Ben-Hassine, Seif

Chabory, Alexandre

Douvenot, Rémi

Morlaas, Christophe

English

Archive Ouverte en Sciences de l'Information et de la Communication

Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
A Stastistical Model for Assessing the Impact of Wind Turbines on
Conventionnal VOR
Alexandre Chabory, Seif Ben Hassine, Christophe Morlaas, Rémi Douvenot
ENAC, TELECOM-EMA, Toulouse, France
Université de Toulouse, France
e-mail: alexandre.chabory@recherche.enac.fr
December 6, 2019
1/29
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
Plan
1 Introduction
2 VOR Error Simulator
3 Probability Distribution for the Multipath Parameters
4 Statistics of the bearing error
5 Simulation
6 Conclusion
2/29
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
Context
Impact of large size obstacles, such as wind turbines, on VOR performances
Multipath⇒ Error in the azimuth assessed by the aircraft receiver
Existing tools
Two steps
Computation of the multipath characteristics: magnitude, phase, azimuth
⇒ Electromagnetic simulation
Computation of the bearing error
⇒ Use of the Odunaiya expression or a receiver model
Example
VERSO: VOR Error Simulator, developed by ENAC, funded by ENAC and DSNA
Limitations
Require high computationnal resources
Require to perfectly know the configuration
Results are highly dependant on the trajectory:
Modification of the trajectory of order few meters
⇒ Change in the multipath phase
⇒ Change in the bearing error
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Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
Objective
Objective
Propose a statistical model for the bearing error with which
The only parameters are the aircraft and wind turbine positions
The other parameters (wind turbine size, materials, ground composition, ...) follow statistical
distributions
Main steps to develop this model
Determine the statistical distributions associated with the multipath parameters
Determine the statistical distribution associated with the bearing error
Perform Monte Carlo simulations with VERSO to assess the parameters of the statistical
distributions
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Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
Plan
1 Introduction
2 VOR Error Simulator
3 Probability Distribution for the Multipath Parameters
4 Statistics of the bearing error
5 Simulation
6 Conclusion
5/29
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
Plan
1 Introduction
2 VOR Error Simulator
3 Probability Distribution for the Multipath Parameters
4 Statistics of the bearing error
5 Simulation
6 Conclusion
6/29
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
General characteristics of wind turbines
Windturbine characteristics
Mast
Metallic with a possible reinforced-concrete lower
part
Conical shape of height from 60 to 140 m
Hub box
Metallic or dielectric, metallic generator
Ovoid or rectangular shape
Blades
Multilayer dielectric : glass or carbon fiber, epoxy,
mix of materials
Lightning protection thin metallic plate or wire
Used model
Mast: metallic conical section
Nacelle: metallic rectangular box
Blade: Simplified multilayer dielectric structure
Lightning protection: metallic wire
Mesh: multilayer-slab or metallic polygonal facets
α
7/29
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
VERSO : VOR ERror SimulatOr
2-rays model
Planar dielectric ground
Physical optics
Planar dielectric ground
Parabolic equation
Dielectric ground with relief
Input/output
Input
VOR station position and radiation pattern
Positions and characteristics of the wind
turbines
Relief
Aircraft trajectory
Output
Scattered field
VOR error
8/29
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
VERSO : VOR ERror SimulatOr
2-rays model
Planar dielectric ground
Two-rays model
Take into account the ground in the VOR station antenna radiation
Calculation of the direct path
9/29
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
VERSO : VOR ERror SimulatOr
optics
Parabolic equation
Dielectric ground with relief
Parabolic equation
Model the propagation VOR station→ wind turbines
⇒ Grazing incidence, significant influence of the ground relief
Split-step-Fourier parabolic equation method:
The relief is accounted
Only the Forward propagation is accounted
2D model (no lateral effect of the relief)
Atmospheric refraction is accounted
10/29
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
VERSO : VOR ERror SimulatOr
Hybridization
Hybridization
On each polygonal facet of the wind turbine, the incident field is interpolated as a plane wave
11/29
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
VERSO : VOR ERror SimulatOr
Physical optics
