Metamodeling Techniques Research Articles

Simulation of Magnetization Errors Using Conformal Mapping Field Computations

Due to their production and magnetization process, rare earth magnets, e.g. NdFeB, exhibit deviations from the targeted ideal remanent magnetic flux-density. As a consequence, the calculation of cogging torque, load torque and force computations of a permanent-magnet synchronous machine by means of finite-element analysis are at best in fair agreement to measurements, since the mentioned variations of the magnet material are not covered by standard simulation models. Actual solutions to consider these variations in the simulation of a permanent-magnet synchronous machine consist either in a full-factorial Monte-Carlo simulation or advanced stochastic analysis techniques such as the creation of polynomial-chaos meta-models. Even meta-model techniques result in an exponential growth of repetitive finite element simulations for a rise in the used polynomial's degree or an increment of the input variables. In order to reduce computation time, this paper unveils a methodology to build the magnet rotor field distribution with consideration of magnet faults semianalytically for calculating arbitrary machine operation points. For this purpose a conformal mapping approach is extended to be applicable to stochastic variations. It is shown, how the conformal mapping assumption of symmetrical field conditions can be overcome. As a result, the proposed approach is applied to the calculation of cogging torques for stochastic varying magnetizations in a permanent synchronous machine.

Metamodeling Based on the Fusion of FEM Simulations Results and Experimental Data

In this Paper an Innovative Multistage Metamodeling Technique is Proposed for Linking Datacoming from Two Different Sources: Simulations and Experiments. the Model is Hierarchical, in Thesense that One Set of Data (the Experiments) is Considered to be more Reliable and it is Labeled as“high-Resolution” and the other Set (the Simulations) is Labeled as “low-Resolution”. the Results Ofexperiments is Obviously Fully Accurate, Except for the only Approximation due to the Measurementsystem and Given the Intrinsically Aleatory Nature of all Real Experiments. in the Proposed Approach,Gaussian Models are Used to Describe Results of Computer Experiments because they are Flexible Andthey can Easily Interpolate Data Coming from Deterministic Simulations. A Second Stage Model is Used,in Order to Link the Prediction of the First Model to the Real Experimental Data. for the Linkage Model,as in the First Stage, a Gaussian Process is Used. in this Second Stage a Random Parameter can be Addedto the Model, Known as Nugget, in Order to take into Account the Process Variability. this Kind Ofmetamodeling can have Different Purposes: Adjusting or Tuning the Simulations, Having a Better Tool Todrive the Design Process, Making an Optimization of a Parameter of Interest. in the Paper, its use Foroptimization of a Single Responsey with Two Design Variables x1 and x2 is Demonstrated. the Approachis Applied for Modeling the Crash Behavior in Three Point Bending of Metal Foam Filled Tubes.

Hexagonal honeycomb cell optimisation by way of meta-model techniques

This paper presents the result of an optimisation study by linear, quadratic, Kriging and radial basis meta-models in order to augment the crashworthiness characteristic of cellular structures. Thin-walled cellular structures (honeycomb) have the ability to absorb impact energy during crashing, thus it is important to enhance the crushing efficiency and optimise the structural reliability. The optimisation carried out in this study is aimed at maximising the energy absorption characteristics using meta-models while considering some limitation on the maximum force as a constraint. Achieving these characteristics is an important factor in crashworthiness analysis, which minimises the damage in dynamic performance. The objective of using various meta-models is to qualify the meta-model in crashworthiness analysis using different point selection schemes and different number of points. The optimisation is performed in two stages; through experimental design methods in which a set of sampling points is selected from design space and polynomial fitting in order to optimise the objective. It is concluded that D-optimal best suits response surface method for model approximation. Kriging performed best by space filling and the best point selection scheme for radial basis surrogate is latin hypercube design. The results show that for optimising the crashworthiness characteristics of honeycomb, Kriging and quadratic response surface (RS) are best, in terms of accuracy and robustness point of view and the radial basis neural network would be the second best. During this optimisation, the RS was combined with detailed geometrically simplified finite element model of honeycomb cell using ANSYS/LS-DYNA, LS-DYNA and LS-opt packages. Approximated functions combined with the finite element analysis were an effective tool to optimise highly non-linear impact problems. This has led to the development of validated algorithm that enabled the development of the optimised solutions.

