Geostatistical seismic inversion and 3D modelling of metric flow units,porosity and permeability in Brazilian presalt reservoir

Flow units(FU)rock typing is a common technique for characterizing reservoir flow behavior,producing reliable porosity and permeability estimation even in complex geological settings.However,the lateral extrapolation of FU away from the well into the whole reservoir grid is commonly a difficult task and using the seismic data as constraints is rarely a subject of study.This paper proposes a workflow to generate numerous possible 3D volumes of flow units,porosity and permeability below the seismic resolution limit,respecting the available seismic data at larger scales.The methodology is used in the Mero Field,a Brazilian presalt carbonate reservoir located in the Santos Basin,who presents a complex and heterogenic geological setting with different sedimentological processes and diagenetic history.We generated metric flow units using the conventional core analysis and transposed to the well log data.Then,given a Markov chain Monte Carlo algorithm,the seismic data and the well log statistics,we simulated acoustic impedance,decametric flow units(DFU),metric flow units(MFU),porosity and permeability volumes in the metric scale.The aim is to estimate a minimum amount of MFU able to calculate realistic scenarios porosity and permeability scenarios,without losing the seismic lateral control.In other words,every porosity and permeability volume simulated produces a synthetic seismic that match the real seismic of the area,even in the metric scale.The achieved 3D results represent a high-resolution fluid flow reservoir modelling considering the lateral control of the seismic during the process and can be directly incorporated in the dynamic characterization workflow.

Hydrological Modelling of the Casamance River in Its Upstream Section (Basin at Kolda Level) to Predict Its Future States as a Function of Different Stresses

Flow records for stations in the Casamance basin are incomplete. Several gaps were noted over the 1980-2021 study period, making this study tedious. The aim of this study is to assess the potential impact of climate change on the flow of the Casamance watershed at Kolda. To this end, hydrological series are simulated and then extended using the GR2M rainfall-runoff model, with a monthly time step. Projected climate data are derived from a multi-model ensemble under scenarios SSP2-4.5 (scenario with additional radiative forcing of 4.5 W/m2 by 2099) and SSP5-8.5 (scenario with additional radiative forcing of 8.5 W/m2 by 2099). An analysis of the homogeneity of the rainfall data series from the Kolda station was carried out using KhronoStat software. The Casamance watershed was then delimited using ArcGIS to determine the morphometric parameters of the basin, which will be decisive for the rest of the work. Next, monthly evapotranspiration was calculated using the formula proposed by Oudin et al. This, together with rainfall and runoff, forms the input data for the model. The GR2M model was then calibrated and cross-validated using various simulations to assess its performance and robustness in the Casamance watershed. The version of the model with the calibrated parameters will make it possible to extend Casamance river flows to 2099. This simulation of future flows with GR2M shows a decrease in the flow of the Casamance at Kolda with the two scenarios SSP2-4.5 and SSP5-8.5 during the rainy period, and almost zero flows during the dry season from the period 2040-2059.

Modelling Land Use/Land Cover Change of River Rwizi Catchment, South-Western Uganda Using GIS and Markov Chain Model

Analysis of catchment Land use/Land cover (LULC) change is a vital tool in ensuring sustainable catchment management. The study analyzed land use/land cover changes in the Rwizi catchment, south western Uganda from 1989-2019 and projected the trend by 2040. Landsat images, field observations, key informant interviews and focus group discussions were used to collect data. Changes in cropland, forestland, built up area, grazing land, wetland and open water bodies were analyzed in ArcGIS version 10.2.2 and ERDAS IMAGINE 14 software and a Markov chain model. All the LULC classes increased in area except grazing land. Forest land and builtup area between 2009-2019 increased by 370.03% and 229.53% respectively. Projections revealed an increase in forest land and builtup area by 2030 and only built up area by 2040. LULCC in the catchment results from population pressure, reduced soil fertility and high value of agricultural products.

