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The high calculation effort for accurate material loss simulation prevents its observation in most magnetic devices. This paper aims at reducing this effort for time periodic applications and so for the steady state of such devices.

The vectorized Jiles-Atherton hysteresis model is chosen for the accurate material losses calculation. It is transformed in the frequency domain and coupled with a harmonic balanced finite element solver. The beneficial Jacobian matrix of the material model in the frequency domain is assembled based on Fourier transforms of the Jacobian matrix in the time domain. A three-phase transformer is simulated to verify this method and to examine the multi-harmonic coupling.

A fast method to calculate the linearization of non-trivial material models in the frequency domain is shown. The inter-harmonic coupling is moderate, and so, a separated harmonic balanced solver is favored. The additional calculation effort compared to a saturation material model without losses is low. The overall calculation time is much lower than a time-dependent simulation.

A moderate working point is chosen, so highly saturated materials may lead to a worse coupling. A single material model is evaluated. Researchers are encouraged to evaluate the suggested method on different material models. Frequency domain approaches should be in favor for all kinds of periodic steady-state applications.

Because of the reduced calculation effort, the simulation of accurate material losses becomes reasonable. This leads to a more accurate development of magnetic devices.

This paper proposes a new efficient method to calculate complex material models like the Jiles-Atherton hysteresis and their Jacobian matrices in the frequency domain.

The purpose of this paper is to propose solutions for both discrete‐time and frequency‐domain designs of unbiased H_∞ functional filters for discrete‐time linear systems affected by bounded norm energy disturbances.

The discrete‐time procedure design is based on the unbiasedness of the functional filter using a Sylvester equation; then the problem is expressed in a singular system one and is solved in terms of linear matrix inequalities (LMIs). The frequency procedure design is derived from discrete‐time domain results by defining some useful matrix fraction descriptions and mainly, establishing the useful and equivalent form of the connecting relationship that parameterizes the dynamics behavior between discrete‐time and z‐domain.

The performance of the proposed approach is illustrated with the aid of a practical example. The proposed methods are easily implementable and concern a more general class of systems, as the transformation of the system in a singular one permits to treat the problem of perturbance advanced.

First, the order of this filter is equal to the dimension of the vector to be estimated, which is benefit in case of control purpose (reduction of time calculation comparing to the full order one). Second, all recent works on the functional filtering consider systems which permit to avoid to have advanced perturbation term in the error dynamics; the authors propose here an approach which resolves the H_∞ filtering problem even when the term is present. In addition, it permit to consider more general class of discrete‐time systems. Furthermore, the LMI approaching the discrete‐time case permits to handle with more general problem (H_∞, L₂−H_∞) than the classical Riccati one.

The non‐linear damping mechanisms are expressed in two general forms: velocity dependent and displacement dependent. The non‐linear damping phenomena are expressed by an array of ‘local constants’, whose value depends upon excitation frequency, excitation amplitude, and type of non‐linearity. Thus, the non‐linear system is replaced by several localized linear systems corresponding to every discrete frequency and amplitude of excitation. Each of the localized linear systems, thus formulated, characterizes the response behaviour of the original non‐linear system, quite accurately in the vicinity of the specific frequency and amplitude of excitation. An algorithm is developed, which expresses the non‐linear damping by an array of ‘local constants’. The algorithm then employs the usual linear design tools to generate the response characteristics almost identical to the response behaviour of the non‐linear system.

This study aims to predict dynamic responses of aileron and spoiler control surfaces in subsonic flight via the use of surrogate models. The prepared reduced order models prove useful when quick estimations for a large number of variations are required.

The linear frequency domain (LFD) method was used for the simulation study. Each surrogate contained a database of 100 control surface dynamic responses over a spectrum of 200 harmonics computed with LFD. To interpolate new results, the DLR surrogate modelling toolbox, SMARTy, was used. The database’s samples were prepared in a Halton sequence, making interpolation reliable. The surrogate’s parameter space was the Mach number, Reynold’s number, angle of attack, control surface deflection angle and the control surface chord length.

The LFD method proved effective for the mentioned purpose: the surrogates were accurate, up to 15% of relative error, in reproducing dynamic responses of aileron and spoiler deflections at low speed, within the limitations of flow field linearity, as well as surrogate prediction capability. The restrictions of the surrogate, and the reasoning thereof, are also presented in detail in the study. Future load alleviation studies are a potential of the findings here.

LFD is an innovative technique for load prediction and alleviation studies. This paper provides a reference for engineers wishing to use the method for the two mentioned control surfaces, or the like.

The purpose of this paper is to mainly review the state-of-the-art developments in the field of hydrodynamics of offshore pipelines, identifying the key tools for analysis of pipeline free spans, their applications, their qualifying characteristics and capabilities and limitations.

These different analytical, numerical and semi-empirical tools available for predicting such hydrodynamic loads and their effects include VIVANA, PIPESIN, VIVSIM, SIMULATOR, FATFREE, amongst others. Inherent in these models are current effects, wave effects and/ or pipe–soil interactions.

Amongst these models, the most attention was given to the new VIVANA model because this model take into account the vortex-induced effects with respect to free-spanning pipelines (which have dominant effect in the span analysis in deep water) better than other semi-empirical models (such as Shear 7). Recent improvements in VIVANA include its ability to have arbitrary variation in speed and direction of current, as well as the ability for calculation of pure IL and combined IL-CF response. Improvements in fatigue assessments at free spans, i.e. pipe–soil interaction have been achieved through the combined frequency domain and non-linear time domain analysis methodology adopted. Semi-empirical models are still the de facto currently used in the design of free-spanning pipelines. However, there is need for further research on free-span hydrodynamic coefficients and on how in-line and cross-flow vibrations interact. Again, there is still the challenge due to VIV complexity in fully understanding the fluid structure interaction problem, as there is no consolidated procedure for its analysis. It has been observed that there is large scatter between the different codes adopted in the prediction of fatigue damage, as there lacks full-scale test data devoted to determination/validation of the coefficients used in the semi-empirical models. A case study of the preliminary design of a typical 48 in. pipeline has been presented in this study to demonstrate the use of the free-span analysis tool, DNV RP F105. Excel spreadsheet has been applied in the execution of formulas.

