Quadratic Transfer Functions Research Articles

A Novel Surrogate-Based Approach to Yield Estimation and Optimization of Microwave Structures Using Combined Quadratic Mappings and Matrix Transfer Functions

Yield estimation and yield-driven design optimization play important roles in microwave design. Existing surrogate-based yield estimation/optimization methods need to develop separate surrogate models or a large surrogate model with high complexity to deal with multiport problems, which is computationally inefficient. This article proposes a novel surrogate-based method to expedite yield estimation/optimization of multiport microwave structures using combined quadratic mappings and matrix-valued transfer functions. For multiport structures, the responses of different transfer functions corresponding to different pairs of input–output ports are computed with separate residues, while the responses of transfer functions for all pairs of input–output ports are computed with a common set of poles. Taking advantage of this, we propose to formulate a set of quadratic functions to map the relationship between the separate residues and statistical/geometrical parameters while employing merely one quadratic function to map the relationship between the common poles and statistical/geometrical parameters. The resultant mappings together with the matrix-format transfer function form an efficient surrogate to expedite the yield estimation and optimization processes for microwave structures. Compared with existing surrogate-based methods, the proposed method can achieve similar yield estimation accuracy in a shorter time due to fewer electromagnetic (EM) simulations. Three microwave structures are used to demonstrate the advantages of the proposed method. Based on accurate yield estimations, we further perform yield-driven design optimization incorporating the proposed surrogate for all the three examples.

Frequency domain modeling of long-span sea-crossing bridge under stochastic wind and waves

In this study, a frequency domain modeling framework that assembles aero- and hydro-dynamic approaches to characterize the structural motions of a long-span sea-crossing bridge under stochastic wind and waves is proposed as an efficient alternative for the conventional time-consuming time domain analysis. The improved quasi-steady buffeting model is employed to investigate the fluctuating wind actions on structural components and the aero-elastic effect of bridge decks. Potential flow theory associated with constant boundary element method is applied to calculate the linear as well as quadratic hydrodynamic transfer functions and both first- and second-order wave loads are considered and coupled in the modeling framework. The proposed methodology is well validated using a benchwork experiment of a flexible cylinder subjected to wind and waves. The dynamic performance of a long-span sea-crossing bridge under extreme wind and wave conditions is modeled using the proposed framework. The effects of wind and waves, different mode combinations, directionality and nonlinear wave loads on global responses are discussed. In the proposed approach, a combination of only a few main modes is necessary to yield plausible displacement responses of bridge deck, while more modes are required to obtain converged internal force responses.

Dynamic Performance Evaluation of an Integrated 15 MW Floating Offshore Wind Turbine Under Typhoon and ECD Conditions

Technology innovation has led to an increase in floating wind turbine size aimed at releasing the pressure on capital cost and increasing its capacity factor. Large-size turbines pose high challenges regarding design with essential structure reliability. The dynamic performance of an integrated 15-megawatt (MW) wind turbine under extreme sea loads is investigated in this paper. Platform motions, mooring system positioning forces, sizeable blades, and tower behaviors are all studied under the targeted typhoon condition and extreme coherent gust with direction change (ECD) wind condition. Potential flow theory is used to analyze the first-order wave load, mean-drift wave load, and second-order difference-frequency wave load on the substructure of the ultra-large 15 MW floating offshore wind turbine (FOWT). The blade element momentum (BEM) theory is adopted for the calculation of the aerodynamic loads on the floating wind turbine, and the finite element method (FEM) is applied to analyze the mooring lines of the floating wind turbine. The results show that the effect of quadratic transfer function (QTF) will significantly increase the dynamic response of FOWT under the typhoon sea state. The ECD wind condition has an influential impact on the motion responses, the axial force of the mooring lines, and structural responses under the normal operating state.

