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A time-varying grey Fourier model (TVGFM(1,1,N)) is proposed for the simulation of variable amplitude seasonal fluctuation time series, as the performance of traditional grey models can't catch the time-varying trend well.

The proposed model couples Fourier series and linear time-varying terms as the grey action, to describe the characteristics of variable amplitude and seasonality. The truncated Fourier order N is preselected from the alternative order set by Nyquist-Shannon sampling theorem and the principle of simplicity, then the optimal Fourier order is determined by hold-out method to improve the robustness of the proposed model. Initial value correction and the multiple transformation are also studied to improve the precision.

The new model has a broader applicability range as a result of the new grey action, attaining higher fitting and forecasting accuracy. The numerical experiment of a generated monthly time series indicates the proposed model can accurately fit the variable amplitude seasonal sequence, in which the mean absolute percentage error (MAPE) is only 0.01%, and the complex simulations based on Monte-Carlo method testify the validity of the proposed model. The results of monthly electricity consumption in China's primary industry, demonstrate the proposed model catches the time-varying trend and has good performances, where MAPE_F and MAPE_T are below 5%. Moreover, the proposed TVGFM(1,1,N) model is superior to the benchmark models, grey polynomial model (GMP(1,1,N)), grey Fourier model (GFM(1,1,N)), seasonal grey model (SGM(1,1)), seasonal ARIMA model seasonal autoregressive integrated moving average model (SARIMA) and support vector regression (SVR).

The parameter estimates and forecasting of the new proposed TVGFM are studied, and the good fitting and forecasting accuracy of time-varying amplitude seasonal fluctuation series are testified by numerical simulations and a case study.

The purpose of this paper is to deal with the correction of the inaccuracies near edges and corners arising from thin shell models by means of an iterative finite element subproblem method. Classical thin shell approximations of conducting and/or magnetic regions replace the thin regions with impedance-type transmission conditions across surfaces, which introduce errors in the computation of the field distribution and Joule losses near edges and corners.

In the proposed approach local corrections around edges and corners are coupled to the thin shell models in an iterative procedure (each subproblem being influenced by the others), allowing to combine the efficiency of the thin shell approach with the accuracy of the full modelling of edge and corner effects.

The method is based on a thin shell solution in a complete problem, where conductive thin regions have been extracted and replaced by surfaces but strongly neglect errors on computation of the field distribution and Joule losses near edges and corners.

This model is only limited to thin shell models by means of an iterative finite element subproblem method.

The developed method is considered to couple subproblems in two-way coupling correction, where each solution is influenced by all the others. This means that an iterative procedure between the subproblems must be required to obtain an accurate (convergence) solution that defines as a series of corrections.

A novel framework for expedited antenna optimization with an iterative prediction-correction scheme is proposed. The methodology is comprehensively validated using three real-world antenna structures: narrow-band, dual-band and wideband, optimized under various design scenarios.

The keystone of the proposed approach is to reuse designs pre-optimized for various sets of performance specifications and to encode them into metamodels that render good initial designs, as well as an initial estimate of the antenna response sensitivities. Subsequent design refinement is realized using an iterative prediction-correction loop accommodating the discrepancies between the actual and target design specifications.

The presented framework is capable of yielding optimized antenna designs at the cost of just a few full-wave electromagnetic simulations. The practical importance of the iterative correction procedure has been corroborated by benchmarking against gradient-only refinement. It has been found that the incorporation of problem-specific knowledge into the optimization framework greatly facilitates parameter adjustment and improves its reliability.

The proposed approach can be a viable tool for antenna optimization whenever a certain number of previously obtained designs are available or the designer finds the initial effort of their gathering justifiable by intended re-use of the procedure. The future work will incorporate response features technology for improving the accuracy of the initial approximation of antenna response sensitivities.

The proposed optimization framework has been proved to be a viable tool for cost-efficient and reliable antenna optimization. To the knowledge, this approach to antenna optimization goes beyond the capabilities of available methods, especially in terms of efficient utilization of the existing knowledge, thus enabling reliable parameter tuning over broad ranges of both operating conditions and material parameters of the structure of interest.

