Nonlinear Harmonics Research Articles

Evaluation of Bonding Strength of Pipeline Coating Based on Circumferential Guided Waves

The anti-corrosion layer of the pipe provides corrosion resistance and extends the lifespan of the whole pipeline. Heat-shrinkable tape is primarily used as the pipeline joint coating material bonded to the pipeline weld connection position after heating. Delineating the bonding strength and assessing the quality of the bonded structure is crucial for pipeline safety. A detection technology based on nonlinear ultrasound is presented to quantitatively evaluate the bonding strength of a steel-EVA-polyethylene three-layer annulus bonding structure. Using the Floquet boundary condition, the dispersion curves of phase velocity and group velocity for a three-layer annulus bonding structure are obtained. Additionally, wave structure analysis is employed in theoretical study to choose guided wave modes that are appropriate for detection. In this paper, guided wave amplitude, frequency attenuation, and nonlinear harmonics are used to evaluate the structural bonding strength. The results reveal that the detection method based on amplitude and frequency attenuation can be used to preliminarily screen the poor bonding, while the acoustic nonlinear coefficient is sensitive to bonding strength changes. This study introduces a comprehensive and precise pipeline joint bonding strength detection system leveraging ultrasonic-guided wave technology for pipeline coating applications. The detection system determines the bonding strength of bonded structures with greater precision than conventional ultrasonic inspection methods.

Experimental Investigation of Nonlinear Forces on a Monopile Offshore Wind Turbine Foundation Under Directionally Spread Waves

Abstract Accurate prediction of nonlinear wave loading is crucial for designing marine and offshore structures, yet it remains a challenging task. Prior research has primarily focused on uni-directional extreme sea states, revealing that linear loading cannot accurately represent the total wave forces acting on offshore wind turbine foundations, with significant contributions from high-order harmonics. This study broadens the scope to include multi-directional and bi-directional wave interactions with monopile offshore wind turbine foundations. We use a phase-based harmonic separation method to isolate harmonic components in the presence of complex wave scenarios. This approach allows for the clear delineation of individual harmonics from the total wave force by controlling the phase of incident focused waves. Remarkably, this method shown effective even with multi-directional and bi-directional spreading. The clean separation of individual harmonics enables the estimation of contributions from each harmonic. Our findings are in line with previous research, showing that nonlinear loading can constitute up to 40% of the total under certain wave conditions. We have also observed that wider wave spreading reduces nonlinear high-order harmonics, and uni-directional waves induce the most severe nonlinear forces. These insights emphasise the importance of accounting for high-order nonlinear wave loading in offshore structure design.

Mitigating Nonlinear Harmonics in Diesel Electrical Ship Network by Model Predictive Control

Mitigating Nonlinear Harmonics in Diesel Electrical Ship Network by Model Predictive Control

Effects of nonlinearity on the crest shape of extreme irregular sea waves: Nonlinear harmonic separation and analysis

This work highlights the effects of nonlinearity on the crest shape of extreme directional water wave events in infinite and finite water depths. HOS-ocean, a High-Order Spectral code developed for solving the deterministic propagation of nonlinear wavefields in open ocean [Ducrozet et al., “HOS-ocean: Open-source solver for nonlinear waves in open ocean based on High-Order Spectral method,” Comput. Phys. Commun. 203, 245–254 (2016)], is used for comparisons with linear simulations. Nonlinear wave harmonics were extracted combining and extending previous methods [Fitzgerald et al., “Phase manipulation and the harmonic components of ringing forces on a surface-piercing column,” Proc. R. Soc. A 470, 20130847 (2014) and Hann et al., “A new set of focused wave linear combinations to extract non-linear wave harmonics,” in Proceedings of 29th International Workshop on Water Waves and Floating Bodies, 2014], showing the contribution of various orders of nonlinearity. The work shows that “walls of water,” [Adcock et al., “Nonlinear dynamics of wave-groups in random seas: Unexpected walls of water in the open ocean,” Proc. R. Soc. A 471, 20150660 (2015) and Adcock et al., “On the shape of large wave-groups on deep water—The influence of bandwidth and spreading,” Phys. Fluids 28, 106601 (2016)], a significant increase in the crest width, are also formulated in finite water depths. Mainly responsible for this is the first order harmonic, with significant energy transfers away from components propagating at an angle, which are more pronounced in finite water depths. As nonlinearity increases, higher order harmonics (>second) become, as expected, more significant. In deep water, rapid energy transfers lead to a broadening of the spectrum which is reflected in the increase in the first order amplitude sum and hence increased crest elevations at the point of the large event. However, in finite water depths, energy transfers are gradually leading to a narrowing of the spectrum around the spectral peak and to a general broadening of the spectrum at the higher harmonics; reflected in the significant decrease in the first order amplitude sum and hence a decrease in crest elevations at the point of the large event, also aided by the larger increase in the out-of-phase difference terms (zeroth harmonic).