Numerical analysis of high‑speed railway slab tracks using calibrated and validated 3D time‑domain modelling

Concrete slabs are widely used in modern railways to increase the inherent resilient quality of the tracks,provide safe and smooth rides,and reduce the maintenance frequency.In this paper,the elastic performance of a novel slab trackform for high-speed railways is investigated using three-dimensional finite element modelling in Abaqus.It is then compared to the performance of a ballasted track.First,slab and ballasted track models are developed to replicate the full-scale testing of track sections.Once the models are calibrated with the experimental results,the novel slab model is developed and compared against the calibrated slab track results.The slab and ballasted track models are then extended to create linear dynamic models,considering the track geodynamics,and simulating train passages at various speeds,for which the Ledsgard documented case was used to validate the models.Trains travelling at low and high speeds are analysed to investigate the track deflections and the wave propagation in the soil,considering the issues associated with critical speeds.Various train loading methods are discussed,and the most practical approach is retained and described.Moreover,correlations are made between the geotechnical parameters of modern high-speed rail and conventional standards.It is found that considering the same ground condition,the slab track deflections are considerably smaller than those of the ballasted track at high speeds,while they show similar behaviour at low speeds.

Implication of community-level ecophysiological parameterization to modelling ecosystem productivity:a case study across nine contrasting forest sites in eastern China

Parameterization is a critical step in modelling ecosystem dynamics.However,assigning parameter values can be a technical challenge for structurally complex natural plant communities;uncertainties in model simulations often arise from inappropriate model parameterization.Here we compared five methods for defining community-level specific leaf area(SLA)and leaf C:N across nine contrasting forest sites along the North-South Transect of Eastern China,including biomass-weighted average for the entire plant community(AP_BW)and four simplified selective sampling(biomass-weighted average over five dominant tree species[5DT_BW],basal area weighted average over five dominant tree species[5DT_AW],biomass-weighted average over all tree species[AT_BW]and basal area weighted average over all tree species[AT_AW]).We found that the default values for SLA and leaf C:N embedded in the Biome-BGC v4.2 were higher than the five computational methods produced across the nine sites,with deviations ranging from 28.0 to 73.3%.In addition,there were only slight deviations(<10%)between the whole plant community sampling(AP_BW)predicted NPP and the four simplified selective sampling methods,and no significant difference between the predictions of AT_BW and AP_BW except the Shennongjia site.The findings in this study highlights the critical importance of computational strategies for community-level parameterization in ecosystem process modelling,and will support the choice of parameterization methods.

Prospect Theory Based Individual Irrationality Modelling and Behavior Inducement in Pandemic Control

Understanding and modeling individuals’behaviors during epidemics is crucial for effective epidemic control.However,existing research ignores the impact of users’irrationality on decision-making in the epidemic.Meanwhile,existing disease control methods often assume users’full compliance with measures like mandatory isolation,which does not align with the actual situation.To address these issues,this paper proposes a prospect theorybased framework to model users’decision-making process in epidemics and analyzes how irrationality affects individuals’behaviors and epidemic dynamics.According to the analysis results,irrationality tends to prompt conservative behaviors when the infection risk is low but encourages risk-seeking behaviors when the risk is high.Then,this paper proposes a behavior inducement algorithm to guide individuals’behaviors and control the spread of disease.Simulations and real user tests validate our analysis,and simulation results show that the proposed behavior inducement algorithm can effectively guide individuals’behavior.

Modelling analysis embodies drastic transition among global potential natural vegetations in face of changing climate

Potential natural vegetation(PNV)is a valuable reference for ecosystem renovation and has garnered increasing attention worldwide.However,there is limited knowledge on the spatio-temporal distributions,transitional processes,and underlying mechanisms of global natural vegetation,particularly in the case of ongoing climate warming.In this study,we visualize the spatio-temporal pattern and inter-transition procedure of global PNV,analyse the shifting distances and directions of global PNV under the influence of climatic disturbance,and explore the mechanisms of global PNV in response to temperature and precipitation fluctuations.To achieve this,we utilize meteorological data,mainly temperature and precipitation,from six phases:the Last Inter-Glacial(LIG),the Last Glacial Maximum(LGM),the Mid Holocene(MH),the Present Day(PD),2030(20212040)and 2090(2081–2100),and employ a widely-accepted comprehensive and sequential classification sy–stem(CSCS)for global PNV classification.We find that the spatial patterns of five PNV groups(forest,shrubland,savanna,grassland and tundra)generally align with their respective ecotopes,although their distributions have shifted due to fluctuating temperature and precipitation.Notably,we observe an unexpected transition between tundra and savanna despite their geographical distance.The shifts in distance and direction of five PNV groups are mainly driven by temperature and precipitation,although there is heterogeneity among these shifts for each group.Indeed,the heterogeneity observed among different global PNV groups suggests that they may possess varying capacities to adjust to and withstand the impacts of changing climate.The spatio-temporal distributions,mutual transitions and shift tendencies of global PNV and its underlying mechanism in face of changing climate,as revealed in this study,can significantly contribute to the development of strategies for mitigating warming and promoting re-vegetation in degraded regions worldwide.

