Nonlinear Surface Research Articles

Machine learning for phase-resolved reconstruction of nonlinear ocean wave surface elevations from sparse remote sensing data

Accurate short-term predictions of phase-resolved water wave conditions are crucial for decision-making in ocean engineering. However, the initialization of remote-sensing-based wave prediction models first requires a reconstruction of wave surfaces from sparse measurements like radar. Existing reconstruction methods either rely on computationally intensive optimization procedures or simplistic modelling assumptions that compromise the real-time capability or accuracy of the subsequent prediction process. We therefore address these issues by proposing a novel approach for phase-resolved wave surface reconstruction using neural networks based on the U-Net and Fourier neural operator (FNO) architectures. Our approach utilizes synthetic yet highly realistic training data on uniform one-dimensional grids, that is generated by the high-order spectral method for wave simulation and a geometric radar modelling approach. The investigation reveals that both models deliver accurate wave reconstruction results and show good generalization for different sea states when trained with spatio-temporal radar data containing multiple historic radar snapshots in each input. Notably, the FNO demonstrates superior performance in handling the data structure imposed by wave physics due to its global approach to learn the mapping between input and output in Fourier space.

Fast construction of cluster interaction matrix for data-driven cluster-based reduced-order model and prediction of elastoplastic stress-strain curves and yield surface

The data-driven cluster-based reduced-order model (CROM) methods[47–50] are very effective for predicting the nonlinear effective properties of heterogeneous materials. The Cluster Interaction Matrix (CIM) in these methods can be regarded as a clustered discrete Green's function and is the critical part of CROM methods, which more and more scholars have realized. However, the explicit expression of Green's function is available only for homogeneous material. The CIM for heterogeneous materials needs to be calculated through numerical approaches, which face the challenge of computational efficiency. Therefore, this paper proposes an efficient method to construct the CIM of heterogeneous materials. By deriving the Green's function in Fourier space under the governing equation of FCA, the CIM of homogeneous materials that can provide the self-equilibrium stress field is calculated efficiently. Then, to avoid the effects of stress averaging on clusters, we augment the proposed cluster-element interaction matrix with the self-equilibrium stress basis vector of heterogeneous material without introducing additional computational cost. Based on the augmented cluster-element interaction matrix, the self-equilibrium stress space is improved, and the CIM of highly heterogeneous materials is calculated using the minimum complementary energy principle. The proposed algorithm significantly improves the offline computational accuracy of FCA, enabling efficient prediction of nonlinear effective properties and yield surface under complex load paths. Numerical examples demonstrate the efficiency and accuracy of the proposed method. In addition, we provide the relationship between the CIMs of a homogeneous material of FCA and SCA. Based on the proposed algorithm in this paper, it can be helpful for other CROM methods.

Additive laser excitation of giant nonlinear surface acoustic wave pulses

Additive laser excitation of giant nonlinear surface acoustic wave pulses

Construction of diverse water wave structures for coupled nonlinear fractional Drinfel’d-Sokolov-Wilson model with Beta derivative and its modulus instability

This paper aims to analyze the coupled nonlinear fractional Drinfel’d-Sokolov-Wilson (FDSW) model with beta derivative. The nonlinear FDSW equation plays an important role in describing dispersive water wave structures in mathematical physics and engineering, which is used to describe nonlinear surface gravity waves propagating over horizontal sea bed. We have applied the travelling wave transformation that converts the FDSW model to nonlinear ordinary differential equations. After that, we applied the generalized rational exponential function method (GERFM). Diverse types of soliton solution structures in the form of singular bright, periodic, dark, bell-shaped and trigonometric functions are attained via the proposed method. By selecting a suitable parametric value, the 3D, 2D and contour plots for some solutions are also displayed to visualize their nature in a better way. The modulation instability for the model is also discussed. The results show that the presented method is simple and powerful to get a novel soliton solution for nonlinear PDEs.

