Tutorials

The tutorials follow VANE’s main path: from an OpenFAST linearization sweep, through the multi-blade transform and the eigenanalysis, to labelled modes, a Campbell diagram, mode-shape views, the error of the azimuth average, and finally the state-space and parameter-varying models used for estimation and control. Each tutorial is one script in the repository’s examples/ folder. Each page shows the code, the output of an actual run and the figure it draws, and explains what the numbers mean. Work through them in order the first time.

#	Tutorial	You learn	Run time
1	Tutorial 1: An OpenFAST linearization sweep	the operating-curve CSV, the settings VANE infers from the deck and the curve, the outcome of each operating point	minutes per point (needs OpenFAST)
2	Tutorial 2: MBC3 transform and eigenanalysis	reading .lin files, the MBC3 transform and azimuth average, frequencies, damping and participation	seconds
3	Tutorial 3: Mode identification and the Campbell diagram	physical labels, tracking across operating points, the Campbell diagram, resonance crossings, tables and the sweep axis	seconds
4	Tutorial 4: Mode shapes	participation charts, 3-D mode-shape views and a VTK animation	seconds
5	Tutorial 5: Azimuth averaging and its error	the blade-number rule for the azimuth count, pinning the azimuth direction, the averaging-error estimate and its check against Floquet exponents	seconds
6	Tutorial 6: State-space, Kalman and LPV export	state-space export, modal reduction, a Kalman filter, mode-tracked and physical-state families	seconds

Before you start

• Install VANE (see Installation) and work from the root of the repository, which holds the examples/ folder.

• Run a script with python examples/<script>.py. Without options, the generated data go to a temporary directory that is deleted at the end, and the figures to docs/tutorials/figures/. --output DIR sends every file to DIR instead. --help lists the options of each script.

• Only tutorial 1 needs OpenFAST. Tutorials 2 to 6 run on small synthetic .lin files that the helper module examples/_synthetic.py writes, because OpenFAST linearization files are not distributed with VANE.

The synthetic turbine

The synthetic turbine has six degrees of freedom: the first tower fore-aft and side-side bending modes, the generator azimuth, and the first flap mode of each of three blades. Each blade is a damped oscillator in its own rotating frame whose frequency rises with rotor speed (centrifugal stiffening). The tower fore-aft mode couples to the three blades equally, the tower side-side mode to each blade through the sine of its azimuth, and a small 3P term modulates the tower fore-aft stiffness. The files are written as OpenFAST writes them: tower states in the fixed frame, blade states in the rotating frame (flag T), with ElastoDyn state descriptions, two inputs (wind speed and collective pitch) and eight outputs. Twelve azimuths make one operating point. Below rated the rotor speed follows a constant tip-speed ratio; above rated (10.6 m/s) it stays at 12.1 rpm.

The numbers resemble a 5 MW-class turbine but describe no real machine, and the model leaves out much of a real linearization (edgewise and second modes, drivetrain, aerodynamic states). It is small enough to follow by hand and has the features the tutorials need: the MBC3 transform splits the flap triplet into regressive, collective and progressive modes, and the tower and the regressive flap mode cross the 3P line in the operating range.

A clean run is not a validation

Every tutorial checks its result against something independent: the frozen-azimuth eigenvalues, the excitation-line arithmetic, an exact eigen-solution, the Floquet exponents, or a simulated truth. Keep that habit for your own models, and see Validation for the evidence behind VANE itself.