diff --git a/.gitattributes b/.gitattributes deleted file mode 100644 index f64cd7159..000000000 --- a/.gitattributes +++ /dev/null @@ -1,2 +0,0 @@ -$ cat .gitattributes -*.* linguist-language=matlab diff --git a/.github/workflows/unix_unit_tests.yml b/.github/workflows/unix_unit_tests.yml index 9a249f8ba..1d24690a5 100644 --- a/.github/workflows/unix_unit_tests.yml +++ b/.github/workflows/unix_unit_tests.yml @@ -2,9 +2,9 @@ name: MHKiT-MATLAB Unix Unit Tests on: push: - branches: [master, develop, ebbflood] + branches: [ master, develop ] pull_request: - branches: [master, develop, ebbflood] + branches: [ master, develop ] jobs: cache_population: @@ -35,7 +35,7 @@ jobs: shell: bash -l {0} run: | conda activate mhkit_conda_env - conda install numpy cython pip pytest hdf5 libnetcdf cftime netcdf4 + conda install numpy==1.24.4 cython pip pytest hdf5 libnetcdf cftime netcdf4 # conda install netcdf4 hdf5 # export PATH="${CONDA_PREFIX}/bin:${CONDA_PREFIX}/Library/bin:$PATH" # so setup.py finds nc-config @@ -67,6 +67,19 @@ jobs: conda activate mhkit_conda_env pip install -e . + - name: Pin scipy version + shell: bash -l {0} + run: | + conda activate mhkit_conda_env + pip uninstall -y scipy + pip install scipy==1.10.1 + + - name: List installed pip modules + shell: bash -l {0} + run: | + conda activate mhkit_conda_env + pip freeze + # Create the cache and add a dummy file # The dummy file ensures that the artifact download - name: Setup mhkit_webread_cache @@ -163,24 +176,24 @@ jobs: - matlab-version: R2020b python-version: 3.9 # Specific versions of tests that fail consistently. Most likely due to the GitHub actions environment - - matlab-version: R2024a # Python netcdf4 pip build error: https://github.com/MHKiT-Software/MHKiT-MATLAB/actions/runs/8789749433/job/24123413351 - python-version: 3.11 - os: macos-13 + # - matlab-version: R2024a # Python netcdf4 pip build error: https://github.com/MHKiT-Software/MHKiT-MATLAB/actions/runs/8789749433/job/24123413351 + # python-version: 3.11 + # os: macos-13 # - matlab-version: R2024a # Working! # python-version: "3.10" # os: macos-13 - - matlab-version: R2024a # Java Segfault on Python initialization: https://github.com/MHKiT-Software/MHKiT-MATLAB/actions/runs/8789749433/job/24123411604 - python-version: 3.9 - os: macos-13 - - matlab-version: R2023b # Python netcd4 pip build error: https://github.com/MHKiT-Software/MHKiT-MATLAB/actions/runs/8789749433/job/24123412889 - python-version: 3.11 - os: macos-13 - - matlab-version: R2023b # Java segfault on Python initialization: https://github.com/MHKiT-Software/MHKiT-MATLAB/actions/runs/8789749433/job/24123412352 - python-version: "3.10" - os: macos-13 - - matlab-version: R2023b # Java segfault on Python initialization: https://github.com/MHKiT-Software/MHKiT-MATLAB/actions/runs/8789749433/job/24123411335 - python-version: 3.9 - os: macos-13 + # - matlab-version: R2024a # Java Segfault on Python initialization: https://github.com/MHKiT-Software/MHKiT-MATLAB/actions/runs/8789749433/job/24123411604 + # python-version: 3.9 + # os: macos-13 + # - matlab-version: R2023b # Python netcd4 pip build error: https://github.com/MHKiT-Software/MHKiT-MATLAB/actions/runs/8789749433/job/24123412889 + # python-version: 3.11 + # os: macos-13 + # - matlab-version: R2023b # Java segfault on Python initialization: https://github.com/MHKiT-Software/MHKiT-MATLAB/actions/runs/8789749433/job/24123412352 + # python-version: "3.10" + # os: macos-13 + # - matlab-version: R2023b # Java segfault on Python initialization: https://github.com/MHKiT-Software/MHKiT-MATLAB/actions/runs/8789749433/job/24123411335 + # python-version: 3.9 + # os: macos-13 runs-on: ${{ matrix.os }} @@ -211,14 +224,14 @@ jobs: shell: bash -l {0} run: | conda activate mhkit_conda_env - conda install numpy cython pip pytest hdf5 libnetcdf cftime netcdf4 + conda install numpy==1.24.4 cython pip pytest hdf5 libnetcdf cftime netcdf4 # conda install netcdf4 hdf5 # export PATH="${CONDA_PREFIX}/bin:${CONDA_PREFIX}/Library/bin:$PATH" # so setup.py finds nc-config # - name: Setup Python ${{ matrix.python-version }} # shell: bash -l {0} # run: | - # conda create --name mhkit_conda_env python=${{ matrix.python-version }} numpy cython pip pytest hdf5 libnetcdf cftime netcdf4 --strict-channel-priority + # conda create --name mhkit_conda_env python=${{ matrix.python-version }} numpy==1.24.4 cython pip pytest hdf5 libnetcdf cftime netcdf4 --strict-channel-priority # conda activate mhkit_conda_env # export PATH="${CONDA_PREFIX}/bin:${CONDA_PREFIX}/Library/bin:$PATH" # so setup.py finds nc-config # pip install -e . --no-deps --force-reinstall @@ -292,6 +305,13 @@ jobs: conda activate mhkit_conda_env pip install -e . + - name: Pin scipy version + shell: bash -l {0} + run: | + conda activate mhkit_conda_env + pip uninstall -y scipy + pip install scipy==1.10.1 + - name: List installed pip modules shell: bash -l {0} run: | diff --git a/.github/workflows/windows_unit_tests.yml b/.github/workflows/windows_unit_tests.yml index b545c1ada..b86fb4478 100644 --- a/.github/workflows/windows_unit_tests.yml +++ b/.github/workflows/windows_unit_tests.yml @@ -2,9 +2,9 @@ name: MHKiT-MATLAB Windows Unit Tests on: push: - branches: [master, develop, ebbflood] + branches: [ master, develop ] pull_request: - branches: [master, develop, ebbflood] + branches: [ master, develop ] jobs: cache_population: @@ -33,8 +33,7 @@ jobs: - name: "Conda install netcdf4, hdf5" run: | conda activate mhkit_conda_env - conda install netcdf4 hdf5 - + conda install numpy==1.24.4 netcdf4 hdf5 - name: Check out MHKiT-MATLAB uses: actions/checkout@v4 @@ -61,6 +60,13 @@ jobs: conda activate mhkit_conda_env pip install -e . + - name: Pin scipy version + shell: bash -l {0} + run: | + conda activate mhkit_conda_env + pip uninstall -y scipy + pip install scipy==1.10.1 + # Create the cache and add a dummy file # The dummy file ensures that the artifact download - name: Setup mhkit_webread_cache @@ -69,7 +75,6 @@ jobs: mkdir mhkit_webread_cache touch mhkit_webread_cache/test.txt echo "Hello World" > mhkit_webread_cache/test.txt - - name: Set up MATLAB uses: matlab-actions/setup-matlab@v2 with: @@ -80,12 +85,10 @@ jobs: shell: pwsh run: > "pyenv(Version='{0}', ExecutionMode='OutOfProcess')" -f (python -c "import sys; print(sys.executable)") | Out-File -FilePath run.m - - name: Check Python System Path shell: bash -l {0} run: | echo "py.sys.path" >> run.m - - name: Add MATLAB test commands shell: bash run: echo "version, @@ -126,6 +129,7 @@ jobs: matlab-version: [R2021b, R2022a, R2022b, R2023a, R2023b, R2024a] mhkit-python-version: ["0.7.0"] exclude: + # Cache population job - matlab-version: R2022a python-version: 3.9 - matlab-version: R2023b @@ -176,20 +180,17 @@ jobs: shell: bash -l {0} run: | conda activate mhkit_conda_env - conda install netcdf4 hdf5 - + conda install numpy==1.24.4 netcdf4 hdf5 - name: Output python executable shell: bash -l {0} run: | conda activate mhkit_conda_env python -c "import sys; print(sys.executable)" - - name: Print Python Version shell: bash -l {0} run: | conda activate mhkit_conda_env python --version - - name: Check out MHKiT-MATLAB uses: actions/checkout@v4 @@ -210,31 +211,34 @@ jobs: run: | conda activate mhkit_conda_env pip install mhkit==$MHKIT_PYTHON_VERSION - - name: pip install mhkit-python-utils module from source shell: bash -l {0} run: | conda activate mhkit_conda_env pip3 install -e . + - name: Pin scipy version + shell: bash -l {0} + run: | + conda activate mhkit_conda_env + pip uninstall -y scipy + pip install scipy==1.10.1 + - name: List installed pip modules shell: bash -l {0} run: | conda activate mhkit_conda_env pip3 freeze - - name: Print MHKiT-Python Version shell: bash -l {0} run: | conda activate mhkit_conda_env python -c "import mhkit; print(mhkit.__version__)" - - name: Verify MHKiT-Python Operation shell: bash -l {0} run: | conda activate mhkit_conda_env python -c "import mhkit; [ED, AP] = mhkit.river.performance.circular(30); print(ED); print(AP);" - - name: Download mhkit_webread_cache artifact uses: actions/download-artifact@v4 with: @@ -255,19 +259,16 @@ jobs: run: | conda activate mhkit_conda_env printf "getenv('path')\nsetenv('path', ['%s;', getenv('path')])\ngetenv('path')\n" $(python -c "import sys; import os; print(os.path.dirname(sys.executable))") >> run.m - # OutOfProcess works reliably on linux, macos, and windows - name: Configure MATLAB pyenv Version and ExecutionMode shell: bash -l {0} run: | conda activate mhkit_conda_env printf "pyenv(Version='%s', ExecutionMode='OutOfProcess')\n" $(python -c "import sys; print(sys.executable)") >> run.m - - name: Check Python System Path shell: bash -l {0} run: | echo "py.sys.path" >> run.m - - name: Add MATLAB test commands shell: bash run: echo "version, diff --git a/.gitignore b/.gitignore index b8b7ac6e2..6fc2860a0 100644 --- a/.gitignore +++ b/.gitignore @@ -1,40 +1,78 @@ -*.xlsm -*.xlsx -*.pyc -test.egg-info/* -*.exe -*.spec -**/build -**./dist/ -**/cache/ -**/static/ -.DS_Store -.DS_Store? -._* -.Spotlight-V100 -.Trashes -ehthumbs.db -Thumbs.db -*.log -*.sql -*.sqlite -*.7z -*.dmg -*.gz -*.iso -*.jar -*.rar -*.tar -*.zip -*~ -*.json -*egg-info -*build -.gitignore - +# MHKiT-MATLAB Specific Files # Test results mhkit/tests/test_results/* -# MHKiT-MATLAB Specific Files # Hindcast data cache mhkit_webread_cache + +# MATLAB + +# Windows default autosave extension +*.asv + +# OSX / *nix default autosave extension +*.m~ + +# Compiled MEX binaries (all platforms) +*.mex* + +# Packaged app and toolbox files +*.mlappinstall +# *.mltbx + +# Generated helpsearch folders +helpsearch*/ + +# Simulink code generation folders +slprj/ +sccprj/ + +# Matlab code generation folders +codegen/ + +# Simulink autosave extension +*.autosave + +# Simulink cache files +*.slxc + +# Octave session info +octave-workspace + +# Python + +# Byte-compiled / optimized / DLL files +__pycache__/ +*.py[cod] +*$py.class + +# C extensions +*.so + +# Distribution / packaging +.Python +eggs/ +.eggs/ +sdist/ +var/ +wheels/ +share/python-wheels/ +*.egg-info/ +.installed.cfg +*.egg + +# MacOS + +# General +.DS_Store +.AppleDouble +.LSOverride + +# Files that might appear in the root of a volume +.DocumentRevisions-V100 +.fseventsd +.Spotlight-V100 +.TemporaryItems +.Trashes +.VolumeIcon.icns +.com.apple.timemachine.donotpresent diff --git a/README.md b/README.md index f74f034de..9fb6721f1 100644 --- a/README.md +++ b/README.md @@ -21,20 +21,22 @@ currently version `0.7.0`. You can achieve this by executing the following comma environment where MHKiT-Python is installed: 1. Uninstall the current version of MHKiT-Python: - ```bash - pip uninstall mhkit - ``` + +```bash +pip uninstall mhkit +``` 2. Install MHKiT-Python version `0.7.0`: - ```bash - pip install mhkit==0.7.0 - ``` + +```bash +pip install mhkit==0.7.0 +``` 3. Verify the MHKiT-Python version: - ```bash - python -c "import mhkit; print(mhkit.__version__)" - ``` +```bash +python -c "import mhkit; print(mhkit.__version__)" +``` ### Software Requirements @@ -43,12 +45,13 @@ compatible versions of Python and MHKiT-Python installed. MHKiT-MATLAB supports the following combinations of MATLAB and Python versions.[^1] -| | R2021b | R2022a | R2022b | R2023a | R2023b | -| ---- | ------ | ------ | ------ | ------ | ------ | -| 3.11 | - | - | - | - | ✓ | -| 3.10 | - | - | ✓ | ✓ | ✓ | -| 3.9 | ✓ | ✓ | ✓ | ✓ | ✓ | -| 3.8 | ✓ | ✓ | ✓ | ✓ | - | +| | R2021b | R2022a | R2022b | R2023a | R2023b | R2024a | +| ---- | ------ | ------ | ------ | ------ | ------ | ------ | +| 3.12 | - | - | - | - | - | - | +| 3.11 | - | - | - | - | ✓ | ✓ | +| 3.10 | - | - | ✓ | ✓ | ✓ | ✓ | +| 3.9 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | +| 3.8 | ✓ | ✓ | ✓ | ✓ | - | - | - ✓: MATLAB/Python versions compatible - `-`: MATLAB/Python versions not compatible @@ -69,30 +72,33 @@ The test matrices below detail the current state of unit testing. An "X" indicat #### Linux (`ubuntu-latest`) -| | R2021b | R2022a | R2022b | R2023a | R2023b | -| ---- | ------ | ------ | ------ | ------ | ------ | -| 3.11 | - | - | - | - | ✓ | -| 3.10 | - | - | ✓ | ✓ | ✓ | -| 3.9 | ✓ | ✓ | ✓ | ✓ | ✓ | -| 3.8 | ✓ | ✓ | ✓ | ✓ | - | +| | R2021b | R2022a | R2022b | R2023a | R2023b | R2024a | +| ---- | ------ | ------ | ------ | ------ | ------ | ------ | +| 3.12 | - | - | - | - | - | - | +| 3.11 | - | - | - | - | ✓ | ✓ | +| 3.10 | - | - | ✓ | ✓ | ✓ | ✓ | +| 3.9 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | +| 3.8 | ✓ | ✓ | ✓ | ✓ | - | - | #### macOS (`macos-latest`) -| | R2021b | R2022a | R2022b | R2023a | R2023b | -| ---- | ------ | ------ | ------ | ------ | -------------------------- | -| 3.11 | - | - | - | - | X[^macos-311-action-error] | -| 3.10 | - | - | ✓ | ✓ | ✓ | -| 3.9 | ✓ | ✓ | ✓ | ✓ | ✓ | -| 3.8 | ✓ | ✓ | ✓ | ✓ | ✓ | +| | R2021b | R2022a | R2022b | R2023a | R2023b | R2024a | +| ---- | ------ | ------ | ------ | ------ | ------ | ------ | +| 3.12 | - | - | - | - | - | - | +| 3.11 | - | - | - | - | ✓ | ✓ | +| 3.10 | - | - | ✓ | ✓ | ✓ | ✓ | +| 3.9 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | +| 3.8 | ✓ | ✓ | ✓ | ✓ | - | - | #### Windows (`windows-latest`) -| | R2021b | R2022a | R2022b | R2023a | R2023b | -| ---- | ------ | ------ | ------ | ------ | --------------------------------- | -| 3.11 | - | - | - | - | X[^windows-gt-2022a-action-error] | -| 3.10 | - | - | X | X | X | -| 3.9 | ✓ | ✓ | X | X | X | -| 3.8 | ✓ | ✓ | X | X | X | +| | R2021b | R2022a | R2022b | R2023a | R2023b | R2024a | +| ---- | ------ | ------ | ------ | ------ | ------ | ------ | +| 3.12 | - | - | - | - | - | - | +| 3.11 | - | - | - | - | ✓ | ✓ | +| 3.10 | - | - | ✓ | ✓ | ✓ | ✓ | +| 3.9 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | +| 3.8 | ✓ | ✓ | ✓ | ✓ | - | - | ### Legend @@ -147,29 +153,3 @@ See [copyright and license](https://mhkit-software.github.io/MHKiT/license.html) [^1]: For a comprehensive list of compatible MATLAB/Python versions, refer to the [MathWorks Python Compatibility Documentation](https://www.mathworks.com/support/requirements/python-compatibility.html). - -[^macos-311-action-error]: - -[macOS Python 3.11 action error](https://github.com/MHKiT-Software/MHKiT-MATLAB/actions/runs/7143629923/job/19455784365#step:20:3373) - - ``` - Python Error: ImportError: - dlopen(/usr/local/miniconda/envs/MHKIT_CONDA_ENV/lib/python3.11/site-packages/netCDF4/_netCDF4.cpython-311-darwin.so, - 0x0002): Symbol not found: (_SSL_get0_group_name) - Referenced from: - '/usr/local/miniconda/envs/MHKIT_CONDA_ENV/lib/libcurl.4.dylib' - Expected in: - '/Users/runner/hostedtoolcache/MATLAB/2023.2.999/x64/MATLAB.app/bin/maci64/libssl.3.dylib' - ``` - -[^windows-gt-2022a-action-error]: - [Windows MATLAB > 2022a action error](https://github.com/MHKiT-Software/MHKiT-MATLAB/pull/108/commits/63fbf91543392e2fc673a67af52e152ff15f2980) - - ``` - Error: Caught "std::exception" Exception message is: - Unable to launch Simple server: Unable to launch C:\Program Files\MATLAB\R2023b\interprocess\bin\win64\pycli\MATLABPyHost.exe - because: Peer process exited before transport type handshake. Exit status: 3221226505 - - ERROR: MATLAB error Exit Status: 0x00000001 - exit status 1 - ``` diff --git a/changelog.md b/changelog.md new file mode 100644 index 000000000..444ee8c60 --- /dev/null +++ b/changelog.md @@ -0,0 +1,18 @@ +# `v0.5.0` + +## New Features + +- Addition of the WEC Design Response Toolbox within the `wave` module #127 + - Estimate extreme sea states based on short term data +- Addition of the Delft3D input and analysis within the `tidal` module #124 + - Analyze modeled river/tidal flow data using same tools as ADCP and resource data + +## Improvements + +- More detailed and complete [installation instructions](https://mhkit-software.github.io/MHKiT/matlab_installation.html) +- Update MATLAB/Python compatibility matrix + +## Fixes + +- Allow user to specific surface elevation generation method #126 +- Properly map the gamma parameter in the `jonswap` function #136 diff --git a/dist/mhkit_python_utils-0.1.0-py3.7.egg b/dist/mhkit_python_utils-0.1.0-py3.7.egg deleted file mode 100644 index 16b05312a..000000000 Binary files a/dist/mhkit_python_utils-0.1.0-py3.7.egg and /dev/null differ diff --git a/examples/data/loads/block_maxima.mat b/examples/data/loads/block_maxima.mat new file mode 100644 index 000000000..9378eeed5 Binary files /dev/null and b/examples/data/loads/block_maxima.mat differ diff --git a/examples/data/loads/example_qoi.mat b/examples/data/loads/example_qoi.mat new file mode 100644 index 000000000..d03a734f0 Binary files /dev/null and b/examples/data/loads/example_qoi.mat differ diff --git a/examples/data/loads/sine_wave.csv b/examples/data/loads/sine_wave.csv new file mode 100644 index 000000000..a22ed9d8c --- /dev/null +++ b/examples/data/loads/sine_wave.csv @@ -0,0 +1,15 @@ +t_peaks,peaks +0.015,0.809016994 +0.035,0.809016994 +0.05,1 +0.065,0.809016994 +0.085,0.809016994 +0.1,1 +0.115,0.809016994 +0.135,0.809016994 +0.15,1 +0.165,0.809016994 +0.185,0.809016994 +0.2,1 +0.215,0.809016994 +0.235,0.809016994 diff --git a/examples/data/loads/ste.mat b/examples/data/loads/ste.mat new file mode 100644 index 000000000..e63d7bb60 Binary files /dev/null and b/examples/data/loads/ste.mat differ diff --git a/examples/data/loads/time_series_for_extremes.txt b/examples/data/loads/time_series_for_extremes.txt new file mode 100644 index 000000000..251cb301f --- /dev/null +++ b/examples/data/loads/time_series_for_extremes.txt @@ -0,0 +1,216010 @@ +0.000000000000000000e+00 1.981130564955001228e-01 +4.999791675346860337e-02 3.702829908768426326e-01 +9.999583350693720674e-02 4.014080685846332375e-01 +1.499937502604058170e-01 1.727952703445220783e-01 +1.999916670138744135e-01 -1.071163373123065060e-01 +2.499895837673430099e-01 -2.651761134854038748e-01 +2.999875005208116341e-01 -2.765758691005939518e-01 +3.499854172742802305e-01 -3.078658245241157054e-01 +3.999833340277488269e-01 -3.084471807485077433e-01 +4.499812507812174234e-01 -2.984649254940145435e-01 +4.999791675346860198e-01 -1.855234972536831950e-01 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Delft3D IO Module