Efficient second-harmonic generation in a lithium niobate metasurface governed by high-Q magnetic toroidal dipole resonances.

Lithium niobate (LN) is an excellent nonlinear optical material due to its large nonlinear coefficient, low loss, and broad optical transparency window. So, it is widely used in the generation of nonlinear harmonics. Magnetic toroidal dipole (MTD) resonance is a special optical resonance mode, which can effectively localize the light field inside the device, thus enhancing the nonlinear effects of the materials. In this work, we numerically study the second-harmonic generation (SHG) effect of the LN metasurface based on the MTD mode with a high quality factor (Q-factor). The designed LN nanorod dimer metasurface supports high Q-factor MTD guided mode resonances (GMRs), which are excited by varying the center spacing of the two nanorods, and the Q-factor can be controlled by the offset distance. The excited MTD can effectively confine the electric field within the device, which enables the LN metasurface SHG conversion efficiency to reach 1.15 × 10-2. In addition, by adjusting the structural parameters, it is possible to effectively modulate the wavelength and conversion efficiency of the SHG. Our results provide a new route for high-quality nonlinear light sources.

Eckart streaming with nonlinear high-order harmonics: An example at gigahertz

Eckart streaming with nonlinear high-order harmonics: An example at gigahertz

Multichannel information transmission via a dual-frequency point space-time coding metasurface

Space-time coding (STC) digital metasurfaces enable dynamic control of nonlinear harmonics. To achieve efficient frequency tuning and harmonic control, we propose a one-bit column-controlled temporal coding dual-frequency point STC digital metasurface. Using a field-programmable gate array (FPGA) to control diode switching, the metasurface is encoded to generate multiple target reflected harmonics as independent information transmission channels. The amplitude intensities of these harmonics are defined as independent binary symbols for transmission. The proposed space-time coding digital metasurface can achieve a phase shift of 180° in its unit structure, with reflectivities above 90% at both operating frequencies. We fabricated the designed metasurface and tested its far-field scattering experimentally. When the incident electromagnetic wave frequency is 4.63 GHz, the predicted results are essentially consistent with the experimental findings.

Nonlinear Harmonics Method for Supercomputer Simulations of Fluid Dynamics in Turbomachines with Higher Accuracy on Unstructured Meshes

Nonlinear Harmonics Method for Supercomputer Simulations of Fluid Dynamics in Turbomachines with Higher Accuracy on Unstructured Meshes

Role of gas composition in weakened nonlinear standing wave excitation and improved plasma radial uniformity in very-high-frequency asymmetric capacitive Ar/CF4 discharges

The higher harmonics generated by nonlinear sheath motion would enhance the standing wave effect, and thus lead to center-peaked plasma density profile in very-high-frequency (VHF) capacitive discharges. In this work, a nonlinear transmission line (NTL) model introduced in Zhou et al (2021 Plasma Sources Sci. Technol. 30 125017) has been extended, with radial transport of various particles and nonlinear sheath motion into account, to investigate the effects of CF4 fraction α on the nonlinear standing wave excitation and plasma radial uniformity in VHF (60 MHz) capacitively coupled Ar/CF4 plasmas at 3 Pa. The results indicate that for pure Ar discharges (i.e. α= 0%), the nonlinearly excited harmonics with short wavelength significantly enhance the electron power absorption at the radial center, resulting in a pronounced central-high plasma density profile. As α increases, the high-order harmonics are gradually damped due to the increase of resistance, as well as the longer wavelength caused by thicker sheath thickness. Thus, the radial profile of the electron absorbed power density shifts from center-peak to edge-high. Besides, at the radial center, the electron density and Ar+ ion density decrease with α , CF3 + ion density shows an increasing trend, while F− ion density initially rises and then decreases. Moreover, the density profiles of all the species become more uniform at higher CF4 fraction, due to the suppressed nonlinear standing wave excitation and the longer wavelength of the nonlinear harmonics.

