[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86525-en":3,"doc-seo-86525-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},86525,2336464648746,"Skyler","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Multidisciplinary Design Optimization of Wave Energy Converter Farms Considering Uncertainty through Polynomial Chaos Expansion","A multidisciplinary design optimization framework under uncertainty is developed for grid-scale wave energy converter (WEC) array farms. Helaving point absorbers are co-designed across coupled disciplines—geometry, hydrodynamics, layout, and trajectory/control—to formulate a control co-design problem jointly optimizing plant and control. Array placement and optimization under uncertain ocean-wave power are shown to outperform optimizing a single WEC before placing it into an array. Power-per-volume is minimized by varying WEC dimensions, array layout, and control gains. Polynomial chaos expansion (PCE) regression quantifies performance variability at each design iteration, yielding designs with reduced sensitivity to wave-environment input changes.","arXiv :2607 . 10962v1 [ ee ss . SY] 13 Jul 2026  \nMultidisciplinary Design Optimization of Wave Energy Converter Farms Considering Uncertainty through Polynomial Chaos Expansion  \nKapil Khanal∗a , Nate DeGoede∗b , Maha N. Hajib  \na Systems Engineering, Cornell University, Ithaca, NY, USA b Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, USA  \nAbstract  \nIn this paper, a multidisciplinary design optimization problem under uncertainty is formulated for wave energy converter array. An array of heaving point absorbers for grid-scale energy production with decision variables and parameters chosen from the coupled disciplines of geometry, hydrodynamics, layout, and trajectory optimization thus resulting in a control co-design formulation of the plant and the control together. We study the benefits of MDO, and WEC farms and show that placing WEC farms in an array and optimizing it under uncertainty is significantly better than optimizing a WEC and placing it in an array. We vary the wave energy converter (WEC) dimensions, array layout, and control gain to minimize the power per volume. Uncertainty in the electrical power is handled using regression based on polynomial chaos expansion (PCE) method at each design iteration. Traditional WEC farm design optimization approaches often neglect the multidisciplinary, coupled nature of WECs and the inherent uncertainty in ocean wave conditions and control responses. This leads to designs that may under perform in real-world environments. In this work, we address this limitation by incorporating uncertainty directly into the design optimization process using the technique of polynomial chaos expansion (PCE) to quantify the variability of the performance due to uncertain wave environment. It is shown that the robustly designed WEC farms are significantly less sensitive to the input variations.  \nKeywords: Multidisciplinary WEC Layout optimization, Sensitivity Analysis, Uncertainty Quantification, Polynomial chaos expansion  \n1. Introduction  \nWave energy converters (WECs) convert the oscillatory motion of ocean waves into usable mechanical or electrical energy (Budal, 1977) . For gridscale deployment, multiple WECs must operate collectively, forming so-called wave farms comprised of arrays of WECs. According to Kilcher et al. (2021), such farms could theoretically supply up to 34% of U.S. electricity demand. Yet, large-scale development remains limited due to high capital costs, permitting challenges, and unresolved technical complexities (Freeman et al. , 2022) .  \nA critical difficulty in designing WEC farms arises from hydrodynamic interactions among devices, identified by Babarit (2013) as the “park effect,\"in which radiated and diffracted waves from one WEC influence the performance of others. These coupled effects mean that total farm power output depends on array geometry, device spacing, control strategy, and the local wave environment. Numerous studies have examined these factors from different perspectives. For example, Bozzi et al. (2017) simulated WEC array configurations under real-sea conditions off the Italian coastline and showed that the dominant wave heading strongly affects optimal layouts; however, their study used brute-force optimization over only four candidate configurations. To reduce computational cost, Giassi and Göteman (2018) applied cluster-based optimization to minimize the levelized cost of electricity (LCOE), while Lyu et al. (2019) employed genetic algorithms to optimize the geometry and layout of three-, five-, and seven-body arrays. Their results demonstrated up to a 39% increase in power production through joint optimization of design variables and further revealed that, under irregular waves with unconstrained impedance-matching and passive-derivative control strategies, the optimal array layout becomes asymmetric. Although these configurations achieved improved hydrodynamic performance, the resulting designs, featuring slightly differ","cbCaiaYf40dwj48W","https://ap.wps.com/l/cbCaiaYf40dwj48W","pdf",5203342,2,1,33,"English","en",105,"# Abstract\n# 1. Introduction\n## Wave energy converter farms and grid-scale deployment\n## Hydrodynamic coupling and the park effect\n## Control co-design and multidisciplinary optimization\n## Uncertainty in wave conditions and control responses\n## MDO formulation and problem setup","[{\"question\":\"What multidisciplinary elements are jointly optimized in the proposed WEC farm framework?\",\"answer\":\"Geometry, hydrodynamics, layout, and trajectory/control are selected as coupled disciplines and optimized together as a control co-design formulation.\"},{\"question\":\"How is uncertainty handled during the design optimization process?\",\"answer\":\"Electrical power uncertainty is incorporated using regression based on polynomial chaos expansion (PCE) at each design iteration to quantify performance variability.\"},{\"question\":\"Why can optimizing an entire WEC array under uncertainty outperform optimizing a single WEC first?\",\"answer\":\"The study finds that robust optimization with uncertainty is significantly better when WECs are placed and optimized as an array, capturing coupled hydrodynamic interactions and environmental variability.\"}]",1784212387,83,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"multidisciplinary-design-optimization-of-wave-energy-converter-farms-considering-uncertainty-through-polynomial-chaos-expansion","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/multidisciplinary-design-optimization-of-wave-energy-converter-farms-considering-uncertainty-through-polynomial-chaos-expansion/86525/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-24","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What multidisciplinary elements are jointly optimized in the proposed WEC farm framework?","Question",{"text":75,"@type":76},"Geometry, hydrodynamics, layout, and trajectory/control are selected as coupled disciplines and optimized together as a control co-design formulation.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is uncertainty handled during the design optimization process?",{"text":80,"@type":76},"Electrical power uncertainty is incorporated using regression based on polynomial chaos expansion (PCE) at each design iteration to quantify performance variability.",{"name":82,"@type":73,"acceptedAnswer":83},"Why can optimizing an entire WEC array under uncertainty outperform optimizing a single WEC first?",{"text":84,"@type":76},"The study finds that robust optimization with uncertainty is significantly better when WECs are placed and optimized as an array, capturing coupled hydrodynamic interactions and environmental 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