# Dynamic Evaluation of Traffic Noise through Standard and Multifractal Models

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## Abstract

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## 1. Introduction

_{den}(day–evening–night) above 55 dB [1].

_{den}and night noise levels L

_{night}.

_{den}> 55 dB and L

_{night}> 50 dB. For the calculations, HA (high annoyance) and HSD (high sleep disturbance) were used, using dose–effect relations set out in this amending to Noise Directive. Finally, the total number of people (N) affected by these harmful effects (HA and HSD) due to road noise (L

_{den}and L

_{night}) was estimated. These indicators are based on previous works that have been endorsed by the WHO [16,17]. Comparison of figures presented in Table 1 and Table 2, suggests either a growth in noise, or a growth in population, or both. The increase of 33,140 people exposed to L

_{den}> 55 dB and 44,588 people exposed to L

_{night}> 50 dB over these 6 years, warns that something needs to be done to reduce noise.

_{den}, L

_{night}) cannot explain by themselves all the adverse effects that traffic noise causes in the population. For this reason, there is a growing need to explore other characteristics of traffic noise that are also causes of annoyance, sleep disturbances, and health problems, for example, low-frequency noise [18,19,20]. Low-frequency content is relatively more dominant indoors and behind noise barriers where mid-high frequency content is reduced. Paradoxically, even if the overall noise level goes down, the annoyance and complaints from people may increase. Moreover, the high spatial–temporal variability of traffic noise makes it advisable to take into account the possibility of using also other noise indicators that can better assess certain aspects of annoyance not clearly included in the static strategic noise maps [21]. Road traffic noise depends on several well-known factors, such as traffic density, vehicle fleet composition, speed, and speed variations. The road surface and the type of tires should also be considered. When the flow of vehicles involves frequent speed changes, including stop and go conditions, it usually involves the generation of noise events [22,23,24]. This adverse phenomenon can be quantified in terms of the levels and number of these noise events using the maximum noise levels L

_{AFmax}exceeding a threshold or time history of L

_{Aeq},

_{T=1s}

_{.}

## 2. Traffic Noise Standard Model

- -
- Carrying out a noise measurement campaign in a section of an avenue in the city of Bacau that stands out for its importance in the strategic noise map of this agglomeration.
- -
- Generation of a VISSIM traffic model for the avenue, with the traffic conditions identified at the moment when the noise measurements are performed;
- -
- Calculation of noise power of traffic flow using DTNA tool (performed in VISSIM-MATLAB combination);
- -
- Recreation of a virtual sound level meter that mimics the actual position of the microphone during the noise/traffic measurement campaign and estimation of noise levels at that point;
- -
- Noise mapping of the avenue using NMPB (French road traffic noise prediction model) and CNOSSOS (Common Noise Assessment methods developed under the European Commission umbrella);
- -
- Statistical and comparative analysis of the two evaluation methods (measurements and simulation);
- -
- Comparative analysis of the different approaches respects the official strategic noise maps.

#### 2.1. Study Area: Marasesti Avenue in Bacau

_{den}indicator, is 29,251. At the same time, the number of people living exposed to more than 60 dBA for the L

_{night}is 36,189. These people live along several arteries of the city including the Calea Marasesti.

- -
- The surface of the avenue is in good condition and is neutral for the generation of noise.
- -
- The traffic flow includes a small percentage of heavy vehicles, mainly composed of buses.
- -
- The avenue is straight and from the perspective of the measuring point, there are no obstacles (upstream/downstream) between the vehicles passing through the avenue and the microphone.
- -
- The surrounding land surface is flat.
- -
- There are no significant vertical reflective surfaces in the vicinity of the sound level meter.
- -
- Regarding noise zoning and city area, it should be noted that the location is in the downtown of the city, and the land use around the avenue is mainly residential. Although, there is an area that must be considered sensitive.
- -
- Lane width is 3.5 m. Speed limit—50 km/h.
- -
- A traffic light is in the area that makes traffic flow not regular with speed changes.

