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 and controller design which minimizes the energy cost and power variation of the Reference Model 3 (RM3) WEC, using a fast simplified frequency domain WEC model.

Context

The project is part of research in the Symbiotic Engineering Analysis (SEA) Lab and has been accepted for publication/presentation in the 2022 ASME IDETC-CIE. At this conference, the work was presented at the DAC-6 session and is publication number 90227. A recording of the conference presentation is available here. The project began as an effort in Cornell course MAE 5350.

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.

Authors

• Rebecca McCabe, rgm222@cornell.edu (Project lead and point of contact) @rebeccamccabe
• Olivia Murphy, om66@cornell.edu (Project contributor) @ommurphy
• Maha Haji, maha@cornell.edu (Advisor) @maha-haji

Disclaimer

The versions of the simulation used in the conference proceedings paper (v1.2) and in the conference video (v1.3) were later found to have a number of errors. These errors have since been corrected, and the current code (v1.4) is correct to the best of the authors' knowledge, within the limitations of the stated assumptions. Known areas for improvement are listed as GitHub issues. If you find any additional errors, please let us know.

Errors that have since been fixed include:

• Incorrect value for young's modulus of steel
• Incorrect implementation of force saturation multiplier
• Wave period and wave height were swapped
• Froude Krylov force coefficient too high
• Incorrect nominal controller design variables and objective values
• Incorrect buckling end condition
• Nominal simulation did not use power saturation
• Incorrect scaling of cost with number of WECs
• Powertrain and transmission loss not accounted for
• Mass of damping plate support tubes not accounted for
• Float maximum displacement constraint not being enforced

Because the results in the official conference proceedings contain these errors, an updated unofficial version of the paper will be posted here in early September 2022, containing corrections.

License

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

File Structure

• inputs: numerical inputs needed to run the optimiztion, simulation, and validation, including wave data, parameters, design variable bounds, and validation values.
• 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.
• 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.
• plots: helper functions to visualize outputs. Start with the script all_figures.m if you want to try out the entire pipeline by running all relevant optimizations to generate every figure in the paper.
• dev: miscellaneous scripts not core to the codebase that were used to inform the development of the simulation.

Dependencies

The following packages are used in this code:

• MATLAB
• Optimization Toolbox
• Global Optimization Toolbox
• Statistics and Machine Learning Toolbox
• Symbolic Math Toolbox

All are required except the symbolic math toolbox, which is used only for code generation and exploratory scripting, not core functionality.

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.