MDOcean

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

More specifically, it is both a multidisciplinary model and a design optimization framework for two-body point absorber WECs.

MDOcean 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.

Features

Model features:

• semi-analytical hydrodynamic model, using the matched eigenfunction expansion method to model linear potential flow
• semi-analytical frequency-domain dynamic model, using describing functions to model drag and saturation nonlinearities
• analytical structural model, using tabulated solutions and the equivalent-thickness method to model stiffened plate ultimate and fatigue limits
• algebraic cost model, with costs scaling with PTO force and power and structural material volume
• algebraic geometry model, calculating common areas and volumes
• (in development) algebraic eco-cost model, with eco-costs scaling with structural material volume, hull area, and maintenance frequency
• (in development) integration with grid model, capturing energy market prices and grid-wide emissions

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.

Optimization features:

• SQP (gradient-based) single-objective optimization
• pattern search (gradient-free) and epsilon constraint SQP (gradient-based) multi-objective optimization
• multi-start to see how starting point affects the optimal result
• derivative-based local sensitivity analysis to see how parameter values affect the optimal result with very little additional computation
• re-optimization-based local sensitivity analysis to see how parameter values affect the optimal result with higher accuracy

Running the single-objective optimization with typical parameters reduces LCOE by 57% compared to the standard RM3 design.

Benchmarking and Validation features:

• Validation of power production and device amplitude against WEC-Sim
• Validation of hydrodynamic coefficents against WAMIT (for RM3 geometry) and existing matched eigenfunction expansion method results (for a benchmark geometry from Chau and Yeung 2012)
• Validation of structural model against FEA results for RM3 geometry from Reference Model report (Neary et. al 2012)
• Validation of economic and geometric outputs against results for RM3 geometry from Reference Model report (Neary et. al 2012)
• Validation that power production does not violate the theoretical radiation limit
• Unit tests, code coverage, and automatic report generation to monitor status of above checks on demand
• Continuous integration with GitHub Actions to monitor status of above checks on every push to GitHub

Academic Context

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

Model journal paper citation (in prep): R. McCabe, M. Dietrich, and M. N. Haji, “Development, Validation, and Benchmarking of a Multidisciplinary Semi-Analytical Model for Wave Energy Converters,” in preparation, 2025. Link to draft paper manuscript.

Optimization journal paper citation (in prep): R. McCabe, M. Dietrich, and M. N. Haji, “Leveraging Multidisciplinary Design Optimization to Advance Wave Energy Converter Viability,” in preparation, 2026. 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.

Code Documentation

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

Installation

Clone the repository via Git. Use the --recursive flag to include submodules.

git clone --recursive https://github.com/symbiotic-engineering/MDOcean.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.

File Structure and Usage

• 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.
• mdocean/analysis: classes for running analyses of various sorts, typically wrappers around functions in the optimization and plots folders. Uses a special cached workflow defined in abstract class GenericAnalysis.m so that changes to cheap post-processing scripts (typically plots) do not require rerunning the expensive analysis (typically optimization).
• 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.

Reproducibility

This project uses Calkit pipelines to ensure all figures and publications are fully reproducible. To reproduce, download calkit and then enter the command calkit run. You can also view the project artifacts on calkit.io. Larger files like images and pdfs are stored in DVC rather than Git.

Software Authors

• Rebecca McCabe, [email protected] (Project lead and point of contact, 2021-present) @rebeccamccabe
• Madison Dietrich, [email protected] (Project contributor, 2023-present) @MadisonDietrich
• Anthony Long, [email protected] (Project contributor, 2025) @anthnlong
• Olivia Murphy, [email protected] (Project contributor, 2021-22) @ommurphy
• Iris Ren, [email protected] (Project contributor, 2024) @irin0012
• Maha Haji, [email protected] (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.

Dependencies

The following packages are used in this code:

Package	Required?
MATLAB	Required for simulation
Statistics and Machine Learning Toolbox	Required for simulation
OpenFLASH	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
SAFE	Optional for sensitivity analysis

The external codes (OpenFLASH, WEC-Sim, and SAFE) are included as submodules for ease of use. The code has been tested on MATLAB 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 [email protected].

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.