Efficient Modeling Method Research Articles

3D electromagnetic modelling for high‐temperature superconducting dynamo flux pumps using T‐A formulation

AbstractA high‐temperature superconducting (HTS) dynamo flux pump can inject DC currents into closed‐loop HTS magnets without contact. It enables the realisation of current‐lead‐free or even through‐wall charging systems for high‐field applications such as nuclear magnetic resonance/magnetic resonance imaging (MRI) magnets, fusion reactors and accelerators. Researchers have proposed many simulation models to understand the working principle of HTS dynamos, few of which are in 3D because of converging problems. Therefore, the influences of many key 3D parameters in the HTS dynamo are scarcely reported. The authors propose an efficient 3D modelling method of the HTS dynamo based on the T‐A formulation. The rotating magnets are modelled by a ring‐shaped permanent magnet with space‐time‐variant remanent flux density to avoid moving meshes. This, together with the T‐A formulation, makes the 3D model efficient and universal. The accuracy of the model is verified by the experimental instantaneous and time‐integrated dynamic voltages. Using this model, the authors present systematic case studies to thoroughly explore the influences of the key parameters of a dynamo flux pump on the dynamic voltage and losses. The proposed modelling method and results could significantly benefit the design and optimisation of HTS dynamos for high‐field magnets.

Modeling of two-stage anaerobic onsite wastewater sanitation system to predict effluent soluble chemical oxygen demand through machine learning

The present research aims to predict effluent soluble chemical oxygen demand (SCOD) in anaerobic digestion (AD) process using machine-learning based approach. Anaerobic digestion is a highly sensitive process and depends upon several environmental and operational factors, such as temperature, flow, and load. Therefore, predicting output characteristics using modeling is important not only for process monitoring and control, but also to reduce the operating cost of the treatment plant. It is difficult to predict COD in a real time mode, so it is better to use Complex Mathematical Modeling (CMM) for simulating AD process and forecasting output parameters. Therefore, different Machine Learning algorithms, such as Linear Regression, Decision Tree, Random Forest and Artificial Neural Networks, have been used for predicting effluent SCOD using data acquired from in situ anaerobic wastewater treatment system. The result of the predicted data using different algorithms were compared with experimental data of anaerobic system. It was observed that the Artificial Neural Networks is the most effective simulation technique that correlated with the experimental data with the mean absolute percentage error of 10.63 and R2 score of 0.96. This research proposes an efficient and reliable integrated modeling method for early prediction of the water quality in wastewater treatment.

A Fast Dynamic Simulation Method of an Active Distribution Network with Distributed Generations Based on Decomposition and Coordination

With the penetration of distributed resources into power distribution networks, power distribution networks are transforming into active distribution networks with a high proportion of distributed generations and power electronic equipment. Efficient modeling and simulation methods are essential to perform dynamic response analysis. In order to satisfy the fast/steady/slow multiple time-scale simulation requirements of active distribution networks, a fast/medium/slow time partition model and a network decoupling method for short line characteristic lines is proposed in this paper. Through the decomposition coordination simulation method, the network is decomposed into multiple regions that can be simulated in parallel. Based on the interconnection of fiber optic network cards, a multi-rate parallel simulation and synchronization strategy is proposed, which significantly improves the simulation speed of active distribution networks while ensuring simulation accuracy. The numerical experiments have been conducted based on a modified IEEE 33-bus and a PG&E 69-bus, and simulation results show the feasibility of the proposed method. The verification results of the example show that using adaptive variable-step-size multi-rate parallel simulation technology can increase the subnet computation-time balance rate and simulation acceleration ratio to 119.90% and 121.31% in the same rate-parallel mode.

Refined modelling methods of structural reinforcements in the analysis of masonry bridges

Masonry arch bridges constitute a large part of today’s Italian architectural heritage. Italy has the highest percentage in Europe of masonry railway bridges with respect to the total. Due to the processes of degradation and to the increased levels of the loads and of the safety requirements, rehabilitation and retrofitting of these bridges is required. Among the available reinforcement techniques, the use of reinforcements with mortar/cement matrix fiber nets has gained great popularity due to the advantages shown over traditional techniques in terms of strength and durability. The FRCM, acronym of “Fiber Reinforced Cementitious Matrix” is a valid reinforcement alternative to the use of polymeric matrix reinforcements, due to its greater compatibility with the masonry support. The Italian technical standards suggest a simplified method for the design of the reinforcement based on empirical coefficients that increase the mechanical properties of the masonry materials, disregarding the consideration of the complex crisis mechanisms occurring, especially in more complex systems like the multi-arch bridges.The object of this work is the definition of a more refined and efficient method for the numerical modeling of FRCM reinforcement in the structural analysis of multi-span masonry arch bridge. Specifically, an equivalent reduced nets embedded in a mortar continuum determined with the area equivalence principle.The model is calibrated based on experimental characterization tests carried out on PBO-Mesh, and on the constituents. A validation test of the model is performed with reference to arch models reinforced with PBO-Mesh experimentally tested.The effectiveness of the proposed approaches is verified analyzing the seismic behavior of a masonry multi-span bridge, also considering the soil-structure interaction.

