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Volume : 44

Part : 2

SB - 19/1/26SB - 19/1/26Proceedings of the Institute of Acoustics

 

 

Modeling the uncertainties of wind farm noise predictions

 

Bill Kayser1, David Ecotière, UMRAE, Cerema, Université Gustave Eiffel, Strasbourg, France

Benoit Gauvreau, UMRAE, Université Gustave Eiffel, Cerema, Bouguenais, France

 

ABSTRACT

 

Representative predictions of wind turbine noise require to accurately model the main mechanisms and characteristics of acoustic emission (i.e. extended sound source with aeroacoustic noise generation) and acoustic propagation in outdoor environment (i.e. ground effects and atmospheric properties). As these phenomena fluctuate over time and space, it leads to great uncertainty on Sound Pressure Level (SPL) estimated at local resident buildings/facades. Such uncertainty is not yet properly quantified by engineering noise prediction models. Thus, this paper presents a modeling tool developed in the framework of the French project PIBE, which aims at quantifying the SPL uncertainty involved in wind farm noise predictions. Ultimately, this modeling tool will be freely available online and will help to better understand the risk of noise pollution at each stage of a wind farm’s life, in order to guarantee compliance with the regulatory requirements concerning the exposure of local populations.

 

1. INTRODUCTION

 

The objective of this paper is to present a method of uncertainty quantification of SPL spread in presence of a wind turbine farm. To do so, the estimation of SPL at a receiver takes into account the aeroacoustic sources at the blades of the wind turbines, [1–3], as well as propagation phenomena between thoses sources and the receivers, i.e. meteorological and ground effects. Such environmental phenomena fluctuate over both time and space, which lead to variable SPL at long range [4–7] and thus to significant SPL uncertainty [8–10].

 

Previous works already focused on sensitivities of environmental parameters in SPL estimation (i.e. determine the parameters that drive uncertainty) [11–13], as well as quantifying SPL uncertainties induced by a single wind turbine for downwind conditions only [14]. This work intends to go further by considering a complete wind turbine farm, even for upwind conditions, which is a key step toward obtaining representative assessments of wind turbine noise.

 

The methodology consists in modeling different scenarios thanks to a stochastic technique based on quasi-Monte Carlo sampling. This allows one to determine the distribution of the SPL induced by the probability distribution of uncertain environmental parameters (e.g. wind properties, ground properties, etc). In practice, thousands of simulations may be required to conduct such uncertainty analysis, which leads to prohibitive calculation costs. As done in [14], one solution is to replace the initial wind turbine noise model by a metamodel that reproduces the expected SPL with highly reduced computational costs and small errors in the SPL estimation. Thus, the metamodel is built to determine the SPL spread at receivers locations in presence of a single wind turbine. Then, the methodology is to conduct uncertainty calculations for each wind turbine of the farm, in order to assess the overall SPL spread at receivers locations near the wind turbine farm.

 

2. THE WIND TURBINE NOISE MODEL

 

2.1. The Source Model

 

The moving monopoles approach [15] is used to model the noise emitted by the wind turbine. It consists in a strip theory that splits each blade into segments of variable chord and span in order to be able to consider a non-uniform incidence flow along the blades. The angle-dependent sound power level of each segment is obtained using Amiet’s theory as detailed in [16]. An attenuation term is used to account for the propagative effects that occurs between the wind turbine and far field receivers. The attenuation term is calculated using a propagation model based on the wide angle parabolic equation (WAPE), derived without the effective sound speed approximation [17]. The summation of the contributions from all blade segments is then performed at the receivers by assuming that all the contributions are uncorrelated [18].

 

The wind turbine has a nominal electrical power of 2.3 MW, a rotor diameter of 93 m, a hub height of 80 m and three blades of 45 m length. The speed of rotation increases linearly from 6 rpm at the cut-in wind speed of 4 m/s measured at the hub height, to 16 rpm at the wind speed of 12 m/s. The reader may refer to [12–14] for details about the wind turbine noise modeling.

 

2.2. Atmospheric Flux Profiles

 

The refraction of the acoustic waves is taken into account through the wind vertical profile U(z) and temperature vertical profile T(z) :

 

 

where Uref (m/s) is the wind speed at height zref (m) above ground level (typical hub height), z (m) is the height above the ground, α is the wind shear factor, T0 (K) is the air temperature at the ground surface, aT (K/m) is a refraction coefficient that determine the influence of temperature profile, and z0 = 0.13hv (m) is the roughness height that depends on vegetation height hv (m).

 

2.3. Atmospheric Absorption

 

The atmospheric absorption is taken into account in accordance with the standard [19] that depends on air temperature T0 (K), atmospheric pressure patm (Pa) and the relative humidity of air hr (%) chosen here as 80 %.

 

2.4. Atmospheric Turbulence Scattering

 

Althought the WAPE model allows for explicitly modeling turbulence scattering by perturbing the acoustic refractive index [20], a large number of realisations (typically 50-100) are needed to end up with SPL estimation. The computational cost of this technique is too high for uncertainty analysis purpose. It was chosen to correct the SPL attenuation in refracting atmosphere that neglect turbulent scattering (SPLnoscatter), by adding a scattering contribution (SPLscatter), as proposed in Harmonoise project [21, 22]. The attenuation term ∆L is thus given by:

 

 

 

where ω = 2π f with f (Hz) the frequency, r (m) the source-receiver distance, and γT a measure of turbulence strength [22].