Microparameters Calibration for Discrete Element Method Based on Gaussian Processes Response Surface Methodology

Microparameter calibration is an important problem that must be solved in the discrete element method. The Gaussian process (GP) response surface methodology was proposed to calibrate the microparameters based on the Bayesian principle in machine-learning methods, which addresses the problems of uncertainty, blindness, and repeatability in microparameter calibration methods. Using the particle flow code (PFC) as an example, the effects of the microparameters on the macroparameters were evaluated using the control-variable method, and the range of the microparameters was determined based on the macroparameters. The uniform design (UD) method and numerical calculation were used to obtain training samples, and a GP response surface methodology suitable for multifactor, multilevel, and nonlinear processes was used to establish the response surface relationships for macro–micro parameters of rock-like materials in discrete element method. According to the macroparameters obtained from the uniaxial experiments conducted on rock specimens, the microparameters were calibrated using the GP response surfaces. Numerical calculations of uniaxial compression and Brazilian splitting were performed using microparameters, and the results were compared with laboratory experiments for verification. The results showed that the relative errors of the GP response surface and laboratory test values were 5.3% for the modulus of elasticity, −7.8% for compressive strength, and −2.6% for tensile strength. The nonlinear GP response surface considered the characteristics of multiple interacting factors, and the established nonlinear response surface relationship between the microparameters and macroparameters can be used for the calibration of microparameters. The accuracy of the microparameters was verified according to the stress–strain curve and failure morphology of the rock specimens. The method of using the GP response surface to establish the macro–micro parameter relationship in the discrete element method can also be extended to other numerical simulation methods and can provide a basis for accurately analysing the microdamage mechanism of rock materials under complex loading conditions.

An accurate and efficient HOS-meshfree CFD coupling method for simulating strong nonlinear wave–body interactions

The study on strong nonlinear wave–structure interaction (WSI) is crucial in ocean engineering. The Smoothed Particle Hydrodynamics (SPH) method is popular in this field because of its advantages in simulating free surface flow. However, to predict the details of WSI, a high resolution of particles is usually required, which results in a huge computational cost. In this paper, a potential-meshfree CFD weak coupling method based on the High Order Spectral (HOS) and SPH method is developed, which combines the advantages of the former in generating nonlinear waves quickly and accurately and the latter in adapting to strong nonlinear free surface problems. The accuracy of the coupling method was verified through the simulations of regular and irregular waves compared with experiment data. It shows the coupling method can effectively improve computational efficiency and extensively reduce the numerical dissipation. Furthermore, a simulation of the interaction between the focus wave and the floating body was conducted by using the coupling method, the original SPH method and the Constrained Interpolation Profile (CIP) method. Among all numerical methods, the coupling method is the best one for predicting the impact pressure of the floating body and is the only one that can capture the second impacting peak.

Simulation of Nonlinear Free Surface Waves using a Fixed Grid Method

The simulation of nonlinear surface waves is of significant importance in safety studies of fluid containers and reservoirs. In this paper, nonlinear free surface flows are simulated using a fixed grid method which employs local exponential basis functions (EBFs). Assuming the flow to be inviscid and irrotational, the velocity potential Laplace’s equation is spatially discretized and solved by considering the nonlinear Bernoulli’s equation for irrotational flow as the boundary condition on the free surface. The nonlinear boundary conditions are imposed through a semi-implicit iterative time marching. The fixed grid feature of the method, based on a Lagrangian description of fluid flow, allows for retaining the portion of the discretization performed in the first time step for the bulk of the fluid. Thus, the portion which pertains to the regions near the moving boundaries is reprocessed during the time marching. The accuracy and efficiency of the existing solution is shown by simulating various problems such as liquid sloshing induced by external excitation of the reservoir or initial deformed shape of liquid, seiche phenomena and solitary wave propagation in a basin with constant depth or with a step, and comparing the results with those which are analytically available or those from available codes such as Abaqus. The proposed method shows far better stability of the results when compared with those of Abaqus which sometimes exhibit divergence after a relatively large number of time steps. For instance, in the propagation of the considered solitary wave in an infinite-like domain problem, the wave height is calculated by the maximum error of 1.6% and 9% using the present method and Abaqus, respectively.

Shock waves in semi-infinite photonic lattices

We investigate the existence, stability and propagation dynamics of shock waves existing in defocusing saturable media modulated by a semi-infinite photonic lattice. Such surface waves consist of modulationally stable pedestals in bulk media and decaying oscillatory tails in semi-infinite photonic lattices. Due to Bragg-type reflection, they are strongly localized at the edge of the optical lattice. The kink steepness, pedestal height and localization degree can be controlled by propagation constant, saturable degree and lattice depth. Two types of kinks, i.e., “out-of-phase” and two branches of “in-phase” shock waves are revealed. Out-of-phase shock waves are stable in a substantial part of their existence domain. While the lower-branch in-phase waves with low energy flow are stable in almost their whole existence domain, the higher-branch in-phase waves are completely unstable. We thus show the first example of stable in-phase shock waves in nonlinear optics. Our findings provide new insight into the dynamics of semi-localized nonlinear surface shock waves or kink solitons.