The following example will familiarize the user with using the Delft3D (mhkit/river/IO/delft_3d)module in MHKiT-MATLAB. The Delft3D module can be used to plot the data from a NetCDF output from Delft3D SNL-D3D-CEC-FM. This example will walk through a flume case with a turbine. The flume is 18 m long, 4 m wide and 2m deep with the turbine placed at 6 m along the length and 3 m along the width. The turbine used for this simulation has a circular cross-section with a diameter of 0.7m, a thrust coefficient of 0.72, and a power coefficient of 0.45. The simulation was run with 5 depth layers and 5-time intervals over 4 min.
This example will show how to create a centerline plot at a desired depth for different variables outputs of Delft3D. It will also show how to make a contour plot of a given plane or depth for the variable output by Delft3D and how to use those variables to calculate turbulence intensity. This module can be helpful to visualize the wake of a turbine and help predict how a turbine will affect the surrounding area.

Loading Data from Delft3D as NetCDF

A NetCDF file has been saved in the MHKiT-MATLAB\examples\data\river\d3d\ directory of a simple flume case with a turbine for reference data. In this code section we define the location of the Delft 3D output NetCDF file and read the file into ds (dataset). Note that this requires having the MHKiT-MATLAB/examples directory within your path. This can be done by navigating to the MHKiT-MATLAB folder within MATLAB, right clicking on the examples folder and adding the folder and subfolder to the path. You can also modify delft_3d_turbine_test_file to point to the turbineTest_map.nc file
Opening a Delft3D NetCFD output file:
delft_3d_turbine_test_file = "examples/data/river/d3d/turbineTest_map.nc";
ds = delft_3d_open_netcdf(delft_3d_turbine_test_file);
There are many variables saved in within the Delft3D NetCDF . Prior to starting data analysis we should verify the input data contains the information needed for further processing.The function delft_3d_get_keys takes a NetCDF object and returns a struct of the available data. In the code section below we pass in the NetCDF dataset and display the output of delft_3d_get_keys.
disp(delft_3d_get_keys(ds));
mesh2d_enc_x: 'x-coordinate' + mesh2d_enc_y: 'y-coordinate' + mesh2d_enc_node_count: 'count of coordinates in each instance geometry' + mesh2d_enc_part_node_count: 'count of nodes in each geometry part' + mesh2d_enc_interior_ring: 'type of each geometry part' + mesh2d_enclosure_container: '' + Mesh2D: '' + NetNode_x: 'x-coordinate' + NetNode_y: 'y-coordinate' + projected_coordinate_system: '' + NetNode_z: 'bed level at net nodes (flow element corners)' + NetLink: 'link between two netnodes' + NetLinkType: 'type of netlink' + NetElemNode: 'mapping from net cell to net nodes (counterclockwise)' + NetElemLink: 'mapping from net cell to its net links (counterclockwise)' + NetLinkContour_x: 'list of x-contour points of momentum control volume surrounding each net/flow link' + NetLinkContour_y: 'list of y-contour points of momentum control volume surrounding each net/flow link' + NetLink_xu: 'x-coordinate of net link center (velocity point)' + NetLink_yu: 'y-coordinate of net link center (velocity point)' + BndLink: 'netlinks that compose the net boundary' + FlowElem_xcc: 'x-coordinate of flow element circumcenter' + FlowElem_ycc: 'y-coordinate of flow element circumcenter' + FlowElem_zcc: 'bed level of flow element' + FlowElem_bac: 'flow element area' + FlowElem_xzw: 'x-coordinate of flow element center of mass' + FlowElem_yzw: 'y-coordinate of flow element center of mass' + FlowElemContour_x: 'list of x-coordinates forming flow element' + FlowElemContour_y: 'list of y-coordinates forming flow element' + FlowElem_bl: 'Initial bed level at flow element circumcenter' + ElemLink: 'flow nodes between/next to which link between two netnodes lies' + FlowLink: 'link/interface between two flow elements' + FlowLinkType: 'type of flowlink' + FlowLink_xu: 'x-coordinate of flow link center (velocity point)' + FlowLink_yu: 'y-coordinate of flow link center (velocity point)' + FlowLink_lonu: 'longitude' + FlowLink_latu: 'latitude' + time: '' + LayCoord_cc: 'sigma layer coordinate at flow element center' + LayCoord_w: 'sigma layer coordinate at vertical interface' + timestep: '' + s1: 'water level' + waterdepth: 'water depth' + unorm: 'normal component of sea_water_speed' + ucz: 'upward velocity on flow element center' + ucxa: 'depth-averaged velocity on flow element center, x-component' + ucya: 'depth-averaged velocity on flow element center, y-component' + ww1: 'upward velocity on vertical interface' + ucx: 'velocity on flow element center, x-component' + ucy: 'velocity on flow element center, y-component' + turkin1: 'turbulent kinetic energy' + vicwwu: 'turbulent vertical eddy viscosity' + tureps1: 'turbulent energy dissipation'

