MDOcean

This is an open source codebase that uses Multidisciplinary Design Optimization (MDO) to optimize an ocean wave energy converter (WEC).

More specifically, it uses the SQP and pattern search algorithms to find the geometry, PTO, and structural design which optimizes the levelized cost of energy, capital cost, and average power of the Reference Model 3 (RM3) WEC, using a fast simplified frequency domain WEC model.

For 210 sea states, the model takes 39 ms to run, which is around a 5 order of magnitude improvement compared to the equivalent ~1 hour set of parallel WEC-Sim MCR simulations.

Context

The project is part of research in the Symbiotic Engineering Analysis (SEA) Lab.

Journal paper citation (in prep): R. McCabe, M. Dietrich, and M. N. Haji, “Leveraging Multidisciplinary Design Optimization and Semi-Analytical Modeling to Advance Wave Energy Converter Viability,” in preparation, 2025. Link to draft paper manuscript.

Conference paper citation: R. McCabe, O. Murphy, and M. N. Haji, “Multidisciplinary Optimization to Reduce Cost and Power Variation of a Wave Energy Converter,” International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, St. Louis, MO, August 14-17, 2022. https://doi.org/10.1115/DETC2022-90227.

A video recording of the conference presentation is available here.

Software Authors - Rebecca McCabe, rgm222@cornell.edu (Project lead and point of contact, 2021-present) @rebeccamccabe - Madison Dietrich, mjd429@cornell.edu (Project contributor, 2023-present) @MadisonDietrich - Olivia Murphy, om66@cornell.edu (Project contributor, 2021-22) @ommurphy - Iris Ren, zr92@cornell.edu (Project contributor, 2024) - Maha Haji, maha@cornell.edu (Advisor, 2021-present) @maha-haji

License

This project is released open-source under the MIT License. The validation folder contains code taken from NREL's WEC-Sim. The Apache 2.0 license for this open source WEC-Sim code is included.

File Structure and Usage

Clone the repository via Git. If you are unfamiliar with Git, click "Code > Download ZIP" to get a .zip file, or try the "Open in MATLAB Online" button above to use the MATLAB Online IDE instead.

• tests: continuous integration tests for validation as well as generating a report to reproduce all figures and results. Running run_tests.m is the easiest way to reproduce all results. The run_slow_tests flag in test.m can be toggled to enable or disable the tests which take longer than a few minutes to run.
• mdocean/inputs: numerical inputs needed to run the optimiztion, simulation, and validation, including wave data, parameters, design variable bounds, and validation values.
• mdocean/simulation: the simulation that takes design variables and parameters as inputs and returns objective and constraint values as outputs, and its validation. The script run_single.m is a good starting point if you want to run the simulation without optimizing.
• mdocean/optimization: scripts and functions to perform single objective and multi-objective optimization and sensitivities. Start with the script gradient_optim.m if you want to run single objective optimization for each of the two objectives. For multi-objective, run pareto_search.m followed by pareto_curve_heuristics.m.
• mdocean/plots: helper functions to visualize outputs. Start with the script all_figures.m if you want to generate specific figures from the paper.
• dev: miscellaneous scripts not core to the codebase that were used to inform the development of the simulation.

If you are running individual scipts/functions, you will need to cd to the mdocean folder and add all subfolders here to the matlab path. This is done automatically if you are running everything at once via run_tests.m.

Documentation Documentation for the function API for this code is in progress at this Sphinx site.

Dependencies

The following packages are used in this code: | Package | Required? | | --- | --- | | MATLAB | Required for simulation | | Statistics and Machine Learning Toolbox | Required for simulation | | Optimization Toolbox | Required for optimization | | Global Optimization Toolbox | Required for optimization | | Symbolic Math Toolbox | Optional for simulation code generation | | Parallel Computing Toolbox | Optional for speedup | | MATLAB Report Generator | Optional for WEC-Sim validation | | Simulink | Optional for WEC-Sim validation | | Simscape | Optional for WEC-Sim validation | | Simscape Multibody | Optional for WEC-Sim validation | | WEC-Sim | Optional for WEC-Sim validation |

The code has been tested on R2022a (Windows) and R2024b (Linux), and likely works on other versions and operating systems.

Contributing

Suggestions, questions, bug reports, and contributions are welcome. Open an issue or pull request. To discuss the possibility of broader collaborations, please email rgm222@cornell.edu.

Funding Acknowledgement

This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE–2139899, and the Cornell Engineering Fellowship. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors(s) and do not necessarily reflect the views of the National Science Foundation.