Second-order difference-frequency wave loads on a floating body in uniform current in the frequency domain

ABSTRACT In this study, a formulation for the second-order difference-frequency wave load in the presence of steady uniform current (or forward speed) is presented, and a practical approximate approach is proposed. A potential flow-based solution is formulated to include terms up to the second-order in wave slope and first-order in current speed. In the uniform-flow approximation, the body disturbed and ship-generated steady flows are neglected, assuming slender bodies and low uniform flow speed. The free-surface integral is not included in evaluating the difference-frequency force quadratic transfer function (QTF) considering its relatively unimportant contribution compared to other terms, which significantly reduces the cost of the computational implementation. The present numerical results compare well against published experimental and numerical result. The importance of directly calculating off-diagonal terms of the QTF in the presence of uniform flow is investigated by comparing the present model with other existing approximation methods and with cases without uniform flow.

A numerical study on self-propulsion performance in regular waves and power prediction in irregular waves

Several numerical studies have been conducted to investigate the methods for self-propulsion performance that changes with the wave conditions using KVLCC2. On comparing the propulsive factors with respect to the wave conditions, self-propulsion performance was observed to undergo changes. It showed that the propulsion efficiency decreases when the added resistance that increases in regular waves, which leads increasement of the required horsepower. Power prediction in the irregular waves was done using the spectral methods as an indirect method, which derives the increase in variables in a target sea state with a quadratic transfer function and wave spectrum. The four spectral methods were considered depending on the parameters used. These can be divided into the methods (SA, TNM, QNM) that use the assumed self-propulsion factors and a proposed method that considers the changes of factors in wave conditions. Consequently, when considering the changes in the self-propulsion factors in the sea state wherein the wave height increases, the power was estimated to be relatively low. This indicates that with increasing wave height, the linear relationship between the variables and the wave height is degraded. This study proposes the necessity of considering the effect of waves on self-propulsion to estimate the realistic power of ships.

Empirical estimation of low-frequency nonlinear hydrodynamic loads on moored structures

Low-frequency (LF) motions of floating structures are commonly modeled as the response of an oscillator to a second-order wave excitation. We present here an empirical method that reliably estimates the oscillators parameters and quadratic transfer function (QTF) used in such models.The method is based on an active stationkeeping system that enables to accurately control external boundary conditions applied on the floating structure in a wave basin. The resulting system can be successively tuned to different frequency ranges of interest. Then, by deconvolution and optimization, LF damping and added-mass loads, as well as a response-independent wave excitation load, can be evaluated. From the wave elevation, and estimated load time series, the difference-frequency QTF is finally estimated by a cross-bi-spectral analysis, including a new treatment of statistical noise.The paper describes the proposed method in details, and illustrates it with the study of a ship-shaped floating unit in a sea-state of relevance for the fatigue design of mooring systems (steep waves, low return period).

Gap resonance from linear to quartic wave excitation and the structure of nonlinear transfer functions

Resonant response of water waves in a narrow gap, with the interaction of multiple highly resonant modes, is an interesting hydrodynamic phenomenon with practical applications. Gap resonances between two identical fixed rectangular boxes are experimentally investigated for unidirectional waves with broadside incidence. We show that gap resonances can be driven through both linear wave excitation and nonlinear processes, i.e. frequency doubling, tripling and quadrupling – apparently new observations. It is striking that the time histories of the gap resonances excited through different nonlinear interactions are remarkably similar to each other. It seems likely that the nonlinear sum-frequency transfer functions for gap resonances depend strongly on the output frequency sum of the interacting linear components, but only weakly on the frequency difference. In terms of their structure in multiple frequency space (at second order the bi-frequency plane for two components), these transfer functions must then have a near-flat form in the direction(s) perpendicular to the leading diagonal. This is supported by our potential flow calculations of the quadratic transfer functions (QTFs). It is therefore convenient to approximate the QTF matrix as ‘flat’ in the direction perpendicular to the leading diagonal. This approximation is justified through experimental data that includes viscous damping. It is too complex, if not impossible, to calculate the full cubic or quartic transfer functions as direct evidence. However, the experimental analysis does provide some support for the near-flat structure being applicable to transfer functions above second order. The flat form approximation greatly reduces lengthy calculations of the high-order transfer functions.