Note: Input NetCDF File Troubleshooting

To avoid code duplication MHKiT-MATLAB performs numerical processing within MHKiT-Python. In the above code section we open the input NetCDF file as a Python object. For troubleshooting purposes it may be necessary to open a NetCDF file directly within MATLAB. The following code section uses the ncinfo function to read a NetCDF into a structure.
% Optional NetCDF check using native MATLAB NetCDF reader
% ds_check = ncinfo(delft_3d_turbine_test_file);
% ds_check.Variables

Seconds Run and Time Index

Within the Delft3D data the time_index variable can be used to pull data from different instances in time. For the example data included there are 5-time steps meaning we have indexes in the range 1 to 5. Each time index has an associated seconds_run that quantifies the number of seconds that passed from the start of the simulation. To get all of the seconds_run for a data set use the function delft_3d_get_all_time the output is an array of all the seconds_run for the input data.
time = delft_3d_get_all_time(ds);
disp(time);
0 60 120 180 240
To get the seconds at a specified index use the function delft_3d_index_to_seconds
seconds_at_index = delft_3d_index_to_seconds(ds, 2);
disp(seconds_at_index);
60
To get the index at a specific elapsed second use the function delft_3d_seconds_to_index. This function will provide the index nearest the input seconds elapsed.
index_at_second = delft_3d_seconds_to_index(ds, 65);
/opt/homebrew/lib/python3.11/site-packages/mhkit/river/io/d3d.py:76: UserWarning: Warning: seconds_run not found. Closest time stampfound {times[idx]} + return _convert_time(data, seconds_run=seconds_run)
disp(index_at_second);
2

Variable Struct From NetCDF

For this example we will create a MATLAB struct from the Delft3D output using the variable 'ucx', the velocity in the x-direction (see available data in previous block output). MHKiT MATLAB's delft_3d_get_all_data_points function will pull all the raw data from the NetCDF file for the specified variable at a specific time index into a structure. The time_index can be used to pull data from a different instances in time (the last valid time_index, time_index=-1, is the default setting). If an integer outside of the valid range is entered the code will output an error with the max valid output listed. The output data from delft_3d_get_all_data_points will be the position (x, y, waterdepth) in meters, the value of vairable in meters per second and the run time of the simulation in seconds or 'x', 'y', 'waterdepth', 'waterlevel', 'ucx', and 'time'. The time run in simulation varies based on the 'time_step'.
% Getting variable data
x_velocity_key = "ucx";
run_timestamps = delft_3d_get_all_time(ds);
seconds_into_simulation = run_timestamps(1, 4);
disp(seconds_into_simulation);
180
In MHKiT-MATLAB we typically return a structure containg the results from a function with multiple outputs. In the code below delft_3d_get_all_data_points returns a struct:
seconds_into_simulation_index = delft_3d_convert_time(ds, seconds_into_simulation);
 
x_velocity_point_data = delft_3d_get_all_data_points(ds, x_velocity_key, seconds_into_simulation_index);
 
disp(x_velocity_point_data);
x: [0.1250 0.3750 0.1250 0.6250 0.3750 0.1250 0.8750 0.6250 0.3750 0.1250 1.1250 0.8750 0.6250 0.3750 0.1250 1.3750 1.1250 0.8750 0.6250 0.3750 0.1250 1.6250 1.3750 1.1250 0.8750 0.6250 0.3750 0.1250 1.8750 1.6250 1.3750 … ] (1×5760 double) + y: [1.1250 1.1250 1.3750 1.1250 1.3750 1.6250 1.1250 1.3750 1.6250 1.8750 1.1250 1.3750 1.6250 1.8750 2.1250 1.1250 1.3750 1.6250 1.8750 2.1250 2.3750 1.1250 1.3750 1.6250 1.8750 2.1250 2.3750 2.6250 1.1250 1.3750 1.6250 … ] (1×5760 double) + waterdepth: [0.1995 0.2000 0.1995 0.2001 0.2000 0.1995 0.2001 0.2001 0.2000 0.1995 0.2000 0.2001 0.2001 0.2000 0.1995 0.2000 0.2000 0.2001 0.2001 0.2000 0.1995 0.2000 0.2000 0.2000 0.2001 0.2001 0.2000 0.1995 0.2000 0.2000 0.2000 … ] (1×5760 double) + waterlevel: [-0.0052 8.1291e-05 -0.0052 5.5880e-04 8.1324e-05 -0.0052 5.0091e-04 5.5884e-04 8.1385e-05 -0.0052 4.4621e-04 5.0097e-04 5.5892e-04 8.1465e-05 -0.0052 3.8288e-04 4.4630e-04 5.0108e-04 5.5902e-04 8.1552e-05 -0.0052 … ] (1×5760 double) + ucx: [0.7179 0.6896 0.7179 0.6942 0.6896 0.7179 0.6919 0.6942 0.6896 0.7179 0.6920 0.6919 0.6942 0.6896 0.7179 0.6915 0.6920 0.6919 0.6942 0.6896 0.7179 0.6911 0.6915 0.6920 0.6919 0.6942 0.6896 0.7179 0.6907 0.6911 0.6915 … ] (1×5760 double) + time: [240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 … ] (1×5760 double)

Figure Output Definitions

In the following code section we define variables that control the figure outputs.
The limits max_plot_vel and min_plot_vel define the vizualization boundaries of the next 3 example plots.
% Setting plot limits
max_plot_vel = 1.25;
min_plot_vel = 0.5;
 
% Defining Figure Size
fig_width = 1200;
fig_height = 400;
The contour_level and grid_size set discrete levels for the output visualizations.
% Set the contour level for all plots below
contour_level = 9;
grid_size = 25;

Plotting a Line Plot Between Two Points

To view the maximum wake effect of the turbine we can plot a velocity down the centerline of the flume. To do this we will create an array between two points down the center of the flume. We will then interpolate the grided data results onto our centerline array. Since the flume is rectangular the centerline points are found by taking the average of the maximum and minimum value for the width, y, and the waterdepth, of the flume. We will then input one array, x, and two points, y and waterdepth into the function delft_3d_create_points to create our centerline array to interpolate over. The function delft_3d_create_points will then output a struct, cline_points, with fieldnames 'x', 'y', and 'waterdepth'.
% Use rectangular grid min and max to find flume centerline
xmax = min(x_velocity_point_data.x);
xmin = max(x_velocity_point_data.x);
 
ymax = min(x_velocity_point_data.y);
ymin = max(x_velocity_point_data.y);
 
waterdepth_max = min(x_velocity_point_data.waterdepth);
waterdepth_min = max(x_velocity_point_data.waterdepth);
 
num_points = 50; % 50 is the numpy default
x = linspace(xmin, xmax, num_points);
y = mean([ymax, ymin]);
waterdepth = mean([waterdepth_max, waterdepth_min]);
cline_points = delft_3d_create_points(x, y, waterdepth);
Next the variable ucx is interpolated onto the created cline_points using the delft_3d_interpolate_to_centerline function and saved as cline_variable. The results are then plotted for velocity in the x direction, ucx, along the length of the flume, x.
points = [x_velocity_point_data.x; x_velocity_point_data.y; x_velocity_point_data.waterdepth];
values = x_velocity_point_data.(x_velocity_key);
xi = [cline_points.x; cline_points.y; cline_points.waterdepth];
cline_variable = delft_3d_interpolate_to_centerline(points, values, xi);
figure('position', [0, 0, fig_width, fig_height]);
plot(x, cline_variable);
grid("on");
xlabel("x [m]")
ylabel("u_x [m/s]")
title(sprintf("Centerline Velocity at: %d s", x_velocity_point_data.time(1)))

Contour Plot for a Given Sigma Layer

Sometimes it is useful to plot only the raw data of a given layer. To do this use delft_3d_get_layer_data, passing a NetCDF object, a key and a layer, to output a single layer of raw data from the NetCDF object. The variable is set to the velocity in the x direction, 'ucx', and the layer of data to plot as 2. Since there are 5 sigma layers in this example layer 2 is approximately the middle layer. layer works as an index that begins at begins at 1 and ends at 5. delft_3d_get_layer_data outputs a struct of layer_data with the fieldnames 'x', 'y', 'waterdepth', 'waterlevel', 'v', and 'time' as the length, width, waterdepth, value, and run time of simulation of the specified variable in this case velocity in the x direction, 'ucx'.
To plot the data the maximum and minimum, max_plot_vel and min_plot_vel, values are pulled from above to limit bounds of the color bar to show the value of the specified variable, in this case it's velocity in the x direction. The type of plot is also defined as a string 'contour' to add to the title of the plot.
layer = 2;
layer_data = delft_3d_get_layer_data(ds, x_velocity_key, layer);
 
% Create a meshgrid using the layers
[x_grid, y_grid] = meshgrid(linspace(min(layer_data.x), max(layer_data.x), grid_size), ...
linspace(min(layer_data.y), max(layer_data.y), grid_size));
v_interp = griddata(layer_data.x, layer_data.y, layer_data.v, x_grid, y_grid);
 
 
% Plot filled contours
figure('position', [0, 0, fig_width, fig_height])
contourf(x_grid, y_grid, v_interp, contour_level, 'LineStyle', 'none');
 
% Add colorbar
h = colorbar;
clim([min_plot_vel, max_plot_vel]); % Set color axis limits
colormap(viridis_colormap(contour_level)); % Set colormap with discrete levels
 
% Add Labels
xlabel('x [m]');
ylabel('y [m]');
title(['Velocity on Layer ', num2str(layer), ' at Time: ', num2str(layer_data.time(1)), ' s']);
% Add units to colorbar
ylabel(h, '$u_x$ [m/s]', 'Interpreter', 'latex');

Plotting a Contour Plot of a given Plane

If you wanted to look at a contour plot of a specific waterdepth you can create a contour plot over given points. Expanding on the centerline array points we can create a grid using the same delft_3d_create_points function by inputting two arrays along the length of the flume, x , and width of the flume, y_contour , and one point for the waterdepth we want to look at. delft_3d_create_points then outputs a struct into contour_points of points to calculate the contour values over with the fieldnames 'x', 'y', and 'waterdepth'.
x2 = linspace(xmin, xmax, 100);
y_contour = linspace(ymin, ymax, 40);
z2 = mean([waterdepth_max, waterdepth_min]);
 
contour_points = delft_3d_create_points(x2, y_contour, z2);
[0, 1, 2]
points = [x_velocity_point_data.x; x_velocity_point_data.y; x_velocity_point_data.waterdepth];
values = x_velocity_point_data.(x_velocity_key);
xi = [contour_points.x; contour_points.y; contour_points.waterdepth];
 
contour_variable = delft_3d_interpolate_to_centerline(points, values, xi);
The results are then plotted. The minimum and maximum values show on the graph are pulled from above (max_plot_vel and min_plot_vel) as in the previous example. The contour plot of the velocity is then output at the center waterdepth of the flume.
[x_grid, y_grid] = meshgrid(linspace(min(contour_points.x), max(contour_points.x), grid_size), ...
linspace(min(contour_points.y), max(contour_points.y), grid_size));
v_interp = griddata(contour_points.x, contour_points.y, contour_variable, x_grid, y_grid);
 
% Plot filled contours
figure('position', [0, 0, fig_width, fig_height])
contourf(x_grid, y_grid, v_interp, contour_level, 'LineStyle', 'none');
colorbar; % Add color bar
clim([min_plot_vel, max_plot_vel]); % Set color axis limits
colormap(viridis_colormap(contour_level));
xlabel('x [m]');
ylabel('y [m]');
title("Velocity of x-y Plane");
 
% Add units label to colorbar
h = colorbar;
ylabel(h, '$u_x$ [m/s]', 'Interpreter', 'latex');

Contour Plot of Turbulent Intensity

Turbulent Intensity is the ratio of the magnitude of turbulent velocity to total velocity. The function delft_3d_calculate_turbulent_intensity takes the inputs of the NetCDF object, the points to calculate over, the time index, and boolean input to output intermediate_values used to calculate turbulent intensity. The fuction then pulls variables 'ucx', 'ucy', 'ucz', and 'turkin1' as the velocity in the x, y, waterdepth and turbulence kinetic energy respectively. The function then calculates and outputs the turbulent intensity into turbulent_intensity, for any given time_index in the data_frame TI. The TI struct also includes the x,y, and waterdepth location. If the intermediate_values boolean is equal to true the turbulent kinetic energy 'turkin1', and velocity in the 'ucx', 'ucy', and 'ucz' direction are also included.
In this example it is calculating the turbulent intensity over the same contour_points used above, however it can also calculate over 'cells', the coordinate system for the raw velocity data, or 'faces', the coordinate system for the raw turbulence data. If nothing is specified for points, 'cells' is the default coordinate system.
Following the same format as the previous two contour plots the limits of the maximum and minimum values are defined by user as well as a string for the type of plot. The code then outputs a contour plot of the turbulent intensity.
turbulent_intensity = delft_3d_calculate_turbulent_intensity(ds, contour_points, true);
points provided
max_plot_ti = 27;
min_plot_ti = 0;
grid_size = 1000;
 
[x_grid, y_grid] = meshgrid(linspace(min(turbulent_intensity.x), max(turbulent_intensity.x), grid_size), ...
linspace(min(turbulent_intensity.y), max(turbulent_intensity.y), grid_size));
v_interp = griddata(turbulent_intensity.x, turbulent_intensity.y, turbulent_intensity.turbulent_intensity, x_grid, y_grid);
 