#### 2.2. Noise Measurement Design

- -
- The position of the microphone was specified following the HARMONOISE methodology [36], 7.5 m from the centerline of the closest lane.
- -
- The measuring point was chosen in front of the stop line of vehicles (the traffic light stop line S–N direction).
- -
- The measurement point was selected away from building facades and vertical walls, and therefore it will not be necessary to correct for reflection.
- -
- The viewing angle of the microphone on the road is greater than 150 degrees.
- -
- The measuring height where the microphone is situated is 1.3 m.

- -
- Noise magnitude (equivalent continuous sound level) is recorded LAeq, T = 1 s. Noise spectra in third-octave bands are also registered but not considered for the study purpose.
- -
- Three measurement campaigns of 1 h and 30 min were carried out on different days. From these campaigns, a record of 1 h duration was extracted (actually a noise time series of 3630 noise data), once all noise anomalies not due to traffic were discarded and it was guaranteed that the vehicle set follows the statistics of the region. When an anomaly is detected, the entire traffic light cycle included is deleted.

- -
- The traffic flow is made up of heavy and light vehicles.
- -
- The capacity of Marasesti Avenue allowed by the traffic signaling cycle and the traffic density at the time of measurement guarantee a fluid traffic flow, far away from congestion.
- -
- The choice of the season of the year in which the noise measurement campaigns are carried out ensures that the tires of the vehicles during the test are not for winter use.

#### 2.3. Complementary Equipment Used to Describe Traffic

- -
- For vehicle speed and acceleration measurements—Radar gun Stalker ATS II + Canon camera.
- -
- For vehicle description and classification of driver’s behavior through video and audio recording—GoPro HERO 2 with a tripod which is a 170° wide-angle lens.

#### 2.4. Dynamic Traffic Noise Assessment (DTNA) Tool

_{WR}is the rolling (tire/road) noise power; A

_{R}and B

_{R}are the coefficients that will change for each frequency band “f” in octaves for each vehicle category; v is the speed of the vehicle, and v

_{ref}is the reference speed.

_{WP}is the propulsion noise power, A

_{P}, B

_{P}, C

_{P}are coefficients that will change for each frequency band “f” in octaves for each vehicle category; v is the speed of the vehicles; v

_{ref}is the reference speed; a represents the acceleration of the vehicle.

_{Aeq}(every 1 s) by the virtual sound level meter, second by second in the analysis time interval (1 h). Figure 3 helps to understand how the noise power distribution, L

_{Aw}, along the avenue, evolves (in this case it was only shown 101 m centered on the measurement point), second by second, during the simulation time. It is interesting to note that the traffic light situation and the duration of the traffic light cycle can be deduced from the graph itself, paying attention to the patterns (periodicities) revealed in the space–time distribution of noise power emissions.

_{Aw}(t, s), the radiated power per meter, and, per second, at 101 m around the measurement point (s = 51 m where is the traffic light). The noise power at the source is due to the traffic composition except for motorcycles and other special vehicles. In the case on the left (a), it is shown the rolling noise, on the center the engine noise, and on the right (c) the total power. The “x” axis is the space (s) that coincides from left to right with the S–N direction. The “y” axis represents the progression in time (t) from the top (1 s) to the bottom (until 3630 s). The colors represent the sound power level from highest (tending towards yellow) to lowest (tending towards dark blue)

#### 2.5. Local Factors

- A technical description of every vehicle class that participates in traffic flow during the time of noise measurements.
- Credible modeling of actions and interactions between vehicles.
- A detailed description of the network, its traffic control features (i.e., signal timing, signs), and rules.
- A correct geographic layout (UTMx and UTMy coordinates) for the construction of the network.
- Traffic volume and composition of the fleet in every link and node of the network.
- Calibration data (traffic counts distinguishing all modes, speed, the length of queues, etc.).

_{AFmax}record is evaluated for noise action plan purposes.

## 3. Model Results

#### 3.1. Results of the Measurement Campaign Traffic Variables

- -
- The traffic signal program remains the same during all noise measurement campaigns. The total cycle time of 110 s is distributed as follows: 86 s of green time, 4 s of yellow, and 20 s of red.
- -
- The queues of vehicles stopped in front of the traffic light have never exceeded seven vehicles.
- -
- No Medium-Heavy vehicles were detected.
- -
- Motorcycles and special vehicles not of interest in the analysis were not taken into account.

