MDOcean documentation
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.
How to Use
Please see the documentation here for instructions on how to run the simulation, optimization, or entire paper-reproduction pipeline. The package calkit is used for single-button reproducibility. Additionally, this page has guidance on how to modify the code to be used for other problems.
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 |
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 |
Optional for WEC-Sim validation |
|
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 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.
Full Function Documentation