130 lines
5.8 KiB
Markdown
130 lines
5.8 KiB
Markdown
# Wind turbine gearbox simulator
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"uncertainties4windturbinegearbox" is a program designed to simulate the uncertainties of a wind turbine gearbox model.
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Its main purpose is the comparison between :
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- Monte Carlo method
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- Generalized Polynomial Chaos method (GPC)
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With this model, proofs that GPC is a valid method are given, with convergence criteria. The wind turbine gearbox model is a 8-DOF gearbox integrated in time with Newmark's scheme. Uncertain parameters are mapped into uniform distributions in the interval $[-1,1]$.
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## Dependencies
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**Development language:** [Octave 11.1.0](https://octave.org/) ("some packages" installed, follow first start requirements, follow the error messages) (add `graphic_toolkit("gnuplot")` in `main`)
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**Compatibility:** [Matlab v2026-a](https://fr.mathworks.com/products/matlab.html) (delete all `graphics_toolkit("gnuplot")` occurrences in the code)
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> Optional: Parallel Computing Toolbox (for `parfor` functions)
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**Plot engine:** [Gnuplot](http://gnuplot.info/) 6.0 patchlevel 4
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**Recommended:** [Inkscape](https://inkscape.org/) can be used for graphs that are printed into `.svg` to be converted into `.pdf`
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**Perspectives:** the code will probably be transferred into Python, as it is free and open source, and coherence with Python machine learning models
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## Usage
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### Run the code
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```bash
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$ git clone https://gitlab.com/afoucaultc/wind_turbine_gearbox
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$ cd wind_turbine_gearbox/uncertainties4windturbinegearbox
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$ mkdir save
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$ mkdir print
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$ octave
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$ octave:1> run main.m
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$ # or run any standalone (starting by a "_")
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$ octave:1> run _[standalone].m
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```
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### Parameters
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Stored in **`parameters.m`**.
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| Variable | Default | Description |
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|---|---|---|
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| `N` | `10000` | Number of Monte Carlo draws |
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| `pmax` | `5` | Maximum polynomial order for CPG |
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| `theta` | `0.01` | Convergence threshold on residual rate |
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| `r_uncertainty` | `20` | ±% variation around nominal values |
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| `newparams` | see file | Cell array of uncertain variable names and nominal values |
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Adding or removing uncertain variables : edit `newparams` array
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```matlab
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newparams = {
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'Z2' , 18 ; % number of teeth (gear 2)
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'b' , 0.1 ; % gear width [m]
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'la1' , 2 ; % shaft 1 length [m]
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% 'kx', 1e8 ; % uncomment to include bearing stiffness
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};
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```
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### OUTPUTS :
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#### Figures (exported to `print/`)
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| File | Content |
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|---|---|
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| `mean_cpg_r=*_p=*_uncertainty=*.pdf` | Mean displacement — CPG vs MC (with 95% CI) |
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| `var_cpg_r=*_p=*_uncertainty=*.pdf` | Standard deviation — CPG vs MC (with 95% CI) |
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| `modes_cpg_r=*_p=*_uncertainty=*.pdf` | Modal energy contribution by polynomial order |
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| `CPG_MC_time.pdf` | Evaluation time — CPG vs MC as a function of sample size |
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| `CPG_polytime.pdf` | Training time of CPG as a function of polynomial order |
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| `MC_convergence.pdf` | Convergence of MC mean estimate vs. number of draws |
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#### Raw values (saved to `save/`)
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| File | Content |
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|---|---|
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| `mc_r=*_N=*.mat` | Full MC workspace |
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| `cpg_r=*_p=*.mat` | Full CPG workspace at converged order |
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### File tree
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```bash
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## Main process
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├── main.m # Main, runs MC then CPG, produces figures
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│ ├── monte_carlo # Monte Carlo
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│ │ ├── method_XiToX.m # Mapping from normalized ξ ∈ [-1,1]^r to physical X
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│ │ └── method_lambda.m # Batch model evaluation over a parameter grid
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│ │ └── model_main.m # Model used (wind turbine gearbox)
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│ │ ├── model_func.m (class) # Function class for model
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│ │ └── model_parameters.m # Parameters for model
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│ └── cpg # GPC
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│ ├── cpg_polyLegendre.m # Legendre polynomials up to order pmax
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│ ├── cpg_polyChaos.m # Multi dimensional chao basis (multi index α)
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│ ├── cpg_gaussColloc.m # Tensor of Gauss collocation grid
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│ ├── method_XiToX.m # Mapping from normalized ξ ∈ [-1,1]^r to physical X
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│ ├── method_lambda.m # Batch model evaluation over a parameter grid
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│ │ └── model_main.m # Model used (wind turbine gearbox)
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│ │ ├── model_func.m (class) # Function class for model
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│ │ └── model_parameters.m # Parameters for model
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│ ├── cpg_modes.m # Stochastic mode computation (Φ \ λ)
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│ ├── cpg_evaluate.m # CPG evaluation on random ξ samples from MC
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│ └── cpg_errors.m # Convergence metrics and stopping criterion
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└── plot_guerine.m # Plots : mean, std and modal energy
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## Standalone functions
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└── _timeaccuracy.m # Compute and plot : time for MC, GPC, convergence MC
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## Rendering folders
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├── print
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│ ├── mean_cpg_r=?_p=?_uncertainty=?.pdf (main)
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│ ├── var_cpg_r=?_p=?_uncertainty=?.pdf (main)
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│ ├── modes_cpg_r=?_p=?_uncertainty=?.pdf (main)
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│ ├── CPG_MC_polytime.pdf (_timeaccuracy)
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│ ├── MC_convergence.pdf (_timeaccuracy)
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│ └── CPG_MC_time.pdf (_timeaccuracy)
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└── save
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├── cpg_r=?_p=?.mat
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└── mc_r=?_N=?.mat
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## Others
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├── octave-workspace
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└── README.md
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```
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## Calculation machine specification
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Hardware: 32Go RAM, Intel(R) Core(TM) i7-7700K CPU @ 4.20GHz, NVIDIA GeForce RTX 4060
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OS: Windows 10, version 22H2 (last update 16/05/2023)
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