Robust expected violation criterion for constrained robust design problems and its application in automotive lightweight design

Metamodeling techniques are commonly used to replace expensive computer simulations in robust design problems. Due to the discrepancy between the simulation model and metamodel, a robust solution in the infeasible region can be found according to the prediction error in constraint responses. In deterministic optimizations, balancing the predicted constraint and metamodeling uncertainty, expected violation (EV) criterion can be used to explore the design space and add samples to adaptively improve the fitting accuracy of the constraint boundary. However in robust design problems, the predicted error of a robust design constraint cannot be represented by the metamodel prediction uncertainty directly. The conventional EV-based sequential sampling method cannot be used in robust design problems. In this paper, by investigating the effect of metamodeling uncertainty on the robust design responses, an extended robust expected violation (REV) function is proposed to improve the prediction accuracy of the robust design constraints. To validate the benefits of the proposed method, a crashworthiness-based lightweight design example, i.e. a highly nonlinear constrained robust design problem, is given. Results show that the proposed method can mitigate the prediction error in robust constraints and ensure the feasibility of the robust solution.

Improving Business Process Model Quality Using Domain Ontologies

This paper addresses the issue of improving quality of business process (BP) models by exploiting domain knowledge. Indeed, business process models reflect the business processes of companies. The success of these processes has a direct and undeniable impact on business operations success. Managing them through their underlying models helps improving their effectiveness, consistency, and transparency. BP modeling aims at a better understanding of processes, allowing deciders to achieve strategic goals of the company. However, several studies from the literature showed that in experienced system analysts often produce low-level quality. This situation is partly due to lack of domain knowledge. In this paper, we propose to support this modeling effort with an approach that uses domain knowledge to improve the semantic quality of BP models. We suggest to use ontologies as a mean to capture domain knowledge and meta-modeling techniques to deal with BP models independently of languages in which they are expressed. Our contribution is threefold: (1) the meta-models describing both a domain ontology and a BP model are described, (2) the alignment between the concepts of both meta-models is defined and illustrated, (3) a set of Object Constraint Language mapping rules is provided. A simple case study illustrates the process.

Tolerance analysis of systems in motion taking into account interactions between deviations

A product’s functionality depends largely on the interaction of its components and their geometries. Hence, tolerance analyses are used to determine the effects of deviations on functional key characteristics of mechanisms. However, possible interactions between the different deviations and the resulting effects on themselves as well as on the functional key characteristics have not yet been considered. This article considers the extension of the existing “integrated tolerance analysis of systems in motion” approach. By means of the methodology, the interactions between appearing deviations can be identified and integrated into a tolerance analysis functional relation. Therefore, the appearing interactions are represented by meta-models that can be easily integrated into the functional relation. Consequently, the product developer is able to gain information about the effects of deviations on functional key characteristics, as well as the effects of the deviations among themselves. In order to show the methodology’s practical use, the interactions between deviations of a nonideal crank mechanism inside a four-stroke combustion engine are considered. For this purpose, two different meta-modeling techniques are used: response surface methodology and artificial neural networks.

On the effect of numerical noise in approximate optimization of forming processes using numerical simulations

The coupling of Finite Element (FE) simulations with approximate optimization techniques is becoming increasingly popular in forming industry. By doing so, it is implicitly assumed that the optimization objective and possible constraints are smooth functions of the design variables and, in case of robust optimization, design and noise variables. However, non-linear FE simulations are known to introduce numerical noise caused by the discrete nature of the simulation algorithms, e.g. errors caused by re-meshing, time-step adjustments or contact algorithms. The subsequent usage of metamodels based on such noisy data reduces the prediction quality of the optimization routine and is known to even magnify the numerical errors. This work provides an approach to handle noisy numerical data in approximate optimization of forming processes, covering several fundamental research questions in dealing with numerical noise. First, the deteriorating effect of numerical noise on the prediction quality of several well-known metamodeling techniques is demonstrated using an analytical test function. Next, numerical noise is quantified and its effect is minimized by the application of local approximation and regularization techniques. A general approximate optimization strategy is subsequently presented and coupling with a sequential update algorithm is proposed. The strategy is demonstrated by the sequential deterministic and robust optimization of 2 industrial metal forming processes i.e. a V-bending application and a cup-stretching application. Although numerical noise is often neglected in practice, both applications in this work show that the general awareness of its presence is highly important to increase the overall accuracy of optimization results.