Evaluation of high-temperature degradation of platen superheater tube in thermoelectric power plant using nonlinear surface ultrasonic waves

The operating conditions of Korean standard coal-fired thermal power plants involve high temperatures, with steam reaching approximately 540 °C. To support the life management of platen superheater (PSH) tubes, which operate under the highest temperature and pressure conditions among boiler tubes, various methods have been used. These methods include visual inspection, thickness measurement, and hardness measurement, which are typically used to conduct lifespan diagnosis on facilities that have been operating for more than 100,000 h or 20 y. This study examined the applicability of a nonlinear ultrasonic technique to evaluate the degradation damage of a PSH tube composed of X20CrMoV12.1 steel in a thermal power plant. The specimens of a PSH tube made of X20CrMoV12.1 steel that has been operating for approximately 20 y (160,000 h) in a Korean standard thermal power plant was obtained from three points, and the nonlinear surface ultrasonic wave was measured. Then, the results of the nonlinear ultrasound, microstructure analysis, and tensile test were compared. Based on where the boiler tube specimen was located, a strong correlation was observed between the ultrasonic nonlinearity parameter and changes in the tensile and yield strengths. These results confirm that the nonlinear ultrasonic method can be used to evaluate the changes in the mechanical properties affected by boiler tube degradation.

The Role of Quadratic-Linearly Radiating Heat Source with Carreau Nanofluid and Exponential Space-Dependent Past a Cone and a Wedge: A Medical Engineering Application and Renewable Energy

A mathematical analysis for a steady, incompressible, laminar Carreau nanofluid flow over a porous cone and wedge is considered. The novelty of this research work is to scrutinize an exponential space-dependent Cattaneo–Christov heat flux and quadratic Rosseland approximation effects. Two-phase nanofluid model, i.e., Brownian motion, and thermophoretic effects are included. This study also employs non-linear thermal radiation and convective surface boundary conditions to investigate heat transport phenomena. The Carreau nanofluid boundary layer equations are derived using the standard boundary layer approximations. By applying the similarity transformations, the managing set of partial differential equations (PDEs) becomes a system of connected non-linear ordinary differential equations (ODEs). The resultant non-linear ODEs are solved numerically utilizing the numerical method, particularly the bvp4c function in MATLAB. The significances of the fluid motion are visualized by sketching several Carreau nanofluid flow’s relevant parameters using graphic outputs. The effects of a wide range of thermophysical variables on liquid properties including velocity, temperature, concentration, skin-friction, Nusselt number, and Sherwood number are investigated and discussed. This study’s findings are compared to previously announced results within a limited range, where strong validation was seen. The results demonstrate that the opposite mechanism is observed with repercussion of Weissenberg number (We) on velocity profile and concentration, the enhancement of We increases the momentum boundary layer while it reduces the concentration boundary layer. The outcomes could be applied to the cooling of equipment, electronics, and various industrial units.

Fuzzy optimal tracking control for nonlinear underactuated unmanned surface vehicles

In this paper, a reinforcement Q-learning fuzzy optimal tracking control method is investigated for nonlinear underactuated unmanned surface vehicles (USVs) with external disturbances. Firstly, the motion dynamics of USVs are described by the Takagi–Sugeno (T–S) fuzzy discrete-time systems. Secondly, by applying parallel distributed compensation (PDC) method and constructing cost function, the existence condition of optimal solutions is derived and reduced to the algebraic Riccati equations (AREs). To solve the solutions of the GAREs, a Q-learning value iteration (VI) algorithm is further developed, which can be implemented by eliminating the demand of initial allowable control policy and system information. The developed strategy has the advantage that the optimal control policy can ensure the USV to be stable and the desired reference signal can also be well tracked by the USV output. Finally, the proposed fuzzy optimal control algorithm is applied to control the USV, the simulation results verify the feasibility of the proposed optimal control algorithm.

