Plugin WindLab

Plugin WindLab
Description
This plugin implement various WindLab features. Plugin version: 1.0 Last modified: 2024-04-15 LabRPS version: All Author: Koffi Daniel
Author
Koffi Daniel
Download
None
Features
Cholesky Decomposition Horizontal Uniform Distribution Vertical Uniform Distribution Uniform Distribution Grid Points Power Law Profile
Plugin Version
1.0
Date last modified
2024-04-15
LabRPS Version(s)
All
Default shortcut
None
See also
None

You can find the source code of this plugin on the following Github repository: Get the code here!. This plugin is one of the official plugins provided by LabRPS. It provides very useful features (tools) for the simulation of random wind velocity. Plugins are very easy to create in LabRPS, therefore, anyone can develop plugin for any random phenomenon in LabRPS. Go to this page to see how to create new plugin for LabRPS. You can get quick assistance from LabRPS community by sending your concern to the community forum.

Cholesky Decomposition

This feature performs the Cholesky decomposition of a positive Hermitian power spectrum matrix and returns the lower triangular matrix (L) of the decomposition. The Cholesky decomposition is a numerical method used to decompose a positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose. Specifically, for a matrix A, the decomposition is given by:

[math]\displaystyle{ \mathbf{A} = \mathbf{L L}^{*}, }[/math]

[math]\displaystyle{ L_{j,j} = \sqrt{ A_{j,j} - \sum_{k=1}^{j-1} L_{j,k}^*L_{j,k} }, }[/math]

[math]\displaystyle{ L_{i,j} = \frac{1}{L_{j,j}} \left( A_{i,j} - \sum_{k=1}^{j-1} L_{j,k}^* L_{i,k} \right) \quad \text{for } i\gt j. }[/math]

where [math]\displaystyle{ L }[/math] is a lower triangular matrix with real and positive diagonal entries, and [math]\displaystyle{ L^* }[/math] denotes the conjugate transpose of [math]\displaystyle{ L }[/math].

The feature is optimized for performance and can handle large matrices efficiently using [math]\displaystyle{ O(n^3) }[/math] computational complexity in the worst case. It checks if the input matrix is indeed positive-definite and Hermitian before performing the decomposition and raises an error if the matrix does not meet these conditions. The feature belong to the PSD Decomposition Method feature group.

Scripting

The feature can be used from the python console as follows:

import WindLab
import WindLabObjects
from LabRPS import Vector as vec
import numpy

 # get an existing WindLab simulation called "Simulation"
 sim = WindLab.getSimulation("Simulation")
    
 # check if the simulation does really exist
 if not sim:
     LabRPS.Console.PrintError("The simulation does not exist.\n")
     # abord the computation
  
 featureType = "Cholesky Decomposition"
 featureGroup = "Spectrum Decomposition Method"
  
 # create the feature and add it to the existing simulation (you may refer to the WindLab Workbench page in 
 # case you don't understand the next line)
 decomposedPSD = WindLabObjects.makeFeature("MyNewFeature", sim.Name, featureType, featureGroup)
    
 # check if the created feature is good
 if not decomposedPSD :
     LabRPS.Console.PrintError("Error on creating the spectrum decomposition method.\n")
     # abord the computation
    
 # get the active simulation points feature and compute the simulation points coordinates
 simPoints = sim.computeLocationCoordinateMatrixP3()

 # use a vector to represent a simulation point based on its coordinates
 v1 = vec(simPoints[0][1], simPoints[0][2], simPoints[0][3])
 v2 = vec(simPoints[1][1], simPoints[1][2], simPoints[1][3])
 v3 = vec(simPoints[2][1], simPoints[2][2], simPoints[2][3])

 # This feature is used to decompose power spectrum matrices which may vary in time. Let's assume that
 # the active power spectrun density function in this example is stationary. Meanning it is not varying in time.
 #Then, we use time instant of 0 second.
 time = 0.0

 # compute the decomposed cross spectrum between points 1 and 3, at time instant of 0 second and for all frequency
 # increments. Note that when the following code is run, WindLab will try to identify the active frequency distribution, 
 # the active power spectrum feature, the active coherence function feature and others. If WindLab fails to find any 
 # of these dependency features, the computation will fails and specific error messages will be sent to the report view.
 # The following function is only one of its functions. There are some other two.
 psd13 = sim.computeDecomposedCrossSpectrumVectorF(v1, v3, time)

 # psd13 can be converted to numpy vector and be used for some other purposes.
 arr = numpy.asarray(psd13)

Horizontal Uniform Distribution

This feature provides an efficient method to distribute random wind simulation points uniformly in space. It allows users to generate a set of points within a 3D spatial domain, ensuring that the points are evenly distributed along a horizontal line that is parallel to one of the coordinate system axis. This uniform distribution is critical in certain simulation methods. For [math]\displaystyle{ n }[/math] simulation points [math]\displaystyle{ (P_1,P_2,P_3,...,P_n) }[/math], the distance [math]\displaystyle{ d_{jk} }[/math] between points [math]\displaystyle{ P_j }[/math] and [math]\displaystyle{ P_k }[/math] must be given by the following formula:

[math]\displaystyle{ d_{jk} = s\times|j-k| }[/math]

where [math]\displaystyle{ s }[/math] is the even space between any two adjacent points.

