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Analytical models are often used in the first steps of the design process. They are associated with optimisation methods to find a solution that fulfil the design specifications. In this paper, the analytical model of an electric motor is built and proposed as a benchmark to highlight the optimisation methods the most fitted to analytical models.

This paper studies the optimal design of a brushless DC wheel motor. First, the analytical model is presented. Each equation used for the sizing is described, including the physical phenomenon associated, the hypotheses done, and some precautions to take before computing. All equations are ordered to ease their resolution, due to a specific procedure which is then described. Secondly, three optimisation problems with an increasing number of parameters and constraints are proposed. Finally, the results found by the sequential quadratic method point out the special features of this benchmark.

The constraint optimisation problem proposed is clearly multimodal as shown in the results of one deterministic method. Many starting points were used to initialise the optimisation methods and lead to two very different solutions.

First, an analytical model for the optimal design is detailed and each equation is explained. A specific procedure is presented to order all equations in order to ease their resolution. Secondly, a multimodal benchmark is proposed to promote the development of hybrid methods and special heuristics.

Analytical target cascading (ATC) is a hierarchical multi‐level design methodology. According to the state‐of‐the‐art, it is confirmed that for problems with unattainable targets, strict design consistency cannot be achieved with finite weighting factors. This paper aims to address these issues.

A new formulation is proposed to improve the ATC convergence. The weighted sum of deviation metric is transformed into a multi‐objective formulation. An original optimization problem with a single global optimal solution is used as a benchmark.

It is found that carrying out an industrial application to design optimally a tram traction system demonstrates the efficiency of the proposed solution.

This paper is of value in showing how to improve the convergence of a multi‐level optimization algorithm by best management of the consistency constraints.

A car alternator with claw poles is typically a 3D device because its shape is not axi‐symmetrical nor XY‐symmetrical. A 3D finite element model can be useful to simulate the thermic behavior of the machine but is rarely available. In this paper, it is shown that a 2D simulation can fit even if all the thermal phenomena relating to the missing direction are neglected. The alternators have been modeled in two different sections to show their respective reliability. Moreover, thermal hybrid conductivities have been defined to take into account the succession of the different materials in the missing direction.

The aim of this paper is to use an analytical multi‐physical model – electromagnetic, mechanic and acoustic – in order to predict the electromagnetic noise of a permanent magnet synchronous machine.

The aim of this work is to develop and use an analytical multi‐physical model – electromagnetic, mechanic and acoustic – of a synchronous machine with permanent magnets. The complete model is coded in order to predict acoustic noise. A study of sensitivity is presented in order to deduce the influential – or significant – factors on the noise. For that, the technique of the experimental designs is used. More particularly, the modeling of the noise will be achieved due to the new “trellis” designs.

Three models are presented: electromagnetic, mechanical of vibration and acoustic. For each of them, comparisons with finite element method and experiments have been made. Several response surfaces are given; they represent the noise according to influential factors, with respect to different speeds of the machine. These surfaces are useful to deduce the parts of the design space to avoid.

Different multi‐physical aspects are considered: electromagnetic, mechanic and acoustic phenomena are taken into account due to a single analytical model. The experimental design method is the privileged tool used to make the complex relationships between the main variables appear.

The paper highlights the process of electric vehicles optimal design as an inverse problem and presents the global constrained optimization as the best way to solve it.

The electric vehicle optimal design is carried out by a new approach. It consists an electric vehicle design model managed by constrained optimization techniques. It includes sizing models for all drive train components and a vehicle dynamic model build in a new “design way” as an energy‐based model using the response surface methodology. The sensitivity of first simple sizing models can be evaluated by the experimental design method, giving information about the most important part of the model that must be improved.

The result shows the superiority of the constrained optimization technique that treats simultaneously the global optimization and the model adjustment. This method of simultaneous resolution is much more powerful than the successive resolution of each subproblem. The proposed “design approach” used for electric vehicle optimal design offer a large potential in the field of the complex systems design.

The electric vehicle design process is treated on a vehicle design model based on a design approach. It allows determining the drive train components specifications for imposed vehicle performances, taking into account the dynamic model of the vehicle and all components interactions. Furthermore, considering fine components sizing models, the components can be sized taking into account the whole system behavior in an optimal global design.

This paper presents two modeling methods applied to induction machine study in order to construct a tool for diagnosis purpose. The first method is based on permeance networks using finite element analysis to calculate magnetic equivalent circuit parameters. The second method consists of the elaboration of an electric equivalent circuit obtained from minimal geometrical knowledge on stator and rotor parts of the machine on study. These two methods are presented and their results are compared with respect to the normal and rotor broken bar operation. For this study, a simple structure induction machine with three stator coils and six rotor bars has been investigated. The presented results concern stator currents and electromagnetic torque for the rated speed and the magnitude of the stator current harmonic components have been compared.