An efficient surrogate model for damage forecasting of composite laminates based on deep learning

In this paper, full-field damage forecasting of a laminated composite structure under different low velocity impact (LVI) conditions is realized through the proposed surrogate model, named VQ-SM. First, an efficient surrogate modelling method is proposed based on the advanced Vector Quantised-Variational AutoEncoder (VQ-VAE) proposed by DeepMind. Second, numerical simulation based on the progressive damage model of composite laminates is performed to obtain the training dataset. After training, the performance of VQ-SM is evaluated compared to the surrogate model without a representation learning process. The results show that VQ-SM has better performance with high-precise and good robustness, trained on the small dataset. Finally, the impact damage field of composite laminates is analyzed based on the surrogate model. The proposed surrogate modelling method provides not only the full-field damage forecast model for composite structures, but also an efficient method of improving the performance of the “generative” surrogate model.

Study on seismic behavior and collapse risk of super high-rise braced mega frame-core tube structural system

The braced mega frame-core tube (BMFCT) structure could provide an efficient lateral-force resisting (LFR) system for high-rise or super high-rise buildings, especially for those higher than 500 m. The BMFCT structure is a dual LFR system, including the outer braced mega frame and the inner core tube. The seismic behavior and design method of this structural system is not clear. In this study, a parametric study based on collapse risk-targeted analysis is conducted to clarify seismic mechanism and performance and to make clear means of matching reasonable stiffness and setting energy-dissipation components. Five comparable BMFCT structures with different mega brace stiffness proportions and frame-tube stiffness ratios are designed. An efficient elasto-plastic modeling method is introduced to establish the accurate FE models. The corresponding collapse risks are calculated through Incremental Dynamic Analysis and fragility theory. The results show that the structural collapse risk increases with the increased frame-tube stiffness ratio. Therefore，the stiffness and bearing capacity of peripheral frames should be strengthened to ensure the structural collapse margin. On the other hand, the collapse resistance capacity gradually decreases with the increasing of the mega brace stiffness. Thus, the stiffness proportion of mega braces should be recommended to meet the basic lateral stiffness requirements, which shall not exceed 35 % of the overall structural stiffness. Moreover, the distribution feature and ideal arrangement of the energy dissipation components are proposed. The seismic design recommendation based on the uniform collapse risk is also proposed for the BMFCT system, which serves a reference for the structural design of super high-rise buildings.

Active learning-driven control point optimization method for efficient modeling of complex stiffened curved shells

The mesh-mapping technique has recently garnered significant attention due to its ability to model stiffened curved shells accurately. The precision of the modeling depends on the number of control points, particularly for complex stiffened curved shells. However, using too many control points results in a time-consuming process of model training and mapping, thereby impeding the structural optimization efficiency. To overcome this challenge, this study proposes an active learning (AL) function that considers the mechanical response and uncertainty of stiffened curved shells. This function is applied to select control points of the radial basis function (RBF) model. The control points with the most substantial AL function value are added to the control point set, and the process is iterated until convergence is achieved. Additionally, the proposed method is compared to other AL strategies to confirm its high efficiency. Furthermore, a data-driven optimization approach, based on the deep neural network method, is employed to minimize the weight of the complex stiffened curved shells. Finally, two engineering examples are presented to verify the effectiveness of the proposed method, which reduces the modeling time by 83.87% and 66.29%, respectively, in comparison to using all control points in mesh-mapping. Additionally, the total time of modeling and optimization is decreased by 42.63% and 59.35%, respectively. In conclusion, the proposed control point optimization method based on active learning-driven for complex stiffened curved shells has substantial potential in efficient modeling, significantly reducing the time of mesh-mapping modeling, and improving engineering’s optimization efficiency.

