Efficient Modeling Method Research Articles

A finite element based state-space approach for vibration analysis of slender explosive clad pipe with partial contact defect

Abstract An efficient modeling method is presented in this paper for vibration analysis of explosive clad pipe with partial contact defect (PCD). The principal purpose is to study the effects of the PCD on the vibration characteristics of explosive clad pipe and to explore effective techniques for detecting the PCD. The slender explosive clad pipe is regarded as two parallel elastic beams continuously joined by a virtual Winkler/Pasternak type viscoelastic layer, and the virtual layer is capable to describe the non-uniform bonding state such as the PCD. By means of finite element method and the standard linear solid (SLS) model, a state-space model of explosive clad pipe with inhomogeneous bonding state is developed for the fields of axial displacement and transverse displacement. The model can reflect the PCD pipe system under different boundary conditions and describe damping behavior of bonding interface. Experiments and numerical examples available in the literature demonstrate the accuracy and reliability of proposed approach. Finally, numerical results are presented and show that the PCD have significant effect on the natural frequencies and forced response in high-frequency domain. A potential method for identifying the length and position of the PCD in explosive clad pipe is also discussed in this paper.

A new and efficient numerical method for the fractional modeling and optimal control of diabetes and tuberculosis co-existence.

The main objective of this research is to investigate a new fractional mathematical model involving a nonsingular derivative operator to discuss the clinical implications of diabetes and tuberculosis coexistence. The new model involves two distinct populations, diabetics and nondiabetics, while each of them consists of seven tuberculosis states: susceptible, fast and slow latent, actively tuberculosis infection, recovered, fast latent after reinfection, and drug-resistant. The fractional operator is also considered a recently introduced one with Mittag-Leffler nonsingular kernel. The basic properties of the new model including non-negative and bounded solution, invariant region, and equilibrium points are discussed thoroughly. To solve and simulate the proposed model, a new and efficient numerical method is established based on the product-integration rule. Numerical simulations are presented, and some discussions are given from the mathematical and biological viewpoints. Next, an optimal control problem is defined for the new model by introducing four control variables reducing the number of infected individuals. For the control problem, the necessary and sufficient conditions are derived and numerical simulations are given to verify the theoretical analysis.

An efficient high-order multiscale finite element method for frequency-domain elastic wave modeling

Solving the frequency-domain elastic wave equation in highly heterogeneous and complex media is computationally challenging. Conventional methods for solving the elastic wave Helmholtz equation usually lead to a large-dimensional linear system that is difficult to solve without specialized and sophisticated techniques. Based on the multiscale finite element theory, we develop a novel method to solve the frequency-domain elastic wave equation in complex media. The key feature of our method is employing high-order multiscale basis functions defined by solving local linear problems to achieve model reduction, which eventually leads to a linear system with significantly reduced dimensions. Solving this reduced linear system therefore results in obvious computational time reduction. We use three 2D examples to verify the accuracy and efficiency of our high-order multiscale finite element method for solving the Helmholtz equation in complex isotropic and anisotropic elastic media. The results show that our new method can approximate the fine-scale reference solution on the coarse mesh with high accuracy and significantly reduced computational time at the linear system solving stage.

Modeling dust dispersion and suspension pattern under turbulence

Controlling dust generation and minimizing volumetric dust concentration, within confined space, are key to the prevention of dust explosion. Dust dispersion pattern under pressure, such as primary explosion or dust leakage from equipment, can be simulated using unsteady state computational fluid dynamics – discrete phase models (CFD-DPMs). Although they offer computational efficiency, DPM simulations do not incorporate particle-wall or particle-particle interactions. In this paper, we therefore adapt the model to include particle-wall interaction based on energy conservation. In a confined volume, to experimentally observe the dust dispersion pattern, a theoretical concentration of 0.05 and 0.10 kg/m3 was generated and the turbulence was created with airflow of 2 and 10 m/s using an air compressor. Similar conditions were used to model the dust dispersion pattern. Our findings show that the dust concentration inside the confined chamber is not evenly distributed throughout its entirety and that explosive dust cloud concentration only takes up to 37.8% of a chamber's volume for a 0.10 kg/m³ injected dust concentration at 10 m/s air velocity. With a decrease in the dust injection rate and air velocity, the dust cloud volume decreased due to lesser amount of particles and low kinetic energy. This study presents an efficient dust dispersion modeling method, and the result shows the dust cloud volume is highly dependent on the dispersion velocity. The predicted dust concentration and the experimental results indicate that this boundary corrected CFD-DPM modeling approach is suitable for dilute particle dispersion flow, where the volume fraction of particles is lower and the adhered particles only form a single particle layer on the wall boundary.