The purpose of this paper is to apply a fast analytical model of the acoustic behaviour of pulse‐width modulation (PWM) controlled induction machines to a fractional‐slot winding machine, and to analytically clarify the interaction between space harmonics and time harmonics in audible electromagnetic noise spectrum.

A multilayer single‐phase equivalent circuit calculates the stator and rotor currents. Air‐gap radial flux density, which is supposed to be the only source of acoustic noise, is then computed with winding functions formalism. Mechanical and acoustic models are based on a 2D ring stator model. A method to analytically derive the orders and frequencies of most important vibration lines is detailed. The results are totally independent of the supply strategy and winding type of the machine. Some variable‐speed simulations and tests are run on a 700 W fractional‐slot induction machine in sinusoidal case as a first validation of theoretical results.

The influence of both winding space harmonics and PWM time harmonics on noise spectrum is exposed. Most dangerous orders and frequencies expressions are demonstrated in sinusoidal and PWM cases. For traditional integral windings, it is shown that vibration orders are necessarily even. When the stator slot number is not even, which is the case for fractional windings, some odd order deflections appear: the radial electromagnetic power can therefore dissipate as vibrations through all stator deformation modes, leading to a potentially lower noise level at resonance.

The analytical research does not consider saturation and eccentricity harmonics which can play a significant role in noise radiation.

The analytical model and theoretical results presented help in designing low‐noise induction machines, and diagnosing noise or vibration problems.

The paper details a fully analytical acoustic and electromagnetic model of a PWM fed induction machine, and demonstrate the theoretical expression of main noise spectrum lines combining both time and space harmonics. For the first time, a direct comparison between simulated and experimental vibration spectra is made.

Discrete highly constrained optimization of induction machine taking into consideration two objective functions: efficiency and total costs of production. The paper aims to discuss these issues.

Interactive and semi-interactive interval-based optimization methods were used. Two concepts of multi-objective discrete optimization were proposed.

Proposed methodology and algorithms allow decision maker (DM) participate in the process of optimal design and therefore decrease the total time of optimization process. The search procedure is straightforward and it does not require special skills of DM. Presented methods were successfully versified for the problem of optimal design with discrete variables.

Three interval algorithms suitable for inverse problems are researched and verified. It generally can be used for multi-objective problems. The dominance principles for interval boxes are showed in the paper. Proposed algorithms are based on the idea of hybridization of exact and evolutionary methods.

Proposed approaches were successfully implemented within computer-aided application which is used by manufacturer of high power induction machine.

The concept of pareto-domination using the interval boxes can be treated as original. The paper researched several elimination rules and discusses the difference between different approaches.

This study aims to examine the association between related party transactions and firm value. The study also investigates the impact of several determinants of this relationship as moderating variables.

The paper uses multiple regression models. In the period from 2018 to 2021, a total of 134 non-financial companies listed on the Saudi Stock Exchange were included in the sample, which consisted of 451 firm-year observations.

This paper finds that related party transactions have a significant negative impact on firm value. Moreover, the negative impact of related party transactions on firm value is increased in the presence of changes in the certain presence of certain moderating variables, such as firm size, leverage and return on assets (ROA). The results of the sensitivity analysis concur with the findings of the basic analysis. There is little evidence in the literature regarding related party transactions and their association with the moderating variables considered in this study.

To the best of the authors’ knowledge, there have been no studies conducted in Saudi Arabia to date that examine the effect of firm size, leverage and ROA on the association between firm value and related party transactions. Consequently, this paper contributes to the limited literature by expanding the existing research and analyzing the impact of firm size, leverage and ROA on the association between related party transactions and firm value.

The aim of the paper is to find the effective algorithms of electromagnetic torque calculation.

The proposed algorithms are related to the analysis of electrical machines using the methods of equivalent magnetic networks. The presented permeance and reluctance networks are formulated using FE methods. Attention is paid to the algorithms of electromagnetic torque calculation for 3D models. The virtual work principle is applied. The principle is adapted to the discrete network models. The network representations of Maxwell's stress formula are given.

The proposed method of electromagnetic torque calculation can be successfully applied in the 3D calculations of rotating electrical machines. It can be used for scalar and vector potential formulations. The obtained results and their comparison with the measurements show that the method is sufficiently accurate.

The presented formulas of electromagnetic torque calculation are universal and can be successfully applied in the FE analysis of electrical machines using nodal and edge elements.