A divergence-free vector finite-element method for efficient 3D magnetotelluric forward modeling

For large-scale magnetotelluric (MT) forward modeling using vector finite-element methods, iterative solvers are commonly applied. However, as frequency decreases close to zero, the iterative solution process struggles to converge. This is mainly caused by the fact that the weak conductivity term in the curl-curl equation governing the electromagnetic (EM) diffusion in the earth fades during the iterative solution for EM fields. This can lead to violation of the divergence-free condition for current and false jumps in the calculated fields. We develop a regularization technique for vector finite-element MT forward modeling, in which a scaled grad-div operator for electrical fields is included in the curl-curl equation to enforce the divergence-free condition explicitly. Because of its use of basis functions, the direct edge element discretization of the scaled term can lead to zero coefficients. To address this, an equivalent substitute of the scaled grad-div operator based on potential representation of electrical fields is used, discretized with node elements. For one specific element, this is finally reduced to a scaled gradient of the surface integral of current across all the surfaces of the element, resulting in better connectivity of the linear system of equations. The correctness of our algorithm is verified with two synthetic models and an inversion model from real data. The numerical performance is compared to the traditional iterative divergence correction technique (and without the application of the divergence correction for one case) for each of the three models. The results indicate that our algorithm is generally more efficient and stable compared to the traditional technique for all models at all periods considered, with significant improvement at long periods.

Efficient 3D Frequency Semi-Airborne Electromagnetic Modeling Based on Domain Decomposition

Landslides are common geological hazards that often result in significant casualties and economic losses. Due to their occurrence in complex terrain areas, conventional geophysical techniques face challenges in early detection and warning of landslides. Semi-airborne electromagnetic (SAEM) technology, utilizing unmanned aerial platforms for rapid unmanned remote sensing, can overcome the influence of complex terrain and serve as an effective approach for landslide detection and monitoring. In response to the low computational efficiency of conventional semi-airborne EM 3D forward modeling, this study proposes an efficient forward modeling method. To handle arbitrarily complex topography and geologic structures, the unstructured tetrahedron mesh is adopted to discretize the earth. Based on the vector finite element formula, the Dual–Primal Finite Element Tearing and Interconnecting (FETI-DP) method is further applied to enhance modeling efficiency. It obtains a reduced order subsystem and avoids directly solving huge overall linear equations by converting the entirety problem into the interface problem. We check our algorithm by comparing it with 1D semi-analytical solutions and the conventional finite element method. The numerical experiments reveal that the FETI-DP method utilities less memory and exhibits higher computation efficiency than the conventional methods. Additionally, we compare the electromagnetic responses with the topography model and flat earth model. The comparison results indicate that the effect of topography cannot be ignored. Further, we analyze the characteristic of electromagnetic responses when the thickness of the aquifer changes in a landslide area. We demonstrate the effectiveness of the 3D SAEM method for landslide detection and monitoring.

Numerical Simulation of 2D Strong Magnetic Field in Space-Wavenumber Mixed Domain

Strong magnetic body has self-demagnetization effect, which is not conducive to processing and interpretation of magnetic measurement data. A 2D numerical simulation method in the spatial-wavenumber mixed domain is proposed to calculate magnetic anomalies of 2D strong magnetic objects. In this method, the partial differential equation satisfying the magnetic potential of 2D strong magnetic body is transformed into independent ordinary differential equation between different wave numbers by 1D FFT, which greatly reduces the computation and storage requirements. The compact operator is used to solve the strong magnetic field by iterative method. The algorithm provides a new efficient and high-precision method for the forward modeling of the 2D magnetic anomalies.

Universal and efficient hybrid modeling and direct slicing method for additive manufacturing processes

Universal and efficient hybrid modeling and direct slicing method for additive manufacturing processes

On the crashworthiness of aperiodic chiral mechanical metamaterials: design and modeling method

Chiral mechanical metamaterial has become topical in energy absorption for the unusual compression-to-twist deformation determined by the asymmetric chirality geometry of their microstructures. However, the insufficient research on the dynamic crash behavior with high nonlinearity and the lack of efficient design and modeling method have blocked the development of chiral mechanical metamaterials considering crashworthiness. In this work, the structure-property relationship of chiral mechanical metamaterials under medium-strain-rate impact was systematically investigated. We proposed an aperiodic framework considering additive manufacturing which enabled both the ordered and disordered chiral mechanical metamaterials utilizing a screw-theory-based assembly rule. The strut components had variable cross-sections and the joints were fillet-enhanced in order to improve the compressive performance. Meanwhile, the corresponding efficient modeling method for finite element analysis (FEA) was introduced. The constitutive relation, damage criteria, and damage revolution of the 316L stainless steel were established considering strain rate effect. Finally, the deformation mechanisms and energy absorbing capabilities of the proposed chiral mechanical metamaterials were demonstrated and discussed based on the mechanical behaviors and the proposed chirality indexes. The numerical results indicated that the proposed design and modeling method provided an effective paradigm for the crashworthiness design of light-weight materials and structures, facilitating the further applications in fields of automobile, civil engineering, aerospace, etc.

