Implementation of the sliding-line technique in a MEC model of a linear bistable actuator

Purpose The aim of this study is to investigate the implementation of the sliding-line technique (SLT) in a generic two-dimensional (2D) nonlinear adaptive magnetic equivalent circuit (MEC) model predicting the electromagnetic force evolution of a linear bistable electromagnetic actuator technology. Design/methodology/approach The developed MEC model considers the saturation effect and the auto-adjustability of the spatial discretisation. The connection between static and mobile zones is ensured by an approach known as “air-gap sliding-line technique”, which is widely used for rotary electric motor models. To the best of the author’s knowledge, that is the first time that the SLT is implemented on an electromagnetic structure with linear motion. Findings It was found that, in case of a linear actuator with a relatively small working stroke, the implementation of the SLT could lead to some non-negligible inaccuracies. Originality/value To solve the above-mentioned problem, it was proposed to investigate the implementation of a single SLT vs double SLT. The results of the MEC models were compared with the 2D finite-element analysis (FEA) as well as with the experimental test results. The developed semi-analytical models can be easily adapted to other topologies of linear electromagnetic machines.

3D full-time anisotropic TEM modelling using a mixed BDF2/SAI method

Transient electromagnetic (TEM) data are affected by resistivity anisotropy, which should be considered in 3D modelling. The influence of anisotropy on full-time response is the main focus of this research. For spatial discretisation of an anisotropic model, the mimetic finite volume approach was applied. The accuracy of the shift-and-invert (SAI) Krylov subspace approach and the two-step backward differentiation formula (BDF2) for modelling 3D full-time electromagnetic data has been demonstrated. However, both algorithms require time-consuming calculations. The SAI technique requires a number of projection subspace constructions, whereas the BDF2 algorithm necessitates numerous coefficient matrix decompositions. We proposed a novel mixed BDF2/SAI algorithm in this paper, which combines the advantages of the two algorithms. The on-time response is computed using BDF2, while the off-time response is computed using the SAI-Krylov subspace method. The forward results of a 1D model with a half-sine waveform demonstrated that the new algorithm is accurate and faster than both the BDF2 algorithm and the SAI algorithm. During the full-time period, the forward results of a 3D anisotropic model with half-sine waveform show that abnormal responses can be induced. It was shown that the relative abnormal of ${{{\bf b}}_{\boldsymbol{z}}}$ is higher during the on-time period, while the relative abnormal of $\partial {{{\bf b}}_{\boldsymbol{z}}}/\partial t$ is higher during the off-time period. Furthermore, the change in relative anomaly is more obvious as the anisotropic block rotates around the x-axis. And the larger the rotation angle, the larger the relative anomaly.

A Linearised θ Numerical Scheme for the Vibrations of Inextensible Beams

A linearised finite element numerical scheme for the vibration of inextensible beams is developed. The proposed scheme is based on the methodology introduced by S. Bartels [15] and satisfies a linearised form of the inextensibility constraint. The time m arching procedure is based on repeated use of the theta-parameter integration quadrature. Three parameters are introduced in total and appropriately selected such that the energy conservation features are improved compared to the Bartels algorithm while the inextensibility constraint is satisfied as accurately as possible. Cubic Hermite polynomials are employed for the spatial discretisation. The Bartels algorithm is retrieved as a special case. Several numerical experiments are presented demonstrating the theoretically predicted enhanced inextensibility mimicking and optimum values of the method parameters are identified.

Technical note: Hydrology modelling R packages – a unified analysis of models and practicalities from a user perspective

Following the rise of R as a scientific programming language, the increasing requirement for more transferable research and the growth of data availability in hydrology, R packages containing hydrological models are becoming more and more available as an open-source resource to hydrologists. Corresponding to the core of the hydrological studies workflow, their value is increasingly meaningful regarding the reliability of methods and results. Despite package and model distinctiveness, no study has ever provided a comparison of R packages for conceptual rainfall–runoff modelling from a user perspective by contrasting their philosophy, model characteristics and ease of use. We have selected eight packages based on our ability to consistently run their models on simple hydrology modelling examples. We have uniformly analysed the exact structure of seven of the hydrological models integrated into these R packages in terms of conceptual storages and fluxes, spatial discretisation, data requirements and output provided. The analysis showed that very different modelling choices are associated with these packages, which emphasises various hydrological concepts. These specificities are not always sufficiently well explained by the package documentation. Therefore a synthesis of the package functionalities was performed from a user perspective. This synthesis helps to inform the selection of which packages could/should be used depending on the problem at hand. In this regard, the technical features, documentation, R implementations and computational times were investigated. Moreover, by providing a framework for package comparison, this study is a step forward towards supporting more transferable and reusable methods and results for hydrological modelling in R.

Ranking earthquake forecasts: On the use of proper scoring rules to discriminate forecasts

<p>Recent years have seen a growth in the diversity of probabilistic earthquake forecasts as well as the advent of them being applied operationally. The growth of their use demands a deeper look at our ability to rank their performance within a transparent and unified framework. Programs such as the Collaboratory Study for Earthquake Predictability (CSEP)  have been at the forefront of this effort. Scores are quantitative measures of how well a dataset can be explained by a candidate forecast and allow forecasts to be ranked. A positively oriented score is said to be proper when, on average, the highest score is achieved by the closest model to the data generating one. Different meanings of closest lead to different proper scoring rules. Here, we prove that the Parimutuel Gambling score, used to evaluate the results of the 2009 Italy CSEP experiment, is generally not proper, and even for the special case where it is proper, it can still be used improperly. We show in detail the possible consequences of using this score for forecast evaluation. Moreover, we show that other well-established scores can be applied to existing studies to calculate new rankings with no requirement for extra information. We extend the analysis to show how much data are required, in principle, to distinguish candidate forecasts and therefore how likely it is to express a preference towards a forecast. This introduces the possibility of survey design with regard to the duration and spatial discretisation of earthquake forecasts. Our findings may contribute to more rigorous statements about the ability to distinguish between the predictive skills of candidate forecasts in addition to simple rankings.</p>

