels (R

^{2}

_{eq})

_{mean}were close to 1, whereas before the optimization the mean value was 0.73.

#### 3.6.3. Comparison of DoE and ANN

^{2}= 0.9995, obtained by the regression of DoE-z versus ANN-z. Thus, the points in the graphs of Figure 10 which are farthest away from the source correspond to the strongest impacts on the response. Figure 10b therefore clearly indicates that the significance of the coded interaction factor AB is low when compared to factors A and B, which is the same result as that obtained by the DoE. This finding is in agreement with the literature, as shown by Montgomery [38], that the magnitude of the interaction effects are generally lower.

## 4. Conclusions

^{2}= 0.99887 and R

^{2}= 0.9877. Thus, for each response variable (TL and AS), the ANN-z and the DoE-z revealed the same ranking, i.e., in order of significance: B, A and AB for the response variable TL, and A, B, and AB for the response variable AS. Thus, the results conclusively indicated that the TL of an acoustic barrier is more strongly influenced by the absorption coefficient of the barrier than by its height, while the AS is more influenced by the height of the barrier than by its absorption coefficient. These results are extremely relevant, since the ANNs used here had not been taught the physics required to calculate sound absorption and sound attenuation. The results were thus obtained based on only the system’s input and output data, indicating the independent linearity given by the non-parameterization of the variables. This method for significance testing using ANNs can be extrapolated to other areas of environmental acoustics and noise control.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Simulation of noise levels in the implementation phase of the highway urbanization project: Earthmoving works in the surroundings of Medianeira School.

**Figure 3.**Simulation of the operationalization phase of the highway reconstruction project in the surroundings of Medianeira School.

**Figure 6.**Noise map of the current situation—without a noise barrier—of sound propagation in front of the educational establishment, i.e., Medianeira School.

**Figure 7.**Noise map calculated with Medianeira School under different conditions: (

**a**) With a 3 m high raw concrete noise barrier; (

**b**) With a 5 m high raw concrete noise barrier; (

**c**) With a 3 m high raw concrete noise barrier insulated with rockwool; and (

**d**) With a 5 m high raw concrete noise barrier insulated with rockwool.

**Figure 8.**Comparison of the significant effects for: (

**a**) Transmission Loss (TL) as a response; (

**b**) area of Acoustic Shadow (AS) as a response.

**Figure 9.**Comparison of the significance effects for factor “A”—Height of the noise barrier using the Modified Profile Method (MPM) with the application of Linear Regression: (

**a**) Transmission Loss as a response; (

**b**) area of the acoustic shadow as a response.

**Figure 10.**Significance effects of factors “A,” “B”, and “AB” on the z-score scale and correlation of the Design of Experiments (DoE) and Artificial Neural Networks (ANN) results. (

**a**) Transmission Loss as a response; (

**b**) Area of the acoustic shadow as a response.

Zone of Use | Daytime 7:01 a.m.–7:00 p.m. | Evening 7:01–10:00 p.m. | Nighttime 10:01 p.m.–7:00 a.m. |
---|---|---|---|

Residential zone | 55 dB(A)* | 50 dB(A) | 45 dB(A) |

Transition and special zones | 60 dB(A) | 55 dB(A) | 50 dB(A) |

Central zone and special sectors | 65 dB(A) | 60 dB(A) | 55 dB(A) |

Industrial and services zone | 70 dB(A) | 60 dB(A) | 60 dB(A) |

Year (*) | Traffic Variables | Established (**) | Condition |
---|---|---|---|

2001 | Percentage of heavy vehicles in relation to total vehicle flow [%] = 31 | 65 dB(A) | Noise polluted |

Mean equivalent sound emission level Leq [dB(A)] = 73 dB(A) | |||

2002 | Percentage of heavy vehicles in relation to the total vehicle flow [%] = 18 | 65 dB(A) | Noise polluted |

Mean equivalent sound pressure level Leq [dB(A)] = 66.8 dB(A) |

Attribute | Qualification |
---|---|

Phase of occurrence | Implementation (work phase); Operationalization |

Area of coverage | Local; Regional |

Nature | Positive; Negative |

Order | First order (direct source); Second order (indirect source) |

Probability of occurrence | Uncertain; Certain |

Duration | Short and medium term; Long term; Immediate |

Importance | Temporary; Permanent |

Possibility of reversal | Minor; Intermediate; Major |

Material * | 250 Hz | 500 Hz | 1000 Hz | 2000 Hz | NRC |
---|---|---|---|---|---|

Smooth Concrete | 0.01 | 0.02 | 0.02 | 0.02 | 0.02 |

Rockwool | 0.50 | 0.5 | 0.52 | 0.60 | 0.53 |

*****)—SoundPlan version 6.2 internal library. NRC: Noise Reduction Coefficient.

Level | Natural Factors | Coded Factors * | ||
---|---|---|---|---|

Barrier Height | NRC | A | B | |

Minimum | 3 m | 0.02 | −1 | −1 |

Maximum | 5 m | 0.45 | +1 | +1 |

*****)—Coded factors A and B stand for the natural factors barrier height and NRC, respectively.

Run | Contrast Input Matrix-X | Output Response Vector–Y | ||||
---|---|---|---|---|---|---|

Mean * | Main Effects | Interaction Effects | Response 1–y_{1} | Response 1–y_{2} | ||

M | A | B | AB | TL | AS | |

1 | 1 | −1 | −1 | 1 | y_{11} | y_{21} |

2 | 1 | 1 | −1 | −1 | y_{12} | y_{22} |

3 | 1 | −1 | 1 | −1 | y_{13} | y_{23} |

4 | 1 | 1 | 1 | 1 | y_{14} | y_{24} |

*****)—To apply Multiple Linear Regression requires a quadratic matrix to determine the independent regressor (${\mathsf{\beta}}_{0}$) from $\mathsf{\beta}={({\mathrm{XX}}^{\mathrm{T}})}^{-1}\mathrm{y}$. This explains the presence of the mean term (M) in the column of 1’s. TL: Transmission Loss, AS: Acoustic Shadow.

