Noise simulation

---

Introduction: The Nature of Noise and Its Impact on Humans

Noise has long been considered an inevitable byproduct of technological progress. However, its effects on humans extend far beyond mere discomfort.

Prolonged exposure to noise can lead to partial or complete hearing loss. Moreover, noise transmits irritation through the auditory system to the central nervous system, affecting internal organs and the overall functional state of the body. People exposed to noise expend 20% more physical effort in their daily activities.

Noise is particularly dangerous during sleep, as it can provoke nightmares and lead to prolonged nervous agitation upon waking. This can, in turn, cause psychological disorders. Therefore, noise imposes significant social and economic damage.

Noise is generated by mechanical oscillations in an elastic medium. These oscillations produce longitudinal sound waves that propagate through the air, reach our ears, and are perceived by the auditory system. The human ear can detect sounds in a frequency range from 16 to 20,000 Hz.

The sound pressure level is measured in decibels (dB) using the formula:

$$L_p = 20 \cdot \log_{10}\left(\frac{P}{P_0}\right)$$

Where:

• Lp — sound pressure level, dB;
• P — sound pressure of the source, Pa;
• P0 — reference sound pressure (at 1000 Hz, Po = 2 × 10⁻⁵ Pa).

Noise Sources and Their Levels

The main noise sources in urban areas include:

• Stationary sources: Transformer substations, industrial plants, construction equipment, ventilation systems, etc.
• Mobile sources: Cars, trams, buses, trains, and aircraft.

Examples of noise levels:

• Winter forest in calm weather: 0 dB;
• Whispering: 20 dB;
• Conversation: 60 dB;
• Motor vehicles: up to 87 dB;
• Tram: up to 90 dB;
• Railroad: up to 93 dB;
• Industrial plants: 80–100 dB.

In recent years, noise levels in large cities have increased by 10–15 dB.

---

Noise Impact Simulation

As part of a project by the IDU team, a noise impact simulation was developed to analyze anthropogenic effects on urban areas. This solution complements the EcoDonut library, which models pollution in soil and water. The primary goal was to create a resource-efficient method to work with geospatial data and simulate sound propagation.

The output of the method is a geolayer containing polygons with attributes indicating the maximum noise level from the source. The acoustic calculations are based on the physical laws of sound wave propagation.

---

Physical Model

Sound waves propagating in the atmosphere decay as they move away from the source due to:

• Absorption of sound energy by the air;
• Reflection and scattering caused by natural or artificial barriers, such as vegetation.

The sound pressure level (L) generated by a noise source at a distance r is determined by the formula:

$$L = L_p - 20 \cdot \log_{10}(r) - b_a \cdot r - b_{\text{veg}}$$

Where:

• L — sound pressure level at the calculation point, dB;
• Lp — sound pressure level of the noise source, dB;
• r — distance from the noise source to the calculation point, m;
• b_a — air absorption coefficient, dB/m;
• b_veg — noise reduction by vegetation barriers, dB.

Noise reduction by vegetation is calculated using the formula:

$$b_{\text{veg}} = 0.08 \cdot r_{\text{veg}} \cdot \left(\frac{f^{1/3}}{8}\right)$$

Where:

• r_veg — width of the vegetation barrier, m;
• f — sound frequency, Hz.

Air Absorption Coefficient

The air absorption coefficient (b_a) depends on the air temperature and sound frequency. Below is a table showing its values for different frequencies and temperatures (with 60% humidity):

Temperature (°C)	63 Hz	125 Hz	250 Hz	500 Hz	1000 Hz	2000 Hz	4000 Hz	8000 Hz
30	0	0.0002	0.0009	0.003	0.0075	0.014	0.025	0.064
20	0	0.0003	0.0011	0.0028	0.0052	0.0096	0.025	0.083
10	0	0.0004	0.001	0.002	0.0039	0.01	0.035	0.125
0	0	0.0004	0.0008	0.0017	0.0049	0.017	0.058	0.156

---

Method Advantages

The method allows noise impact modeling with consideration for:

• Distance attenuation;
• Influence of natural barriers (vegetation);
• Obstructions like buildings or other solid objects in the sound path;
• Atmospheric parameters such as temperature and humidity.