Simultaneously Interactions of Ultra‐Low‐Frequency Waves and Whistler Waves, and Whistler Waves and Quasi‐Electrostatic Whistler Harmonics in the Earth's Magnetosheath

AbstractIdentifying how different wave modes interaction with each other is an important topic in space physics. Using measurements from the Magnetospheric Multiscale (MMS) mission, we report an event in the Earth's magnetosheath where ultra‐low‐frequency (ULF) waves, whistler waves, and quasi‐electrostatic whistler harmonics were observed simultaneously. Specifically, our analyses show that the parallel components of ULF waves modulate the electron butterfly distributions which provide the free energy to the excitation of the observed whistler waves. Meanwhile, quasi‐electrostatic waves sharing frequencies that are nearly integral multiples of the frequency of the observed whistlers are identified as nonlinear harmonics of whistler waves. The close correlations between the whistler waves and the electric field harmonics, as well as the high bicoherence indexes within the frequency ranges of the whistlers and harmonics, suggest the significant nonlinear couplings between the whistler waves and quasi‐electrostatic whistler harmonics. Our work provides new insights to the interactions between waves at different frequency bands.

Radar Micro-Doppler Signature Generation Based on Time-Domain Digital Coding Metasurface.

Micro-Doppler effect is a vital feature of a target that reflects its oscillatory motions apart from bulk motion and provides an important evidence for target recognition with radars. However, establishing the micro-Doppler database poses a great challenge, since plenty of experiments are required to get the micro-Doppler signatures of different targets for the purpose of analyses and interpretations with radars, which are dramatically limited by high cost and time-consuming. Aiming to overcome these limits, a low-cost and powerful simulation platform of the micro-Doppler effects is proposed based on time-domain digital coding metasurface (TDCM). Owing to the outstanding capabilities of TDCM in generating and manipulating nonlinear harmonics during wave-matter interactions, it enables to supply rich and high-precision electromagnetic signals with multiple micro-Doppler frequencies to describe the micro-motions of different objects, which are especially favored for the training of artificial intelligence algorithms in automatic target recognition and benefit a host of applications like imaging and biosensing.

Time-varying coding digital double-layered Huygens' metasurface for high-efficiency harmonic frequency conversion

Time-varying metasurfaces offer an efficient means of controlling nonlinear harmonics by manipulating component geometries and modulating signals. This ability renders them valuable across various fields, such as wireless communication, radar sensing, and biological monitoring. However, most of the energy in time-varying metasurfaces is concentrated in the fundamental wave, as well as scattered at various harmonic orders, which reduces the energy efficiency at the desired harmonic. Existing approaches have employed time-varying coding digital metasurfaces to achieve efficient harmonic conversion but are primarily designed for reflection. Reflection-based designs require a feed source to excite the metasurface, which can cause certain shielding effects and limit their application in specific scenarios. Thus, designing transmissive time-varying coding digital metasurfaces for efficient harmonic conversion is currently an urgent problem that needs to be addressed. To solve this problem, this paper develops a time-varying coding digital double-layered Huygens' metasurface, which achieves efficient conversion of the desired transmitted harmonics. The unit structure of the metasurface consists of a pair of reverse-symmetric split rings located on the upper and lower sides of a dielectric substrate, enabling nearly non-reflective Huygens' resonance. Based on a continuous periodic phase modulation strategy, we achieved efficient conversion of transmitted harmonics by loading a time-varying voltage (phase) modulation signal with a 5-bit resolution bit width onto the designed double-layered Huygens' metasurface. This study presents a solution for designing a transmissive time-varying coding digital metasurface to achieve efficient conversion of harmonics, thereby enhancing the application capabilities of time-varying coding digital metasurfaces.