Descriptor | Setups Used in This Work |
---|---|

Architecture | Multilayer Perceptron |

Training method | Supervised |

Topology 1 | 3-5-5-1 |

Topology 2 | 3-10-10-1 |

Topology 3 | 3-15-15-1 |

Topology 4 | 3-20-20-1 |

Topology 5 | 3-25-25-1 |

Topology 6 | 3-30-30-1 |

Training algorithm | Error backpropagation with Levenberg-Marquardt |

Activation Functions on the 1° e 2° hidden layers | Hyperbolic tangent |

Activation function on output layer | Linear Function |

Legislation and Standards | Period | Maximum Value [dB(A)] | % Compliance | Acoustic Situation |
---|---|---|---|---|

Law No. 10625 (SZ-BR-476–special zone of BR-476) | Daytime | 65 | 16 | Clearly polluted |

Law No. 10625 (SEZ–special educational zone) | Daytime | 60 | 0 | Clearly polluted |

NBR-10151 standard (mixed zone) | Daytime | 65 | 16 | Clearly polluted |

NBR-10151 (with special buildings) | Daytime | 55 | 0 | Clearly polluted |

Legislation and Standards | Period | Maximum Value [dB(A)] | % Compliance | Acoustic Situation |
---|---|---|---|---|

Law No. 10625 (SZ-BR-476–special zone of BR-476) | Daytime | 65 | 13 | Clearly polluted |

Law No. 10625 (SEZ–special educational zone) | Daytime | 60 | 0 | Clearly polluted |

NBR-10151 standard (mixed zone) | Daytime | 65 | 13 | Clearly polluted |

NBR-10151 (with special buildings) | Daytime | 55 | 0 | Clearly polluted |

Legislation and Standards | Period | Maximum Value [dB(A)] | % Compliance | Acoustic Situation |
---|---|---|---|---|

Curitiba Law No. 10625 (SEZ) | Daytime | 60 | 13 | Clearly polluted |

NBR-10151 (with special buildings) | Daytime | 55 | 0 | Clearly polluted |

Attribute | Qualification | |
---|---|---|

Phase of occurrence | Implementation | Operationalization |

Area of coverage | Local | Local |

Nature | Negative | Negative |

Order | First order | First order |

Probability of occurrence | Certain | Certain |

Beginning | Immediate | In the short term |

Duration | Temporary | Permanent |

Importance | Major | Major |

Possibility of reversal | Reversible | Reversible |

Run | Run Order | Mean | Main Effects | Interaction Effect | Response | ||
---|---|---|---|---|---|---|---|

M | A | B | AB | TL | AS—m^{2} | ||

1 | 2 | 1 | −1 | −1 | 1 | 6 | 76,551 |

2 | 1 | 1 | 1 | −1 | −1 | 3 | 67,063 |

3 | 4 | 1 | −1 | 1 | −1 | 12 | 76,976 |

4 | 3 | 1 | 1 | 1 | 1 | 9 | 66,920 |

Qualifiers | Topologies | |||||
---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | |

ANN* | 50 | 50 | 50 | 50 | 50 | 50 |

(ANN_{eq})_{mean} | 34 | 34 | 30 | 29 | 30 | 33 |

MSE* | 7.13 | 7.92 | 8.40 | 6.15 | 6.94 | 6.72 |

(MSE_{eq})_{mean} | 4.17 | 3.08 | 1.82 | 1.32 | 1.23 | 4.48 |

R^{2} | 0.88 | 0.74 | 0.71 | 0.90 | 0.70 | 0.67 |

(R^{2}_{eq})_{mean} | 0.99 | 0.96 | 1.00 | 1.00 | 0.99 | 0.80 |

**Table 14.**Comparison of the results of the effects of significance applying ANN and Design of Experiments (DoE).

Qualifiers | Medianeira School | z-Score Results | Error in z-Score | |||||||
---|---|---|---|---|---|---|---|---|---|---|

TL | AS | TL | AS | TL | AS | |||||

DoE | ANN | DoE | ANN | DoE | ANN | DoE | ANN | DoE | ANN | |

A | −1.50 | −0.91 | −4943 | −2274.33 | −0.87 | −0.87 | −1.16 | −1.16 | 0% | −0.07% |

B | 3.00 | 1.70 | 13.50 | −218.17 | 1.09 | 1.09 | 0.62 | 0.57 | 0% | 7.74% |

AB | 0.00 | 0.16 | −199.00 | −203.63 | −0.21 | −0.21 | 0.54 | 0.58 | 0% | −7.72% |

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## Share and Cite

**MDPI and ACS Style**

Zannin, P.H.T.; Do Nascimento, E.O.; Da Paz, E.C.; Do Valle, F.
Application of Artificial Neural Networks for Noise Barrier Optimization. *Environments* **2018**, *5*, 135.
https://doi.org/10.3390/environments5120135

**AMA Style**

Zannin PHT, Do Nascimento EO, Da Paz EC, Do Valle F.
Application of Artificial Neural Networks for Noise Barrier Optimization. *Environments*. 2018; 5(12):135.
https://doi.org/10.3390/environments5120135

**Chicago/Turabian Style**

Zannin, Paulo Henrique Trombetta, Eriberto Oliveira Do Nascimento, Elaine Carvalho Da Paz, and Felipe Do Valle.
2018. "Application of Artificial Neural Networks for Noise Barrier Optimization" *Environments* 5, no. 12: 135.
https://doi.org/10.3390/environments5120135