This approach is efficient for working with large geospatial datasets and provides flexible parameter customization for simulation.

Calculation Algorithm and Example Usage

Key Steps:

1. Calculate the maximum propagation distance.
   Using parameters like the initial source loudness (source_noise_db), target loudness (target_noise_db), and simulation step (db_sim_step), the algorithm computes distances at which sound reaches intermediate loudness levels.

2. Use visibility polygons.
   The "visibility polygon" function identifies zones of direct sound propagation without reflections.

3. Account for reflections.
   "Significant" points from visibility polygons (e.g., those capable of creating reflections) are selected. New visibility polygons are created for subsequent reflections.

4. Handle obstacles.
   Each obstacle has an absorption coefficient. The default value is 0.05 for smooth concrete. Using this coefficient, the algorithm adjusts sound levels after reflections.

Algorithm Complexity

The computational complexity increases with:

• Obstacle geometry complexity. More obstacles result in more reflection points.
• Source and environment characteristics. Greater propagation distances and higher numbers of reflections (reflection_n) require more resources.

Optimization

To accelerate the process:

• Reduce target_noise_db (target loudness).
• Set low reflection_n values (1–3 reflections).
• Simplify obstacle geometry.

---

Example Usage

Below is an example of using the simulate_noise function and a description of its parameters.

# Simulate noise propagation using the `simulate_noise` function

# Parameters:
# - source_points: GeoDataFrame containing the noise sources' coordinates.
# - obstacles: GeoDataFrame describing obstacles (e.g., buildings).
# - source_noise_db: Initial noise level of the source (95 dB in this example).
# - geometric_mean_freq_hz: Geometric mean sound frequency (2000 Hz).
# - standart_absorb_ratio: Obstacle absorption coefficient (default is 0.05, smooth concrete).
# - trees: GeoDataFrame for trees (None if trees are not considered).
# - tree_resolution: Resolution for simulating tree effects (value of 4).
# - air_temperature: Air temperature in °C (set to 20).
# - target_noise_db: Target noise level to simulate (40 dB).
# - db_sim_step: Simulation step for noise reduction (1 dB).
# - reflection_n: Maximum number of reflections (4).
# - dead_area_r: Radius of "dead zones" where reflections are ignored (5 meters).

noise = simulate_noise(
    source_points=start_p,            # Noise source points
    obstacles=obstacles,              # Obstacles
    source_noise_db=95,               # Source noise level
    geometric_mean_freq_hz=2000,      # Geometric mean sound frequency
    standart_absorb_ratio=0.05,       # Obstacle absorption coefficient
    trees=trees,                      # Trees
    tree_resolution=4,                # Tree resolution
    air_temperature=20,               # Air temperature
    target_noise_db=40,               # Target noise level
    db_sim_step=1,                    # Simulation step
    reflection_n=4,                   # Number of reflections
    dead_area_r=5                     # Dead zone radius
)

Results

Let us consider three simulation scenarios for a noise source with a power of 95 dB, an average frequency of 2000 Hz, and an ambient temperature of 20°C:

Scenario 1: Without Trees

The sound wave propagates without considering additional environmental elements. Zones of direct and reflected sound impact are formed solely due to obstacles, such as buildings.

Scenario 2: With Trees

Accounting for trees near the source demonstrates a noticeable reduction in noise levels due to sound absorption by foliage and soil.

Scenario 3: Increased Wall Absorption to 0.5

When the wall absorption coefficient is increased from 0.05 (smooth concrete) to 0.5 (e.g., porous material or vertical gardens), the noise level behind obstacles decreases significantly.