Properties

• DataFirstPoint: This is a point in 3D space representing the first point the distribution will start from.
• DataSpacing: This is the even space between any two adjacent points in the distribution.

Scripting

import WindLab
import WindLabObjects
from LabRPS import Vector as vec
import numpy

 # get an existing WindLab simulation called "Simulation"
 sim = WindLab.getSimulation("Simulation")
    
 # check if the simulation does really exist
 if not sim:
     LabRPS.Console.PrintError("The simulation does not exist.\n")
     # abord the computation
  
 featureType = "Horizontal Distribution"
 featureGroup = "Location Distribution"
  
 # create the feature and add it to the existing simulation (you may refer to the WindLab Workbench page in 
 # case you don't understand the next line)
 unifSimPoints= WindLabObjects.makeFeature("MyNewFeature", sim.Name, featureType, featureGroup)
    
 # check if the created feature is good
 if not unifSimPoints:
     LabRPS.Console.PrintError("Error on creating the uniform points feature.\n")
     # abord the computation
 # let's set the first point of the distribution (x =0, y = 0, z = 80m)
 simPoints.FirstPoint = vec(0,0,80000)

 # let's set the spacing (s = 10m)
 simPoints.Spacing = '10m'

 # compute the simulation points coordinates. WindLab will internally use the "unifSimPoints" feature.
 simPoints = sim.computeLocationCoordinateMatrixP3()

 # now you can convert the coordinate matrix to numpy array and use it for any other purposes
 arr = numpy.asarray(simPoints)

Vertical Uniform Distribution

This feature provides an efficient method to distribute random wind simulation points uniformly in space. It allows users to generate a set of points within a 3D spatial domain, ensuring that the points are evenly distributed along a vertical line. This uniform distribution is critical in certain simulation methods. For [math]\displaystyle{ n }[/math] simulation points [math]\displaystyle{ (P_1,P_2,P_3,...,P_n) }[/math], the distance [math]\displaystyle{ d_{jk} }[/math] between points [math]\displaystyle{ P_j }[/math] and [math]\displaystyle{ P_k }[/math] must be given by the following formula:

[math]\displaystyle{ d_{jk} = s\times|j-k| }[/math]

where [math]\displaystyle{ s }[/math] is the even space between any two adjacent points.

Properties

• DataLowestPoint: This is a point in 3D space representing the lowest point the distribution will start from. In many applications, this point should not be lower than 10 meters.
• DataSpacing: This is the even space between any two adjacent points in the distribution.

Scripting

import WindLab
import WindLabObjects
from LabRPS import Vector as vec
import numpy

 # get an existing WindLab simulation called "Simulation"
 sim = WindLab.getSimulation("Simulation")
    
 # check if the simulation does really exist
 if not sim:
     LabRPS.Console.PrintError("The simulation does not exist.\n")
     # abord the computation
  
 featureType = "VerticalDistribution"
 featureGroup = "Location Distribution"
  
 # create the feature and add it to the existing simulation (you may refer to the WindLab Workbench page in 
 # case you don't understand the next line)
 unifSimPoints= WindLabObjects.makeFeature("MyNewFeature", sim.Name, featureType, featureGroup)
    
 # check if the created feature is good
 if not unifSimPoints:
     LabRPS.Console.PrintError("Error on creating the uniform points feature.\n")
     # abord the computation
 # let's set the first point of the distribution (x =0, y = 0, z = 30m)
 simPoints.LowestPoint = vec(0,0,30000)

 # let's set the spacing (s = 10m)
 simPoints.Spacing = '10m'

 # compute the simulation points coordinates. WindLab will internally use the "unifSimPoints" feature.
 simPoints = sim.computeLocationCoordinateMatrixP3()

 # now you can convert the coordinate matrix to numpy array and use it for any other purposes
 arr = numpy.asarray(simPoints)

Uniform Distribution

This feature may be seen as a general form of the horizontal and the vertical distribution features. It allows users to generate a set of points within a 3D spatial domain, ensuring that the points are evenly distributed along a line parallel to one of the coordinate system axis. For [math]\displaystyle{ n }[/math] simulation points [math]\displaystyle{ (P_1,P_2,P_3,...,P_n) }[/math], the distance [math]\displaystyle{ d_{jk} }[/math] between points [math]\displaystyle{ P_j }[/math] and [math]\displaystyle{ P_k }[/math] must be given by the following formula:

[math]\displaystyle{ d_{jk} = s\times|j-k| }[/math]

where [math]\displaystyle{ s }[/math] is the even space between any two adjacent points.