Second-order monopile wave loads at linear cost

A method to compute the second-order free surface elevation, depth integrated force and mud line moment for a slender circular vertical cylinder is presented. The method is valid for unidirectional irregular waves and includes inertia loads and viscous loads.We first derive the linear transfer functions for free surface elevation, depth-integrated force and moment from the complex Fourier amplitudes of the velocity potential. Next, the second-order contributions are expressed through closed form quadratic transfer functions, which are further diagonalized through eigen decomposition. Hereby the second-order contributions can be computed as products of pseudo time series calculated by FFT, with the eigenvectors acting as transfer functions on the linear Fourier amplitudes.For a sample 3-hour sea state, we find that eight eigen vectors are sufficient to achieve an accuracy of 1% for the maximum peak value of force and moment and 1.3% for free surface elevation, relative to the standard deviation of each signal. These results are obtained 2500 faster than with the conventional approach and we demonstrate that the computational effort of the new method scales like O(NlogN), similar to linear wave loads, where N is the number of frequencies. For the eight mode approximation, the error bound of 1% for loads and 4% for free surface elevation are found to hold across various values of the normalized peak wave number from shallow to deep water. The accuracy is adjustable through the number of modes and is found to be independent of the time series length. The methods potential in practical design is discussed.

Identification of wave drift force QTFs for the INO WINDMOOR floating wind turbine based on model test data and comparison with potential flow predictions

The paper presents a comparison between empirical and numerical quadratic transfer functions (QTFs) of the horizontal wave drift loads on the INO WINDMOOR floating wind turbine. The empirical QTFs are determined from cross bi-spectral analysis of model test data obtained in an ocean basin. Validation of the identified QTF is provided by comparing low frequency motions reconstructed from the empirical QTF with measurements. The numerical QTFs are calculated by a panel code that solves the wave-structure potential flow problem up to the second order. Systematic comparisons between numerical and empirical QTFs allows identification of tendencies of empirical QTFs and limitations of the second order potential flow predictions. The study is limited to hydrodynamic loads from waves only, i.e. without current. For small seastates, the results indicate that the second order potential flow predictions of the surge QTFs agree quite well with the wave drift coefficients identified empirically from the model test data. For moderate and high seastates, second order predictions underestimate the surge wave drift coefficients for all compared diagonals of the QTFs. The discrepancies between predictions and empirical coefficients are not small, especially at the lower frequency range (below around 0.10 Hz) where the potential flow wave drift forces tend to zero.

Validation and application of nonlinear hydrodynamics from CFD in an engineering model of a semi-submersible floating wind turbine

Nonlinear hydrodynamics play a significant role in accurate prediction of the dynamic responses of floating wind turbines (FWTs), especially near the resonance frequencies. This study investigates the use of computational fluid dynamics (CFD) simulations to improve an engineering model (based on potential flow theory with Morison-type drag) by modifying the second-order difference-frequency quadratic transfer functions (QTFs) and frequency-dependent added mass and damping for a semi-submersible FWT. The results from the original and modified engineering models are compared to experimental data from decay tests and irregular wave tests. In general, the CFD results based on forced oscillation tests suggest increasing the frequency-depending added mass and damping at low frequencies compared to first order potential flow theory. The modified engineering model predicts natural periods close to the experimental results in decay tests (within 5%), and the underprediction of the damping is reduced compared to the original engineering model. The motions, mooring line tensions and tower-base loads in the low-frequency response to an irregular wave are underestimated using the original engineering model. The additional linear damping increases this underestimation, while the modified QTFs based on CFD simulations of a fixed floater in bichromatic waves result in larger difference-frequency wave loads. The combined modifications give improved agreement with experimental data in terms of damage equivalent loads for the mooring lines and tower base.