Outlines a general methodology for the solution of the system of algebraic equations arising from the discretization of the field equations governing coupled problems. Considers that this discrete problem is obtained from the finite element discretization in space and the finite difference discretization in time. Aims to preserve software modularity, to be able to use existing single field codes to solve more complex problems, and to exploit computer resources optimally, emulating parallel processing. To this end, deals with two well‐known coupled problems of computational mechanics – the fluid‐structure interaction problem and thermally‐driven flows of incompressible fluids. Demonstrates the possibility of coupling the block‐iterative loop with the nonlinearity of the problems through numerical experiments which suggest that even a mild nonlinearity drives the convergence rate of the complete iterative scheme, at least for the two problems considered here. Discusses the implementation of this alternative to the direct coupled solution, stating advantages and disadvantages. Explains also the need for online synchronized communication between the different codes used as is the description of the master code which will control the overall algorithm.

This paper aims to propose a semi-analytical benchmarking framework for enthalpy-based methods used in problems involving phase change with latent heat. The benchmark is based on a class of semi-analytical solutions of spatially symmetric Stefan problems in an arbitrary spatial dimension. Via a public repository this study provides a finite element numerical code based on the FEniCS computational platform, which can be used to test and compare any method of choice with the (semi-)analytical solutions. As a particular demonstration, this paper uses the benchmark to test several standard temperature-based implementations of the enthalpy method and assesses their accuracy and stability with respect to the discretization parameters.

The class of spatially symmetric semi-analytical self-similar solutions to the Stefan problem is found for an arbitrary spatial dimension, connecting some of the known results in a unified manner, while providing the solutions’ existence and uniqueness. For two chosen standard semi-implicit temperature-based enthalpy methods, the numerical error assessment of the implementations is carried out in the finite element formulation of the problem. This paper compares the numerical approximations to the semi-analytical solutions and analyzes the influence of discretization parameters, as well as their interdependence. This study also compares accuracy of these methods with other traditional approach based on time-explicit treatment of the effective heat capacity with and without iterative correction.

This study shows that the quantitative comparison between the semi-analytical and numerical solutions of the symmetric Stefan problems can serve as a robust tool for identifying the optimal values of discretization parameters, both in terms of accuracy and stability. Moreover, this study concludes that, from the performance point of view, both of the semi-implicit implementations studied are equivalent, for optimal choice of discretization parameters, they outperform the effective heat capacity method with iterative correction in terms of accuracy, but, by contrast, they lose stability for subcritical thickness of the mushy region.

The proposed benchmark provides a versatile, accessible test bed for computational methods approximating multidimensional phase change problems. The supplemented numerical code can be directly used to test any method of choice against the semi-analytical solutions.

While the solutions of the symmetric Stefan problems for individual spatial dimensions can be found scattered across the literature, the unifying perspective on their derivation presented here has, to the best of the authors’ knowledge, been missing. The unified formulation in a general dimension can be used for the systematic construction of well-posed, reliable and genuinely multidimensional benchmark experiments.

To propose novel predictor‐corrector time‐integration algorithms for pseudo‐dynamic testing.

The novel predictor‐corrector time‐integration algorithms are based on both the implicit and the explicit version of the generalized‐α method. In the non‐linear unforced case second‐order accuracy, stability in energy, energy decay in the high‐frequency range as well as asymptotic annihilation are distinctive properties of the generalized‐α scheme; while in the non‐linear forced case they are the limited error near the resonance in terms of frequency location and intensity of the resonant peak. The implicit generalized‐α algorithm has been implemented in a predictor‐one corrector form giving rise to the implicit IPC‐ρ_∞ method, able to avoid iterative corrections which are expensive from an experimental standpoint and load oscillations of numerical origin. Moreover, the scheme embodies a secant stiffness formula able to approximate closely the actual stiffness of a structure. Also an explicit algorithm has been implemented, the EPC‐ρ_b method, endowed with user‐controlled dissipation properties. The resulting schemes have been tested experimentally both on a two‐ and on a six‐degrees‐of‐freedom system, exploiting substructuring techniques.