% Plot filled contours
figure('position', [0, 0, fig_width, fig_height]);
contourf(x_grid, y_grid, v_interp, contour_level, 'LineStyle', 'none');
colorbar; % Add color bar
clim([min_plot_ti, max_plot_ti]); % Set color axis limits
colormap(viridis_colormap(contour_level)); % Set colormap (optional)
xlabel('x [m]');
ylabel('y [m]');
title("Turbulent Intensity");
 
% Add units label to colorbar
h = colorbar;
ylabel(h, 'Turbulent Intensity [%]');

Comparing Face Data to Cell Data

In Delft3D there is a staggered grid where some variables are stored on the faces and some are stored on the cells. The delft_3d_calculate_variable_interpolation function allows you to linearly interpolate face data onto the cell locations or vice versa. For this example, we input the variable names, 'ucx', 'ucy','ucz', and 'turkin1', which are pulled from the NetCDF object (ds) and are to be interpolated on to the coordinate system 'faces'. The output is a struct of interpolated data that we store in var_interpolation.
variables = {'turkin1', 'ucx', 'ucy', 'ucz'};
 
var_interpolation = delft_3d_calculate_variable_interpolation(ds, variables, "faces", "nearest");
Near the boundaries interpolation will sometimes return negative values. When calculating turbulent intensity, negative turbulent kinetic energy values (turkin1) are invalid and must be filtered out. The function delft_3d_cleanup_turbulent_kinetic_energy takes an array of turbulent kinetic energy values and a negative threshold and converts values below the threshold to NaN and values between the threshold and 0 to 0. In the following code section we modify the turkin1 fieldname of var_interpolation by passing the turkin1 array and a threshold of -0.001.
% Set turkin1 values below this threshold to NaN and values between this
% threshold and 0 to 0
kinetic_energy_cleanup_threshold = -0.001;
var_interpolation.turkin1 = delft_3d_cleanup_turbulent_kinetic_energy(var_interpolation.turkin1, kinetic_energy_cleanup_threshold);
To calculate turbulent intensity the magnitude of the velocity is calculated with 'ucx', 'ucy', 'ucz' and saved as u_mag. Turbulent intensity is then calculated with u_mag and turkin1 and saved as turbulent_intensity.
We now have 'ucx' and 'turkin1' on the same grid so then can be compared and used in calculations.
% Calculating the root mean squared velocity
var_interpolation.u_mag = delft_3d_calculate_unorm(var_interpolation.ucx, var_interpolation.ucy, var_interpolation.ucz);
 
% Calculating turbulent intensity as a percent
var_interpolation.turbulent_intensity = (sqrt(2/3 * var_interpolation.turkin1) ./ var_interpolation.u_mag) * 100;

Plotting Turbulent Intensity

When plotting data using delft_3d_calculate_variable_interpolation it is helpful to define points to interpolate onto as the 'cell' and 'face' grids contain a 3 dimensional grid of points. In this next example we will use the delft_3d_calculate_variable_interpolation function to plot a contour plot of tubulent intesity normal to turbine (y-waterdepth cross section) n turbine diameters downstream of the turbine.
As stated in the intro, the turbine is located at 6m along the length turbine_x_loc with a diameter of 0.7m (turbine_diameter). Similar to the previous example, we input the variable names variables 'ucx', 'ucy','ucz', and 'turkin1', which are pulled from the NetCDF object (ds). Unlike the previous example, the points are defined as sample_points created using create_points from x_sample, y_sample, and waterdepth_sample with x_sample at a constant point of 1 (N) turbine diameters downstream of the turbine (6.7m) and y_sample and waterdepth_sample being arrays between the minimum and maximum values for that flume dimension. The interpolated data is the saved from delft_3d_calculate_variable_interpolation as Var_sample and used to calculate turbulent intensity as in the previous example. The data is then plotted along the y and waterdepth axis.
turbine_x_loc = 6;
turbine_diameter = 0.7;
N = 1;
x_sample = turbine_x_loc + N * turbine_diameter;
y_samples = linspace(ymin, ymax, 40);
waterdepth_samples = linspace(waterdepth_min, waterdepth_max, 256);
 
variables = {'turkin1', 'ucx', 'ucy', 'ucz'};
sample_points = delft_3d_create_points(x_sample, y_samples, waterdepth_samples);
[0, 1, 2]
Var_sample = delft_3d_calculate_variable_interpolation(ds, variables, sample_points, "nearest");
points provided
Var_sample.u_mag = delft_3d_calculate_unorm(Var_sample.ucx, Var_sample.ucy, Var_sample.ucz);
Var_sample.turbulent_intensity = sqrt(2/3 * Var_sample.turkin1) ./ Var_sample.u_mag * 100;
grid_size = 100;
 
[x_grid, y_grid] = meshgrid(linspace(min(Var_sample.y), max(Var_sample.y), grid_size), ...
linspace(min(Var_sample.waterdepth), max(Var_sample.waterdepth), grid_size));
v_interp = griddata(Var_sample.y, Var_sample.waterdepth, Var_sample.turbulent_intensity, x_grid, y_grid);
contour_level = 10;
% Plot filled contours
figure('position', [0, 0, fig_width - 300, fig_height]);
contourf(x_grid, y_grid, v_interp, contour_level, 'LineStyle', 'none');
colorbar; % Add color bar
clim([min_plot_ti, max_plot_ti]); % Set color axis limits
colormap(viridis_colormap(contour_level)); % Set colormap (optional)
xlabel('y [m]');
ylabel('z [m]');
title("Turbulent Intensity");
 
% Add units label to colorbar
h = colorbar;
ylabel(h, 'Turbulent Intensity [%]');
This sample data used in this example is not spatial or temporally resolved and is for demonstration purposes only. In this example there are 5 sigma layers. The low level of discretization can be seen in in the sharp edges in the turbulent intensity plot above around the turbine.
+
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MHKiT Environmental Contours

Environmental contours of extreme sea states can be used as a part of reliability-based design for offshore structures, including wave energy converters (WECs). Environmental contours provide estimations of extreme sea states based on short-term data (e.g., 10 years used to estimate a 100-year event). These environmental contours describe extreme sea states by characterizing the resource, defining sea states for extreme condition analysis, and developing a framework for analyzing survivability of a design.
MHKiT includes functions adapted from the WDRT for creating environmental contours of extreme sea states using a principal component analysis (PCA) methodology, with additional improvements for characterizing the joint probability distribution of sea states. As a demonstration, this notebook will walk through the following steps to find a 100-year sea state for NDBC buoy 46022 using 16 years of spectral wave density data.
  1. Request Spectral Wave Density Data from NDBC
  2. Calculate Hm0 and Te using the requested data
  3. Find the data's 100-year contour
  4. Plot the data and the 100-year contour

1. Request Spectral Wave Density Data from NDBC

MHKiT can be used to request historical data from the National Data Buoy Center (NDBC). This process is split into the following steps:

Query available NDBC data

The NDBC_available_data function requires a parameter to be specified and optionally the user may provide a station ID as a string. We are interested in historical spectral wave density data 'swden' (from which we may calculate Hm0 and Te). Additionally, we will specify the buoy number as '46022' to only return data associated with this site.
% Specify the parameter as spectral wave density and the buoy number to be 46022
parameter = 'swden';
buoy_number = '46022';
available_data= NDBC_available_data(parameter,"buoy_number", buoy_number);
Data request URL: https://www.ndbc.noaa.gov/data/historical/swden
available_data
available_data = struct with fields:
Station_id: [25×1 string] - year: [25×1 double] - file: [25×1 string] -

Select years of interest

The NDBC_available_data function has returned a Table with columns 'Station_id', 'year', and 'file'. In this case, the years returned from NDBC_available_data span 1996 to the last complete year the buoy was operational (currently 2019 for 46022). For demonstration, we have decided we are interested in the data between the years 1996 and 2012 so we will create a new filenames_of_interest variable which only contains filenames of years less than 2013.
% Slice the available data to only include through year 2012
rows = (available_data.year < 2013) ;
filenames_of_interest = available_data.file(rows);
filenames_of_interest
filenames_of_interest = 17×1 string
"46022w1996.tx…
"46022w1997.tx…
"46022w1998.tx…
"46022w1999.tx…
"46022w2000.tx…
"46022w2001.tx…
"46022w2002.tx…
"46022w2003.tx…
"46022w2004.tx…
"46022w2005.tx…

Request Data from NDBC

To get the NDBC data we can use the NDBC_request_data function to iterate over each buoy id and year in passed filenames. This function will return the parameter data as a structure of structures which may be accessed by buoy id and then the year for multiple buoys or just the year for a single buoy. An additional data column called 'time' is created with time in datetime format.
ndbc_requested_data = NDBC_request_data(parameter, filenames_of_interest);

2. Calculate Hm0 and Te using the NDBC Data

A sea state may be characterized by significant wave height (Hm0) and energy period (Te). Using the historical spectral wave density data from NDBC, we can calculate these variables using MHKiT. Both Hm0 and Te return a single value for a given time (e.g., DateTime index).
Hm0 = [];
Te = [];
for field = fieldnames(ndbc_requested_data)'
Hm0 = [Hm0 ; significant_wave_height(ndbc_requested_data.(field{1}))];
Te = [Te ; energy_period(ndbc_requested_data.(field{1}))];
end

3. Find the 100-year contour line

With the sea state data calculated, we can now use the modified I-FORM method to define reliability for a 100-year sea state based on the 17 years of spectral wave density data obtained from NDBC for buoy 46022. Reliability is the likelihood that a certain event will not occur in a given period. The period will define a line of constant probability in the joint probability of Hm0 and Te but individually each component different reliability (marginal distribution) which we can find by evaluating a normal cumulative distribution function (CDF). This CDF returns each component's quantiles along the iso-reliability line that finally allows us to calculate each sea state value (e.g., the 100-year contour values for Hm0 and Te).
For more detail on the environmental contour method used here please refer to: Eckert-Gallup et. al 2016
To apply the environmental contours function we will specify a 100-year sea state, the sea state data (Hm0, Te), and the time difference between measurements (dt in seconds).
% Return period (years) of interest
period = 100 ;
 
% Remove Hm0 Outliers and NaNs
filter = Hm0 < 20;
Hm0 = Hm0(filter);
Te = Te(filter);
[row, col] = find(~isnan(Te));
Hm0 = Hm0(row);
Te = Te(row);
[row, col] = find(~isnan(Hm0));
Hm0 = Hm0(row);
Te = Te(row);
 
% Delta time of sea-states in seconds
dt = ndbc_requested_data.year_1996.time(2)- ndbc_requested_data.year_1996.time(1);
dt= seconds(dt);
 
% Get the contour values
contour = environmental_contour(Hm0, Te, dt, period);

4. Plot overlay of the data and contour

Lastly we can use the MHKiT graphics module to create a contour plot which shows the data and resultant contour line.
plot_environmental_contours(Te,Hm0,contour.contour2,contour.contour1,"x_label",...
'Energy Period (s)', "y_label",'Significant Wave Height (m)',"data_label",'NDBC 46022',...
"contour_label",'100 Year Contour');
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MHKiT Environmental Contours

Environmental contours of extreme sea states can be used as a part of reliability-based design for offshore structures, including wave energy converters (WECs). Environmental contours provide estimations of extreme sea states based on short-term data (e.g., 10 years used to estimate a 100-year event). These environmental contours describe extreme sea states by characterizing the resource, defining sea states for extreme condition analysis, and developing a framework for analyzing survivability of a design.
MHKiT includes functions adapted from the WDRT for creating environmental contours of extreme sea states using a principal component analysis (PCA) methodology, with additional improvements for characterizing the joint probability distribution of sea states. As a demonstration, this notebook will walk through the following steps to find a 100-year sea state for NDBC buoy 46022 using 16 years of spectral wave density data.
  1. Request Spectral Wave Density Data from NDBC
  2. Calculate Hm0 and Te using the requested data
  3. Find the data's 100-year contour
  4. Plot the data and the 100-year contour

1. Request Spectral Wave Density Data from NDBC

MHKiT can be used to request historical data from the National Data Buoy Center (NDBC). This process is split into the following steps:

Query available NDBC data

The NDBC_available_data function requires a parameter to be specified and optionally the user may provide a station ID as a string. We are interested in historical spectral wave density data 'swden' (from which we may calculate Hm0 and Te). Additionally, we will specify the buoy number as '46022' to only return data associated with this site.
% Specify the parameter as spectral wave density and the buoy number to be 46022
parameter = 'swden';
buoy_number = '46022';
available_data= NDBC_available_data(parameter,"buoy_number", buoy_number);
Data request URL: https://www.ndbc.noaa.gov/data/historical/swden
available_data
available_data = struct with fields:
Station_id: [28×1 string] + year: [28×1 double] + file: [28×1 string] +

Select years of interest

The NDBC_available_data function has returned a Table with columns 'Station_id', 'year', and 'file'. In this case, the years returned from NDBC_available_data span 1996 to the last complete year the buoy was operational (currently 2019 for 46022). For demonstration, we have decided we are interested in the data between the years 1996 and 2012 so we will create a new filenames_of_interest variable which only contains filenames of years less than 2013.
% Slice the available data to only include through year 2012
rows = (available_data.year < 2013) ;
filenames_of_interest = available_data.file(rows);
filenames_of_interest
filenames_of_interest = 17×1 string
"46022w1996.tx…
"46022w1997.tx…
"46022w1998.tx…
"46022w1999.tx…
"46022w2000.tx…
"46022w2001.tx…
"46022w2002.tx…
"46022w2003.tx…
"46022w2004.tx…
"46022w2005.tx…