COMPARING THE DISCONTINUOUS GALERKIN AND HIGH-ORDER DIAMOND DIFFERENCING METHODS FOR THE TRANSPORT EQUATION ON A LOZENGE-BASED HEXAGONAL GEOMETRY

This paper presents an implementation and a comparison of two spatial discretisation schemes over a hexagonal geometry for the two-dimensional discrete ordinates transport equation. The methods are a high-order Discontinuous Galerkin (DG) finite element scheme and a high-order Diamond Differencing (DD) scheme. The DG method has been, and is being, studied on the hexagonal geometry, also called a honeycomb mesh – but not the DD method. In this research effort, it was chosen to divide the hexagons into (at least) three lozenges. An affine transformation is then applied onto said lozenges to cast them into the reference quadrilaterals usually studied in finite elements. In practice, this effectively means that the equations used in Cartesian geometry have their terms and operators altered using the Jacobian matrix of the transformation. This was implemented in the discrete ordinates solver of the code DRAGON5. Two 2D benchmark problems were then used for the verification and validation, including one based on the Monju 3D reactor benchmark. It was found that the diamond-differencing scheme seemed better. It converged much faster towards the solution at comparable mesh refinements for first-order expansion of the flux. Even if this difference was not present for second-order, DG was slower, about two to four times slower.

Risk Oriented Earthquake Hazard Assessment: Influence of Spatial Discretisation and Non-ergodic Ground-Motion Models

Three important aspects of ground-motion modelling for regional or portfolio risk analyses are discussed. The first issue is the treatment of discretisation of continuous ground-motion fields for generating spatially correlated discrete fields. Shortcomings of the present approach in which correlation models based upon point estimates of ground motions are used to represent correlations within and between spatial regions are highlighted. It is shown that risk results will be dependent upon the chosen spatial resolution if the effects of discretisation are not adequately treated. Two aspects of non-ergodic groundmotion modelling are then discussed. Correlation models generally used within risk modelling are traditionally based upon very simple partitioning of ground-motion residuals. As regional risk analyses move to non-ergodic applications where systematic site effects are considered, these correlation models (both inter-period and spatial models) need to be revised. The nature of these revisions are shown herein. Finally, evidence for significantly reduced between-event variability within earthquake sequences is presented. The ability to progressively constrain location and sequence-dependent systematic offsets from ergodic models as earthquake sequences develop can have significant implications for aftershock risk assessments.

Numerical Modeling of Non-Affine Viscoelastic Fluid Flow Including Viscous Dissipation Through a Square Cross-Section Duct: Heat Transfer Enhancement due to the Inertia and the Elastic Effects

Non-isothermal laminar flow of a viscoelastic fluid including viscous dissipation through a square cross–section duct is analyzed. Viscoelastic stresses are described by Giesekus modele orthe Phan-Thien–Tanner model and the solvent shear stress is given by the linear Newtonian constitutive relationship. The flow through the tube is governed by the conservation equations of energy, mass, momentum associated with to one non–affine rheological model mentioned above. The mixed type of the governing system of equations (elliptic–parabolic–hyperbolic) requires coupling between discretisation methods designed for elliptic–type equations and techniques adapted to transport equations. To allow appropriate spatial discretisation of the convection terms, the system is rewritten in a quasi-linear first-order and homogeneous form without the continuity and energy equations. With the rheological models of the Giesekus type, the conformation tensor is by definition symmetrical and positive-definite, with the PTT model the hyperbolicity condition is subject to restrictions related to the rheological parameters. Based on this hyperbolicity condition, the contribution of the hyperbolic part is approximated by applying the characteristic method to extract pure advection terms which are then discretized by high ordre schemes WENO and HOUC. The algorithm thus developed makes it possible, to avoid the problems of instabilities related to the high Weissenberg number without the use of any stabilization method. Finally, a Nusselt number analysis is given as a function of inertia, elasticity, viscous dissipation, for constant solvent viscosity ratio and constant material and rheological parameters.

Hydrology modelling R packages: a unified analysis of models and practicalities from a user perspective

Following the rise of R as a scientific programming language, the increasing requirement for more transferable research, and the growth of data availability in hydrology, R packages containing hydrological models are becoming more and more available to hydrologists. Corresponding to the core of the hydrological studies workflow, their value is increasingly meaningful regarding the reliability of methods and results. Despite package and model distinctiveness, no study has ever provided a comparison of R packages for conceptual rainfall-runoff modelling from a user perspective, contrasting their philosophy, model characteristics and ease of use. We have selected eight packages based on our ability to consistently run their models on simple hydrology modelling examples. We have uniformly analysed the exact structure of seven of the hydrological models integrated in these R packages in terms of conceptual storages and fluxes, spatial discretisation, data requirements and output provided. The analysis showed that very different modelling choices are associated with these packages, which emphasises various hydrological concepts. These specificities are not always sufficiently well explained by the package documentation. Therefore a synthesis of the package functionalities was performed from a user perspective. This synthesis helps inform selection of what packages could/should be used depending on the problem at hand. In this regard, technical features, documentation, R implementations and computational times were investigated. Moreover, by providing a framework for package comparison, this study is a step forward towards supporting more transferable and reusable methods and results for hydrological modelling in R.