#### 3.2. Results of the Noise Measurements Campaign

#### 3.3. Noise Results Coming from Traffic Noise Simulation in the Selected Area

_{Aeq},

_{T=3630s}= 68.6 dBA, arithmetic mean 65.77 dBA, standard deviation = 5.32 dBA.

#### 3.4. Noise Maps

_{AW}(noise power per meter) remains constant along the avenue. Examining the average sound power along the 401 m of the simulated path during the 3630 s of analysis, it can be extracted that the noise fluctuations describe a periodicity that corresponds to the traffic light period.

## 4. Analysis and Discussion

#### 4.1. Validation of the Model Using Noise Variations within Inter-Cycles of Traffic Lights

_{Aeq},

_{T=1s}= 102.9 dBA), which are due to ambulance sirens and high power motorcycles, the distribution shown in Figure 7 was obtained. It has an asymmetrical shape with two humps. This distribution shape allows understanding that there are at least two sources of noise in the area and that it has two mixed distributions. The first and most important source caused by the traffic on the avenue as it passes through the measuring point could be visually assigned at approximately 68 dBA. The second, the background noise, is the noise caused in the moments in which by different causes the main noise is turned off and loses importance. Then, not from other avenues and the Marasesti avenue itself but out of the limits of the 401 m analyzed, etc. This begins to stand out in special situations when there is no traffic in the area near the sound level meter, or, for example, when the traffic light is red, with the vehicles stopped.

- Splitting both time series (simulated and real) into intervals of 110 s, which coincide with the red-green-yellow-red traffic signal cycle, in such a way that it extract both the L
_{Aeq}, for each of the cycles (inter-cycles analysis). - The cycle of the passage of the ambulance was eliminated from the real series measured, not only by the anomaly detected but because the traffic is altered, and the normal flow of vehicles is altered by the presence of the ambulance.
- It was added energetically to the simulated data series, 50 dBA, which corresponds to the lowest and prolonged L
_{Aeq}level of background noise measured during the measurement period. This also eliminates the presence of zeros. Another possibility (not contemplated in this study) is to take into account only the green time in the analysis. - Noise data is energetically averaged within each cycle.

_{Aeq}of the estimated traffic flow for each of these cycles. After processing the data, Figure 12 shows the distribution of the new series.

_{o}is the null hypothesis whose formulation is “The two series are part of the same population and their distribution is identical”, this would be the evidence that the results of the simulation are representing acoustically what is happening on the Bacău’s Marasesti Avenue. A Kolmogorov–Smirnov test for two independent samples SPSS results is presented (Table 5).

_{o}cannot be rejected. Therefore, it can be affirmed that both data series belong to the same process and it can be affirmed with a 95% level of significance that the simulated series perfectly predicts the results obtained directly from the environmental noise measurements. Mann–Whitney and Wald–Wolfowitz tests both for independent samples confirmed the result.

#### 4.2. Dynamic Maps for Action Plans Using Noise Variations within Intra-Cycles of Traffic Lights

## 5. Multifractal Model

#### 5.1. From Differentiability to Nondifferentiability in a Hydrodynamic Approach

^{l}is the spatial coordinate of multifractal type, t is the temporal coordinate of a non-multifractal type which is also an affine parameter of the movement curves, $\lambda $ is a parameter associated with the multifractal–non-multifractal scale transitions, $f\left(\alpha \right)$ is the singularity spectra of $\alpha $ order of the multifractal dimension D

_{F}and $\alpha $ is the singularity index of the multifractal dimension [53,57,58]. Moreover, Equation (3) corresponds to the multifractal conservation law of specific momentum and Equation (4) corresponds to the multifractal conservation law of state density.

_{F}< 2 for correlative processes, D

_{F}> 2 for noncorrelative processes etc. In such a conjecture, operating with the singularity spectrum f(α) it is possible to identify not only the “areas” of the complex fluid dynamics that are characterized by a certain multifractal dimension, but also the number of “areas” whose multifractal dimensions are situated in an interval of values. Moreover, through f(α) it is possible to identify classes of universality in the complex fluid dynamics laws, even when regular or strange attractors have different aspects [57,58].