Properties

• DataFirstPoint: This is a point in 3D space representing the first point the distribution will start from. This should be the lowest point in case the distribution is parallel to the vertical axis and should not be lower than 10 meters in many application.
• DataSpacing: This is the even space between any two adjacent points in the distribution.
• DataDirection: Its value can be X, Y or Z. This is the axis the points distribution is parallel to.

Scripting

This feature can be used to produce vertical distribution as we did before in the Vertical Distribution feature.

import WindLab
import WindLabObjects
from LabRPS import Vector as vec
import numpy

 # get an existing WindLab simulation called "Simulation"
 sim = WindLab.getSimulation("Simulation")
    
 # check if the simulation does really exist
 if not sim:
     LabRPS.Console.PrintError("The simulation does not exist.\n")
     # abord the computation 
  
 featureType = "UniformDistribution"
 featureGroup = "Location Distribution"
  
 # create the feature and add it to the existing simulation (you may refer to the WindLab Workbench page in 
 # case you don't understand the next line)
 unifSimPoints= WindLabObjects.makeFeature("MyNewFeature", sim.Name, featureType, featureGroup)
    
 # check if the created feature is good
 if not unifSimPoints:
     LabRPS.Console.PrintError("Error on creating the uniform points feature.\n")
     # abord the computation

 # set the direction of the distribution to be vertical
  simPoints.Direction= 'Z'

 # let's set the first point of the distribution (x =0, y = 0, z = 30m)
 simPoints.FirstPoint = vec(0,0,30000) # This is the lowest point in this case (Direction = 'Z')

 # let's set the spacing (s = 10m)
 simPoints.Spacing = '10m'

 # compute the simulation points coordinates. WindLab will internally use the "unifSimPoints" feature.
 simPoints = sim.computeLocationCoordinateMatrixP3()

 # now you can convert the coordinate matrix to numpy array and use it for any other purposes
 arr = numpy.asarray(simPoints)

Grid Points

This feature allows users to generate a set of grid points within a 3D spatial domain, ensuring that the points are evenly distributed in a plane parallel to one of the coordinate system planes (XY Plane, YZ Plane, XZ Plane).

Properties

• DataSpacing1: This is the points spacing along one of the axis forming the plane.
• DataSpacing2: This is the points spacing along the second axis.
• DataLength1: This is the length within points are distributed along one of the axis forming the plane.
• DataLength2: This is the length within points are distributed along the second axis.
• DataCenterPoint: This is the center of the grid around which the points are generated. It is a 3D point.
• DataNumberOfPoints: This is the resulting total number of points in the grid. This is a read only property for internal use. User cannot change its value directly.

Scripting

The following script shows how this feature can be created and used.

import WindLab
import WindLabObjects
from LabRPS import Vector as vec
import numpy

 # get an existing WindLab simulation called "Simulation"
 sim = WindLab.getSimulation("Simulation")
    
 # check if the simulation does really exist
 if not sim:
     LabRPS.Console.PrintError("The simulation does not exist.\n")
     # abord the computation 
  
 featureType = "Grid Points"
 featureGroup = "Location Distribution"
  
 # create the feature and add it to the existing simulation (you may refer to the WindLab Workbench page in 
 # case you don't understand the next line)
 unifSimPoints= WindLabObjects.makeFeature("MyNewFeature", sim.Name, featureType, featureGroup)
    
 # check if the created feature is good
 if not unifSimPoints:
     LabRPS.Console.PrintError("Error on creating the uniform points feature.\n")
     # abord the computation

 # set the plan the points grid is parallel to
  simPoints.LocationPlan= 'YZ Plane'

 # let's set the center point of the distribution (x =0, y = 0, z = 0)
 simPoints.CenterPoint = vec(0,0,0) 

 # let's set the spacing1 (s1 = 10m)
 simPoints.Spacing1 = '10m'

 # let's set the spacing2 (s2 = 10m)
 simPoints.Spacing2 = '10m'

 # let's set the length1 (l1 = 200m)
 simPoints.Length1= '200m'

 # let's set the length2 (l2 = 200m)
 simPoints.Length2= '200m'

 # compute the simulation points coordinates. WindLab will internally use the "unifSimPoints" feature.
 simPoints = sim.computeLocationCoordinateMatrixP3()

 # now you can convert the coordinate matrix to numpy array and use it for any other purposes
 arr = numpy.asarray(simPoints)

General Distribution

When the simulation points distribution is more general and does not follow any of the previous uniform distribution, this feature can be used. This feature allows users to input simulation points one by one using their coordinates based on the vector dialog shown below:

