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1. A time domain approach for the optimal control of wave energy converter arrays

   https://doi.org/10.36688/ewtec-2023-472  

   Shabara, Mohamed; Abdelkhalik, Ossama (September 2023, Proceedings of the European Wave and Tidal Energy Conference)

   Wave energy converters typically use various control methods to extract energy from ocean waves. The objective of the control system is to optimize the energy extraction process, taking into account the dynamics of the system and the wave conditions. The task of deriving the optimal control laws of wave energy converter arrays for regular and irregular waves using the Pontryagin minimum principle was previously investigated in the literature. The result is a combination between the singular arc and bang-bang control laws. For irregular waves, some complexity arises due to the radiation state-space representation, which requires ignoring the hydrodynamic coupling terms related to the added mass and radiation-damping coefficients; this reduces the computational complexity of the control force but adversely affects the solution's accuracy. Also, the derived control laws are specific to a particular wave condition. Recently, the optimal control of a flexible buoy wave energy converter was derived using the convolution representation for the radiation force. In this work, the optimal control laws of flexible buoy wave energy converters are modified to simulate wave energy converter arrays; then, the results are compared to those obtained by dropping the hydrodynamic radiation coupling terms. Although using a convolution representation adds computational complexity to the optimal control problem, it generates an equation that is generic to any wave condition, can be used with any wave spectrum, and provides an expression for the switching condition. 

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2. On-demand harmonic wave suppression in non-Hermitian space-time-periodic phased arrays

   https://doi.org/10.1088/1361-665X/acd597  

   Adlakha, R; Nouh, M (May 2023, Smart Materials and Structures)

   Abstract Phased arrays have been a cornerstone of non-destructive evaluation, sonar communications, and medical imaging for years. Conventional arrays work by imparting a static phase gradient across a set of transducers to steer a self-created wavefront in a desired direction. Most recently, space-time-periodic (STP) phased arrays have been explored in the context of multi-harmonic wave beaming. Owing to the STP phase profile, multiple scattered harmonics of a single-frequency input are generated which propagate simultaneously in different directional lanes. Each of these lanes is characterized by a principal angle and a distinct frequency signature that can be computationally predicted. However, owing to the Hermitian (real) nature of the spatiotemporal phase gradient, waves emergent from the array are still bound to propagate simultaneously along up- and down-converted directions with a perfectly symmetric energy distribution. Seeking to push this boundary, this paper presents a class of non-Hermitian STP phased arrays which exercise a degree of unprecedented control over the transmitted waves through an interplay between gain, loss, and coupling between its individual components. A complex phase profile under two special symmetries, parity-time (PT) and anti-PT, is introduced that enables the modulation of the amplitude of various harmonics and decouples up- and down-converted harmonics of the same order. We show that these arrays provide on-demand suppression of either up- or down-converted harmonics at an exceptional point—a degeneracy in the parameter space where the system’s eigenvalues and eigenvectors coalesce. An experimental prototype of the non-Hermitian array is constructed to illustrate the selective directional suppression via time-transient measurements of the out-of-plane displacements of an elastic substrate via laser vibrometry. The theory of non-Hermitian phased arrays and their experimental realization unlock rich opportunities in precise elastoacoustic wave manipulation that can be tailored for a diverse range of engineering applications. 

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3. Transition Wave Interference in Multistable Mechanical Metamaterials

   https://doi.org/10.1115/1.4067856  

   Bonthron, Michael; Tubaldi, Eleonora (May 2025, Journal of Applied Mechanics)

   Mechanical metamaterials with multiple stable configurations offer a promising avenue for the design and development of adaptable materials with unprecedented levels of control over physical properties. Specifically, arrays of bistable beam elements represent a unique metamaterial platform with tunable transition waves offering means of passive control, sensing, and memory effects of environmental conditions. Although previous studies have mainly investigated transition waves triggered by a static input in nonlinear metamaterials, the dynamic properties of these structures and the interference of colliding waves are still unknown. Here, we investigate the dynamic properties of arrays of bistable beam elements which are important keys in the further development of applications of these metastructures. We determine the critical force and the optimal location to apply a force to trigger a transition wave and characterize the natural frequencies of the metamaterial. Moreover, we study the interference between two transition waves simultaneously actuated at both ends of the one-dimensional multistable array. Our new insights on the nonlinear dynamic responses of multistable metamaterials pave the way for the ability to design and program adaptable structures with enhanced energy absorption, vibration isolation, and wave steering capabilities. 