Investigation of Maxima Assumptions in Modelling Tropical Cyclone- Induced Hazards in the South China Sea

The present study aims to examine the suitability of two commonly used assumptions that simplify modelling metoceanconditions for designing offshore wind turbines in the South China Sea (SCS). The first assumption assumes thatjoint N-year extreme wind and wave events can be independently estimated and subsequently combined. The secondone assumes peak wind and waves can be modelled as occurring simultaneously during a tropical cyclone (TC) event.To better understand the potential TC activity, a set of 10000 years synthetic TC events are generated. The wind fieldmodel and the Mike 21 spectral wave model are employed to model the TC-induced hazards. Subsequently, theeffect of the assumptions is evaluated by analyzing the peak structural response of both monopile and semisubmersibleoffshore wind turbines during TC events. The results demonstrate that the examined assumptions are generally accurate.By assessing the implications of these assumptions, valuable insights are obtained, which can inform andimprove the modelling of TC-induced hazards in the SCS region.

Discrete Element Modelling of Damage Evolution of Concrete Considering Meso-Structure of ITZ

The mechanical properties of interfacial transition zones(ITZs)have traditionally been simplified by reducing the stiffness of cement in previous simulation methods.A novel approach based on the discrete element method(DEM)has been developed for modeling concrete.This new approach efficiently simulates the meso-structure of ITZs,accurately capturing their heterogeneous properties.Validation against established uniaxial compression experiments confirms the precision of thismodel.The proposedmodel canmodel the process of damage evolution containing cracks initiation,propagation and penetration.Under increasing loads,cracks within ITZs progressively accumulate,culminating in macroscopic fractures that traverse themortarmatrix,forming the complex,serpentine path of cracks.This study reveals four distinct displacement patterns:tensile compliant,tensile opposite,mixed tensile-shear,and shear opposite patterns,each indicative of different stages in concrete’s damage evolution.The widening angle of these patterns delineates the progression of cracks,with the tensile compliant pattern signaling the initial crack appearance and the shear opposite pattern indicating the concrete model’s ultimate failure.

Numerical Modelling of Coupled Heat and Mass Transfer in Porous Materials: Application to Cinder Block Bricks

In this work, we present numerical modelling of coupled heat and mass transfer within porous materials. Our study focuses on cinder block bricks generally used in building construction. The material is assumed to be placed in air. Moisture content and temperature have been chosen as the main transfer drivers and the equations governing these transfer drivers are based on the Luikov model. These equations are solved by an implicit finite difference scheme. A Fortran code associated with the Thomas algorithm was used to solve the equations. The results show that heat and mass transfer depend on the temperature of the air in contact with the material. As this air temperature rises, the temperature within the material increases, and more rapidly at the material surface. Also, thermal conductivity plays a very important role in the thermal conduction of building materials and influences heat and mass transfer in these materials. Materials with higher thermal conductivity diffuse more heat.

A framework for dynamic modelling of railway track switches considering the switch blades,actuators and control systems

The main contribution of this paper is the development and demonstration of a novel methodology that can be followed to develop a simulation twin of a railway track switch system to test the functionality in a digital environment.This is important because,globally,railway track switches are used to allow trains to change routes;they are a key part of all railway networks.However,because track switches are single points of failure and safety-critical,their inability to operate correctly can cause significant delays and concomitant costs.In order to better understand the dynamic behaviour of switches during operation,this paper has developed a full simulation twin of a complete track switch system.The approach fuses finite element for the rail bending and motion,with physics-based models of the electromechanical actuator system and the control system.Hence,it provides researchers and engineers the opportunity to explore and understand the design space around the dynamic operation of new switches and switch machines before they are built.This is useful for looking at the modification or monitoring of existing switches,and it becomes even more important when new switch concepts are being considered and evaluated.The simulation is capable of running in real time or faster meaning designs can be iterated and checked interactively.The paper describes the modelling approach,demonstrates the methodology by developing the system model for a novel“REPOINT”switch system,and evaluates the system level performance against the dynamic performance requirements for the switch.In the context of that case study,it is found that the proposed new actuation system as designed can meet(and exceed)the system performance requirements,and that the fault tolerance built into the actuation ensures continued operation after a single actuator failure.