Dynamics of a Y-shaped semi-submersible floating wind turbine: a comparison of concrete and steel support structures

ABSTRACT Concrete semi-submersible floating wind turbines (FWTs) have generated increasing interest in the offshore wind energy industry due to their superiority over steel structures in aspects of construction and maintenance. However, the influence of construction materials on the dynamics of FWTs was scarcely studied before. The dynamics of two FWTs, mounted on a concrete and a steel Y-shaped semi-submersible platform respectively, are investigated by means of 1:60 scale combined wind and wave model tests and coupled multi-body simulations. The results indicate that the steel structure with a lower centre of gravity exhibits advantages in platform pitch motion alleviation. The steel structure is also subjected to lower pitch-induced tower base loads and nacelle acceleration than its concrete counterpart. However, an opposite trend is found in the wave-frequency responses, leading to an insignificant difference of tower base loads and nacelle acceleration between the two structures. ABBREVIATIONS: FWTs: Floating wind turbines; CoG: Centre of gravity; CoB: Centre of buoyancy; LCP3: Lightweight prestressed concrete platform; HSP3: High-strength steel platform; WTWF: Wind tunnel and wave flume joint laboratory; ROC: Rated operational condition; JONSWAP; Joint North Sea Wave Observation Projection; RAO: Response amplitude operator; BEM: Blade element momentum theory; DOF: Degree of freedom; GDW: Generalised dynamic wake theory; PSD: Power spectral density; QTF: Quadratic transfer function

Analysis of difference-frequency wave loads and quadratic transfer functions on a restrained semi-submersible floating wind turbine

One of the concerns regarding numerical simulation of floating wind turbines (FWTs) in waves is underprediction of resonant responses in the low-frequency range. In the present work, the difference-frequency wave loads on a restrained semi-submersible FWT subject to bichromatic waves are investigated by higher-fidelity tools (Computational Fluid Dynamics, CFD) and simplified engineering tools based on potential flow theory with Morison type drag. The effects of mean pitch angle (trim) and the wave force distribution on the multimember semisubmersible are assessed. Compared to the CFD results, wave loads estimated by engineering models are in good agreement at the wave frequencies, while slightly larger differences occur at the surge and pitch natural frequencies. The most significant underprediction of the surge force at the surge natural frequency occurs in the heave plate of the floater. Compared to the upright floater, the increased wave loads on the trimmed floater at the surge natural frequency are more significant than those at the pitch natural frequency. Furthermore, quadratic transfer functions (QTFs) are estimated based on the CFD model with a set of bichromatic wave cases. A new approach is found to use the CFD results to modify the QTFs in lower-fidelity engineering tools. This approach is validated against experimental measurements in irregular waves. Good agreement is achieved between measured and numerically estimated difference-frequency wave loads by engineering tools with modified QTFs.

Second-order sum- and difference-frequency bichromatic wave forces on three-dimensional bodies in a channel

In Huang and Teng (2020), the effects of the channel walls on the second-order hydrodynamic characteristics of three-dimensional bodies in monochromatic incident waves were investigated. To ensure the high accuracy and efficiency of the calculation, robust numerical algorithms have been developed to treat the troublesome integrals over the free surface, body surface and up- and down-wave vertical surfaces involved in the second-order analysis. In the present study, Huang and Teng (2020)'s work is extended to the cases of bichromatic incident waves, and some improvements in the numerical algorithms are made. The expressions of the locked potentials including both the propagating and evanescent modes are derived. Since the up- and down-wave vertical surfaces are allowed to be placed close to the body, the calculation of the free surface integral can be performed in a small region, and an analytical method is developed to directly evaluate the up- and down-wave vertical surface integrals. After solving the boundary integral equation, the sum- and difference-frequency radiation and diffraction potentials are obtained explicitly. Numerical results for the quadratic transfer functions of the second-order free surface elevation, pressure and force are given for a series of geometries in channels.