Finite Element Analysis-Based Blast Performance Evaluation for Reinforced Concrete Columns with Shear and Flexure Failure Modes

Blast loads have significantly damaged non-ductile reinforced concrete building structures with seismically deficient column details, which have lower shear capacity than the building structures with the current code-required details. This paper aims to evaluate the blast performance of non-ductile (shear-governed) and ductile (flexure-governed) RC columns using ductility- and residual capacity-based performance limits. To accomplish this research goal, the shear- and flexure-governed RC column models were developed using a finite element method and validated with previous experimental results. The efficient blast modeling method representing the reflected and incident waves was implemented in the validated column models, and these were simulated under various blast loading scenarios. The blast-induced responses for each column were investigated and utilized to determine the performance levels using the two different performance limits. The flexure-governed column model has higher performance levels than the shear-governed column model because of the lower ductility capacity of the shear-governed column model. The residual capacity-based performance level of the shear-governed column was underestimated compared to the ductility-based limits specified in a current design code.

Universal machine learning for the response of atomistic systems to external fields

Machine learned interatomic interaction potentials have enabled efficient and accurate molecular simulations of closed systems. However, external fields, which can greatly change the chemical structure and/or reactivity, have been seldom included in current machine learning models. This work proposes a universal field-induced recursively embedded atom neural network (FIREANN) model, which integrates a pseudo field vector-dependent feature into atomic descriptors to represent system-field interactions with rigorous rotational equivariance. This “all-in-one” approach correlates various response properties like dipole moment and polarizability with the field-dependent potential energy in a single model, very suitable for spectroscopic and dynamics simulations in molecular and periodic systems in the presence of electric fields. Especially for periodic systems, we find that FIREANN can overcome the intrinsic multiple-value issue of the polarization by training atomic forces only. These results validate the universality and capability of the FIREANN method for efficient first-principles modeling of complicated systems in strong external fields.

Deep learning-based modeling method for probabilistic LCF life prediction of turbine blisk

Turbine blisk is one of the typical components of gas turbine engines. The fatigue life of turbine blisk directly affects the reliability and safety of both turbine blisk and aeroengine whole-body. To monitor the performance degradation of an aeroengine, an efficient deep learning-based modeling method called convolutional-deep neural network (C-DNN) method is proposed by absorbing the advantages of both convolutional neural network (CNN) and deep neural network (DNN), to perform the probabilistic low cycle fatigue (LCF) life prediction of turbine blisk regarding uncertain influencing parameters. In the C-DNN method, the CNN method is used to extract the useful features of LCF life data by adopting two convolutional layers, to ensure the precision of C-DNN modeling. The two close-connected layers in DNN are employed for the regression modeling of aeroengine turbine blisk LCF life, to keep the accuracy of LCF life prediction. Through the probabilistic analysis of turbine blisk and the comparison of methods (ANN, CNN, DNN and C-DNN), it is revealed that the proposed C-DNN method is an effective mean for turbine blisk LCF life prediction and major factors affecting the LCF life were gained, and the method holds high efficiency and accuracy in regression modeling and simulations. This study provides a promising LCF life prediction method for complex structures, which contribute to monitor health status for aeroengines operation.

Kinetostatics modeling and elasto-geometrical calibration of overconstrained parallel manipulators

Overconstrained parallel manipulators have garnered increasing attention due to their higher stiffness resulting from redundant wrenches and improved performance by eliminating clearances and backlashes through forced assembly, as compared to non-overconstrained counterparts. However, a challenge arises in calibrating these manipulators due to non-ideal geometry, which introduces mechanical strains in the structure. Consequently, identifying the geometrical errors of the manipulators becomes difficult without considering the effect of elastic deformations. The primary contribution of this work is to propose an efficient kinetostatic modeling and elasto-geometrical calibration method that enables simultaneous identification of both geometric parameters and compliance parameters in overconstrained parallel manipulators. Initially, a kinetostatic model considering both geometric errors and flexible deformations is proposed using an error equivalent method. Subsequently, a unified error model encompassing geometric and compliance parameters is derived through projection operations. To validate the effectiveness of the proposed method, experiments are conducted on a 3-DOF translational manipulator. The results demonstrate a significant reduction in residual errors of the manipulator using the proposed approach.