Modelling the monthly hydrological balance using Soil and Water Assessment Tool(SWAT)model:A case study of the Wadi Mina upstream watershed

Modelling the hydrological balance in semi-arid zones is essential for effective water resource management,encompassing both surface water and groundwater.This study aims to model the monthly hydrological water cycle in the Wadi Mina upstream watershed(northwest Algeria)by applying the Soil and Water Assessment Tool(SWAT)hydrological model.SWAT modelling integrates spatial data such as the Digital Elevation Model(DEM),land use,soil types and various meteorological parameters including precipitation,maximum and minimum temperatures,relative humidity,solar radiation and wind speed.The SWAT model was calibrated and validated using data from January 2012 to December 2014,with a calibra-tion period from January 2012 to August 2013 and a validation period from September 2013 to December 2014.Sensitivity and parameter calibration were conducted using the SWAT-SA program,and model performance evaluation relied on comparing the observed discharge at the outlet of the basin with model-simulated discharge,assessed through statistical coefficients including Nash-Sutcliffe Efficiency(NSE),coefficient of determination(R2)and Percent Bias(PBAIS).Calibration results indicated favourable objec-tive function values(NSE=0.79,R2=0.93,PBAIS=-8.53%),although a slight decrease was observed during validation(NSE=0.69,R2=0.86,and PBAIS=-11.41%).The application of the SWAT model to the Wadi Mina upstream watershed highlighted its utility in simulating the spatial distribution of different components of the hydrological balance in this basin.The SWAT model revealed that approximately 71%of the precipitation in the basin evaporates,while only 29%contributes to surface runoff or infiltration into the soil.

Modelling the viscoplastic behaviour of Callovo-Oxfordian claystone with consideration of damage effect

In order to evaluate the performance of deep geological disposal of radioactive waste,an underground research laboratory(URL)was constructed by Andra in the Callovo-Oxfordian(COx)claystone formation at the Meuse/Haute-Marne(MHM).The construction of URL induced the excavation damage of host formations,and the ventilation in the galleries desaturated the host formation close to the gallery wall.Moreover,it is expected that the mechanical behaviour of COx claystone is time-dependent.This study presents a constitutive model developed to describe the viscoplastic behaviour of unsaturated and damaged COx claystone.In this model,the unsaturation effect is considered by adopting the Bishop effective stress and the van Genuchten(VG)water retention model.In terms of the viscoplastic behaviour,the nonstationary flow surface(NSFS)theory for unsaturated soils is used with consideration of the coupled effects of strain rate and suction on the yield stress.A progressive hardening law is adopted.Meanwhile,a non-associated flow rule is used,which is similar to that in Barcelona basic model(BBM).In addition,to describe the damage effect induced by suction change and viscoplastic loading,a damage function is defined based on the crack volume proportion.This damage function contains two variables:unsaturated effective stress and viscoplastic volumetric strain,with the related parameters determined based on the mercury intrusion porosimetry(MIP)tests.For the model validation,different tests on COx claystone under different loading paths are simulated.Comparisons between experimental and simulated results indicated that the present model is able to well describe the viscoplastic behaviour of damaged COx claystone,including swelling/shrinkage,triaxial extension and compression,and triaxial creep.

Enhanced UAV Pursuit-Evasion Using Boids Modelling:A Synergistic Integration of Bird Swarm Intelligence and DRL

TheUAV pursuit-evasion problem focuses on the efficient tracking and capture of evading targets using unmanned aerial vehicles(UAVs),which is pivotal in public safety applications,particularly in scenarios involving intrusion monitoring and interception.To address the challenges of data acquisition,real-world deployment,and the limited intelligence of existing algorithms in UAV pursuit-evasion tasks,we propose an innovative swarm intelligencebased UAV pursuit-evasion control framework,namely“Boids Model-based DRL Approach for Pursuit and Escape”(Boids-PE),which synergizes the strengths of swarm intelligence from bio-inspired algorithms and deep reinforcement learning(DRL).The Boids model,which simulates collective behavior through three fundamental rules,separation,alignment,and cohesion,is adopted in our work.By integrating Boids model with the Apollonian Circles algorithm,significant improvements are achieved in capturing UAVs against simple evasion strategies.To further enhance decision-making precision,we incorporate a DRL algorithm to facilitate more accurate strategic planning.We also leverage self-play training to continuously optimize the performance of pursuit UAVs.During experimental evaluation,we meticulously designed both one-on-one and multi-to-one pursuit-evasion scenarios,customizing the state space,action space,and reward function models for each scenario.Extensive simulations,supported by the PyBullet physics engine,validate the effectiveness of our proposed method.The overall results demonstrate that Boids-PE significantly enhance the efficiency and reliability of UAV pursuit-evasion tasks,providing a practical and robust solution for the real-world application of UAV pursuit-evasion missions.