#### 5.2. Acoustic Waves Approximation of Multifractal Type

^{,}” the perturbed values, and ${c}_{s}$ the velocity of the acoustic wave in the complex fluid. By operating with these relations in Equations (7) and (8), and using the procedure from [48], we obtain the propagation equation of the acoustic waves of multifractal type:

_{F}= 2, and $\lambda =\raisebox{1ex}{$h$}\!\left/ \!\raisebox{-1ex}{$2{m}_{0}$}\right.$, where h is the Planck constant and m

_{0}is the rest mass of the complex fluid structural units) the generating condition of “Acoustic Black Hole” implies:

#### 5.3. Pulsation–Velocity Correlation through Patches of Riemann Type

## 6. Model Results Analysis

## 7. Conclusions

_{Aeq}of the total traffic which passes through the avenue and the simulated noise data L

_{Aeq}of the total traffic of the same avenue generated with the dynamic traffic noise simulation method, are equal. The validation of the dynamic traffic noise assessment tool shows that this traffic noise prediction method is suitable for the evaluation of action plan effectiveness against urban noise, and specifically, this has been proven for the city of Bacau when cars use summer tires. The mathematical model was developed based on Cayley–Klein-type absolute geometries that implied harmonic mappings between the usual space and the Lobacevsky plane in a Poincaré metric. This allowed studying the isomorphism of two groups of SL(2R) type, and through Stoka formalism showcased joint invariant functions that allow associations of pulsations–velocities manifolds type. Based on the complexity of our model and its multitude of degrees of freedom, the multifractal approach can be used through the fractality degree of each acoustic wave to simulate external constraints that can be found in real ones. Therefore, the multifractal approach of acoustic waves propagation and their sources in the traffic area offers another perspective of traffic noise interpretation and simulation.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**3-D representation of the study area imported from CADNA (Computer Aided Noise Abatement software).

**Figure 2.**Camera for video-audio recording and the sound level meter B&K 2270 (

**a**). Radar gun Stalker ATS II and Canon camera (

**b**).

**Figure 6.**Noise measurements in the exterior once the anomalies produced by ambulances, sirens, motorcycles, and other events that cannot be simulated in VISSIM have been corrected.

**Figure 7.**L

_{Aeq},

_{T=1s}distribution per noise level classes, once the noise anomalies have been corrected.

**Figure 8.**The 3630 values of L

_{Aeq},

_{T=1s}recorded by the virtual sound level meter located in the same position as the real one shown in Figure 2.

**Figure 10.**L

_{Aeq},

_{T=1h}noise map built with collected traffic information recovered during the measurements campaign. On the left (

**a**), the map prepared with the provisional traffic noise model NMPB06. On the right (

**b**), the map prepared with the current traffic noise model CNOSSOS.

**Figure 11.**Mapping the noise variations within traffic light intra-cycles. The figures show the averaged lower (

**a**) and higher (

**b**) noise level maps (two of the 110 possible) during the hour of simulation.

**Figure 12.**Distribution of L

_{Aeq}, T = 110 synchronized with the traffic light for both the simulated series (red) and the series measured (in blue) corrected for the anomalies.

**Figure 13.**Sound pressure level difference along the Marasesti Avenue between the maximum (in blue) and minimum (in red) intra-cycle noise maps with respect to the noise map carried out with the averaged traffic data for the measurement interval and without the presence of the traffic light.

**Figure 14.**Time-series of $Re{h}_{c0}$ for different values of $\Omega $ and $r$: (

**a**) $\Omega =7.8,r=0.1;0.5;0.9$; (

**b**) $\Omega =9.7,r=0.1;0.5;0.9$.

**Figure 15.**Simulated noise generate by combinatorial mixing of single-fractal systems from the multifractal theoretical model by superposition of signals (

**a**) and polynomial mixing (

**b**).

**Table 1.**Summary of results L

_{den}and L

_{night}of exposure to noise to traffic noise within the Bacau urban area [14].