Request Data from NDBC

To get the NDBC data we can use the NDBC_request_data function to iterate over each buoy id and year in passed filenames. This function will return the parameter data as a structure of structures which may be accessed by buoy id and then the year for multiple buoys or just the year for a single buoy. An additional data column called 'time' is created with time in datetime format.
ndbc_requested_data = NDBC_request_data(parameter, filenames_of_interest);

2. Calculate Hm0 and Te using the NDBC Data

A sea state may be characterized by significant wave height (Hm0) and energy period (Te). Using the historical spectral wave density data from NDBC, we can calculate these variables using MHKiT. Both Hm0 and Te return a single value for a given time (e.g., DateTime index).
Hm0 = [];
Te = [];
for field = fieldnames(ndbc_requested_data)'
Hm0 = [Hm0 ; significant_wave_height(ndbc_requested_data.(field{1}))];
Te = [Te ; energy_period(ndbc_requested_data.(field{1}))];
end

3. Find the 100-year contour line

With the sea state data calculated, we can now use the modified I-FORM method to define reliability for a 100-year sea state based on the 17 years of spectral wave density data obtained from NDBC for buoy 46022. Reliability is the likelihood that a certain event will not occur in a given period. The period will define a line of constant probability in the joint probability of Hm0 and Te but individually each component different reliability (marginal distribution) which we can find by evaluating a normal cumulative distribution function (CDF). This CDF returns each component's quantiles along the iso-reliability line that finally allows us to calculate each sea state value (e.g., the 100-year contour values for Hm0 and Te).
For more detail on the environmental contour method used here please refer to: Eckert-Gallup et. al 2016
To apply the environmental contours function we will specify a 100-year sea state, the sea state data (Hm0, Te), and the time difference between measurements (dt in seconds).
% Return period (years) of interest
period = 100 ;
 
% Remove Hm0 Outliers and NaNs
filter = Hm0 < 20;
Hm0 = Hm0(filter);
Te = Te(filter);
[row, col] = find(~isnan(Te));
Hm0 = Hm0(row);
Te = Te(row);
[row, col] = find(~isnan(Hm0));
Hm0 = Hm0(row);
Te = Te(row);
 
% Delta time of sea-states in seconds
dt = ndbc_requested_data.year_1996.time(2)- ndbc_requested_data.year_1996.time(1);
dt= seconds(dt);
 
% Get the contour values
contour = environmental_contours(Hm0, Te, dt, period, "PCA");

4. Plot overlay of the data and contour

Lastly we can use the MHKiT graphics module to create a contour plot which shows the data and resultant contour line.
plot_environmental_contours(Te,Hm0,contour.contour2,contour.contour1,"x_label",...
'Energy Period (s)', "y_label",'Significant Wave Height (m)',"data_label",'NDBC 46022',...
"contour_label",'100 Year Contour');

+
\ No newline at end of file diff --git a/examples/extreme_response_contour_example.mlx b/examples/extreme_response_contour_example.mlx new file mode 100644 index 000000000..ad1cc1c98 Binary files /dev/null and b/examples/extreme_response_contour_example.mlx differ diff --git a/examples/extreme_response_full_sea_state_example.html b/examples/extreme_response_full_sea_state_example.html new file mode 100644 index 000000000..6888a5c6d --- /dev/null +++ b/examples/extreme_response_full_sea_state_example.html @@ -0,0 +1,443 @@ + +Extreme Conditions Modeling - Full Sea State Approach

Extreme Conditions Modeling - Full Sea State Approach

Extreme conditions modeling consists of identifying the expected extreme (e.g. 100-year) response of some quantity of interest, such as WEC motions or mooring loads. Three different methods of estimating extreme conditions were adapted from WDRT: full sea state approach, contour approach, and MLER design wave. This noteboook presents the full sea state approach.
The full sea state approach consists of the following steps:
  1. Take N samples to represent the sea state. Each sample represents a small area of the sea state and consists of a representative (H, T) pair and a weight W associated with the probability of that sea state area.
  2. For each sample (H, T) calculate the short-term (e.g. 3-hours) extreme for the quantity of interest (e.g. WEC motions or mooring tension).
  3. Integrate over the entire sea state to obtain the long-term extreme. This is a sum of the products of the weight of each sea state times the short-term extreme.
See more details and equations in
[1] Coe, Ryan G., Carlos A. Michelén Ströfer, Aubrey Eckert-Gallup, and Cédric Sallaberry. 2018. “Full Long-Term Design Response Analysis of a Wave Energy Converter.” Renewable Energy 116: 356–66.
NOTE: Prior to running this example it is recommended to become familiar with environmental_contours_example.ipynb and short_term_extremes_example.ipynb since some code blocks are adapted from those examples and used here without the additional description.

Obtain and Process NDBC Buouy Data

The first step will be obtaining the environmental data and creating the contours. See environmental_contours_example.ipynb for more details and explanations of how this is being done in the following code block.
% Specify the parameter as spectral wave density and the buoy number to be 46022
parameter = 'swden';
buoy_number = '46022';
available_data= NDBC_available_data(parameter,"buoy_number", buoy_number);
Data request URL: https://www.ndbc.noaa.gov/data/historical/swden
 
% Slice the available data to only include through year 2012
rows = (available_data.year < 2013) ;
filenames_of_interest = available_data.file(rows);
 
ndbc_requested_data = NDBC_request_data(parameter, filenames_of_interest);
 
Hm0 = [];
Te = [];
for field = fieldnames(ndbc_requested_data)'
Hm0 = [Hm0 ; significant_wave_height(ndbc_requested_data.(field{1}))];
Te = [Te ; energy_period(ndbc_requested_data.(field{1}))];
end
 
% Remove Hm0 Outliers and NaNs
filter = Hm0 < 20;
Hm0 = Hm0(filter);
Te = Te(filter);
[row, ~] = find(~isnan(Te));
Hm0 = Hm0(row);
Te = Te(row);
[row, col] = find(~isnan(Hm0));
Hm0 = Hm0(row);
Te = Te(row);
 
% Delta time of sea-states in seconds
dt = ndbc_requested_data.year_1996.time(2)- ndbc_requested_data.year_1996.time(1);
dt = seconds(dt);

1. Sampling

The first step is sampling the sea state to get samples (H, T) and associtated weights. For this we will use the waves.contours.samples_full_seastate function. We will sample 20 points between each return level, for 10 levels ranging from 0.001—100 years return periods. For more details on the sampling approach see
[1] Coe, Ryan G., Carlos A. Michelén Ströfer, Aubrey Eckert-Gallup, and Cédric Sallaberry. 2018. “Full Long-Term Design Response Analysis of a Wave Energy Converter.” Renewable Energy 116: 356–66.
[2] Eckert-Gallup, Aubrey C., Cédric J. Sallaberry, Ann R. Dallman, and Vincent S. Neary. 2016. “Application of Principal Component Analysis (PCA) and Improved Joint Probability Distributions to the Inverse First-Order Reliability Method (I-FORM) for Predicting Extreme Sea States.” Ocean Engineering 112 (January): 307–19.
% return levels
levels = [0.001; 0.01; 0.05; 0.1; 0.5; 1; 5; 10; 50; 100];
 
% points per return level interval
npoints = 20;
 
% create samples
[sample_hs, sample_te, sample_weights] = samples_full_seastate( ...
Hm0, Te, npoints, levels, dt, "PCA", 250);
We will now plot the samples alongside the contours. First we will create the different contours using contours.environmental_contours. See environmental_contours_example.ipynb for more details on using this function. There are 20 samples, randomly distributed, between each set of return levels.
Hm0_contours = zeros(length(levels),1000);
Te_contours = zeros(length(levels),1000);
for p = 1:length(levels)
contour = environmental_contours(Hm0, Te, dt, levels(p), "PCA", "return_fit",true);
Hm0_contours(p,:) = contour.contour1;
Te_contours(p,:) = contour.contour2;
end
 
plot_environmental_contours(sample_te,sample_hs,Te_contours,Hm0_contours,"x_label",...
'Energy Period (s)', "y_label",'Significant Wave Height (m)',"data_label",'NDBC 46022',...
"contour_label",string(levels'));

2. Short-Term Extreme Distributions

Many different methods for short-term extremes were adapted from WDRT, and a summary and examples can be found in short_term_extremes_example.ipynb. The response quantity of interest is typically related to the WEC itself, e.g. maximum heave displacement, PTO extension, or load on the mooring lines. This requires running a simulation (e.g. WEC-Sim) for each of the 200 (H, T) sampled sea states.
For the sake of example we will consider the wave elevation as the quantity of interest (can be thought as a proxy for heave motion in this example). Wave elevation time-series for a specific sea state can be created quickly without running any external software.
NOTE: The majority of the for loop below is simply creating the synthetic data (wave elevation time series). In a realistic case the variables time and data describing each time series would be obtained externally, e.g. through simulation software such as WEC-Sim or CFD. For this reason, the details of creating the synthetic data are not presented here, instead assume for each sea state there is time-series data available.
The last lines of the for-loop create the short-term extreme distribution from the time-series using the loads.extreme.short_term_extreme function. The short-term period will be 3-hours and we will use 1-hour "simulations" and the Weibull-tail-fitting method to estimate the 3-hour short-term extreme distributions for each of the 200 samples.
For more details on short-term extreme distributions see short_term_extremes_example.ipynb and
[3] Michelén Ströfer, Carlos A., and Ryan Coe. 2015. “Comparison of Methods for Estimating Short-Term Extreme Response of Wave Energy Converters.” In OCEANS 2015 - MTS/IEEE Washington, 1–6. IEEE.
NOTE: For calculating the short_term_extreme of each state, we set the optional argument output_py to true in order to return the native python output that we can then feed into our long term extreme function. Consequently, we can put arbitrary inputs to the x and method inputs of the short_term_extreme function.
% create the short-term extreme distribution for each sample sea state
t_st = 3.0 * 60.0 * 60.0;
gamma = 3.3;
t_sim = 1.0 * 60.0 * 60.0;
 