Enhancing Stochastic Kriging Metamodels with Gradient Estimators

Stochastic kriging is a new metamodeling technique for effectively representing the mean response surface implied by a stochastic simulation; it takes into account both stochastic simulation noise and uncertainty about the underlying response surface of interest. We show theoretically, through some simplified models, that incorporating gradient estimators into stochastic kriging tends to significantly improve surface prediction. To address the issue of which type of gradient estimator to use, when there is a choice, we briefly review stochastic gradient estimation techniques; we then focus on the properties of infinitesimal perturbation analysis and likelihood ratio/score function gradient estimators and make recommendations. To conclude, we use simulation experiments with no simplifying assumptions to demonstrate that the use of stochastic kriging with gradient estimators provides more reliable prediction results than stochastic kriging alone.

Metamodelling with independent and dependent inputs

In the cases of computationally expensive models the metamodelling technique which maps inputs and outputs is a very useful and practical way of making computations tractable. A number of new techniques which improve the efficiency of the Random Sampling-High dimensional model representation (RS-HDMR) for models with independent and dependent input variables are presented. Two different metamodelling methods for models with dependent input variables are compared. Both techniques are based on a Quasi Monte Carlo variant of RS-HDMR. The first technique makes use of transformation of the dependent input vector into a Gaussian independent random vector and then applies the decomposition of the model using a tensored Hermite polynomial basis. The second approach uses a direct decomposition of the model function into a basis which consists of the marginal distributions of input components and their joint distribution. For both methods the copula formalism is used. Numerical tests prove that the developed methods are robust and efficient.

Multi-Dimensional Global Approximation Method Based Improved MARS

Global approximation for a complex “black-box” model (like a simulation model) with large domain or multi-dimensions can be applied in many fields such as parameter experiment, sensibility analysis, real-time simulation, and design/control optimization. For multi-dimensional global approximation, MARS (multi-variant adaptive regression splines) has unquestionable predominance over other common-used metamodel techniques. However, MARS has its own inevitable drawbacks which limit the range of its applications. This paper proposes a multi-dimensional global approximation method based improved MARS .Some tests and applications are given to prove the performance of the method.

Comparison between neural network and response surface metamodels based on D-optimal designs

In this paper, two metamodelling techniques namely, the neural network and the response surface methodology are used and compared to approximate a multidimensional function to predict the springback amount of metallic sheets in the bending process. The training data required to train the two metamodelling techniques were generated using a verified non-linear finite element algorithm developed in this research. The algorithm is based on the updated Lagrangian formulation, which takes into consideration geometrical, material non-linearity, and contact. A neural network algorithm based on the back propagation algorithm has been developed. This research utilises computer generated D-optimal designs to select training examples for both metamodelling techniques so that a comparison between the two techniques can be considered as fair. Results from this research showed that the neural network metamodels outperform the response surface metamodels.

Meta-modeling Optimization of the Cutting Process During Turning Titanium Metal Matrix Composites (Ti-MMCs)

The Outstanding characteristics of titanium metal matrix composites (Ti-MMCs) have brought them up as promising materials in different industries, such as aerospace and biomedical. They exhibit high mechanical and physical properties, in addition to their low weight, high stiffness and high wear resistance. The presence of the ceramic reinforcements in a metallic matrix further contributes to these preferable properties. However, the high abrasive nature of the ceramic particles limits greatly the machinability of this class of material, as they induce significant tool wear and poor surface finish. In this study an attempt is made to find the optimum cutting conditions in terms of minimizing the tool wear and surface roughness during machining Ti-MMCs. Meta-modeling optimization in performed to achieve the goal.In this study the three independent parameters under consideration are the cutting speed, feed rate and the depth of cut. The response parameters are the surface roughness and the tool wear rate. The independent parameters are divided into a set of levels at which the experiments are conducted. At each experimental condition the two response parameters are measured. Kriging meta-modeling technique is used to fit a model to the response parameters in the multi-dimensional space. These models are used, in turn, within a multi-objective optimization algorithm to find the optimum cutting condition space. The above-mentioned algorithm is based on an evolutionary multi-objective search technique known as SPEA (Strength Pareto Evolutionary Algorithm).