Key Issues for Modelling, Operation, Management and Diagnosis of Lithium Batteries: Current States and Prospects

1 Introduction.With the continuous growth of the global population,the energy demand continues to increase.However,due to the dominance of fossil fuels in global energy and fossil fuels are non-renewable,it has led to the global energy crisis[1].Besides,the use of fossil fuels will generate a mass of air pollutants(e.g.,carbon dioxide,sulfur dioxide,etc.),which will cause serious environmental pollution,climate change[2],etc.To resolve the aforementioned issues,countries around the world have implemented a variety of measures hoping to fundamentally adjust the global energy structure and achieve sustainable development.Thereinto,“Paris Agreement”reached in 2015 under the framework of“United Nations Framework Convention on Climate Change”aims to control the increase in the average temperature of the globe to within 2°C below preindustrial levels,and thereafter to peak global greenhouse gas emissions as soon as possible,continuously decreasing thereafter[3].United Kingdom plans to reduce the average exhaust emissions of“new cars”to approximately 50–70 g/km by 20230,which is roughly half of what it is now[4].In addition,China proposed a plan at“United Nations General Assembly”in 2020 to peak carbon dioxide emissions by 2030 and strive to achieve carbon neutrality by 2060.It is a fact that the whole world is committed to changing the current energy structure,protecting the Earth’s ecology,and achieving global sustainable development[5].

Nucleation of Supercooled Water by Neutrons: Latitude Dependence and Implications for Cloud Modelling

It has recently been shown that incident particles, neutrons, can initiate the freezing in a supercooled water volume. This new finding may have ramifications for the interpretation of both experimental data on the nucleation of laboratory samples of supercooled water and perhaps more importantly on the interpretation of ice nucleation involved in cloud physics. For example, if some fraction of the cloud nucleation previously attributed to dust, soot, or aerosols has been caused by cosmogenic neutrons, fresh consideration is required in the context of climate models. Moreover, as cosmogenic neutrons, most being muon-induced, have much greater flux at high latitudes, estimates of ice nucleates in these regions may be larger than required to accurately model cloud and condensation properties. This discrepancy has been pointed out in IPCC reports. Our paper discusses the connection between the new concept of neutrons nucleating supercooled water and the need for a new source of nucleation in high latitude clouds, ideally causing others to review current data, or to analyse future data with this idea in mind. .

Assessment of sediment connectivity using modelling and field-based approaches in the Slavíč River catchment(MoravskoslezskéBeskydy Mts,Czech Republic)

Mountain streams act as conveyors of sediments within the river continuum,where the physical transport of sediments between river reaches through the catchment or between individual parts(e.g.,between hillslopes and channels)of the catchment is assumed.This study focused on sediment connectivity analysis in the SlavíčRiver catchment in the MoravskoslezskéBeskydy Mts in the eastern part of the Czech Republic.The connectivity index and connectivity index target modelling were combined with an analysis of anthropogenic interventions.Additionally,field mapping,grain size of bed sediments and stream power analysis were used to obtain information about connectivity in the catchment.Based on the analysis and obtained results,terrain topography is the current main driving factor affecting the connectivity of sediment movement in the SlavíčRiver catchment.However,the modelling provided valuable information about high sediment connectivity despite different recent land use conditions(highly forested area of the catchment)than those in historical times from the 16th to 19th centuries when the SlavíčRiver catchment was highly deforested and sediment connectivity was probably higher.The analysis of anthropogenic interventions,field mapping,grain size of bed sediments and stream power analysis revealed more deceleration of sediment movement through the catchment,decreased sediment connectivity with bed erosion,and gradual river channel process transformation in some reaches.Field mapping has identified various natural formations and human-induced changes impacting the longitudinal and lateral connectivity in the SlavíčRiver.For instance,embankments along 48%of the river's length,both on the right and left banks,significantly hinder lateral sediment supply to the channel.Stream power index analysis indicates increased energy levels in the flowing water in the river's upper reaches(up to 404.8 W m^(-2)).This high energy is also observed in certain downstream sections(up to 337.6 W m^(-2)),where it is influenced by human activities.These conditions lead to intensified erosion processes,playing a crucial role in sediment connectivity.Similar observations were described in recent studies that pointed out the long-term human interventions on many streams draining European mountains,where a decrease in sediment connectivity in these streams is linked with sediment deficits and the transformation of processes forming channels.