for i=1:length(sample_hs)
tp = sample_te(i) / (0.8255 + 0.03852 * gamma - 0.005537 * gamma^2 + 0.0003154 * gamma^3);
% time & frequency arrays
df = 1.0 / t_sim;
T_min = tp / 10.0; % s
f_max = 1.0 / T_min;
Nf = int32(f_max / df) + 1;
time = linspace(0, t_sim, 2 * Nf + 1);
f = linspace(0.0, f_max, Nf);
fprintf("Sea state %g/%g. (Hs, Te) = (%.2f m, %.2f s). Tp = %.2f s\n",i,200,sample_hs(i),sample_te(i),tp);
% spectrum
S = jonswap_spectrum(f, tp, sample_hs(i), gamma);
% 1-hour elevation time-series
data = surface_elevation(S, time);
% 3-hour extreme distribution
ste_all{i} = short_term_extreme(time, data.elevation, t_st, "peaks_weibull_tail_fit", 100, "cdf", "output_py",true);
end
Sea state 1/200. (Hs, Te) = (2.87 m, 10.18 s). Tp = 11.26 s +Sea state 2/200. (Hs, Te) = (3.23 m, 10.46 s). Tp = 11.57 s +Sea state 3/200. (Hs, Te) = (3.78 m, 10.59 s). Tp = 11.72 s +Sea state 4/200. (Hs, Te) = (3.49 m, 9.51 s). Tp = 10.53 s +Sea state 5/200. (Hs, Te) = (3.12 m, 9.07 s). Tp = 10.04 s +Sea state 6/200. (Hs, Te) = (2.53 m, 9.01 s). Tp = 9.97 s +Sea state 7/200. (Hs, Te) = (2.78 m, 8.23 s). Tp = 9.11 s +Sea state 8/200. (Hs, Te) = (2.41 m, 8.94 s). Tp = 9.89 s +Sea state 9/200. (Hs, Te) = (2.32 m, 7.81 s). Tp = 8.64 s +Sea state 10/200. (Hs, Te) = (2.04 m, 8.03 s). Tp = 8.89 s +Sea state 11/200. (Hs, Te) = (1.66 m, 7.45 s). Tp = 8.25 s +Sea state 12/200. (Hs, Te) = (1.48 m, 7.66 s). Tp = 8.48 s +Sea state 13/200. (Hs, Te) = (2.35 m, 9.11 s). Tp = 10.08 s +Sea state 14/200. (Hs, Te) = (2.35 m, 9.12 s). Tp = 10.09 s +Sea state 15/200. (Hs, Te) = (2.11 m, 9.11 s). Tp = 10.08 s +Sea state 16/200. (Hs, Te) = (2.21 m, 9.32 s). Tp = 10.32 s +Sea state 17/200. (Hs, Te) = (2.25 m, 9.37 s). Tp = 10.37 s +Sea state 18/200. (Hs, Te) = (2.37 m, 9.16 s). Tp = 10.14 s +Sea state 19/200. (Hs, Te) = (2.38 m, 9.19 s). Tp = 10.17 s +Sea state 20/200. (Hs, Te) = (2.39 m, 9.20 s). Tp = 10.18 s +Sea state 21/200. (Hs, Te) = (4.44 m, 13.23 s). Tp = 14.64 s +Sea state 22/200. (Hs, Te) = (4.62 m, 12.60 s). Tp = 13.95 s +Sea state 23/200. (Hs, Te) = (3.92 m, 10.88 s). Tp = 12.04 s +Sea state 24/200. (Hs, Te) = (4.38 m, 10.45 s). Tp = 11.56 s +Sea state 25/200. (Hs, Te) = (4.60 m, 9.34 s). Tp = 10.34 s +Sea state 26/200. (Hs, Te) = (3.24 m, 8.11 s). Tp = 8.98 s +Sea state 27/200. (Hs, Te) = (3.20 m, 7.16 s). Tp = 7.92 s +Sea state 28/200. (Hs, Te) = (2.37 m, 6.24 s). Tp = 6.91 s +Sea state 29/200. (Hs, Te) = (2.15 m, 6.98 s). Tp = 7.72 s +Sea state 30/200. (Hs, Te) = (1.55 m, 5.77 s). Tp = 6.39 s +Sea state 31/200. (Hs, Te) = (1.14 m, 5.86 s). Tp = 6.48 s +Sea state 32/200. (Hs, Te) = (1.04 m, 6.56 s). Tp = 7.26 s +Sea state 33/200. (Hs, Te) = (0.80 m, 7.16 s). Tp = 7.92 s +Sea state 34/200. (Hs, Te) = (0.52 m, 8.36 s). Tp = 9.26 s +Sea state 35/200. (Hs, Te) = (1.00 m, 8.74 s). Tp = 9.67 s +Sea state 36/200. (Hs, Te) = (1.22 m, 10.30 s). Tp = 11.40 s +Sea state 37/200. (Hs, Te) = (1.50 m, 10.77 s). Tp = 11.92 s +Sea state 38/200. (Hs, Te) = (1.84 m, 13.76 s). Tp = 15.23 s +Sea state 39/200. (Hs, Te) = (2.14 m, 14.16 s). Tp = 15.67 s +Sea state 40/200. (Hs, Te) = (3.64 m, 13.32 s). Tp = 14.74 s +Sea state 41/200. (Hs, Te) = (0.40 m, 11.12 s). Tp = 12.31 s +Sea state 42/200. (Hs, Te) = (0.73 m, 11.89 s). Tp = 13.16 s +Sea state 43/200. (Hs, Te) = (1.23 m, 13.83 s). Tp = 15.31 s +Sea state 44/200. (Hs, Te) = (2.74 m, 15.95 s). Tp = 17.65 s +Sea state 45/200. (Hs, Te) = (3.90 m, 15.72 s). Tp = 17.40 s +Sea state 46/200. (Hs, Te) = (4.60 m, 15.40 s). Tp = 17.05 s +Sea state 47/200. (Hs, Te) = (5.08 m, 14.47 s). Tp = 16.01 s +Sea state 48/200. (Hs, Te) = (5.74 m, 12.87 s). Tp = 14.24 s +Sea state 49/200. (Hs, Te) = (6.28 m, 12.58 s). Tp = 13.92 s +Sea state 50/200. (Hs, Te) = (5.22 m, 9.61 s). Tp = 10.64 s +Sea state 51/200. (Hs, Te) = (4.59 m, 8.55 s). Tp = 9.46 s +Sea state 52/200. (Hs, Te) = (3.85 m, 7.33 s). Tp = 8.11 s +Sea state 53/200. (Hs, Te) = (2.66 m, 5.95 s). Tp = 6.59 s +Sea state 54/200. (Hs, Te) = (2.13 m, 5.38 s). Tp = 5.95 s +Sea state 55/200. (Hs, Te) = (1.81 m, 5.17 s). Tp = 5.72 s +Sea state 56/200. (Hs, Te) = (1.33 m, 5.11 s). Tp = 5.65 s +Sea state 57/200. (Hs, Te) = (0.91 m, 5.41 s). Tp = 5.99 s +Sea state 58/200. (Hs, Te) = (0.71 m, 6.13 s). Tp = 6.78 s +Sea state 59/200. (Hs, Te) = (0.37 m, 6.53 s). Tp = 7.23 s +Sea state 60/200. (Hs, Te) = (0.42 m, 7.52 s). Tp = 8.32 s +Sea state 61/200. (Hs, Te) = (0.41 m, 13.51 s). Tp = 14.95 s +Sea state 62/200. (Hs, Te) = (0.75 m, 14.83 s). Tp = 16.41 s +Sea state 63/200. (Hs, Te) = (2.15 m, 16.55 s). Tp = 18.32 s +Sea state 64/200. (Hs, Te) = (3.37 m, 17.22 s). Tp = 19.05 s +Sea state 65/200. (Hs, Te) = (4.01 m, 17.20 s). Tp = 19.03 s +Sea state 66/200. (Hs, Te) = (6.27 m, 16.59 s). Tp = 18.35 s +Sea state 67/200. (Hs, Te) = (6.33 m, 15.75 s). Tp = 17.43 s +Sea state 68/200. (Hs, Te) = (6.78 m, 14.08 s). Tp = 15.58 s +Sea state 69/200. (Hs, Te) = (6.28 m, 11.10 s). Tp = 12.29 s +Sea state 70/200. (Hs, Te) = (5.70 m, 9.76 s). Tp = 10.80 s +Sea state 71/200. (Hs, Te) = (5.07 m, 8.50 s). Tp = 9.41 s +Sea state 72/200. (Hs, Te) = (4.14 m, 7.24 s). Tp = 8.02 s +Sea state 73/200. (Hs, Te) = (3.38 m, 6.33 s). Tp = 7.00 s +Sea state 74/200. (Hs, Te) = (2.79 m, 5.68 s). Tp = 6.28 s +Sea state 75/200. (Hs, Te) = (1.65 m, 4.95 s). Tp = 5.47 s +Sea state 76/200. (Hs, Te) = (1.61 m, 4.99 s). Tp = 5.53 s +Sea state 77/200. (Hs, Te) = (1.15 m, 4.90 s). Tp = 5.42 s +Sea state 78/200. (Hs, Te) = (0.60 m, 5.13 s). Tp = 5.68 s +Sea state 79/200. (Hs, Te) = (0.25 m, 5.88 s). Tp = 6.50 s +Sea state 80/200. (Hs, Te) = (0.17 m, 6.27 s). Tp = 6.94 s +Sea state 81/200. (Hs, Te) = (0.78 m, 16.17 s). Tp = 17.89 s +Sea state 82/200. (Hs, Te) = (1.97 m, 17.29 s). Tp = 19.14 s +Sea state 83/200. (Hs, Te) = (3.66 m, 18.06 s). Tp = 19.98 s +Sea state 84/200. (Hs, Te) = (4.52 m, 19.50 s). Tp = 21.57 s +Sea state 85/200. (Hs, Te) = (6.21 m, 18.91 s). Tp = 20.92 s +Sea state 86/200. (Hs, Te) = (7.49 m, 16.74 s). Tp = 18.52 s +Sea state 87/200. (Hs, Te) = (8.16 m, 15.00 s). Tp = 16.60 s +Sea state 88/200. (Hs, Te) = (7.65 m, 13.41 s). Tp = 14.84 s +Sea state 89/200. (Hs, Te) = (7.20 m, 11.74 s). Tp = 12.99 s +Sea state 90/200. (Hs, Te) = (6.61 m, 10.39 s). Tp = 11.50 s +Sea state 91/200. (Hs, Te) = (5.05 m, 8.41 s). Tp = 9.31 s +Sea state 92/200. (Hs, Te) = (4.24 m, 7.09 s). Tp = 7.85 s +Sea state 93/200. (Hs, Te) = (3.56 m, 6.19 s). Tp = 6.85 s +Sea state 94/200. (Hs, Te) = (2.61 m, 5.36 s). Tp = 5.93 s +Sea state 95/200. (Hs, Te) = (1.94 m, 4.82 s). Tp = 5.34 s +Sea state 96/200. (Hs, Te) = (1.40 m, 4.45 s). Tp = 4.93 s +Sea state 97/200. (Hs, Te) = (1.36 m, 4.71 s). Tp = 5.22 s +Sea state 98/200. (Hs, Te) = (0.72 m, 4.61 s). Tp = 5.10 s +Sea state 99/200. (Hs, Te) = (0.67 m, 4.84 s). Tp = 5.36 s +Sea state 100/200. (Hs, Te) = (0.07 m, 5.34 s). Tp = 5.91 s +Sea state 101/200. (Hs, Te) = (0.23 m, 17.16 s). Tp = 18.99 s +Sea state 102/200. (Hs, Te) = (2.04 m, 19.19 s). Tp = 21.24 s +Sea state 103/200. (Hs, Te) = (2.49 m, 19.57 s). Tp = 21.65 s +Sea state 104/200. (Hs, Te) = (6.08 m, 19.65 s). Tp = 21.74 s +Sea state 105/200. (Hs, Te) = (6.77 m, 19.04 s). Tp = 21.07 s +Sea state 106/200. (Hs, Te) = (8.08 m, 18.35 s). Tp = 20.30 s +Sea state 107/200. (Hs, Te) = (8.66 m, 15.55 s). Tp = 17.21 s +Sea state 108/200. (Hs, Te) = (8.18 m, 12.97 s). Tp = 14.36 s +Sea state 109/200. (Hs, Te) = (8.06 m, 12.36 s). Tp = 13.68 s +Sea state 110/200. (Hs, Te) = (6.49 m, 9.89 s). Tp = 10.95 s +Sea state 111/200. (Hs, Te) = (5.13 m, 7.71 s). Tp = 8.53 s +Sea state 112/200. (Hs, Te) = (4.07 m, 6.58 s). Tp = 7.28 s +Sea state 113/200. (Hs, Te) = (3.18 m, 5.54 s). Tp = 6.13 s +Sea state 114/200. (Hs, Te) = (3.04 m, 5.36 s). Tp = 5.93 s +Sea state 115/200. (Hs, Te) = (1.95 m, 4.52 s). Tp = 5.01 s +Sea state 116/200. (Hs, Te) = (1.40 m, 4.24 s). Tp = 4.69 s +Sea state 117/200. (Hs, Te) = (0.97 m, 4.20 s). Tp = 4.65 s +Sea state 118/200. (Hs, Te) = (0.75 m, 4.31 s). Tp = 4.77 s +Sea state 119/200. (Hs, Te) = (0.51 m, 4.55 s). Tp = 5.03 s +Sea state 120/200. (Hs, Te) = (0.06 m, 5.15 s). Tp = 5.70 s +Sea state 121/200. (Hs, Te) = (1.41 m, 19.66 s). Tp = 21.76 s +Sea state 122/200. (Hs, Te) = (2.54 m, 20.29 s). Tp = 22.46 s +Sea state 123/200. (Hs, Te) = (3.47 m, 21.14 s). Tp = 23.39 s +Sea state 124/200. (Hs, Te) = (7.10 m, 20.16 s). Tp = 22.31 s +Sea state 125/200. (Hs, Te) = (8.64 m, 19.45 s). Tp = 21.53 s +Sea state 126/200. (Hs, Te) = (9.72 m, 17.61 s). Tp = 19.48 s +Sea state 127/200. (Hs, Te) = (9.35 m, 16.58 s). Tp = 18.34 s +Sea state 128/200. (Hs, Te) = (8.45 m, 13.05 s). Tp = 14.44 s +Sea state 129/200. (Hs, Te) = (7.97 m, 11.42 s). Tp = 12.64 s +Sea state 130/200. (Hs, Te) = (6.37 m, 9.31 s). Tp = 10.30 s +Sea state 131/200. (Hs, Te) = (6.28 m, 8.86 s). Tp = 9.80 s +Sea state 132/200. (Hs, Te) = (4.57 m, 6.78 s). Tp = 7.50 s +Sea state 133/200. (Hs, Te) = (3.53 m, 5.70 s). Tp = 6.30 s +Sea state 134/200. (Hs, Te) = (2.70 m, 4.83 s). Tp = 5.34 s +Sea state 135/200. (Hs, Te) = (2.55 m, 4.62 s). Tp = 5.11 s +Sea state 136/200. (Hs, Te) = (1.61 m, 4.09 s). Tp = 4.53 s +Sea state 137/200. (Hs, Te) = (1.14 m, 4.12 s). Tp = 4.56 s +Sea state 138/200. (Hs, Te) = (0.97 m, 3.90 s). Tp = 4.32 s +Sea state 139/200. (Hs, Te) = (0.42 m, 4.09 s). Tp = 4.52 s +Sea state 140/200. (Hs, Te) = (0.08 m, 4.49 s). Tp = 4.97 s +Sea state 141/200. (Hs, Te) = (0.25 m, 19.72 s). Tp = 21.82 s +Sea state 142/200. (Hs, Te) = (2.18 m, 21.97 s). Tp = 24.31 s +Sea state 143/200. (Hs, Te) = (3.88 m, 22.22 s). Tp = 24.59 s +Sea state 144/200. (Hs, Te) = (7.30 m, 22.13 s). Tp = 24.49 s +Sea state 145/200. (Hs, Te) = (9.22 m, 20.77 s). Tp = 22.98 s +Sea state 146/200. (Hs, Te) = (9.69 m, 19.12 s). Tp = 21.16 s +Sea state 147/200. (Hs, Te) = (10.60 m, 17.39 s). Tp = 19.24 s +Sea state 148/200. (Hs, Te) = (10.20 m, 14.75 s). Tp = 16.32 s +Sea state 149/200. (Hs, Te) = (8.50 m, 11.62 s). Tp = 12.86 s +Sea state 150/200. (Hs, Te) = (7.08 m, 9.44 s). Tp = 10.45 s +Sea state 151/200. (Hs, Te) = (6.06 m, 8.16 s). Tp = 9.03 s +Sea state 152/200. (Hs, Te) = (5.13 m, 7.16 s). Tp = 7.92 s +Sea state 153/200. (Hs, Te) = (3.76 m, 5.57 s). Tp = 6.16 s +Sea state 154/200. (Hs, Te) = (3.00 m, 4.84 s). Tp = 5.35 s +Sea state 155/200. (Hs, Te) = (2.24 m, 4.31 s). Tp = 4.77 s +Sea state 156/200. (Hs, Te) = (1.55 m, 3.85 s). Tp = 4.27 s +Sea state 157/200. (Hs, Te) = (1.48 m, 3.89 s). Tp = 4.31 s +Sea state 158/200. (Hs, Te) = (0.76 m, 3.83 s). Tp = 4.24 s +Sea state 159/200. (Hs, Te) = (0.40 m, 4.06 s). Tp = 4.49 s +Sea state 160/200. (Hs, Te) = (0.22 m, 4.18 s). Tp = 4.62 s +Sea state 161/200. (Hs, Te) = (0.65 m, 22.88 s). Tp = 25.32 s +Sea state 162/200. (Hs, Te) = (3.04 m, 23.41 s). Tp = 25.90 s +Sea state 163/200. (Hs, Te) = (4.59 m, 23.43 s). Tp = 25.92 s +Sea state 164/200. (Hs, Te) = (8.08 m, 22.66 s). Tp = 25.08 s +Sea state 165/200. (Hs, Te) = (10.23 m, 20.21 s). Tp = 22.37 s +Sea state 166/200. (Hs, Te) = (10.97 m, 19.67 s). Tp = 21.76 s +Sea state 167/200. (Hs, Te) = (10.73 m, 16.24 s). Tp = 17.97 s +Sea state 168/200. (Hs, Te) = (10.20 m, 13.75 s). Tp = 15.22 s +Sea state 169/200. (Hs, Te) = (10.02 m, 12.77 s). Tp = 14.13 s +Sea state 170/200. (Hs, Te) = (7.91 m, 10.02 s). Tp = 11.09 s +Sea state 171/200. (Hs, Te) = (6.50 m, 8.46 s). Tp = 9.36 s +Sea state 172/200. (Hs, Te) = (5.40 m, 7.21 s). Tp = 7.98 s +Sea state 173/200. (Hs, Te) = (3.84 m, 5.51 s). Tp = 6.10 s +Sea state 174/200. (Hs, Te) = (3.11 m, 4.86 s). Tp = 5.38 s +Sea state 175/200. (Hs, Te) = (2.28 m, 4.15 s). Tp = 4.59 s +Sea state 176/200. (Hs, Te) = (1.58 m, 3.72 s). Tp = 4.12 s +Sea state 177/200. (Hs, Te) = (1.27 m, 3.64 s). Tp = 4.03 s +Sea state 178/200. (Hs, Te) = (0.96 m, 3.60 s). Tp = 3.99 s +Sea state 179/200. (Hs, Te) = (0.73 m, 3.72 s). Tp = 4.12 s +Sea state 180/200. (Hs, Te) = (0.20 m, 4.00 s). Tp = 4.43 s +Sea state 181/200. (Hs, Te) = (0.76 m, 23.17 s). Tp = 25.64 s +Sea state 182/200. (Hs, Te) = (3.91 m, 24.51 s). Tp = 27.12 s +Sea state 183/200. (Hs, Te) = (7.32 m, 24.46 s). Tp = 27.07 s +Sea state 184/200. (Hs, Te) = (9.48 m, 23.50 s). Tp = 26.01 s +Sea state 185/200. (Hs, Te) = (11.81 m, 21.25 s). Tp = 23.52 s +Sea state 186/200. (Hs, Te) = (12.09 m, 19.36 s). Tp = 21.43 s +Sea state 187/200. (Hs, Te) = (12.01 m, 16.87 s). Tp = 18.67 s +Sea state 188/200. (Hs, Te) = (10.65 m, 13.32 s). Tp = 14.74 s +Sea state 189/200. (Hs, Te) = (10.36 m, 13.08 s). Tp = 14.47 s +Sea state 190/200. (Hs, Te) = (8.78 m, 10.69 s). Tp = 11.83 s +Sea state 191/200. (Hs, Te) = (6.12 m, 7.75 s). Tp = 8.57 s +Sea state 192/200. (Hs, Te) = (4.99 m, 6.40 s). Tp = 7.09 s +Sea state 193/200. (Hs, Te) = (4.18 m, 5.61 s). Tp = 6.21 s +Sea state 194/200. (Hs, Te) = (2.87 m, 4.41 s). Tp = 4.87 s +Sea state 195/200. (Hs, Te) = (2.43 m, 4.09 s). Tp = 4.53 s +Sea state 196/200. (Hs, Te) = (1.67 m, 3.61 s). Tp = 3.99 s +Sea state 197/200. (Hs, Te) = (1.48 m, 3.53 s). Tp = 3.91 s +Sea state 198/200. (Hs, Te) = (0.92 m, 3.44 s). Tp = 3.81 s +Sea state 199/200. (Hs, Te) = (0.45 m, 3.53 s). Tp = 3.90 s +Sea state 200/200. (Hs, Te) = (0.30 m, 3.67 s). Tp = 4.06 s