Computational-Efficient Thermal Estimation for IGBT Modules Under Periodic Power Loss Profiles in Modular Multilevel Converters

One of the next challenges for modular multilevel converters (MMCs) is how to the size the critical components to their limits with reduced design margins, while at the same time fulfilling the reliability target. To do it confidently, better thermal modeling with quantitative uncertainty analysis is necessary to support the decision-making during the product design stage. Regarding the conversion of long-term mission profiles into thermal profiles for reliability evaluation, this paper proposes a computationally efficient thermal modeling method for insulated-gate bipolar transistor modules in MMCs. The proposed method considers the impact of the inherent thermal unbalance and has minimum computation with quantitative error analysis. Finally, both simulations and experiments have verified the theoretical results.

An efficient kriging modeling method for high-dimensional design problems based on maximal information coefficient

Kriging, one of the most popular surrogate models, is widely used in computationally expensive optimization problems to improve the design efficiency. However, due to the “curse-of-dimensionality,” the time for generating the kriging model increases exponentially as the dimension of the problem grows. When it comes to the cases that the kriging model needs to be frequently constructed, such as sequential sampling for kriging modeling or global optimization based on kriging model, the increased modeling time should be taken into consideration. To overcome this challenge, we propose a novel kriging modeling method which combines kriging with maximal information coefficient (MIC). Taking the features of the optimized hyper-parameters into consideration, MIC is utilized for estimating the relative magnitude of hyper-parameters. Then this knowledge of hyper-parameters is incorporated into the maximum likelihood estimation problem to reduce the dimensionality. In this way, the high dimensional optimization can be transformed into a one-dimensional optimization, which can significantly improve the modeling efficiency. Five representative numerical examples from 20-D to 80-D and an industrial example with 35 variables are used to show the effectiveness of the proposed method. Results show that compared with the conventional kriging, the modeling time of the proposed method can be ignored, while the loss of accuracy is acceptable. For the problems with more than 40 variables, the proposed method can even obtain a more accurate kriging model with given computational resources. Besides, the proposed method is also compared with KPLS (kriging combined with the partial least squares method), another state-of-the-art kriging modeling method for high-dimensional problems. Results show that the proposed method is more competitive than KPLS, which means the proposed method is an efficient kriging modeling method for high-dimensional problems.

Efficient reliability analysis of dynamic k-out-of-n heterogeneous phased-mission systems

In this paper, an efficient analytical modeling method is proposed for reliability analysis of k-out-of-n phased-mission systems (PMSs). A PMS is a system involving multiple, consecutive and non-overlapping phases of tasks during its mission, which abounds in complex technological systems such as aerospace systems, nuclear power plants, and high-performance computing systems. Due to dynamics in the system configuration and component behavior as well as statistical dependences across phases, exact reliability evaluation of a PMS is a time-consuming and complicated task. This paper proposes a new efficient multi-valued decision diagram (MDD) based method for the reliability analysis of a special class of non-repairable PMSs called k-out-of-n PMS where the same number of components n is involved in all the phases but the required number of working components k may vary from phase to phase. Particularly, a new MDD generation method is proposed for a fast construction of the PMS MDD model. The system components are not necessarily identical; they can be heterogeneous in their failure time distributions. Examples are provided to demonstrate the application and advantages of the proposed methodology.

Efficient modeling of flexural and shear behaviors in reinforced concrete beams and columns subjected to low-velocity impact loading