Planar dielectric ground
Physical optics
Multilayer-slab or metallic polygonal facets with an incident plane wave
Currents calculation using the physical optics approximation
Fast calculation of the radiation integrals
Hypotheses: large enough wind turbines, no multiple scattering, planar dielectric ground
12/29
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
VERSO : VOR ERror SimulatOr
2-rays model
Planar dielectric ground
Physical optics
Planar dielectric ground
Parabolic equation
Dielectric ground with relief
VOR error
Scattered field are clustered with respect to their azimuth of arrival
⇒ List of multipath: amplitude an, phase θn, azimuth φn
Conventional VOR error formula (a similar formula exists for Doppler VOR)
εC = tan−1
( ∑N
n=1 an cos(θn − θ0) sin(ϕn − ϕ0)
a0 +
∑N
n=1 an cos(θn − θ0) cos(ϕn − ϕ0)
)
13/29
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
In-flight measurement campaign
Figure 1: Windfarm located at 5 km from the VORC
station in Boulogne-sur-Mer.
0 2 000 4 0001 000 3 000 5 000
0
−40
−20
−50
−30
−10
10
Figure 2: Relief from the VOR station to the wind turbines.
Parameters
Antenna of the Boulogne-sur-Mer VORC
(113.8 MHz)
9 wind turbines on 3 radials
Mast : ground diameter = 7.5 m, top
diameter = 2 m, height = 98 m
Nacelle : 4 m× 11 m× 4 m
Blades : length = 35.5 m
Three in-flight campaigns:
Without wind turbines up to a distance of
15 km from the VOR (May 2009) ;
With wind turbines masts at approximately
5 km from the VOR (July 2012) ;
With complete wind turbines (November
2012).
Ground with relief
14/29
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
Simulated and measured VOR errors on radial ϕ = −10◦
0 20 40 6010 30 50
0
−2
−1
1
−1.5
−0.5
0.5
1.5
(a) without wind turbines
0 20 4010 30 505 15 25 35 45
0
−2
−1
1
−1.5
−0.5
0.5
1.5
Measurement
Simulation
(b) masts
0 20 4010 30 505 15 25 35 45
0
−2
2
−3
−1
1
3
Measurement
Simulation
(c) wind turbines
Analysis
Good agreement for the error envelop and maximal value
Relatively strong residual error without wind turbines (other scatterers, noise)
Rapid oscillations due to complex combination of multipath with various phases. Difficult to
reproduce exactly in simulation
Computation time = 13 min
15/29
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
Complementary analyses via simulations
Influence of the aircraft trajectory
Configuration
Two simulation campaigns with slight
changes in the aircraft trajectories
Results
Significant modification of the error
⇒ Difficult to compare results for nearby
trajectories
16/29
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
Plan
1 Introduction
2 VOR Error Simulator
3 Probability Distribution for the Multipath Parameters
4 Statistics of the bearing error
5 Simulation
6 Conclusion
17/29
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
Statistical Description of the Configuration
Objective
For one wind turbine of known approximate position and at a given observation point, determine the
statistics of the multipath parameters (a1, θ1, φ1)
Statistical Parameters
Ground composition
Dry, wet, fresh water, sea water, ...
⇒ Discrete uniform ditribution
Windturbine position
Variation about the average position
⇒ Normal distribution
Wind turbine characteristics
14 distances
Mast length, hub box size, ...
4 angles
Blade orientation, rotor orientation, ...
⇒ Uniform and normal distributions
18/29
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
Probability Distribution for the Multipath Parameters
Multipath Amplitude
Statistical variations of the wind turbine characteristics
Total wind Turbine scattering: Sum of the Scattering of the wind turbine components
Central limit theorem ⇒ Multipath amplitude follows a Rayleigh distribution
Multipath Azimuth
Wind turbine position: normal distribution of standard deviation σw
σw ≪ distance VOR wind turbine
Azimuth of the multipath = Azimuth of the average position of the wind turbine
19/29
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
Probability Distribution for the Multipath Parameters
Configuration
Wind turbine position: normal distribution
of standard deviation σw
r distance from VOR to aircraft
rw1, rw2 distances from VOR to windturbine and from windturbine
to aircraft
Hypothesis σw ≪ rw1, rw2
rw1
r
VOR
Wind turbine
rw2 phi'
Distribution for the path length
Multipath length with respect to the direct path
d = rw1 + rw2 − r
Taylor series for σw ≪ rw1, rw2 ⇒ d follows a normal distribution of std
σd = 2 sin
(
|φ′|
2
)
σW
with φ′ angle between
the VOR - Wind turbine axis
the Wind turbine - Aircraft axis
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
Probability Distribution for the Multipath Parameters