3. Long-Term Extreme Distribution

Finally we integrate the weighted short-term extreme distributions over the entire sea state space to obtain the extreme distribution, assuming a 3-hour sea state coherence. For this we use the full_seastate_long_term_extreme function. The integral reduces to a sum over the 200 bins of the weighted short-term extreme distributions.
Similar to the short-term extreme functions, the output of long-term extreme function is a probability distribution. Here, we will look at the survival function and the 100-year return level.The value of the survival function at a given return level (e.g. 100-years) may be calculated using the return_year_value function.
t_st_hr = t_st / (60.0 * 60.0);
t_return_yr = 100.0;
probability_of_exceedance = 1 / (t_return_yr * 365.25 * 24 / t_st_hr);
x_t = full_seastate_long_term_extreme(ste_all, sample_weights, 1-probability_of_exceedance, "ppf");
fprintf("100-year elevation: %.3f meters", x_t)
100-year elevation: 10.299 meters
% plot survival function
x = linspace(0, 20, 1000);
lte_sf = full_seastate_long_term_extreme(ste_all, sample_weights, x, "sf");
figure;
semilogy(x, lte_sf);
xlabel('elevation [m]'); ylabel('survival function (1-cdf)'); ylim([1e-10, 1]); xlim([0, x(end)]);
% add 100-year return level to plot
hold on
st_sf = full_seastate_long_term_extreme(ste_all, sample_weights, x_t, "sf");
xline(x_t, '--')
yline(st_sf, '--')
+
+ +
\ No newline at end of file diff --git a/examples/extreme_response_full_sea_state_example.mlx b/examples/extreme_response_full_sea_state_example.mlx new file mode 100644 index 000000000..7041ebc0e Binary files /dev/null and b/examples/extreme_response_full_sea_state_example.mlx differ diff --git a/examples/river_example.mlx b/examples/river_example.mlx index 579e97f73..1820fbfd7 100644 Binary files a/examples/river_example.mlx and b/examples/river_example.mlx differ diff --git a/examples/short_term_extremes_example.html b/examples/short_term_extremes_example.html new file mode 100644 index 000000000..a81046d5c --- /dev/null +++ b/examples/short_term_extremes_example.html @@ -0,0 +1,322 @@ + +MHKiT Short-term Extreme Loads

MHKiT Short-term Extreme Loads

Short-term extreme loads are typically required as part of a long-term extreme load estimate. A short-term extreme distribution is a probability distribution for the extreme value of a short-term (e.g. 3-hours) time-series.
MHKiT includes functions adapted from the WDRT for estimating the short-term extreme distribution. Several methods are included, which can be divided into two main approaches:
  1. Block maxima: approximate the short-term extreme distribution directly by fitting a probability distribution to the maxima from N distinct short-term blocks.
  2. Peaks distribution: approximate the short-term extreme distribution from the distribution of peaks from a time-series of arbitrary length.
The two sets of methods will be demonstrated.
NOTE: This notebook will walk through the two different approaches, and each method in them. The short-term extremes will be obtained step-by-step showing the intermediate outputs. However, a convenience function, the loads.extreme.short_term_extreme function, can be be used directly in a single step. For this usage jump to the last section. It is recommended that you go over this entire example to understand what is going on "under the hood" prior to using this convenience function.
The quantity (load) of interest can be anything related to the WEC, such as position (e.g. PTO extension, heave displacement), velocity, structural load, mooring loads, etc. For this example we will use the wave elevation as the quantity of interest, since such time-series can be easily created without having to run a WEC-modeling software. The short-term period of interest will be 3-hours.
An important pre-processing step is making the time-series zero-mean. In this case, since wave elevation is zero-mean no pre-processing is needed.
We first define the short-term period (3 hours).
% short-term period in seconds
t_st = 3.0 * 60.0 * 60.0
t_st = 10800
The methods based on peaks distributions require a single time series of any length while the methods based on block maxima require N time series of length equal to the short-term time period.
We will now create N=10 time series of length equal to the short-term period (3 hours). For block maxima methods we will use all 10 and for peaks distribution methods we will only use the first hour of the first time-series. For the block maxima we use N=10 for speed considerations, but note that this would be inadequately small for most real applications.
For the sake of example we will consider the wave elevation as the quantity of interest (can be thought as a proxy for heave motion in this example). Wave elevation time-series for a specific sea state can be created quickly without running any external software.
NOTE: The code below is simply creating the synthetic data (wave elevation time series). In a realistic case the time series would be obtained externally, e.g. through simulation software such as WEC-Sim or CFD. For this reason the details of creating the synthetic data are not presented here, instead assume for the quantity of interest there are ten 3-hours time-series available.
We start by creating the ten 3-hour time-series of the quantity of interest. We do this with a list comprehension and using the wave.resource.surface_elevation function. The result is a list of 10 different time-series. Alternatively we could have created a single time-series of length N times the short-term period (30 hours) and used the extreme.block_maxima function to split it into blocks and return the block maxima.
% JONSWAP spectrum for creating short-term time-series
T_min = 1; % s
Tp = 8; % s
Hs = 1.5; % m
df = 1/t_st;
f_max = 1/T_min;
Nf = f_max/df + 1;
f = linspace(0.0, f_max, Nf);
S = jonswap_spectrum(f, Tp, Hs);
 
% time in seconds
time = linspace(0, t_st, 2*Nf+1);
 
% qoi timeseries
qoi_timeseries = surface_elevation(S, time);
qoi = qoi_timeseries.elevation;
We can view the different time-series. Change value of i below to plot a different time-series. Below we plot both the full 3 hours time series and the first 2 minutes to get a better look at the behavior of the response.
figure;
plot(time, qoi)
title("Full 3 hours"); xlabel("time [s]"); ylabel("elevation [m]")
figure;
plot(time(1:120), qoi(1:120))
title("First 2 minutes"); xlabel("time [s]"); ylabel("elevation [m]")

Block Maxima

The short-term extreme distribution can be estimated directly from N time-series of short-term period. These time-series can be obtained, for instance, from N distinct simulations of the quantity of interest, or alternatively by dividing a long time-series of the quantity of interest into blocks of length equal to the short-term period. In this example we will divide our 3 hour time series into 10-minute segments for speed considerations, but this would be inadequately small for most real applications.