Detailed finite element (FE) models with 3-D solid elements are typically used to simulate impact behaviors of reinforced concrete (RC) beams and columns. However, the method usually requires a substantial amount of time and effort to model concrete and reinforcement and conduct nonlinear contact-impact analyses. Also, the accuracy of the method cannot be guaranteed due to the limitations in concrete material models implemented in general-purpose FE codes. In this paper, an efficient modeling method is proposed to capture both flexural and shear behaviors of RC beams and columns under low-velocity impact loading. A macroelement-based contact model was developed in the proposed method to capture interaction behaviors between impacting objects and RC members. In the contact model, a compression-only spring with an initial gap behavior was used to account for the stiffness and the kinematic response of an impacting object, and a combination of an elastic spring and a viscous damper in parallel was employed to simulate the contact stiffness and damping. By properly approximating the strain-rate effects, traditional fiber-section elements were demonstrated to be capable of predicting impact-induced flexural failures for RC members. On this basis, a general approach for both flexural- and shear-critical RC columns under impact loading was presented with the inclusion of additional shear springs in the fiber-section elements. Nearly fifty impact tests on RC beams and columns reported in the literature were employed to validate the proposed modeling method. Comparisons between the experimental and numerical results indicate that failure modes of the impacted members can be identified explicitly by the use of the proposed modeling method. Also, reasonable agreements were achieved for the impact forces and the impact-induced responses obtained from the impact tests and the analyses. The proposed method can be readily implemented without coding in any FE software as long as traditional fiber-section elements, and discrete macroelements are available. This feature would offer an advantage for the applications of the proposed method such as when assessing the structural response and vulnerability of a bridge structure subjected to vessel and vehicle collisions.

An Efficient Modeling Method for Large-Scale Complex Finite-Element Electric Field Numerical Calculation

In the process of solving electric field of the large-scale complex finite-element models, the fine control of the mesh on the outer surface of metal entity models is often difficult. Therefore, considering the basic geometric structure of the equipment, an efficient finite-element modeling method based on multilayer external surround entities (MESE) is proposed. Taking a simple 2-D model as an example, the algorithm of MESE generation, the principle of region division and related operation flow are introduced. The correctness of the method is validated through the typical case of parallel cylindrical conductors model, and the number of MESE is discussed as well. The proposed method is applied to the surface electric field calculation of the ±1100 kV ultrahigh-voltage direct current converter station valve hall. The calculated maximum electric field strength is 14.2 kV/cm. Furthermore, compared with the submodel method, the accuracy and efficiency of the proposed method are verified.

Efficient 3D lateral analysis of cold-formed steel buildings

Non-structural components contribute significantly to the lateral stiffness of a cold-formed steel (CFS) building structure, but are cumbersome to model explicitly in the structural analysis. They are therefore commonly ignored in a 3D structural analysis, and their benefits are lost to the design. This paper proposes an efficient modelling method that enables practical and accurate 3D elastic analysis of a multi-storey CFS building structure to study its lateral behaviour within the serviceability limit state. Each shear or gravity wall is represented by an equivalent shear modulus four-node orthotropic shell element, which incorporates the lateral stiffness (or flexibility) contributions of all components including sheathing, braces and fasteners as present in the wall. The equivalent shear modulus is determined from the experimental test of a representative wall panel, or from the analysis of a finely detailed finite element model of the panel. The resulting two-storey building model, which has much fewer degrees of freedom compared to conventional models, is verified against full-scale shake table test results with respect to the natural period, the peak storey drift and the peak floor acceleration at two different construction phases. This paper demonstrates that the proposed modelling method not only saves analysis time considerably through the drastic reduction of degrees of freedom, but also compares favourably against a published modelling method in terms of accuracy and modelling efforts.

Using High Performance Computing for Liquefaction Hazard Assessment with Statistical Soil Models

Conventional methods for liquefaction assessment using engineering indices such as Factor of safety against Liquefaction (FL) tend to overestimate liquefaction hazards. The soil dynamics analysis-based assessment with automatic modeling is more rational and robust. Soil properties are known for large uncertainties. Rather than deterministic soil models, statistical models for soil parameters should be considered. With automatic modeling, a large number of statistic models can be generated without difficulty. The problem becomes how to assess liquefaction hazard with statistic models in an efficient way. Using high performance computing, we develop an efficient liquefaction assessment method for statistical modeling of soils. A high parallel efficiency can be achieved and a large number of statical models of the order of 104 can be simulated within a reasonable time span. The method developed in this paper can be used as an efficient tool for unravelling critical parameters of soil liquefaction.