Power quality stabilization system for grid connected large-scale solar power system

This paper presents solution to power quality issues when integrating a 1.5 MW photovoltaic array (PVA) with a unified power quality conditioner (UPQC) into the power grid. A modified unit vector template control scheme is used to generate a reference load voltage signal, and a synchronous reference frame (SRF) is created using a low-pass filter to control UPQC. Furthermore, the PVA is interfaced with the grid through a common DC link of shunt and series converters. The series converter mitigates power quality problems allied with the grid side, such as 3rd, 5th, and 7th harmonics, voltage sag, and voltage swell, by introducing signals in phase and out of phase voltage, respectively, at the point of common coupling (PCC). The shunt converter mitigates nonlinear load current harmonics and compensates for reactive power using SRF. The suggested methodology is implemented using MATLAB Simulink with both linear and nonlinear loads under different power quality conditions. Total harmonic distortions are maintained below 5% at PCC, as per IEEE-519 standards.

Tension evaluation of prestressed strand based on combined features of nonlinear ultrasonic mixing

The estimation of prestressed strand stress levels is of great significance in ensuring the structurally reasonable performance of post-tensioned concrete structures, cable-stayed bridges, and arch bridges. This paper proposes a method to evaluate the remaining tensile stress on the strand through the ultrasonic mixing technique. The relationship between the strand tension and the nonlinear harmonics is established based on the theory of contact acoustic nonlinearity, and the acoustic nonlinear parameters at different tension levels are investigated by finite element analysis and step-loading experiments. The results show that the nonlinear parameters follow a power-law decrease with the increase in the tensile stress. To overcome the shortage of decreasing sensitivity of theoretical nonlinear parameters in monitoring early loosening, support vector regression is introduced to utilize complex high-order nonlinear generations in stress evaluation. With this approach, the accuracy of early-stage stress evaluation based on wave mixing has been remarkably improved.

Concurrent UPQC Schemes for the Power Quality Improvement in Solar Photovoltaic Systems

Aims: Aim of this research is to propose a novel concurrent UPQC scheme for improving the power quality issues in grid integrated solar photovoltaic (PV) systems. Background: The power quality is a major issue for the grid integration of renewable energy sources. Issues like voltage sag, voltage swell, harmonics & non-linear load variations are certainly observed in the distributed energy system and it is mandated that any system has to depend on advanced controllers to improve power quality and stabilize the electrical parameters. Controller related power quality improvements are a bit easier to design but the tuning of power is difficult in this aspect. Objective: In order to overcome the aforesaid limitation, this particular paper proposes a new concurrent UPQC scheme for improving the four different power quality issues in grid integrated solar photovoltaic (PV) system such as voltage sag, voltage swell, non-linear load variations and current harmonics. Methods: The operating regions of each power quality issues are examined in the I-V curves of PV specifications and the new operating modes of PV systems are mapped for every quality improvement considering the power, current and frequency of the grid and load as well. The pool of solutions is developed from the real power, reactive power and converter duty cycle and verified with the proposed solutions. Additionally, the designed switching frequency of the proposed system has a 5% variation for practical irradiance. The PV uniform irradiance profile matches the real power for various proposed concurrent UPQC schemes. Results: Finally, the simulation results are presented to validate the operation of the proposed concurrent UPQC schemes for PV system. The comparative study of the proposed concurrent UPQC scheme for PV system with appropriate literature is presented. The superiority of the proposed schemes infers studying the odd harmonic components up to 100th order after implementing the proposed concurrent UPQC scheme for PV system. Conclusion: From the measured results, it is concluded that a new concurrent optimization scheme enhances the operation of solar PV system that integrates with the grid. The power quality issues like voltage & current swell, voltage & current sag, voltage imbalance, and harmonics are reduced compared to existing methods. The validation of the schemes is achieved through the group constraints and the operating slopes in each region.