An MDA‐based framework for collaborative business process modelling

PurposeThis paper aims to present a new approach for developing a framework based on a model driven architecture (MDA) for the modelling of technology‐independent collaborative processes.Design/methodology/approachThe paper suggests a new collaborative process modelling approach based on an MDA and a metamodelling technique. The research method, based on the design science approach, was started by identifying the characteristics of the collaborative processes, which distinguish them from the classical intraorganizational ones. Then, the generic collaborative business process (CBP) modelling framework is developed based on MDA approach and definition of a set of transformation rules through three layers: business, process, and technical. After that, the core component of the framework was the proposition of a generic CBP metamodel at PIM/MDA level. The specific collaboration participant's business processes (expressed as BPMN model) are generated from the generic CBP model represented as an UML2 Profile activity diagram, which is compliant to CBP metamodel. Finally, as proof‐of‐concept, the architecture of an Eclipse‐based open development platform is developed implementing an e‐Procurement collaborative process.FindingsThe proposed framework for CBP modelling and the generic CBP metamodel contribute towards a more efficient methodology and have consequences for BPM‐related collaboration, facilitating the B2B processes modelling and implementation. In order to demonstrate and evaluate the practical applicability of the framework, the architecture of an Eclipse‐based open development platform is developed implementing a collaborative business application on the basis of an e‐Procurement use case.Research limitations/implicationsThere is a need to focus future research efforts on the improvement of the semi‐automatic transformation phase from public to private processes which needs human intervention by adding a suitable interfaces at both sides of the B2B interaction. In addition, the problem of semantic heterogeneities regarding the partner's business process elements (business documents, activity/task names) should be tackled by developing an approach that uses ontology.Practical implicationsBusiness processes developers find a B2B technology‐independent solution for implementing and using interorganizational information systems.Originality/valueThe paper provides a framework that enables the CBP modelling and integrates a generic CBP metamodel. Currently, to the best of the authors' knowledge, such a generic metamodel and his instantiation have not so far been developed.

A Performance Modeling Language for Automotive Embedded Control Systems Based on UML

To improve the timing related performance of the embedded software of automotive control system, a performance modeling language has been developed based on UML (Unified Modeling Language) using meta-modeling technique. The proposed language consists of three kinds of meta-models used to define the high-level modeling paradigms for software structure, target platform and runtime system respectively. The modeling environment configured by the proposed language and software modules of functional model importation, components allocation, task forming and timing analysis can reuse the existing functional models, add timing requirement as well as resource constraints, and fulfill formal timing analysis at an early design stage. As results, the reliability of the automotive embedded control software can be improved and the development cycle and cost can also be reduced.

Multi-Point Sequential Sampling Method for Complex Engineering Optimization Problems

Metamodeling techniques are commonly used to replace expensive computer simulations in complex engineering optimization problems. Due to the discrepancy between the simulation model and metamodel, the prediction error in predicted responses may lead to a wrong solution. To balance the predicted mean and prediction error, the efficient global optimization (EGO) algorithm using Kriging predictor can be used to explore the design space and find next sample to adaptively improve the fitting accuracy of the predicted responses. However in conventional EGO algorithm, adding one point per iteration may be not efficient for the complex engineering problems. In this paper, a new multi-point sequential sampling method is proposed to include multiple points per iteration. To validate the benefits of the proposed multi-point sequential sampling method, a mathematical example and a highly-nonlinear automotive crashworthiness design example are illustrated. Results show that the proposed method can efficiently mitigate the prediction error and find the global optimum using fewer iterations.

A meta-modelling strategy to identify the critical offshore conditions for coastal flooding

Abstract. High water level at the coast may be the result of different combinations of offshore hydrodynamic conditions (e.g. wave characteristics, offshore water level, etc.). Providing the contour of the "critical" set of offshore conditions leading to high water level is of primary importance either to constrain early warning networks based on hydro-meteorological forecast or observations, or for the assessment of the coastal flood hazard return period. The challenge arises from the use of computationally intensive simulators, which prevent the application of a grid approach consisting in extracting the contour through the systematic evaluation of the simulator on a fine design grid defined in the offshore conditions domain. To overcome such a computational difficulty, we propose a strategy based on the kriging meta-modelling technique combined with an adaptive sampling procedure aiming at improving the local accuracy in the regions of the offshore conditions that contribute the most to the estimate of the targeted contour. This methodology is applied to two cases using an idealized site on the Mediterranean coast (southern France): (1) a two-dimensional case to ease the visual analysis and aiming at identifying the combination of offshore water level and of significant wave height; (2) a more complex case aiming at identifying four offshore conditions (offshore water level and offshore wave characteristics: height, direction and period). By using a simulator of moderate computation time cost (a few tens of minutes), the targeted contour can be estimated using a cluster composed of a moderate number of computer units. This reference contour is then compared with the results of the meta-model-based strategy. In both cases, we show that the critical offshore conditions can be estimated with a good level of accuracy using a very limited number (of a few tens) of computationally intensive hydrodynamic simulations.

