DVGeometryCST
- class pygeo.parameterization.DVGeoCST.DVGeometryCST(datFile, numCST=8, idxChord=0, idxVertical=1, comm=mpi4py.MPI.COMM_WORLD, isComplex=False, debug=False, tolTE=60.0)[source]
This class implements a 2D geometry parameterisation based on Brenda Kulfan’s CST (Class-Shape Transformation) method. This class can work with 3D coordinates but will only change the point coordinates in one direction.
The CST equation is as follows:
\(y(x) = C(x) * S(x) + y_\text{te}x\)
Where C is the class function:
\(C(x) = (x^{N1} + (1 - x)^{N2})\)
And S is the shape function, in this case a summation of Bernstein polynomials:
\(S(x) = \sum_i^n w_i \binom{n}{i}x^i(1-x)^{n-i}\)
Here x is the normalized chordwise coordinate, ranging from 0 to 1 from front to the rear of the shape.
Assumptions about the point sets being added:
Dat file is ordered continuously around the airfoil and the beginning and end of the list is the trailing edge (no jumping around, but CW vs. CCW does not matter)
Geometry is exclusively an extruded shape (no spanwise changes allowed)
Airfoil’s leading edge is on the left (min x) and trailing edge is on the right (max x)
Airfoil is not rotated (trailing edge and leading edge are close to y equals zero)
- Parameters
- datFilestr
Filename of dat file that represents the initial airfoil. The coordinates in this file will be used to determine the camber line, which is the dividing line to distinguish upper and lower surface points.
- numCSTint or list of two ints
Number of CST parameters to use for the initial fit and the DVs (if DVs with type
"upper"
or"lower"
are added). IfnumCST
is an int, the value will be used for both upper and lower. If it is a two-item list, the first value defines the number of upper CST coefficients and the second is the number of lower coefficients, by default 8.- idxChordint, optional
Index of the column in the point set to use as the chordwise (x in CST) coordinates, by default 0
- idxVerticalint, optional
Index of the column in the point set to use as the vertical (y in CST) airfoil coordinates, by default 1
- commMPI communicator, optional
Communicator for DVGeometryCST instance, by default MPI.COMM_WORLD
- isComplexbool, optional
Initialize variables to complex types where necessary, by default False
- debugbool, optional
Show plots when addPointSet is called to visually verify that it is correctly splitting the upper and lower surfaces of the airfoil points, by default False
- tolTEfloat, optional
Tolerance used to detect trailing edge corners on the airfoil. The value represents the angle difference in degrees between adjacent edges of the airfoil, by default 60 deg.
- addDV(dvName, dvType, lowerBound=None, upperBound=None, scale=1.0, default=None)[source]
Add design variables to the DVGeometryCST object. For upper and lower CST coefficient DVs, the number of design variables is defined using the
numCST
parameter in DVGeoCST’s init function.- Parameters
- dvNamestr
A unique name to be given to this design variable group
- dvTypestr
Define the type of CST design variable being added. Either the upper/lower surface class shape parameter DV can be defined (e.g.,
"N1_upper"
), or the DV for both the upper and lower surfaces’ class shape parameter can be defined (e.g.,"N1"
), but not both. The options (not case sensitive) are"upper"
: upper surface CST coefficients (specifydvNum
to define how many)"lower"
: lower surface CST coefficients (specifydvNum
to define how many)"N1"
: first class shape parameter for both upper and lower surfaces (adds a single DV)"N2"
: second class shape parameter for both upper and lower surfaces (adds a single DV)"N1_upper"
: first class shape parameters for upper surface (adds a single DV)"N1_lower"
: first class shape parameters for lower surface (adds a single DV)"N2_upper"
: second class shape parameters for upper surface (adds a single DV)"N2_lower"
: second class shape parameters for lower surface (adds a single DV)"chord"
: chord length in whatever units the point set length is defined and scaled to keep the leading edge at the same position (adds a single DV)
- lowerBoundfloat or ndarray, optional
The lower bound for the variable(s). This will be applied to all shape variables
- upperBoundfloat or ndarray, optional
The upper bound for the variable(s). This will be applied to all shape variables
- scalefloat, optional
The scaling of the variables. A good approximate scale to start with is approximately 1.0/(upper-lower). This gives variables that are of order ~1.0.
- defaultndarray, optional
Default value for design variable (must be same length as number of DVs added).
- Returns
- Nint
The number of design variables added.
- addPointSet(points, ptName, boundTol=1e-10, **kwargs)[source]
Add a set of coordinates to DVGeometry. The is the main way that geometry in the form of a coordinate list is given to DVGeometry to be manipulated.