The analytical findings and the tests have indicated that the proposed numerical strategies enhance the performance of the pseudo‐dynamic test (PDT) method even in an environment characterized by considerable experimental errors. Moreover, the schemes have been tested numerically on strongly non‐linear multiple‐degrees‐of‐freedom systems reproduced with the Bouc‐Wen hysteretic model, showing that the proposed algorithms reap the benefits of the parent generalized‐α methods.

Further developments envisaged for this study are the application of the IPC‐ρ_∞ method and of EPC‐ρ_b scheme to partitioned procedures for high‐speed pseudo‐dynamic testing with substructuring.

The implicit IPC‐ρ_∞ and the explicit EPC‐ρ_b methods allow a user to have defined dissipation which reduces the effects of experimental error in the PDT without needing onerous iterations.

The paper proposes novel time‐integration algorithms for pseudo‐dynamic testing. Thanks to a predictor‐corrector form of the generalized‐α method, the proposed schemes maintain a high computational efficiency and accuracy.

This paper is concerned with rank analysis of rectangular matrix of a homogeneous set of incremental equations regarded as an element of continuation method. The rank analysis is based on a known feature that every rectangular matrix can be transformed into the matrix of echelon form. By inspection of the rank, correct control parameters are chosen and this allows not only for rounding limit and turning points but also for branch‐switching near bifurcation points.

Two common fixed grid enthalpy methods used in the numerical modelling of phase change problems are the apparent heat capacity and the source based methods. In this paper, a general enthalpy method that includes as subsets both apparent heat capacity and source based methods, is derived. Following this, an optimal enthalpy scheme is identified. The superiority of the optimal scheme over the apparent heat capacity and the source based schemes is illustrated by solving sample phase change problems.

Effective explicit algorithms for integrating complex elastoplastic constitutive models, such as those belonging to the Cam clay family, are described. These automatically divide the applied strain increment into subincrements using an estimate of the local error and attempt to control the global integration error in the stresses. For a given scheme, the number of substeps used is a function of the error tolerance specified, the magnitude of the imposed strain increment, and the non‐linearity of the constitutive relations. The algorithms build on the work of Sloan in 1987 but include a number of important enhancements. The steps required to implement the integration schemes are described in detail and results are presented for a rigid footing resting on a layer of Tresca, Mohr‐Coulomb, modified Cam clay and generalised Cam clay soil. Explicit methods with automatic substepping and error control are shown to be reliable and efficient for these models. Moreover, for a given load path, they are able to control the global integration error in the stresses to lie near a specified tolerance. The methods described can be used for exceedingly complex constitutive laws, including those with a non‐linear elastic response inside the yield surface. This is because most of the code required to program them is independent of the precise form of the stress‐strain relations. In contrast, most of the implicit methods, such as the backward Euler return scheme, are difficult to implement for all but the simplest soil models.

This paper aims to provide a new method to design a fuel efficient control strategy such as J₂ perturbation for deploying a constellation into a specified configuration. The nonspherical perturbation, mainly J₂ perturbation, is the dominant perturbation for low-Earth-orbit (LEO) satellites of a constellation. This perturbation can be utilized in the control strategy to lower fuel consumption enormously.

The relationship of the coupled variables, the relative right ascension of ascending node (RAAN) and the relative phase (RP), are analyzed. First-order approximation expressions of the relative RAAN (RRAAN) and the relative phase (RP) with respect to the semimajor axis are derived. According to the Gauss’ variational equations, the reduced explicit functions of these variables in regard to each active control are established. Based on these functions, control strategy design methods, including the preliminary planning and iterative corrections, are proposed. The numerical simulation is carried out to verify the proposed method.

The results indicate that the constellation can be deployed accurately about the semimajor axis, the RRAAN and the relative phase (RP) by the developed fuel efficient control strategy.

The proposed control strategy is limited for the orbital altitude where the J₂ perturbation is dominant.

The proposed effective method is applicable for the engineers planning an orbital control strategy of deploying satellites of a constellation.

The new control strategy can realize utilization of J₂ perturbation and an accurate deployment, simultaneously. Further, this paper provides practical help for satellite engineers.