Applying metamodeling techniques in the design and optimization of train wheel detector

PurposeIn writing this paper, the authors investigated the use of electromagnetic sensors in axle counter applications by means of train wheel detection. The purpose of this paper is to improve the detection capability of train wheel detectors, by installing them in the optimal orientation and position, using finite element modeling (FEM) in combination with metamodeling techniques. The authors compare three common metamodeling techniques for the special case of wheel detector orientation: response surface methodology; multivariate adaptive regression splines; and kriging.Design/methodology/approachAfter analyzing the effective parameters of a train wheel detector, an appropriate method for decreasing the system susceptibility to electromagnetic noises is presented.FindingsThe results were validated using a laboratory‐based system and also the results of field tests carried out on the Iranian railway network. The results of the study suggest that the FEM method and a metamodeling technique can reduce the computational efforts and processing time.Originality/valueIn this paper, combination of FEM and metamodeling approaches are used to optimize the railway axle counter coils orientation, which is more insusceptible to electromagnetic noise than initial arrangement used by some signallers.

Comparative study of metamodeling techniques for reliability analysis using evidence theory

Different from classical probability theory, evidence theory has been proposed to handle uncertainties with incomplete or imprecise information. Evidence theory has a flexible framework to represent different types of uncertainties, and has been introduced to perform reliability analysis and design. However, its application for reliability analysis is still a challenging problem due to excessive computational cost. The coupling of the discontinuous nature of uncertainty representation in evidence theory with practical complex problem makes the computational cost extremely prohibitive. To improve its practical utility, metamodels are always used to replace the actual limit-state function to reduce the computational cost. In this paper, we systematically compare three selected metamodeling techniques - quadratic polynomial without cross terms (termed as polynomial approach), radial basis function (RBF), high-dimensional model representation combined with moving least square (HDMR-MLS) - to test the average analysis accuracy and robustness using six representative reliability problems. The objective of this research is to study applicability of different metamodeling techniques for reliability analysis using evidence theory, conclude their overall performances under different test cases, and further investigate their advantages and disadvantages for predicting low failure-probability problems.

순차적 크리깅 메타모델의 민감도 검증법

메타모델은 설계 프레임워크 안에서 높은 효율성과 우수한 예측 능력, 타 프로그램과 쉬운 연동성때문에 공학분야에서 지난 10 년간 최적설계 기법들과 함께 발전해왔다. 메타모델을 구성하기 위해서는 실험계획법, 메타모델링 기법, 검증법과 같은 절차가 요구된다. 검증법은 메타모델의 정확성을 판단하기 때문에 순차적 크리깅 메타모델에서 정확한 크리깅 메타모델을 구성하기 위한 표본점의 개수를 결정한다. 크리깅 메타모델과 같은 보간모델은 표본점에서의 응답을 항상 지나기 때문에 기존 방법으로 메타모델의 정확성을 판단하기 위해서는 추가적인 해석이나 메타모델의 재구성이 요구된다. 본 연구에서는 이러한 추가적인 해석과 메타모델의 재구성을 요구하지 않는 메타모델의 해석적 민감도를 이용하는 민감도 검증법을 제안한다. 14 개의 2 차원 수학예제와 공학예제를 이용하여 이 방법의 타당성을 검증한다.

A comparative study of the scalability of alternative metamodelling techniques

Metamodels, also known as surrogate models, can be used in place of computationally expensive simulation models to increase computational efficiency for the purposes of design optimization or design space exploration. The accuracy of these metamodels varies with the scale and complexity of the underlying model. In this article, three metamodelling methods are evaluated with respect to their capabilities for modelling high-dimensional, nonlinear, multimodal functions. Methods analyzed include kriging, radial basis functions, and support vector regression. Each metamodelling technique is used to model a set of single output functions with dimensionality ranging from fifteen to fifty independent variables and modality ranging from one to ten local maxima. The number of points used to train the models is increased until a predetermined error threshold is met. Results show that kriging metamodels perform most consistently across a variety of functions, although radial basis functions and support vector regression are very competitive for highly multimodal functions and functions with large local gradients, respectively. Support vector regression metamodels consistently offer the shortest build and prediction times when applied to large scale multimodal problems.