Note
Even if
isComplex=True
, the imaginary portion of coordinates passed in here is ignored when determining if a given point is on the upper or lower surface.- Parameters
- pointsarray, size (N,3)
The coordinates to embed.
- ptNamestr
A user supplied name to associate with the set of coordinates. This name will need to be provided when updating the coordinates or when getting the derivatives of the coordinates.
- boundTolfloat, optional
Small absolute deviation by which the airfoil coordinates can exceed the initial minimum and maximum x coordinates, by default 1e-10.
- kwargs
Any other parameters are ignored.
- addVariablesPyOpt(optProb)[source]
Add the current set of variables to the optProb object.
- Parameters
- optProbpyOpt_optimization class
Optimization problem definition to which variables are added
- static computeCSTCoordinates(x, N1, N2, w, yte, dtype=<class 'float'>)[source]
Compute the vertical coordinates of a CST curve.
This function assumes x has been normalized to the range [0,1].
- Parameters
- xndarray (# pts,)
x coordinates at which to compute the CST curve height
- N1float
First class shape parameter
- N2float
Second class shape parameter
- wndarray (# coeff,)
CST coefficient array
- ytefloat
y coordinate of the trailing edge (used to define trailing edge thickness). Note that the trailing edge will be twice this thick, assuming the same
yte
value is used for both the upper and lower surfaces.- dtypetype, optional
Type for instantiated arrays, by default float
- Returns
- ndarray (# pts,)
y coordinates of the CST curve
- static computeCSTdydN1(x, N1, N2, w, dtype=<class 'float'>)[source]
Compute the derivatives of the height of a CST curve with respect to N1
Given \(y = C(x, N1, N2) * S(x)\)
\(\frac{dy}{dN1} = S(x) * \frac{dC}{dN1} = S(x) * C(x, N1, N2) * \ln{x}\)
This function assumes x has been normalised to the range [0,1].
- Parameters
- xndarray (# pts,)
x coordinates at which to compute the CST curve height
- N1float
First class shape parameter
- N2float
Second class shape parameter
- wndarray (# coeff,)
CST coefficient array
- dtypetype, optional
Type for instantiated arrays, by default float
- Returns
- ndarray (# pts,)
Derivative of the y coordinates with respect to the first class shape parameter
- static computeCSTdydN2(x, N1, N2, w, dtype=<class 'float'>)[source]
Compute the derivatives of the height of a CST curve with respect to N2
Given \(y = C(x, N1, N2) * S(x)\)
\(\frac{dy}{dN2} = S(x) * \frac{dC}{dN2} = S(x) * C(x, N1, N2) * \ln(1-x)\)
This function assumes x has been normalised to the range [0,1].
- Parameters
- xndarray (# pts,)
x coordinates at which to compute the CST curve height
- N1float
First class shape parameter
- N2float
Second class shape parameter
- wndarray (# coeff,)
CST coefficient array
- dtypetype, optional
Type for instantiated arrays, by default float
- Returns
- ndarray (# pts,)
Derivative of the y coordinates with respect to the second class shape parameter
- static computeCSTdydw(x, N1, N2, w, dtype=<class 'float'>)[source]
Compute the derivatives of the height of a CST curve with respect to the shape function coefficients
Given \(y = C(x) * sum [w_i * p_i(x)]\)
\(\frac{dy}{dw_i} = C(x) * p_i(x)\)
This function assumes x has been normalized to the range [0,1].
Only the shape of w is used, not the values.
- Parameters
- xndarray (# pts,)
x coordinates at which to compute the CST curve height
- N1float
First class shape parameter
- N2float
Second class shape parameter
- wndarray (# coeff,)
CST coefficient array
- dtypetype, optional
Type for instantiated arrays, by default float
- Returns
- ndarray (# coeff, # pts)
Derivatives of the y coordinates with respect to the CST coefficients
- static computeCSTfromCoords(xCoord, yCoord, nCST, N1=0.5, N2=1.0, dtype=<class 'float'>)[source]
Compute the CST coefficients that fit a set of airfoil coordinates (either for the upper or lower surface, not both).
This function internally normalizes the x and y-coordinates.
- Parameters
- xCoordndarray
Upper or lower surface airfoil x-coordinates (same length as yCoord vector).
- yCoordndarray
Upper or lower surface airfoil y-coordinates (same length as xCoord vector).
- nCSTint
Number of CST coefficients to fit.