Drivers for Inter-city Innovation Networks Across Chinese Cities:Modelling Physical Versus Intangible Effects

Cross-region innovation is widely recognized as an important source of the long-term regional innovation capacity.In the recent past,a growing number of studies has investigated the network structure and mechanisms of cross-region innovation collaboration in various contexts.However,existing research mainly focuses on physical effects,such as geographical distance and high-speed railway connections.These studies ignore the intangible drivers in a changing environment,the more digitalized economy and the increasingly solidified innovation network structure.Thus,the focus of this study is on estimating determinants of innovation networks,especially on intangible drivers,which have been largely neglected so far.Using city-level data of Chinese patents(excluding Hong Kong,Macao,and Taiwan Province of China),we trace innovation networks across Chinese cities over a long period of time.By integrating a measure on Information and Communications Technology(ICT)development gap and network structural effects into the general proximity framework,this paper explores the changing mechanisms of Chinese innovation networks from a new perspective.The results show that the structure of cross-region innovation networks has changed in China.As mechanisms behind this development,the results confirm the increasingly important role of intangible drivers in Chinese inter-city innovation collaboration when controlling for effects of physical proximity,such as geographical distance.Since digitalization and coordinated development are the mainstream trends in China and other developing countries,these countries'inter-city innovation collaboration patterns will witness dramatic changes under the influence of intangible drivers.

Modelling and Sizing of a Floor Reinforced by Ballasted Columns Intended to Support a Tank

This work aims to study the modeling and sizing of a floor reinforced by ballasted columns. We are studying the system of reinforcement by ballasted columns because this technique is able to replace deep foundations that are technically difficult to realize and their cost is higher. The modelling and dimensioning of foundations on a ballasted column will be an important contribution to the state of the art of this method because it will highlight the mode of transfer of loads, and will expose the induced deformations by also allowing to verification criteria of bearing capacity and allowable settlement according to geometric information of the model. The columns on a substrate located at 9 m have a length of 9 m and a diameter of 40 cm and were obtained by incorporating ballast of granular class 0/31.5 of internal friction angle of 38˚ and a density weight of 21 kN/m3. The choice of this method is based on the geotechnical characteristics of the initial soil. Thus, identification and characterization tests were carried out to estimate the bearing capacity and the settlement giving respectively 125 kPa and 57 cm. These results show the ground does not have sufficient mechanical properties to withstand the loads transmitted by the tank. By adopting the reinforcement of the soil with ballasted columns, numerical calculations show that after applying a load equal to 265.1 KPa, 20 cm vertical settlement and 17 cm horizontal displacement were obtained. This is in the tolerable deformation range for our tank, namely, less than 20 cm. Analytically, in addition to reducing settlement, ballasted columns, Due to their high stiffness, they have effectively contributed to the increase of the permissible soil stress up to 257 kPa.

Contribution to the Full 3D Finite Element Modelling of a Hybrid Stepping Motor with and without Current in the Coils

The paper presents our contribution to the full 3D finite element modelling of a hybrid stepping motor using COMSOL Multiphysics software. This type of four-phase motor has a permanent magnet interposed between the two identical and coaxial half stators. The calculation of the field with or without current in the windings (respectively with or without permanent magnet) is done using a mixed formulation with strong coupling. In addition, the local high saturation of the ferromagnetic material and the radial and axial components of the magnetic flux are taken into account. The results obtained make it possible to clearly observe, as a function of the intensity of the bus current or the remanent induction, the saturation zones, the lines, the orientations and the magnetic flux densities. 3D finite element modelling provide more accurate numerical data on the magnetic field through multiphysics analysis. This analysis considers the actual operating conditions and leads to the design of an optimized machine structure, with or without current in the windings and/or permanent magnet.