# Adaptive stratified importance sampling: hybridization of extrapolation and importance sampling Monte Carlo methods for estimation of wind turbine extreme loads

## Abstract

Wind turbine extreme load estimation is especially difficult because turbulent inflow drives nonlinear turbine physics and control strategies; thus there can be huge differences in turbine response to essentially equivalent environmental conditions. The two main current approaches, extrapolation and Monte Carlo sampling, are both unsatisfying: extrapolation-based methods are dangerous because by definition they make predictions outside the range of available data, but Monte Carlo methods converge too slowly to routinely reach the desired 50-year return period estimates. Thus a search for a better method is warranted. We introduce an adaptive stratified importance sampling approach that allows for treating the choice of environmental conditions at which to run simulations as a stochastic optimization problem that minimizes the variance of unbiased estimates of extreme loads. Furthermore, the framework, built on the traditional bin-based approach used in extrapolation methods, provides a close connection between sampling and extrapolation, and thus allows the solution of the stochastic optimization (i.e., the optimal distribution of simulations in different wind speed bins) to guide and recalibrate the extrapolation. Results show that indeed this is a promising approach, as the variance of both the Monte Carlo and extrapolation estimates are reduced quickly by the adaptive procedure. We conclude, however,more »

- Authors:

- National Renewable Energy Lab. (NREL), Golden, CO (United States)

- Publication Date:

- Research Org.:
- National Renewable Energy Lab. (NREL), Golden, CO (United States)

- Sponsoring Org.:
- USDOE Office of Energy Efficiency and Renewable Energy (EERE)

- OSTI Identifier:
- 1472240

- Report Number(s):
- NREL/JA-2C00-72435

Journal ID: ISSN 2366-7451

- Grant/Contract Number:
- AC36-08GO28308

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Wind Energy Science (Online)

- Additional Journal Information:
- Journal Name: Wind Energy Science (Online); Journal Volume: 3; Journal Issue: 2; Journal ID: ISSN 2366-7451

- Publisher:
- European Wind Energy Association - Copernicus

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 17 WIND ENERGY; 97 MATHEMATICS AND COMPUTING; wind turbines; load estimation; sampling; extreme loads

### Citation Formats

```
Graf, Peter, Dykes, Katherine, Damiani, Rick, Jonkman, Jason, and Veers, Paul. Adaptive stratified importance sampling: hybridization of extrapolation and importance sampling Monte Carlo methods for estimation of wind turbine extreme loads. United States: N. p., 2018.
Web. doi:10.5194/wes-3-475-2018.
```

```
Graf, Peter, Dykes, Katherine, Damiani, Rick, Jonkman, Jason, & Veers, Paul. Adaptive stratified importance sampling: hybridization of extrapolation and importance sampling Monte Carlo methods for estimation of wind turbine extreme loads. United States. doi:10.5194/wes-3-475-2018.
```

```
Graf, Peter, Dykes, Katherine, Damiani, Rick, Jonkman, Jason, and Veers, Paul. Wed .
"Adaptive stratified importance sampling: hybridization of extrapolation and importance sampling Monte Carlo methods for estimation of wind turbine extreme loads". United States. doi:10.5194/wes-3-475-2018. https://www.osti.gov/servlets/purl/1472240.
```

```
@article{osti_1472240,
```

title = {Adaptive stratified importance sampling: hybridization of extrapolation and importance sampling Monte Carlo methods for estimation of wind turbine extreme loads},

author = {Graf, Peter and Dykes, Katherine and Damiani, Rick and Jonkman, Jason and Veers, Paul},

abstractNote = {Wind turbine extreme load estimation is especially difficult because turbulent inflow drives nonlinear turbine physics and control strategies; thus there can be huge differences in turbine response to essentially equivalent environmental conditions. The two main current approaches, extrapolation and Monte Carlo sampling, are both unsatisfying: extrapolation-based methods are dangerous because by definition they make predictions outside the range of available data, but Monte Carlo methods converge too slowly to routinely reach the desired 50-year return period estimates. Thus a search for a better method is warranted. We introduce an adaptive stratified importance sampling approach that allows for treating the choice of environmental conditions at which to run simulations as a stochastic optimization problem that minimizes the variance of unbiased estimates of extreme loads. Furthermore, the framework, built on the traditional bin-based approach used in extrapolation methods, provides a close connection between sampling and extrapolation, and thus allows the solution of the stochastic optimization (i.e., the optimal distribution of simulations in different wind speed bins) to guide and recalibrate the extrapolation. Results show that indeed this is a promising approach, as the variance of both the Monte Carlo and extrapolation estimates are reduced quickly by the adaptive procedure. We conclude, however, that due to the extreme response variability in turbine loads to the same environmental conditions, our method and any similar method quickly reaches its fundamental limits, and that therefore our efforts going forward are best spent elucidating the underlying causes of the response variability.},

doi = {10.5194/wes-3-475-2018},

journal = {Wind Energy Science (Online)},

number = 2,

volume = 3,

place = {United States},

year = {2018},

month = {7}

}

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