Number of People Exposed to Different Noise Levels (L_{den}) | Number of People Exposed to Different Noise Levels (L_{nigh}_{t}) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

Year | 55–59 dB | 60–64 dB | 65–69 dB | 70–74 dB | >75 dB | 50–54 dB | 55–59 dB | 60–64 dB | 65–69 dB | >70 dB |

2012 | 19,800 | 25,800 | 21,500 | 20,000 | 9200 | 21,800 | 20,800 | 19,200 | 16,000 | 1000 |

2018 | 34,912 | 36,654 | 36,635 | 19,541 | 1698 | 34,496 | 31,991 | 25,802 | 4769 | 10 |

**Table 2.**Summary of results of the total number of people affected by the harmful effect due to traffic noise within the Bacau urban area.

High Annoyance (HA) Strategic Noise Map Indicator (L _{den}) | High Sleep Disturbance (HSD) Strategic Noise Map Indicator (L _{night}) | |||
---|---|---|---|---|

Year | Total number N of people at risk of a harmful effect due to traffic noise | Percentage of people at risk of a harmful effect due to traffic noise for L_{den} greater than 55 dB | Total number N of people at risk (AR) of a harmful effect due to traffic noise | Percentage of people at risk of a harmful effect due to traffic noise for L_{nigh}_{t} greater than 50 dB |

2012 | 2286.1 | 0.2374 | 7031.5 | 0.2901 |

2018 | 2705.6 | 0.2090 | 7463.6 | 0.2787 |

Traffic Flow Direction | No. of Cars (during 1 h) | No. of Heavy Vehicles (during 1 h) |
---|---|---|

N–S carriageway | 814 | 20 |

S–N (carriageway close to the sound level meter) | 770 | 20 |

Driving Behavior Type | Cruising Speed (km/h) | Percentage of Cars |
---|---|---|

Calm | <45 | 23% |

Normal | 45–55 | 43% |

Aggressive | >55 | 34% |

Variable | Group | N |
---|---|---|

L_{Aeq,T=110 s} | 1. Simulation | 34 |

2. Measurement | 34 | |

3. Total | 68 |

Variable L_{Aeq},_{T=110 s} | ||
---|---|---|

Maximum limit differences | Absolute | 0.283 |

Positive | 0.283 | |

Negative | −0.029 | |

Z Kolmogorov–Smirnov | 1.119 | |

Sig. Asymptotic (bilateral) | 0.163 | |

a. Group variable: GROUP |

Complex Fluid | Particle Mass (kg) | Particle Radius (m) | Diffusion Coefficient (m^{2}/s) | Collapse Length of the Acoustic Wave (m) |
---|---|---|---|---|

Electronic fluid | ~10^{−30} | ~3 × 10^{−4} | ~10^{−7} | |

Ionic fluid | ~10^{−27} | ~3 × 10^{−7} | ~10^{−10} | |

Tropospheric fluid with particles of various sizes and densities | 10^{−8} | 1.56 × 10^{−4} | ~10^{−5} | |

10^{−7} | 2.53 × 10^{−6} | ~10^{−7} | ||

10^{−6} | 1.29 × 10^{−6} | ~10^{−9} | ||

10^{−5} | 1.19 × 10^{−8} | ~10^{−11} |

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**MDPI and ACS Style**

Petrovici, A.; Cueto, J.L.; Nedeff, V.; Nava, E.; Nedeff, F.; Hernandez, R.; Bujoreanu, C.; Irimiciuc, S.A.; Agop, M.
Dynamic Evaluation of Traffic Noise through Standard and Multifractal Models. *Symmetry* **2020**, *12*, 1857.
https://doi.org/10.3390/sym12111857

**AMA Style**

Petrovici A, Cueto JL, Nedeff V, Nava E, Nedeff F, Hernandez R, Bujoreanu C, Irimiciuc SA, Agop M.
Dynamic Evaluation of Traffic Noise through Standard and Multifractal Models. *Symmetry*. 2020; 12(11):1857.
https://doi.org/10.3390/sym12111857

**Chicago/Turabian Style**

Petrovici, Alina, Jose Luis Cueto, Valentin Nedeff, Enrique Nava, Florin Nedeff, Ricardo Hernandez, Carmen Bujoreanu, Stefan Andrei Irimiciuc, and Maricel Agop.
2020. "Dynamic Evaluation of Traffic Noise through Standard and Multifractal Models" *Symmetry* 12, no. 11: 1857.
https://doi.org/10.3390/sym12111857