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Concurrent Geometry, Control, and Layout Optimization of Wave Energy Converter Farms in Probabilistic Irregular Waves using Surrogate Modeling

Saeed Azad, Daniel R. Herber, Suraj Khanal, Gaofeng Jia

Abstract

A promising direction towards improving the performance of wave energy converter (WEC) farms is to leverage a system-level integrated approach known as control co-design (CCD). A WEC farm CCD problem may entail decision variables associated with the geometric attributes, control parameters, and layout of the farm. However, solving the resulting optimization problem, which requires the estimation of hydrodynamic coefficients through numerical methods such as multiple scattering (MS), is computationally prohibitive. To mitigate this computational bottleneck, we construct data-driven surrogate models (SMs) using artificial neural networks in combination with concepts from many-body expansion. The resulting SMs, developed using an active learning strategy known as query by committee, are validated through a variety of methods to ensure acceptable performance in estimating the hydrodynamic coefficients, (energy-related) objective function, and decision variables. To rectify inherent errors in SMs, a hybrid optimization strategy is devised. It involves solving an optimization problem with a genetic algorithm and SMs to generate a starting point that will be used with a gradient-based optimizer and MS. The effectiveness of the proposed approach is demonstrated by solving a series of optimization problems with increasing levels of integration. For a layout optimization study, the framework offers a 91-fold increase in computational efficiency compared to MS. Previously unexplored investigations of much further complexity are also performed, leading to a concurrent geometry, control, and layout optimization of WEC devices in probabilistic irregular waves. The scalability of the method is evaluated by increasing the farm size to include 25 devices. The results indicate promising directions toward a practical framework for integrated WEC farm design with more tractable computational demands.

Concurrent Geometry, Control, and Layout Optimization of Wave Energy Converter Farms in Probabilistic Irregular Waves using Surrogate Modeling

Abstract

A promising direction towards improving the performance of wave energy converter (WEC) farms is to leverage a system-level integrated approach known as control co-design (CCD). A WEC farm CCD problem may entail decision variables associated with the geometric attributes, control parameters, and layout of the farm. However, solving the resulting optimization problem, which requires the estimation of hydrodynamic coefficients through numerical methods such as multiple scattering (MS), is computationally prohibitive. To mitigate this computational bottleneck, we construct data-driven surrogate models (SMs) using artificial neural networks in combination with concepts from many-body expansion. The resulting SMs, developed using an active learning strategy known as query by committee, are validated through a variety of methods to ensure acceptable performance in estimating the hydrodynamic coefficients, (energy-related) objective function, and decision variables. To rectify inherent errors in SMs, a hybrid optimization strategy is devised. It involves solving an optimization problem with a genetic algorithm and SMs to generate a starting point that will be used with a gradient-based optimizer and MS. The effectiveness of the proposed approach is demonstrated by solving a series of optimization problems with increasing levels of integration. For a layout optimization study, the framework offers a 91-fold increase in computational efficiency compared to MS. Previously unexplored investigations of much further complexity are also performed, leading to a concurrent geometry, control, and layout optimization of WEC devices in probabilistic irregular waves. The scalability of the method is evaluated by increasing the farm size to include 25 devices. The results indicate promising directions toward a practical framework for integrated WEC farm design with more tractable computational demands.
Paper Structure (28 sections, 31 equations, 19 figures, 11 tables, 1 algorithm)

This paper contains 28 sections, 31 equations, 19 figures, 11 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Wave Climate and Modeling
  4. Wave-Structure Interactions
  5. Linear Potential Flow Theory
  6. Hydrodynamic and Hydrostatic Forces
  7. Multiple Scattering
  8. Dynamics and Control of WECs
  9. Array Considerations
  10. Surrogate Models for Hydrodynamic Interactions
  11. Artificial Neural Networks.
  12. Many-body Expansion.
  13. Constructing Surrogate Models
  14. Surrogate Model Structure
  15. Developing Training Data and ANNs
  16. ...and 13 more sections

Figures (19)

  • Figure 1: The general framework for the concurrent plant, control, and layout optimization using surrogate modeling and principles of MBE. The joint probability distribution of significant wave heights and wave periods for various US locations are constructed based on historical data.
  • Figure 2: Joint distribution of $H_s$ and $T_p$ for the first year of the study at the selected site locations on the Alaskan Coast, East Coast, Pacific Islands, and West Coast based on data from storlazzi2015futureerikson2016wave.
  • Figure 3: Illustration of WEC and its layout considerations.
  • Figure 4: Illustration of many-body expansion principle.
  • Figure 5: ANN model performance for estimation of various hydrodynamic coefficients of a single WEC, characterized in the plant design space through expected MSE. A different number of samples is intelligently selected for each model.
  • ...and 14 more figures