- N1float, optional
First class shape parameter to assume in fitting, by default 0.5
- N2float, optional
Second class shape parameter to assume in fitting, by default 1.0
- dtypetype, optional
Type for instantiated arrays, by default float
- Returns
- np.ndarray (nCST,)
CST coefficients fit to the airfoil surface.
- static computeClassShape(x, N1, N2, dtype=<class 'float'>)[source]
Compute the class shape of a CST curve
- Parameters
- xndarray (# pts,)
x coordinates at which to compute the CST curve height
- N1float
First class shape parameter
- N2float
Second class shape parameter
- dtypetype, optional
Type for instantiated arrays, by default float
- Returns
- ndarray (# pts,)
y coordinates of the class shape
- static computeShapeFunctions(x, w, dtype=<class 'float'>)[source]
Compute the Bernstein polynomial shape function of a CST curve
This function assumes x has been normalized to the range [0,1].
- Parameters
- xndarray (# pts,)
x coordinates at which to compute the CST curve height
- wndarray (# coeff,)
CST coefficient array
- dtypetype, optional
Type for instantiated arrays, by default float
- Returns
- ndarray (# coeff, # pts)
Bernstein polynomials for each CST coefficient
- getNDV()[source]
Return the total number of design variables this object has.
- Returns
- nDVint
Total number of design variables
- getValues()[source]
Generic routine to return the current set of design variables. Values are returned in a dictionary format that would be suitable for a subsequent call to setValues()
- Returns
- dvDictdict
Dictionary of design variables
- getVarNames(**kwargs)[source]
Return a list of the design variable names. This is typically used when specifying a wrt= argument for pyOptSparse.
Examples
>>> optProb.addCon(.....wrt=DVGeo.getVarNames())
- static plotCST(upperCoeff, lowerCoeff, N1=0.5, N2=1.0, nPts=100, ax=None, **kwargs)[source]
Simple utility to generate a plot from CST coefficients.
- Parameters
- upperCoeffndarray
One dimensional array of CST coefficients for the upper surface.
- lowerCoeffndarray
One dimensional array of CST coefficients for the lower surface.
- N1float
First class shape parameter.
- N2float
Second class shape parameter.
- nPtsint, optional
Number of coordinates to compute on each surface.
- axmatplotlib Axes, optional
Axes on which to plot airfoil.
- **kwargs
Keyword arguments passed to matplotlib.pyplot.plot
- Returns
- matplotlib Axes
Axes with airfoil plotted
- setDesignVars(dvDict)[source]
Standard routine for setting design variables from a design variable dictionary.
- Parameters
- dvDictdict
Dictionary of design variables. The keys of the dictionary must correspond to the design variable names. Any additional keys in the dictionary are simply ignored.
- totalSensitivity(dIdpt, ptSetName, comm=None, **kwargs)[source]
This function computes sensitivity information. Specifically, it computes the following: \(\frac{dX_{pt}}{dX_{DV}}^T \frac{dI}{d_{pt}}\)
- Parameters
- dIdptarray of size (Npt, 3) or (N, Npt, 3)
This is the total derivative of the objective or function of interest with respect to the coordinates in ‘ptSetName’. This can be a single array of size (Npt, 3) or a group of N vectors of size (N, Npt, 3). If you have many to do, it is faster to do many at once.
- ptSetNamestr
The name of set of points we are dealing with
- kwargs
Any other parameters ignored, but this is maintained to allow the same interface as other DVGeo implementations.
- Returns
- dIdxDictdict
The dictionary containing the derivatives, suitable for pyOptSparse
- totalSensitivityProd(vec, ptSetName, **kwargs)[source]
This function computes sensitivity information. Specifically, it computes the following: \(\frac{dX_{pt}}{dX_{DV}} \times\mathrm{vec}\). This is useful for forward AD mode.
- Parameters
- vecdictionary whose keys are the design variable names, and whose
values are the derivative seeds of the corresponding design variable.
- ptSetNamestr
The name of set of points we are dealing with
- kwargs
Any other parameters ignored, but this is maintained to allow the same interface as other DVGeo implementations.
- Returns
- xsdotarray (Nx3)
Array with derivative seeds of the surface nodes.
- update(ptSetName, **kwargs)[source]
This is the main routine for returning coordinates that have been updated by design variables.
- Parameters
- ptSetNamestr
Name of point-set to return. This must match ones of the given in an
addPointSet()
call.- kwargs
Any other parameters ignored, but this is maintained to allow the same interface as other DVGeo implementations.
- Returns
- pointsndarray (N x 3)
Updated point set coordinates.