On the probability of down-crossing and up-crossing rogue waves

By means of the direct numerical simulation of directional waves on the surface of deep water, it is shown that extreme waves can exhibit such asymmetry that the occurrence of deeper troughs is several times more likely on the wave rear slopes. This effect becomes most pronounced in the case of steep short-crested waves. It is not related to the Benjamin–Feir instability but is a result of complex contribution from nonlinear combination harmonics, mainly cubic in nonlinearity. The discovered asymmetry can lead to remarkably different estimates of the rogue wave probability based on either down- or up-zero-crossing methods for individual wave selection, commonly used in the oceanography.

Enhanced Position Estimation Based on Frequency Adaptive Generalized Comb Filter for Interior Permanent Magnet Synchronous Motor Drives

Accurate rotor position estimation is critical to ensure the high-performance operation of position sensorless interior permanent magnet synchronous motor (IPMSM) drives. However, the back electromotive force (BEMF) estimated by the model-based observers is usually nonideal, which may further degrade the position estimation accuracy. In this paper, a frequency adaptive generalized comb filter (FAGCF) with a quadrature phase-locked loop (PLL) is adopted to suppress the rotor position estimation errors by filtering out the dominant distortions in the BEMF, including the (6k±1)th harmonics caused by inverter nonlinearity and flux spatial harmonics, as well as the DC offset from the inaccurate current measurements. This proposed filter is constructed by multiple digital delay blocks and therefore has the advantage of easy implementation with less online parameters tuning effort. Meanwhile, a linearized model is derived for PLL parameter design, with which the stability of the FAGCF-PLL position estimation system can also be analyzed theoretically. The effectiveness of the proposed sensorless control strategy has been validated with the experimental results on a 1.5-kW IPMSM drive.

Contributions of Nonlinear Spectral Components to the Probability Distribution of Rogue Waves Based on the Results of Numerical Simulation of the Euler Equations

The contributions of various wave components (second, third and difference harmonics) to the formation of probability distributions of extreme wave heights, as well as amplitudes of crests and troughs, are evaluated based on the direct numerical simulation of irregular nonlinear deep water waves within three-dimensional potential equations of hydrodynamics. The simulation results taking into account 4- and 5-wave nonlinear interactions are analyzed. Different non-linear harmonics participate in the formation of the probability distributions in nontrivial way, essentially not satisfying the principles of linear superposition and ordering of the contribution by the parameter of weak nonlinearity.

Nonlinear high-order harmonics correction for phase measuring profilometry

Gamma nonlinearity severely affects the accuracy of phase measuring profilometry (PMP). Through averaging two phase maps with inverse errors, conventional methods including double phase-shifting (DPS) and Hilbert transform (HT) only compensate the fundamental harmonic while leaving high-order harmonics. To address this issue, this paper presents an efficient high-order harmonics correction (HHC) method. The averaged phase is encoded into factitious fringes on the computer. Then we directly apply HT on these factitious fringes to generate transformed fringes, while the addition of the ideal phase and residual harmonics is converted to multiplication. Finally, the residual high-order harmonics are suppressed, and the corrected phase is calculated using the phase-shifting algorithm. In comparison to conventional DPS and HT methods, the proposed HHC method can efficiently correct the residual high-order harmonics, thereby enhancing the measuring accuracy.

An Optimized PLL With Time Delay and Harmonic Suppression for Improved Position Estimation Accuracy of PMSM Based on Levenberg–Marquardt

This paper proposes an optimized phase-locked loop (OPLL) based on Levenberg-Marquardt (LM) to improve the estimation accuracy of the sliding mode observer (SMO) based position estimator. The position estimation suffers from dc bias caused by digital control delay, and harmonic caused by inverter nonlinearity and flux spatial harmonics. The OPLL is constructed with two parts to overcome the above negative effects. The delay phase is preliminarily calculated based on linear prediction, so as to compensate for the lag phase in the estimated back electromotive force (back-EMF); secondly, the objective function is built based on the reference and feedback position error, the former contains an unknown harmonic. The objective function can be minimized by the LM to solve for the harmonic amplitude, then the obtained harmonic is used to offset the harmonic components in the estimated position. Wherein, the required partial derivatives of the LM method can be deduced based on the transfer function of PLL and the delay-compensated back-EMF to achieve a stable update of harmonic amplitude. Finally, the corresponding comparative experiments in steady-state and dynamic conditions proved the superiority of the proposed method applied to permanent magnet synchronous motors.