 

2.5. Ground Properties

 

The ground influence on sound propagation (sound absorption and scattering by surface roughness) is taken into account using an effective admittance model [12, 23]. The sound absorption is modeled through the Miki’s impedance model [24] that depends on the airflow resistivity parameter σ:

 

 

Note that Miki’s model should be used in the frequency validity domain: f > 0.01 σ / ρ0 [25] where ρ0 = 1.24 kg·m−3 is the density of air.

 

The scattering by ground roughness is taken into account through an effective admittance term (see [14]) that depends on 2 parameters: σh (m) which is the standard deviation of the ground roughness heights and lc (m) which is the correlation length of the horizontal variations of the ground.

 

3. METAMODELING

 

The objective of the metamodel is to reproduce the behavior of the original physic-based model with a reduced computation time (a fraction of a second for each calculation) and reasonable accuracy (less than 1 dB of error). The output of the physic-based model is a 2D (x,z) SPL map with x ∈ [500; 3000] m and z ∈ [0; 10] m, with a resolution of 0.5 m. A direct application of metamodeling is to reproduce the behavior of each acoustic receiver using a statistical emulator, which in itself would not drastically reduce computation time because of the excessive number of receivers considered (5001 in x × 20 in z = 100020 receivers). Thus, the SPL maps need to be represented by a limited number of scalars (i.e. on the order of ten), which will become the emulated quantities. The method consists of three steps, as detailed in [14] and recalled below.

 

3.1. Training Sample

 

The first step of building the metamodel is to generate a training sample Y composed of N SPL maps calculated with the physic-based model. The N SPL maps explore the input set space of the physic based model thanks to a Latin-Hypercube Sampling [26]. The centered training sample is created by removing the mean of the training sample from each SPL map y in the full training sample Y.

 

3.2. Output Dimension Reduction

 

Reduction of dimension of the physic-based model outputs through a principal component analysis [27] of the centered training sample . Then, each SPL map y can be defined as a linear combination of principal components Ψ on a reduced subspace such that y =Σa × Ψ. Each principal component Ψ can be represented in the same form as an SPL map (5001 × 20 elements, they can be seen as "elementary maps"), and the scalar members of a are coefficients that represent the weight of each component Ψ in the SPL map y.

 

3.3. Kriging Interpolation

 

For each new SPL map calculation, it is only necessary to determine the coefficients a because the principal components Ψ are already known. A fast statistical emulator based on kriging interpolation [28] is then used to emulate the relation between the projection coefficients a and the inputs X. Krigin interpolation is a linear interpolation method (meaning that predictions at a target point are linear combinations of the training data), that is unbiased so that the predictions at training points match with the data.

 

4. UNCERTAINTY ANALYSIS

 

The objective of uncertainty analysis is to determine the probability distribution ℙ(y) of the output y of the model (i.e. SPL), induced by the probability distributions ℙ(X) of the uncertain parameters X (i.e. environmental parameters). The distribution ℙ(y) is estimated numerically by sampling the distributions of the inputs ℙ(X) to propagate the uncertainty of the inputs X.

 

4.1. Input Parameters Interval Values

 

The input parameters interval values are chosen to be representative of wind turbine context, for temperate climate. The table 1 presents these intervals.

 

Quasi-Monte Carlo Sobol sequences [29] are then used to generate samples distributed according to the probability distributions of these input parameters ℙ(X). The Sobol sequences are deterministic versions of the Monte Carlo method that provide a faster convergence, up to a factor of 10 compared to the classical Monte Carlo method, with a lower discrepancy [30]. When the distribution laws of the input parameter are not known, we recommend using a uniform distribution so as not to favor any particular condition. It should be noted that this choice of uniformity may lead to overestimation of the uncertainties.

 

4.2. Uncertainty Analysis for a Whole Wind Farm

 

The metamodel is built to model the SPL emitted by a single wind turbine, in a 2D (x,z) domain where x ∈ [500; 3000] m and z ∈ [0; 10] m. In order to assess the SPL uncertainty for a whole wind

 

Table 1: Set of inputs X, whose interval values are chosen to be representative of wind turbine context and temperate climate conditions.

 

 

farm, the methodology is to conduct uncertainty analysis for each wind turbine of the farm. Then, the contributions of each wind turbine i is considered at the receivers of interest, taking into account the different propagation angles θi  between the wind turbines and the receivers. The Figure 1 illustrates this approach.

 

 

Figure 1: Schematics of the methodology for a wind farm composed of 2 wind turbines.

 

5. CONCLUSIONS

 

This work takes place in the context of uncertainty estimation of wind turbine noise. This paper presented a methodology in order to build a fast metamodel for wind turbine noise estimation. The metamodel will consider bot downwind and upwind conditions, and its low computational cost will allow to perform uncertainty analysis for a whole wind turbine farm. Ultimately, the metamodel will be freely available as an online tool, which will help to better understand the risk of noise pollution of wind farms.

 

ACKNOWLEDGEMENTS

 

This research is funded by the French National Agency for Research in the framework of the PIBE project (contract ANR-18-CE04-0011).

 

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1 bill.kayser@cerema.fr