Experimental and numerical studies on the low-frequency responses of a spar-type floating offshore wind turbine

Accurate modeling of low-frequency (LF) wave loads and responses is important but challenging in the design of spar-type floating offshore wind turbines (FOWTs), especially for shallow and intermediate water depths. A 6 MW spar-type FOWT system designed for a water depth of 100 m is investigated both experimentally and numerically to study the nonlinear hydrodynamics responses in waves. The second-order LF wave loads are modeled in the time-domain tool FAST using two different methods based on full Quadratic Transfer Functions (QTF) and Newman's approximation, respectively. To account for viscous effects in calculating the LF responses, linear and quadratic damping models calibrated from model tests are comparatively studied and the latter is found to be more suitable and easier to implement in the time-domain simulations. It is demonstrated that it is crucial to include the 2nd order difference-frequency wave excitation in the analysis of motions in both horizontal and vertical planes. With the considered water depth, a full QTF method is seen to greatly improve the prediction of LF responses compared with Newman's approximation. In general, it is observed that the wave-frequency (WF) responses are higher in amplitude than the LF responses for surge and heave, while the LF pitch motions are higher than the corresponding WF contribution.

Second-order wave run-up on a vertical cylinder adjacent to a plane wall based on the application of quadratic transfer function in bi-directional waves

A numerical model was developed in this study to simulate the wave diffraction caused by an arbitrarily shaped structure in the presence of bi-directional incident waves based on a higher-order boundary element method (HOBEM). Based on the developed model, the wave elevation quadratic transfer function (QTF) in bi-directional waves, which is defined as the second-order wave elevation caused by two incident waves of unit amplitude from two directions, can be determined. The developed model was subsequently used to investigate the wave interaction with a cylinder situated near a vertical wall. The image principle was applied to transform the original problem into an equivalent one of wave diffraction caused by two symmetrical cylinders in open seas exposed to bi-directional incident waves. The second-order wave run-up on the cylinder can then be determined using the wave elevation QTF obtained from an analysis of the equivalent problem. A detailed numerical analysis was then conducted. Numerical results revealed that the presence of the vertical wall can apparently disturb the wave diffraction process from the cylinder, and lead to significantly amplified second-order wave elevation within the region between the wall and cylinder. In addition, the respective contribution from the first- and second-order components to the overall wave elevation around the cylinder was discussed.

Effects of second-order hydrodynamics on an ultra-large semi-submersible floating offshore wind turbine

Second-order wave loads on floating offshore wind turbine (FOWT) may excite severe resonance at the eigenfrequencies of the floating system and cause fatigue damage. The hydrodynamic coefficients including first- and second-order wave force transfer functions are calculated, and fully coupled time-domain simulation by FAST is conducted for selected environmental conditions. Each load case is simulated without second-order loads, and with difference-frequency full quadratic transfer functions (QTFs), sum-frequency full QTFs, and complete second-order solution. The effect of second-order difference- and sum-frequency wave loads on the dynamic behaviors of the 10 MW semi-submersible FOWT is discussed. Subsequently, the effect of second-order wave loads on the structural fatigue behavior of the 10 MW and 5 MW semi-submersible FOWTs is investigated and compared by computing ultimate and damage-equivalent loads (DELs). The results show that ignoring second-order difference-frequency wave loads may underestimate the low-frequency responses, and second-order sum-frequency wave loads significantly affect the structural dynamics of the 10 MW FOWT. In addition, the effect of second-order wave loads on the fatigue damage of the 5 MW and 10 MW semi-submersible FOWTs are significantly different.

Validation of drift motions for a semi-submersible floating wind turbine and associated challenges

In the EU H2020 project LIFES50+, a 1:36 scaled model test campaign was carried out for the NAUTILUS-DTU10 semi-submersible floating offshore wind turbine with active ballast. This paper concentrates on the modelling capabilities of a state-of-the-art time domain simulation model FAST8 for floating offshore wind turbines and specific challenges associated with the validation process. For the modelling, the platform is considered as a rigid body, and the frequency dependant radiation damping, added mass, and wave excitation are evaluated with a panel code using potential theory. The results from the scaled model are compared to the simulations, looking into the effects on the platform when the first order radiation-diffraction hydrodynamics through the Cummins equation, the mean drift coefficients from the nearfield solution for Newman’s approximation of the second-order difference-frequency wave forces, and full quadratic transfer function (QTF) are taken into account. Moreover, viscous forces on the floating platform are modelled through Morison elements with coefficients of drag. Frequency domain analysis of the motions showed good agreement after modifications of the coefficients of drag of the Morison elements for tests performed with a pink wave spectrum. On the other hand, the extreme wave test showed large discrepancies between results and simulations, which could not be overcome by the inclusion of the QTFs or tuning of the coefficients of drag which model the viscous forces. This is followed by a discussion of the challenges in the modelling approach, and other validation techniques are proposed for future research. The main goal is to define the Morison elements for the floater, and tune the drag coefficients to enable the numerical tool to capture the floater’s motions. The effect of the change of the coefficients on the simulation outputs are shown.