Distribution for the phase
Relative phase of the multipath arg ejkd , with d normal distribution
For σd ≥ λ/2, almost uniform phase on 0, 2pi
Domain of uniform phase
Uniform phase except for |φ′| ≤ 2 arcsin
(
λ
4σw
)
When φ′ → 0, the error is null from Odunaiya expression
VOR
Wind turbine
phi'
For σw of few λ, uniform phase except in a region where the bearing error is weak
Example: For σw = 4λ ≈ 10 m, Uniform phase except for |φ′| ≤ 7◦
Conclusion
Rayleigh relative amplitude
Constant azimuth
Uniform relative phase
Need for only one parameter to characterize the multipath
⇒ The parameter of the Rayleigh distribution
21/29
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
Plan
1 Introduction
2 VOR Error Simulator
3 Probability Distribution for the Multipath Parameters
4 Statistics of the bearing error
5 Simulation
6 Conclusion
22/29
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
Statistics of the bearing error
One wind turbine
General Odunaiya expression
εC = tan−1
( ∑N
n=1 an cos(θn − θ0) sin(ϕn − ϕ0)
a0 +
∑N
n=1 an cos(θn − θ0) cos(ϕn − ϕ0)
)
Expression for one weak multipath
εC =
a1
a0
cos(θ1 − θ0) sin(φ1 − φ0)
a1/a0 Rayleigh distribution of parameter σ θ1 − θ0 uniform distribution on 0, 2pi
Conclusion εC centered normal distribution of standard deviation
σε = σ| sin(φ1 − φ0)|
Several wind turbines
Independant distributions for the multipath of each wind turbine
Conclusion εC centered normal distribution of standard deviation
σε =
√√√√ N∑
n=1
σ2n sin
2(φ1 − φ0)
23/29
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
Plan
1 Introduction
2 VOR Error Simulator
3 Probability Distribution for the Multipath Parameters
4 Statistics of the bearing error
5 Simulation
6 Conclusion
24/29
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
Test-Case
Configuration
Deterministic parameters
VOR Station of power 50 W and frequency 113 MHz
Aircraft position : Half sphere of radius 10 km centered on the Wind Turbine
Windturbine at 3 km from the VOR, on radial 90◦
Statistical parameters
Wind turbine characteristics: database of 2000 wind turbines installed in the Norh of France
Monte Carlo simulations
Objective: assess the parameter of the Rayleigh distribution
VERSO is run for several samples of the input parameters
Convergence test: estimated value variations weaker than 5% during the 10 last iterations
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Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
Rayleigh parameter
Results
Complete half-sphere
0 50 100 150 200 250 300 350
φobs(°)
−24
−22
−20
−18
−16
St
d 
de
vi
at
io
n 
(d
B)
For θ = 88◦
Comments
Low Elevation: strong multipath due to the mast
Medium elevation: residual contribution due to the blades
Near zenith: spurious increase of the relative multipath in the blind cone
26/29
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
Bearing Error
Results
Complete half-sphere
0 50 100 150 200 250 300 350
φobs(°)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
St
d 
de
vi
at
io
n 
(°
)
For θ = 88◦
Comments
Low Elevation: strong multipath due to the mast
Medium elevation: residual contribution due to the blades
Near zenith: spurious increase of the relative multipath in the blind cone
27/29
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
Plan
1 Introduction
2 VOR Error Simulator
3 Probability Distribution for the Multipath Parameters
4 Statistics of the bearing error
5 Simulation
6 Conclusion
28/29
Introduction VOR Error Simulator Probability Distribution for the Multipath Parameters Statistics of the bearing error Simulation Conclusion
Conclusion
Conclusion
Multipath Probability Distribution
For a wind turbine of known approximated position and at a given obesrvation point, the multipath is
so that
Uniform relative phase
Constant relative azimuth
Rayleigh relative amplitude
Parameter of the Rayleigh distribution via Monte Carlo Simulation
Bearing error Probability Distribution
For one wind turbine, centered normal distribution
For several wind turbines, centered normal distribution if multipath are independant
Future works
Develop a method to avoid to run one MC simulation per wind turbine and per aircraft positions
⇒ Huge computation resources
Include the terrain relief
Similar work for Doppler VOR
29/29


A Stastistical Model for Assessing the Impact of Wind Turbines on Conventionnal VOR

https://hal-enac.archives-ouvertes.fr/hal-02458579/file/presentation_stat_vor_chabory.pdf

A Stastistical Model for Assessing the Impact of Wind Turbines on Conventionnal VOR

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Archive Ouverte en Sciences de l'Information et de la Communication