This review paper is the first of its kind to study the state-of-the-art development in pipeline free-span analysis models and demonstrate the use of analysis tool, DNV for MAFSL calculation. Hence, information obtained from this paper would be invaluable in assisting designers both in the industry and academia.

In marine structures, the long‐term non‐stationary response of flexible lines, due to random environmental loads, may be regarded as successive short‐term stationary processes in which current, wind and ocean wave conditions remain constant. The power spectrum of each stationary process can be characterized by its linear and non‐linear energy components: the linear energy defines a Gaussian process, and the additional nonlinear energy characterizes a non‐Gaussian process. Within this scope, digital bispectral analysis has enabled one to describe non‐linear stationary response of flexible lines in the frequency domain, so that the complex coefficients of a quadratic model, in the frequency domain, can be estimated. The real and symmetrical matrix constructed from these coefficients has eigenvalues and eigenvectors useful to describe the characteristic function of the response from where the probability density function can be obtained by using a fast Fourier transform algorithm. The bases of the method presented here have already been treated, in a similar but pure algebraic method, to obtain the asymptotic probability function applicable to the response of non‐linear systems in closed form.

This paper aims to build an accurate mathematical model which is necessary for control design and attitude estimation of a miniature unmanned rotorcraft and its subsequent conversion to an autonomous vehicle.

Frequency-domain system identification of a small-size flybar-less remote controlled helicopter is carried out based on the input–output data collected from flight tests of the instrumented vehicle. A complete six degrees of freedom quasi-steady dynamic model is derived for hover and cruise flight conditions.

The veracity of the developed model is ascertained by comparing the predicted model responses to the actual responses from flight experiments and from statistical measures. Dynamic stability analysis of the vehicle is carried out using eigenvalues and eigenvectors. The identified model represents the vehicle dynamics very well in the frequency range of interest.

The model needs to be augmented with additional terms to represent the high-frequency dynamics of the vehicle.

Control algorithms developed using the first principles model can be easily reconfigured using the identified model, because the model structure is not altered during identification.

This paper gives a practical solution for model identification and stability analysis of a small-scale flybar-less helicopter. The estimated model can be easily used in developing control algorithms.

The purpose of this paper is to discuss the capability of nonlinear frequency domain (NLFD) method in predicting surface pressure coefficient presented in the time domain in unsteady transonic flows.

In this research, the solution and spatial operator are approximated by discrete form of Fourier transformation and resulting nonlinear equations are solved by use of pseudo‐spectral approach. Considered transonic flows involve different flow pattern on the airfoil surfaces. One of the test cases involves moving shocks on both lower and upper airfoil surfaces and in the two other test cases a moving shock occurs only on the upper surface.

Pressure distributions presented in the time domain using NLFD are compared with three test cases. Results show that NLFD predicts reasonable pressure distributions in time domain except in vicinity of shock positions. Although this method may predict unfair results near shock positions, however gives good estimates for global properties such as lift coefficient.

In the previous works on NLFD method, the flow field results have been limited to representing the pressure in the frequency domain or global coefficients such as lift coefficients. No details of pressure distributions in the time domain have been provided in such investigations. In this research, by presenting the pressure in the time domain, the conditions on which good pressure distributions are obtained are demonstrated.

This paper aims to propose a fast and accurate simulation of large-scale induction heating problems by using nonlinear reduced-order models.

A projection space for model order reduction (MOR) is quickly generated from the first kernels of Volterra’s series to the problem solution. The nonlinear reduced model can be solved with time-harmonic phasor approximation, as the nonlinear quadratic structure of the full problem is preserved by the projection.

The solution of induction heating problems is still computationally expensive, even with a time-harmonic eddy current approximation. Numerical results show that the construction of the nonlinear reduced model has a computational cost which is orders of magnitude smaller than that required for the solution of the full problem.

Only linear magnetic materials are considered in the present formulation.

The proposed MOR approach is suitable for the solution of industrial problems with a computing time which is orders of magnitude smaller than that required for the full unreduced problem, solved by traditional discretization methods such as finite element method.

The most common technique for MOR is the proper orthogonal decomposition. It requires solving the full nonlinear problem several times. The present MOR approach can be built directly at a negligible computational cost instead. From the reduced model, magnetic and temperature fields can be accurately reconstructed in whole time and space domains.

To develop a subdomain perturbation technique to calculate skin and proximity effects in inductors within frequency and time domain finite element (FE) analyses.

A reference limit eddy current FE problem is first solved by considering perfect conductors via appropriate boundary conditions. Its solution gives the source for eddy current FE perturbation subproblems in each conductor with its actual conductivity. Each of these problems requires an appropriate mesh of the associated conductor and its surrounding region.

The skin and proximity effects in inductors can be accurately determined in a wide frequency range, allowing for a precise consideration of inductive phenomena as well as Joule losses calculations in thermal coupling.

The developed subdomain method allows to accurately determine the current density distributions and ensuing Joule losses in conductors of any shape, not only in the frequency domain but also in the time domain. It extends the domain of validity and applicability of impedance boundary condition techniques. It also allows the solution process to be lightened, as well as efficient parameterized analyses on signal forms and conductor characteristics.