Efficient surrogate modeling methods for large-scale Earth system models based on machine-learning techniques

Abstract. Improving predictive understanding of Earth system variability and change requires data–model integration. Efficient data–model integration for complex models requires surrogate modeling to reduce model evaluation time. However, building a surrogate of a large-scale Earth system model (ESM) with many output variables is computationally intensive because it involves a large number of expensive ESM simulations. In this effort, we propose an efficient surrogate method capable of using a few ESM runs to build an accurate and fast-to-evaluate surrogate system of model outputs over large spatial and temporal domains. We first use singular value decomposition to reduce the output dimensions and then use Bayesian optimization techniques to generate an accurate neural network surrogate model based on limited ESM simulation samples. Our machine-learning-based surrogate methods can build and evaluate a large surrogate system of many variables quickly. Thus, whenever the quantities of interest change, such as a different objective function, a new site, and a longer simulation time, we can simply extract the information of interest from the surrogate system without rebuilding new surrogates, which significantly reduces computational efforts. We apply the proposed method to a regional ecosystem model to approximate the relationship between eight model parameters and 42 660 carbon flux outputs. Results indicate that using only 20 model simulations, we can build an accurate surrogate system of the 42 660 variables, wherein the consistency between the surrogate prediction and actual model simulation is 0.93 and the mean squared error is 0.02. This highly accurate and fast-to-evaluate surrogate system will greatly enhance the computational efficiency of data–model integration to improve predictions and advance our understanding of the Earth system.

Investigation into Joint Stiffness for Finite Element Modelling of the Dynamic Behaviour of a Structure with Bolted Joints

Accurate representation of the joint stiffness of bolted joints in the finite element (FE) model of a jointed structure is vital to ensure the accuracy and reliability of the predicted dynamic behaviour of the structure. The aim of this work was to put forward an efficient FE modelling method embodying the representation of the joint stiffness for the investigation of an assembled structure with bolted joints. The predicted FE results were compared with those obtained from the experimental modal analysis (EMA). EMA was performed to measure the natural frequencies and mode shapes of the structure with bolted joints. The calculated total error from the comparison of the natural frequencies between the FE and EMA were recorded. The results of the investigation showed that there is a noticeable contribution of the joint stiffness in the representation of the structure with bolted joints in developing the efficient FE modelling method.

Effects of mass scaling on finite element simulation of the cold roll-beating forming process

The cold roll-beating forming is a cold plastic forming technology for shaping external teeth of parts. The study aims to improve the simulation efficiency of the cold roll-beating forming process. Based on the principle of the roll-beating forming process, the finite element model of a representative simplified tooth groove forming process was established. Through the simulation results, the forming force and the metal plastic deformation are clearly revealed. Meanwhile, the effect of mass scaling on simulation efficiency and precision are discussed. And the experiments are carried out on a specialized forming equipment. Comparing finite element results with the experimental results, it shows the reasonable selection of mass scaling can effectively improve the simulation efficiency with the certain calculation precision. This study provides a reasonable and efficient finite element model and numerical calculation method for relative researches of cold roll-beating forming technology.

An efficient method for numerical modeling of thin air layer drag reduction on flat plate and prediction of flow instabilities

Experimental researches on flat plates and ship models show that among many different methods of drag reduction, Air Layer Drag Reduction (ALDR) seems to be one of the most efficient methods. The physics behind different phenomena in this method is not completely clear and numerical modeling can help resolving this manner. There is a lack of exact numerical modeling of this flow because of its complexity and huge numerical cost due to the two-phase instabilities in case of DNS. Also common CFD simulations using URANS models involve significant errors. In this paper an efficient method for numerical modeling of ALDR is introduced which is a combination of linear stability and URANS modeling of the flowfield. The base flow is extracted from CFD which is used in linear stability analysis as the basis which results the frequency of the most unstable mode. The final CFD simulation is then carried out plus an additional perturbation term with that specific frequency. Results show that the implementation of this strategy significantly improves the results of the numerical modeling compared to the experimental results. The predicted flowfields also show some new aspects of physics of ALDR that had not been previously shown in experimental tests.

A new closed-form calculation of envelope surface for modeling face gears

Envelope approaches have been widely applied in mechanical engineering to build mathematical and 3D models, which are fundamental elements for the design and manufacturing. It is difficult to obtain both models of face gears since their tooth surfaces are derived from a complex double envelope generation process: the face gear generation with a shaper, and the shaper generation with a rack cutter. According to this process, the conventional approaches calculate the face gear tooth surface from the well-known nonlinear equation of meshing. To avoid this problem, a completely new calculation method of envelope surface is established according to the geometry characteristic of the shaper tooth surface, so the mathematical model of the face gear tooth surface can be directly represented as a closed-form (explicit) rather than implicit one. This method is available to the face gear drives with general spur pinions or the involute helical pinion. Furthermore, an efficient approach is developed to automatically generate the 3D models of face gears. The presented work has two main contributions: (1) the closed-form envelope approach is beneficial to general envelope calculations; (2) The efficient modeling method can also be applied to other types of gear.