1. Find the maximum of each block

The first step is to get the maximum in each block, i.e. in each of the 10-minute time series. We can use the block_maxima funtion to do this for us.
% split time series into 10-minute (600s) segments
block_max = block_maxima(time, qoi', 600);
We can also visualize this result, which represents the maximum elevation of each 10-minute segment for the 3 hour period we are analyzing.
figure;
plot(block_max, 'o'); grid on; xticks(0:1:19); ylim([0,2])
xlabel('block #'); ylabel('block max elevation [m]'); title('Block maxima')

2. Fit a distribution to the block maxima

We can now get the short-term extreme distribution by fitting either a generalized extreme value distribution or a Gumbel (right) distributions to these N=18 maxima. We will compare both methods.
% generalized extreme value distribution
x = linspace(0,3,1000);
ste_gev_pdf = ste_block_maxima_gev(block_max, x, "pdf");
ste_gev_cdf = ste_block_maxima_gev(block_max, x, "cdf");
ste_gum_pdf = ste_block_maxima_gumbel(block_max, x, "pdf");
ste_gum_cdf = ste_block_maxima_gumbel(block_max, x, "cdf");
The outputs of these functions are probability distributions. Here we will plot the CDF and PDF and print the 95% interval for both methods.
% plot cdf and pdf
subplot(1,2,1); hold on;
plot(x,ste_gev_pdf); xlabel('elevation [m]'); ylabel('PDF')
plot(x,ste_gum_pdf); xlabel('elevation [m]'); ylabel('PDF')
legend('GEV','Gumbel')
subplot(1,2,2); hold on;
plot(x,ste_gev_cdf); xlabel('elevation [m]'); ylabel('CDF')
plot(x,ste_gum_cdf); xlabel('elevation [m]'); ylabel('CDF')
fprintf('GEV:\n 95 percent interval: (%.3f m, %.3f m)',ste_block_maxima_gev(block_max, 0.025, "ppf"),ste_block_maxima_gev(block_max, 0.975, "ppf"))
GEV: + 95 percent interval: (1.081 m, 1.459 m)
fprintf('GUMBEL:\n 95 percent interval: (%.3f m, %.3f m)',ste_block_maxima_gumbel(block_max, 0.025, "ppf"),ste_block_maxima_gumbel(block_max, 0.975, "ppf"))
GUMBEL: + 95 percent interval: (1.084 m, 1.483 m)

Peaks Distribution

The block maxima approach is the most direct way to approximate the short-term extreme but it requires a lot of data (N timeseries of length equal to the short-term period). An alternative approach approximates the short-term extreme from a timeseries of arbitrary length, even shorter than the short-term period, by fitting a distribution to the peaks of the timeseries.
To demonstrate these methods we will approximate the 3-hour short-term extreme distribution from a single 1-hour timeseries.
We start by generating this 1-hour response timeseries.
t_end = 1.0 * 60.0 * 60.0;
qoi_1hr = qoi(1:t_end);
time_1hr = time(1:t_end);
% visualize
figure;
plot(time_1hr, qoi_1hr)
title("1 hour"); xlabel("time [s]"); ylabel("elevation [m]")

1. Find the global peaks

The global peaks are the maximum between succesive zero-upcrossings. We use the extreme.global_peaks function to find these peaks.
[t_peaks, qoi_peaks] = global_peaks(time_1hr, qoi_1hr);
npeaks = length(qoi_peaks)
npeaks = 305
We will plot the entire time-series and the global peaks and then zoom in on the first 2 minutes.
figure; hold on;
plot(time_1hr, qoi_1hr)
title("1 hour"); xlabel("time [s]"); ylabel("elevation [m]")
scatter(t_peaks, qoi_peaks)
yline(0)
figure; hold on;
plot(time_1hr, qoi_1hr)
title("1 hour"); xlabel("time [s]"); ylabel("elevation [m]")
scatter(t_peaks, qoi_peaks, 'filled')
yline(0)
xlim([0,120])

2. Fit a distribution to the peaks

MHKiT has three methods for doing this.
  1. Fit a Weibull distribution to all the peaks.
  2. Weibull tail fit: seven different weibull distributions are fit to successively smaller subsets of the highest peaks, and the peak distribution is taken as the average of these sevenn
  3. Peaks over threshold: a generalized Pareto distribution is fit to all peaks above a certain threshold, typically taken as 1.4 standard deviations above the mean.
We will now compare the results from these three methods. For the peaks over threshold we will take the threshold (variable thresh below) to be 1.4 standard deviations above the mean. Note in this example, we are also storing the python statistical object. This is something we will need in the step!
% Weibull
[peaks_w_pdf, peaks_w] = peaks_distribution_weibull(qoi_peaks, x, "pdf");
peaks_w_cdf = peaks_distribution_weibull(qoi_peaks, x, "cdf");
% Weibull tail fit
[peaks_wtf_pdf, peaks_wtf] = peaks_distribution_weibull_tail_fit(qoi_peaks, x, "pdf");
peaks_wtf_cdf = peaks_distribution_weibull_tail_fit(qoi_peaks, x, "cdf");
% peaks over threshold
thresh = mean(qoi_peaks) + 1.4 * std(qoi_peaks);
[peaks_pot_pdf, peaks_pot] = peaks_distribution_peaks_over_threshold(qoi_peaks, x, "pdf", "threshold", thresh);
peaks_pot_cdf = peaks_distribution_peaks_over_threshold(qoi_peaks, x, "cdf", "threshold", thresh);
We will plot both the PDF and CDF of the peaks distribution, and obtain the 95% interval for each distribution. Note however that for the peaks over threshold method the distribution is only defined for values over the threshold, and many of the functionalities that require the entire distribution are therefore not available.
% plot cdf and pdf
subplot(1,2,1); hold on;
plot(x,peaks_w_pdf); xlabel('elevation [m]'); ylabel('PDF')
plot(x,peaks_wtf_pdf); xlabel('elevation [m]'); ylabel('PDF')
plot(x,peaks_pot_pdf,'green'); xlabel('elevation [m]'); ylabel('PDF')
legend('Weibull','WTF','POT')
subplot(1,2,2); hold on;
plot(x,peaks_w_cdf); xlabel('elevation [m]'); ylabel('CDF')
plot(x,peaks_wtf_cdf); xlabel('elevation [m]'); ylabel('CDF')
plot(x,peaks_pot_cdf, 'green'); xlabel('elevation [m]'); ylabel('CDF')
s1 = sprintf('Weibull:\n 95 percent interval: (%.3f m, %.3f m)\n',peaks_distribution_weibull(qoi_peaks,0.025,"ppf"),peaks_distribution_weibull(qoi_peaks,0.975,"ppf"));
s2 = sprintf('Weibull tail fit:\n 95 percent interval: (%.3f m, %.3f m)',peaks_distribution_weibull_tail_fit(qoi_peaks,0.025,"ppf"),peaks_distribution_weibull_tail_fit(qoi_peaks,0.975,"ppf"));
disp([s1, s2])
Weibull: + 95 percent interval: (0.055 m, 1.122 m) +Weibull tail fit: + 95 percent interval: (0.049 m, 1.101 m)

3. Obtain the short-term extreme distribution from the peaks distribution

We do this using the peaks distribution and an approximation for the number of peaks per short-term period. We use the extreme.ste_peaks function to obtain an approximation for the number of peaks in a short-term period.
N_st = number_of_short_term_peaks(npeaks, t_end, t_st);
fprintf("Approximate number of peaks in a (3-hours) short-term period: %d",N_st)
Approximate number of peaks in a (3-hours) short-term period: 915
%
ste_w_pdf = ste_peaks(peaks_w, N_st, x, "pdf");
ste_w_cdf = ste_peaks(peaks_w, N_st, x, "cdf");
ste_wtf_pdf = ste_peaks(peaks_wtf, N_st, x, "pdf");
ste_wtf_cdf = ste_peaks(peaks_wtf, N_st, x, "cdf");
ste_pot_pdf = ste_peaks(peaks_pot, N_st, x, "pdf");
ste_pot_cdf = ste_peaks(peaks_pot, N_st, x, "cdf");
 
% plot cdf and pdf
figure;
subplot(1,2,1); hold on;
plot(x,ste_w_pdf); xlabel('elevation [m]'); ylabel('PDF')
plot(x,ste_wtf_pdf); xlabel('elevation [m]'); ylabel('PDF')
plot(x,ste_pot_pdf, 'green'); xlabel('elevation [m]'); ylabel('PDF')
legend('Weibull','WTF','POT')
subplot(1,2,2); hold on;
plot(x,ste_w_cdf); xlabel('elevation [m]'); ylabel('CDF')
plot(x,ste_wtf_cdf); xlabel('elevation [m]'); ylabel('CDF')
plot(x,ste_pot_cdf, 'green'); xlabel('elevation [m]'); ylabel('CDF')

The short_term_extreme function

This example showed step-by-step how to estimate the short-term extreme using different methods. However for most use cases the results from the intermediate steps are not of interest. The estimated short-term extreme distribution can be obtained directly from a time-series of the response using the short_term_extreme function. For the methods based on fitting the peaks the time-series can be of arbitrary length, while for methods based on block maxima it should be many times longer than the short-term period.
Note: This function is provided for convenience but the user should be aware of what is going on "under the hood" and ensure the method they choose is appropriate. For instance if using a block maxima method it is good practice to have at least 20 short-term periods worth of data.
As an example the Weibull tail fit approximation of the short-term extreme distribution can be obtained in a single step. The function takes the time series (time, response), the desired short-term period, and the method as inputs.
ste_wtf = short_term_extreme(time_1hr, qoi_1hr, t_st, "peaks_weibull_tail_fit", x, "pdf");
+
+ +
\ No newline at end of file diff --git a/examples/short_term_extremes_example.mlx b/examples/short_term_extremes_example.mlx new file mode 100644 index 000000000..ae13680b3 Binary files /dev/null and b/examples/short_term_extremes_example.mlx differ diff --git a/examples/tidal_example.html b/examples/tidal_example.html index 865098b32..69fc1a250 100644 --- a/examples/tidal_example.html +++ b/examples/tidal_example.html @@ -1,4 +1,14 @@ +<<<<<<< HEAD +Example: MHKiT-MATLAB Tidal Module

Example: MHKiT-MATLAB Tidal Module

The following example will familiarize the user with the MHKiT tidal module by stepping through the calculation of the velocity duration curve. The data file used in this example is stored in the \MHKiT\examples\data directory.

Load Data from NOAA-Currents

This example uses 1 year of data from the NOAA-Currents sites. A map of available currents stations is available at https://tidesandcurrents.noaa.gov/map/. The tidal io module includes two functions to import data: request_noaa_data which pulls data from the website, and read_noaa_json which loads a json file. The request function can save the json file for later use.
For simplicity, this example loads data from a json file into a MATLAB Series. This data contains 1 year of 6-minute averaged data from the Southampton Shoal Channel LB 6 (Station Number: s08010) in San Francisco Bay. The data includes 6-minute averaged direction [degrees] and speed [cm/s] indexed by time. The structure names returned by NOAA are 'd' for direction and 's' for speed. Since MHKIT uses SI units, speed is converted to m/s.
% Create a file name to save the requested data to
relative_file_name = "data/tidal/s08010.json"; % South Hampton Shoal LB
current_dir = fileparts(matlab.desktop.editor.getActiveFilename);
full_file_name = fullfile(current_dir, relative_file_name);
 
data = read_noaa_json(full_file_name)
% Example of how you could request NOAA-Currents data
%data = request_noaa_data("s08010","currents","20161101","20180401","write_json",currents_file);
 
 
% Convert discharge data from cm/s to m/s
data.s = data.s/100.;
The request_noaa_data has returned a Matlab Structure of time series data between November of 2016 and March of 2018. The time series data points are 6-minute averaged direction [degrees] and speed [cm/s] data indexed by time. The structure key names returned by NOAA are 'd' for direction and 's' for speed. The speed returned from NOAA is in cm/s so we converted this to m/s.

Principal Flow Directions

An initial data check may look at the time series data to identify data gaps. To consider the velocity in one of the principal flow directions we apply the principal_flow_directions function. This function returns 2 directions (in degrees) corresponding to the flood and ebb directions of the tidal site. Principal flow directions are calculated based on the highest frequency directions. These directions are often close to 180 degrees apart, but are not required to be.
The plot_current_timeseries function plots velocity in either direction using the speed timeseries.
% We need to specify a histogram bin width for the directions to calculate
% the principal flow direction
width_direction = 1; % [degrees]
 
% Two principal directions are calculated based on the highest frequency
% direction
% One direction is the flood, the other is tide or ebb.
% they are 180 degrees apart, but not required to be
[direction1, direction2] = principal_flow_directions(data.d,width_direction);
 
% Set the flood and ebb directions based on site knowledge
flood = direction1 ; %flow into
ebb = direction2 ; % flow out
 
 
%plot the time series of current data using the flood direction
plot_current_timeseries(data,flood);
The plot above shows that the NOAA site request did not return data for most of early and mid-2017. The IEC standard recommends a minimum of 1 year of 10-minute averaged data (See IEC 201 for full description). For the purposes of demonstration this dataset is sufficient. To look at a specific month we can slice the dataset before passing to the plotting function.
% Slice December of 2017 out of the full dataset
start = posixtime(datetime('2017-12-01','InputFormat','yyyy-MM-dd'));
stop = posixtime(datetime('2017-12-31','InputFormat','yyyy-MM-dd'));
index = data.time > start & data.time < stop ;
datadec.time = data.time(index);
datadec.s = data.s(index);
datadec.d = data.d(index);
 
plot_current_timeseries(datadec,flood);

Joint Probability Distribution

Direction and velocity can be viewed as a joint probability distribution on a polar plot. This plot helps visually show the flood and ebb directions and the frequency of particular directional velocities.
% Set the joint probability bit widths
width_direction = 1 ; %[degrees]
width_velocity = 0.1 ; %[m/s]
 
% Plot the joint probability distribution
figure;
plot_joint_probability_distribution(data,width_direction,width_velocity);

Rose Plot

A rose plot shows the same information as the joint probability distribution, but the probability is now the r-axis, and the velocity is the contour value. As compared to a joint probability distribution plot, a rose plot can be more readable when using larger bins sizes.
% A rose plot is more readable using larger bin sizes than the jpd plot
width_direction = 10; % [degrees]
width_velocity = 0.25; %[m/s]
 
%plot the rose plot
%f2= figure;
figure;
plot_rose(data,width_direction,width_velocity,"flood_ebb",[flood,ebb]);

Velocity Duration Curve

The velocity duration curve shows the probability of achieving a particular velocity value. After computing the exceedance probability, the rank order of velocity values can be plotted as follows.
% Calculate the exceedance probability of the data
data.Discharge = data.s; % need to change structure name for exceedance probability function
F = exceedance_probability(data);
 
% Plot the VDC
 
plot_velocity_duration_curve(data.s,F.F);
+======= Example: MHKiT-MATLAB Tidal Module