MULTI-LINEAR-ELEMENT DEPTH-INTEGRATED MODELS FOR FLOWS WITH A FREE SURFACE

In this study, we derive a new set of depth-integrated models for solving unsteady flows that satisfy the Euler equations and nonlinear free surface boundary conditions in the sigma -coordinates. One of the obvious differences between the present approach and the ones directly solving the 3D Euler equations using Finite Element Method (FEM) is that in the present model the vertical velocity and the pressure field are eliminated by integrating the continuity equation and vertical momentum equation, respectively. Therefore, the present models only solve the horizontal velocity components and the free surface displacement in the two-dimensional horizontal (2DH) space. The new models are also more advantageous in using fewer elements in the vertical direction while achieving better performance. At this stage, the capability and application of the new models in dealing with free surface wave propagation problems are addressed.

An LMI adaptive-barrier function global sliding mode control of uncertain nonlinear systems with input saturation

This paper proposes a barrier function-based adaptive control strategy with a nonlinear sliding surface for a class of uncertain dynamic systems with input saturation. Its main objectives are to ensure robustness to parametric and non-parametric uncertainties whilst eliminating the reaching phase. A global nonlinear switching surface is defined and an adaptive barrier function sliding mode control approach is derived. The barrier strategy is adopted to ensure the convergence of the states to the desired values without overestimating the control gains. System stability is analyzed using the Lyapunov stability theory. The control parameters are obtained using the linear matrix inequality (LMI) approach. The control law is designed to remove the reaching phase. The effectiveness of the proposed approach was validated using a simulation study. The proposed control approach can easily be implemented to various nonlinear uncertain systems.

Nonlinear plasma surface modification of polylactide to promote interaction with fibroblasts

AbstractSurface modification of polylactide films was performed using a dielectric barrier discharge (DBD) with the aim of increasing proliferative activity of human fibroblasts on these films. It has been shown that during the plasma treatment of the polylactide film, nonlinear processes occur depending on the processing time. The effect of the dielectric barrier discharge on the modification of polylactide films was evaluated using IR spectroscopy, AFM, XPS, TSDC, and the wetting angle of the surface. The optimal processing time in DBD of polylactide films is 3 min for this installation, the proliferative activity increases by 10% compared to the original film. This treatment time provides an increased concentration of oxygen‐containing groups, optimal relief, and free surface energy of 55 mJ/m2 on the surface.Highlights The biocompatibility of the polylactide film was improved by 10% used DBD. The optimal processing time of PLA films in DBD is 3 min. The functionalization of the polylactide surface occurs non‐linearly.

Micro-polar liquid flows with magnetohydrodynamic (MHD) mixed convection due to a nonlinear stretched sheet in a convective state

The topic of this study is the flow of a micro-polar liquid toward a nonlinear stretched surface using magnetohydrodynamics (MHDs). The analysis presents the effects of some important parameters on fluid flow. The mixed convection phenomena are used to examine the characteristics of heat transmission. By using the appropriate transformations, dimensional nonlinear equations can be transformed into dimensionless expressions. The governing dimensionless problems are solved using the modified Laplace decomposition approach by examining the effects of various boundary factors on flow and heat transfer.

Quick clay monitoring using distributed acoustic sensing: A case study from Rissa, Norway

Quick clay avalanche is one of the most devastating landslide types worldwide. Hence, an early warning system is in demand to mitigate the fatal consequences caused by such events. To address this, distributed acoustic sensing data are collected in an area containing quick clay deposits between July 2021 and February 2022 in Rissa, Norway, while a new road is constructed on the quick clay. Road construction can induce unwanted changes to the mass balance in the clay, and previous landslides have been triggered by such changes. For this purpose, passive and active data are collected to test and compare various analysis methods. Using extracted Rayleigh wave dispersion from active sledgehammer shots, shear-wave velocity depth profiles covering the first 15 m could be estimated and compared using a linearized and a nonlinear surface wave inversion method. Furthermore, ambient noise crosscorrelation is used to obtain the dispersion from the ambient noise and associated shear-wave velocity profiles, providing two possible data collection methods for the early warning system. The obtained dispersion curves and the estimated shear-wave velocity profiles show small time-lapse variation during the acquisition period (up to approximately 23 m/s), where the variation is within one standard deviation. Such a small variation suggests that the construction work and the extra load added to the quick clay do not alter the quick clay’s properties. Nevertheless, the obtained results capture the nonrepeatability effects within the acquisition period and provide reference curves for the study area at undisturbed conditions and valuable information for future comparisons to refer to potential failure scenarios. This is the first step in exploring an early warning system for quick clay landslides using fiber-optic cables. Further work will investigate the possibility of automatizing the system and improving the accuracy of the sensing system.