QSAR model for predicting neuraminidase inhibitors of influenza A viruses (H1N1) based on adaptive grasshopper optimization algorithm

ABSTRACT High-dimensionality is one of the major problems which affect the quality of the quantitative structure–activity relationship (QSAR) modelling. Obtaining a reliable QSAR model with few descriptors is an essential procedure in chemometrics. The binary grasshopper optimization algorithm (BGOA) is a new meta-heuristic optimization algorithm, which has been used successfully to perform feature selection. In this paper, four new transfer functions were adapted to improve the exploration and exploitation capability of the BGOA in QSAR modelling of influenza A viruses (H1N1). The QSAR model with these new quadratic transfer functions was internally and externally validated based on MSEtrain, Y-randomization test, MSEtest, and the applicability domain (AD). The validation results indicate that the model is robust and not due to chance correlation. In addition, the results indicate that the descriptor selection and prediction performance of the QSAR model for training dataset outperform the other S-shaped and V-shaped transfer functions. QSAR model using quadratic transfer function shows the lowest MSEtrain. For the test dataset, proposed QSAR model shows lower value of MSEtest compared with the other methods, indicating its higher predictive ability. In conclusion, the results reveal that the proposed QSAR model is an efficient approach for modelling high-dimensional QSAR models and it is useful for the estimation of IC50 values of neuraminidase inhibitors that have not been experimentally tested.

Real-time nonlinear cylinder wave force reconstruction in stochastic wave field considering second-order wave effects

This study provides a novel method for reconstructing real-time nonlinear wave forces on a large-scale circular cylinder by considering second-order wave effects. Potential theory is utilized for deriving the expression of wave forces with the measured data of wave elevation. Approximate expressions of quadratic transfer functions are built with undetermined coefficients, which are resolved by using the historical data of measured wave elevation. Two different algorithms, including fast Fourier transform (FFT) and recursive least squares (RLS), are adopted for real-time reconstruction. Hydrodynamic tests are conducted in the wave flume on a circular cylinder to examine the effectiveness of the nonlinear reconstruction method. Comparative results demonstrate that the accuracy of real-time reconstructed wave forces is significantly enhanced by the present method. The over-prediction errors at force crests and the under-prediction errors at force troughs have been reduced. Furthermore, comparative results show that the nonlinear method implemented by the FFT algorithm provides more accurate results, whereas the RLS algorithm is more time cost efficient.

Analysis of various transfer functions for binary owl search algorithm in feature selection problem

ABSTRACT Owl Search Algorithm (OSA) is a recently proposed nature-inspired meta-heuristic algorithm which is easily implementable and exhibits great potential for solving continuous optimization problems. In our earlier work, a binary version of owl search algorithm (BOSA), with transfer functions for mapping the continuous solution space into a binary one, has been developed and applied in optimal feature subset selection problem. In our preliminary simulation experiments, it was found that the performance of the solution depends on the type of transfer function used. In this work, an extensive analysis of various types of transfer functions and their respective effects on the selection of optimal feature subset has been studied by simulation experiments with multiple benchmark datasets. Transfer functions of three different families, S-shaped, V-shaped and quadratic, are used for designing eleven BOSA models, each of which is made by combining individual transfer function. The performances of the proposed wrapper based feature subset selection algorithm based on several BOSA models have been evaluated by simulation experiments with twenty datasets for finding out the best model. The best observed BOSA model has also been compared with other similar meta-heuristics algorithms for feature subset selection. Experimental results show that the feature subset selected by BOSA with quadratic transfer function produces the highest classification accuracy with the minimum number of selected features compared to other algorithms.