Statistical Evaluation of Radiofrequency Exposure during Magnetic Resonant Imaging: Application of Whole-Body Individual Human Model and Body Motion in the Coil.

The accurate estimation of patient’s exposure to the radiofrequency (RF) electromagnetic field of magnetic resonance imaging (MRI) significantly depends on a precise individual anatomical model. In the study, we investigated the applicability of an efficient whole-body individual modelling method for the assessment of MRI RF exposure. The individual modelling method included a deformable human model and tissue simplification techniques. Besides its remarkable efficiency, this approach utilized only a low specific absorption rate (SAR) sequence or even no MRI scan to generate the whole-body individual model. Therefore, it substantially reduced the risk of RF exposure. The dosimetric difference of the individual modelling method was evaluated using the manually segmented human models. In addition, stochastic dosimetry using a surrogate model by polynomial chaos presented SAR variability due to body misalignment and tilt in the coil, which were frequently occurred in the practical scan. In conclusion, the dosimetric equivalence of the individual models was validated by both deterministic and stochastic dosimetry. The proposed individual modelling method allowed the physicians to quantify the patient-specific SAR while the statistical results enabled them to comprehensively weigh over the exposure risk and get the benefit of imaging enhancement by using the high-intensity scanners or the high-SAR sequences.

Computationally efficient simulation method for conductivity modeling of 2D-based conductors

Macroscopic materials made of two-dimensional components such as flakes of graphene or transition metal dichalcogenides represent a material class with great potential for large-scale applications. Depending on the structure, they can inherit the exceptional properties of the nanoscale building blocks while developing new features on the macroscopic scale. Supported by theoretical considerations and finite element analysis, we developed a network simulation method to model 2D-based electrical conductors. Here, we systematically explain the technical and methodological details of our approach, using the example of graphene-based conductor materials. Apart from the raw material properties, we discuss the importance of homogeneity and internal structure of the material. Our findings are supported by finite element analysis. We demonstrate the application of our method by studying the intricate interaction of several material parameters and the resulting effect on the macroscopic network. Finally, we provide guidelines for adapting our method to different physical situations.

Scaled sequential threshold least-squares (S2TLS) algorithm for sparse regression modeling and flight load prediction

This paper presents a Scaled Sequential Thresholded Least Squares (S2TLS) algorithm to construct sparse regression models for flight load prediction. The combined use of a sparsification parameter λ and a magnification factor χ is proposed to tune both the model complexity and the regressor complexity. A bumpiness function is introduced to preferentially select simple regressors to improve model prediction. A cost function J consisting of the estimation residual and the bumpiness is then proposed to determine parameters (χ, λ) satisfying balanced performance. Parametric analysis is undertaken to investigate the effect of χ and λ on sparse regression performance. It is found that the optimal solution is hidden within a trench-like region of the (χ, λ) domain. Two methods using different optimization variables and algorithms are then presented to search for optimal combinations of λ and χ. Case studies are performed, and model results are compared against the test and CFD data of flight loads. Excellent agreement is observed, and the data (even with significant complications) is well bounded by the 95% confidence interval. Importantly, the underlying load-driving factors can be successfully identified. The new S2TLS algorithm represents a robust, efficient, and accurate method for flight load modeling and prediction.

Standardized modelling and economic optimization of multi-carrier energy systems considering energy storage and demand response

The integration energy and information technology has prompted the development of the multi-carrier energy system. Energy hub model is widely used in the multi-carrier energy system study. However, it is the difficult to formulate coupling matrix and optimize operation state of complex energy hub model. This paper proposes an efficient standardized multi-step modelling method and linearized optimization method for the energy hub model. Firstly, a complex energy hub model is separated into several simple energy hub models based on nodes arrangement and virtual nodes insertion methods; then the coupling matrix of each simple energy hub model can be easily modelled; the coupling matrix of the complex energy hub model can be obtained by multiplying the coupling matrix of each simple energy hub model. In addition, energy storage, demand response and renewable energy are considered and integrated in the energy hub model. Further, the nonlinear optimal operation model of energy hub is reformulated to a linear programming problem by using variable substitution in each simple energy hub model. Cases study is performed on a resident district in a city of China on a typical summer day with the energy storage devices, demand response and renewable energy considered. Compared with the traditional calculation method, the computational burden is significantly reduced based on the proposed calculation method, which can guarantee the global optimal operation decision.