Properties

• DataLocations: This is a list holding the simulation points

Scripting

The following script shows how this feature can be created and used.

import WindLab
import WindLabObjects
from LabRPS import Vector as vec
import numpy

 # get an existing WindLab simulation called "Simulation"
 sim = WindLab.getSimulation("Simulation")
    
 # check if the simulation does really exist
 if not sim:
     LabRPS.Console.PrintError("The simulation does not exist.\n")
     # abord the computation 
  
 featureType = "General Distribution"
 featureGroup = "Location Distribution"
  
 # create the feature and add it to the existing simulation (you may refer to the WindLab Workbench page in 
 # case you don't understand the next line)
 genSimPoints= WindLabObjects.makeFeature("MyNewFeature", sim.Name, featureType, featureGroup)
    
 # check if the created feature is good
 if not genSimPoints:
     LabRPS.Console.PrintError("Error on creating the uniform points feature.\n")
     # abord the computation

 # create the simulation points by their coordinates
 v1 = vec(0, 0, 35000)
 v2 = vec(0, 0, 40000)
 v3 = vec(0, 0, 140000)

 # add the points to the locations
 loc.Locations = [v1, v2, v3]

 # compute the simulation points coordinates. WindLab will internally use the "genSimPoints" feature
 simPoints = sim.computeLocationCoordinateMatrixP3()

 # now you can convert the coordinate matrix to numpy array and use it for any other purposes
 arr = numpy.asarray(simPoints)

Power Law Profile

This feature is designed to compute the wind speed at a given height based on the power law mean wind profile, which is commonly used to model the variation of wind speed with height in the atmospheric boundary layer. This model is essential in fields such as wind energy, structural engineering, and environmental science. The power law formula that governs the relationship between wind speed and height is expressed as:

[math]\displaystyle{ U(z) = U(z_0)\times\left( \frac{{z-\phi}}{z_0} \right)^\alpha }[/math]

where:

• [math]\displaystyle{ U(z) }[/math] is the wind speed at height [math]\displaystyle{ z }[/math],
• [math]\displaystyle{ U(z_0) }[/math] is the reference wind speed at a known reference height [math]\displaystyle{ z_0 }[/math],
• [math]\displaystyle{ \alpha }[/math] is the power law exponent, a dimensionless constant that varies depending on terrain and atmospheric conditions,
• [math]\displaystyle{ \phi }[/math] is the zero plan displacement,
• [math]\displaystyle{ z }[/math] is the height at which the wind speed is to be calculated.

Properties

• DataReferenceHeight: This is a reference height.
• DataReferenceSpeed: This is the reference wind speed at the reference height.
• DataDimensionlessPower: This is the power law exponent.
• DataZeroPlanDisplacement: This is the zero plan displacement.

Scripting

The following script shows how this feature can be created and used.

import WindLab
import WindLabObjects
from LabRPS import Vector as vec
import numpy

 # get an existing WindLab simulation called "Simulation"
 sim = WindLab.getSimulation("Simulation")
    
 # check if the simulation does really exist
 if not sim:
     LabRPS.Console.PrintError("The simulation does not exist.\n")
     # abord the computation 
  
 featureType = "Power Law Profile"
 featureGroup = "Mean Wind Profile"
  
 # create the feature and add it to the existing simulation (you may refer to the WindLab Workbench page in 
 # case you don't understand the next line)
 meanSpeed= WindLabObjects.makeFeature("MyNewFeature", sim.Name, featureType, featureGroup)
    
 # check if the created feature is good
 if not meanSpeed:
     LabRPS.Console.PrintError("Error on creating the uniform points feature.\n")
     # abord the computation

 meanSpeed.ReferenceHeight = '10.00 m'
 meanSpeed.ReferenceSpeed = '30.00 m/s'
 meanSpeed.DimensionlessPower = 0.12
 meanSpeed.ZeroPlanDisplacement = '0.0 m'

 # In WindLab, mean wind velocity can vary with time. In case the user desires a time dependent mean wind speed,  
 # a modulation function can be used for this purpose. The feature account for this. When the Stationarity property of the parent 
 # simulation of this feature is false, the feature identify the active modulation function and use it to produce non-stationary 
 # mean wind speed. But for this example we shall use time instant of 0 second.
 time = 0.0

 # compute the mean wind speeds at time instant of 0 second and for all simulation points
 # Note that when the following code is run, WindLab will try to identify the active locations distribution,
 # it will also try to identity the active modulation function in case the parent simulation is non-stationary. 
 # If WindLab fails to find these dependency features, the computation will fails and specific error messages will be sent to the report view.
 meanValues = sim.computeMeanWindSpeedVectorP(time)

 # now you can convert the coordinate matrix to numpy array and use it for any other purposes
 arr = numpy.asarray(meanValues )