Mechanics, modeling, and shape optimization of electrostatic zipper actuators

Generating actuation for haptic feedback is a major challenge for wearable devices and soft robotics. Current methods such as piezoelectric, pneumatic, or responsive material actuators are limited by the response time, power consumption, and their reliance on external mechanisms such as pumps or large voltage amplifiers. The emerging technology of electrostatic zipper actuators, where a dielectric-filled pouch is sandwiched between flexible conducting electrodes, is a promising alternative. However, the voltage required to actuate such systems remains in the relatively large kilovolt range. Additionally, there do not currently exist efficient modeling methods to explore more effective designs. Our work looks to address both of these issues. We start by discussing the mechanics of the zipping phenomenon which leads to actuation. Then, we formulate a novel mechanics model for these systems. By considering an elastic plate coupled with the electrostatic interactions, we develop an efficient and robust numerical method to simulate the actuation process. We then verify the model by demonstrating excellent agreement to analytical predictions for simplified cases. As the complex physics of such systems create challenges for intuitive design, we turn to optimal design methods. We formulate the shape optimization problem through the method of mappings to design actuators for maximum actuation pressure and work of actuation. Our method navigates the trade-offs between zipping susceptibility and volume displacement, and we explore optimal designs for various geometric and loading scenarios. Finally, we discuss further directions and open problems relevant to the industrial deployment of zipper actuators moving forward.

A fast evaluation method of surrogate model based on active subspace dimension reduction

Aimed at the problem of high-dimensional uncertainty quantification commonly existing in engineering complex shapes, traditional methods are often time-consuming and energy-consuming. So the paper proposes an efficient surrogate model method based on active subspace dimension reduction. The method uses active subspace to achieve feature dimension reduction and construct surrogate model, and develops a fast evaluation method of 1-D active subspace based on polynomial least squares decomposition to solve the difficult derivative problems. The detailed implementation process of the method is given in the paper, and the feasibility of the method is verified by examples such as the ablation thermal response and RAE2822 airfoil. It provides a solution for the quantification of multivariate uncertainty in engineering.

Accurate and Efficient Surrogate Model-Assisted Optimal Design of Flux Reversal Permanent Magnet Arc Motor

An accurate and efficient surrogate model plays a significant role in the optimal design of electrical motors. This paper presents an accurate and efficient surrogate modeling method for a flux reversal permanent magnet arc motor (FR-PMAM) based on machine learning algorithm. Specifically, the motor topology and the optimized design of the FR-PMAM are firstly illustrated. Then, the PM magnetic motive force-permeance model is developed to select structural parameters of FR-PMAM. After that, a finite-element analysis (FEA) model of FR-PMAM is calculated to obtain sample data. A machine learning algorithm random forest is introduced into the field of motor optimal design for the first time to evaluate the contribution of each parameter to the design objectives. Based on the sample data, an efficient machine learning algorithm CatBoost is innovatively employed to establish the accurate and efficient surrogate model of the FR-PMAM that can capture the complex function relationship between output objectives and input parameters. Subsequently, an improved genetic algorithm with the elitist reservation strategy is adopted to obtain the optimal combination of the structural parameters of FR-PMAM. Finally, a prototype of the FR-PMAM is manufactured. The FEA and experimental results validate the effectiveness of the investigated surrogate modeling method.

An efficient gradient-enhanced kriging modeling method assisted by fast kriging for high-dimension problems

PurposeThe modeling cost of the gradient-enhanced kriging (GEK) method is prohibitive for high-dimensional problems. This study aims to develop an efficient modeling strategy for the GEK method.Design/methodology/approachA two-step tuning strategy is proposed for the construction of the GEK model. First, an auxiliary kriging is built efficiently. Then, the hyperparameter of the kriging model is served as a good initial guess to that of the GEK model, and a local optimal search is further used to explore the search space of hyperparameter to guarantee the accuracy of the GEK model. In the construction of the auxiliary kriging, the maximal information coefficient is adopted to estimate the relative magnitude of the hyperparameter, which is used to transform the high-dimension maximum likelihood estimation problem into a one-dimensional optimization. The tuning problem of the auxiliary kriging becomes independent of the dimension. Therefore, the modeling efficiency can be improved significantly.FindingsThe performance of the proposed method is studied with analytic problems ranging from 10D to 50D and an 18D aerodynamic airfoil example. It is further compared with two efficient GEK modeling methods. The empirical experiments show that the proposed model can significantly improve the modeling efficiency without sacrificing accuracy compared with other efficient modeling methods.Originality/valueThis paper developed an efficient modeling strategy for GEK and demonstrated the effectiveness of the proposed method in modeling high-dimension problems.