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4. Statistical and Dynamical Characteristics of Extreme Wave Crests Assessed with Field Measurements from the North Sea

   https://doi.org/10.1175/JPO-D-22-0125.1  

   Malila, Mika P; Barbariol, Francesco; Benetazzo, Alvise; Breivik, Øyvind; Magnusson, Anne Karin; Thomson, Jim; Ward, Brian (February 2023, Journal of Physical Oceanography)

   Abstract Wave crests of unexpected height and steepness pose a danger to activities at sea, and long-term field measurements provide important clues for understanding the environmental conditions that are conducive to their generation and behavior. We present a novel dataset of high-frequency laser altimeter measurements of the sea surface elevation gathered over a period of 18 years from 2003 to 2020 on an offshore platform in the central North Sea. Our analysis of crest height distributions in the dataset shows that mature, high sea states with high spectral steepness and narrow directional spreading exhibit crest height statistics that significantly deviate from standard second-order models. Conversely, crest heights in developing sea states with similarly high steepness but wide directional spread correspond well to second-order theory adjusted for broad frequency bandwidth. The long-term point time series measurements are complemented with space–time stereo video observations from the same location, collected during five separate storm events during the 2019/20 winter season. An examination of the crest dynamics of the space–time extreme wave crests in the stereo video dataset reveals that the crest speeds exhibit a slowdown localized around the moment of maximum crest elevation, in line with prevailing theory on nonlinear wave group dynamics. Extending on previously published observations focused on breaking crests, our results are consistent for both breaking and nonbreaking extreme crests. We show that wave crest steepness estimated from time series using the linear dispersion relation may overestimate the geometrically measured crest steepness by up to 25% if the crest speed slowdown is not taken into account. Significance StatementBetter understanding of the statistics and dynamical behavior of extreme ocean surface wave crests is crucial for improving the safety of various operations at sea. Our study provides new, long-term field evidence of the combined effects of wave field steepness and directionality on the statistical distributions of crest heights in storm conditions. Moreover, we show that the dynamical characteristics of extreme wave crests are well described by recently identified nonlinear wave group dynamics. This finding has implications, for example, for wave force calculations and the treatment of wave breaking in numerical wave models. 

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5. Integrated Design for Wave Energy Converter Farms: Assessing Plant, Control, Layout, and Site Selection Coupling in the Presence of Irregular Waves

   https://doi.org/10.1115/DETC2024-143179  

   Azad, Saeed; Khanal, Suraj R; Herber, Daniel R; Jia, Gaofeng (August 2024, American Society of Mechanical Engineers)

   Abstract A promising direction towards reducing the levelized cost of energy for wave energy converter (WEC) farms is to improve their performance. WEC design studies generally focus on a single design domain (e.g., geometry, control, or layout) to improve the farm’s performance under simplifying assumptions, such as regular waves. This strategy, however, has resulted in design recommendations that are impractical or limited in scope because WEC farms are complex systems that exhibit strong coupling among geometry, control, and layout domains. In addition, the location of the candidate site, which has a large impact on the performance of the farm, is often overlooked. Motivated by some of the limitations observed in WEC literature, this study uses an integrated design framework, based on simultaneous control co-design (CCD) principles, to discuss the impact of site selection and wave type on WEC farm design. Interactions among plant, control, and layout are also investigated and discussed using a wide range of simulations and optimization studies. All of the studies were conducted using frequency-domain heaving cylinder WEC devices within a farm with a linear reactive controller in the presence of irregular probabilistic waves. The results provide high-level guidelines to help the WEC design community move toward an integrated design perspective. 

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