Memory-friendly fixed-point iteration method for nonlinear surface mode oscillations of acoustically driven bubbles: from the perspective of high-performance GPU programming

A fixed-point iteration technique is presented to handle the implicit nature of the governing equations of nonlinear surface mode oscillations of acoustically excited microbubbles. The model is adopted from the theoretical work of Shaw [1], where the dynamics of the mean bubble radius and the surface modes are bi-directionally coupled via nonlinear terms. The model comprises a set of second-order ordinary differential equations. It extends the classic Keller–Miksis equation and the linearized dynamical equations for each surface mode. Only the implicit parts (containing the second derivatives) are reevaluated during the iteration process. The performance of the technique is tested at various parameter combinations. The majority of the test cases needs only a single reevaluation to achieve 10-9 error. Although the arithmetic operation count is higher than the Gauss elimination, due to its memory-friendly matrix-free nature, it is a viable alternative for high-performance GPU computations of massive parameter studies.

Optimal Sizing of Trailing Edge Flaps for Helicopter Vibration Reduction: A Response Surface Approach

On-blade active trailing edge flaps are considered for helicopter vibration reduction. A Pareto optimal multi-objective optimization approach is used to obtain the spanwise and chordwise dimensions of single and dual trailing- edge flaps. The objective of this study is to simultaneously achieve minimum hub vibration levels and minimize the flap actuation power requirement. Helicopter aeroelastic analysis is used in conjunction with an optimal controller to minimize hub vibration and flap power levels. It is found that nonlinear polynomial response surfaces based on L9 orthogonal array could adequately describe both the objectives. An intense sampling of the surrogate objective space is used to obtain optimal design points for the mutually conflicting objectives. A Pareto optimal design reduces vibration levels by about 70% and also reduces flap actuation power requirement by about 20%, in comparison to the initial design. The present study leads to an optimal design of trailing edge flaps which expend less power and can be further explored for self-powered control surfaces towards a self-powered smart blade design concept. The optimal designs are robust to uncertainty introduced by manufacturing.

Entropy Generation in a Magnetohydrodynamic Hybrid Nanofluid Flow over a Nonlinear Permeable Surface with Velocity Slip Effect

The current study is designed to model the hydrothermal feature of a hybrid nano liquid slip flows over a permeable expanding/contracting surface with entropy generation. The model incorporates Cu-Al2O3 nanoparticles with water as the host liquid to simulate the flow. Additional impacts incorporated into the novelty of the model are viscous dissipation and Joule heating. The model is transformed appropriately to its dimensionless form using similarity quantities and the solution is numerically obtained using the spectral quasi-linearization method (SQLM). The impact of pertinent factors on the flow characteristics is communicated through graphs for the hybrid nano-suspension to discuss the hydrothermal variations. The friction factor and the rate of heat transport are also discussed with sensible judgment through tables. To ensure the code validity, a comparison with earlier studies is conducted and excellent consensus is accomplished. The result explored that diminution in the irreversibility ratio is witnessed for rising magnetic field strength along the free stream, distance away from the permeable surface as the heat dissipation to the surrounding decelerates. Also, the augmented nonlinearity parameter intensified the heat transfer rate for about 2.79% of the hybrid nano-suspension.

A fully nonlinear BEM-beam coupled solver for fluid–structure interactions of flexible ships in waves

A fully nonlinear hydroelastic numerical method is proposed for the fluid–structure interactions of elastic ships. The boundary value problem is solved by the three-dimensional boundary element method. To simulate the instantaneous evolution on the free surface, an effective mesh optimization solution consisting of the local coordinate system and an elastic mesh technique has been developed. The mixed Eulerian–Lagrangian method is implemented to update the fully nonlinear free surface conditions in the local coordinate system. The hull structure is simplified as a non-uniform Timoshenko beam, and the modal superposition approach is adopted to analyse the symmetric responses in the head sea. Convergence of the model is evaluated for mesh resolutions and the time step size, and then comprehensive investigations of vertical motions as well as vertical bending moment are carried out for an advancing ship in a range of wave frequencies. The numerical solutions are compared with the experimental data and a satisfactory agreement is demonstrated. The distribution of high-order harmonics and whipping responses are predicted by the amplitude spectrum, in which the water entry and water exit are considered. The high-frequency vertical bending moments are investigated, in which the effects of higher harmonics and whipping responses are addressed.