Use Of Metamodels Research Articles

TSI metamodels-based multi-objective robust optimization

Purpose – This paper aims to deal with an efficient strategy for robust optimization when a large number of uncertainties are taken into account. Design/methodology/approach – ANOVA analysis is used in order to perform a variance-based decomposition and to reduce stochastic dimension based on an appropriate criterion. A massive use of metamodels allows reconstructing response surfaces for sensitivity indexes in the design variables plan. To validate the proposed approach, a simplified configuration, an inverse problem on a 1D nozzle flow, is solved and the performances compared to an exact Monte Carlo reference solution. Then, the same approach is applied to the robust optimization of a turbine cascade for thermodynamically complex flows. Findings – First, when the stochastic dimension is reduced, the error on the variance between the reduced and the complete problem was found to be roughly estimated by the quantity (1−T¯ TSI )×100, where T¯ TSI is the summation of TSI concerning the variables respecting the TSI criterion. Second, the proposed strategy allowed obtaining a converged Pareto front with a strong reduction of computational cost by preserving the same accuracy. Originality/value – Several articles exist in literature concerning robust optimization but very few dealing with a global approach for solving optimization problem affected by a large number of uncertainties. Here, a practical and efficient approach is proposed that could be applied also to realistic problems in engineering field.

A system of entities for enterprise business models

A business model of a modern enterprise is a base element for the most adequate and reasonable reaction to a change in the enterprise's socio-economic environment. To achieve desired results, this reaction should take into account enterprise features. The use of metamodeling and systems theory allows one to create an integrated system of business models. Such models are based on enterprise features and are implemented using a common set of entities for all business models.

Thermal building simulation using the UKCP09 probabilistic climate projections

This article investigates how to use UK probabilistic climate-change projections (UKCP09) in rigorous building energy analysis. Two office buildings (deep plan and shallow plan) are used as case studies to demonstrate the application of UKCP09. Three different methods for reducing the computational demands are explored: statistical reduction (Finkelstein-Schafer [F-S] statistics), simplification using degree-day theory and the use of metamodels. The first method, which is based on an established technique, can be used as reference because it provides the most accurate information. However, it is necessary to automatically choose weather files based on F-S statistic by using computer programming language because thousands of weather files created from UKCP09 weather generator need to be processed. A combination of the second (degree-day theory) and third method (metamodels) requires only a relatively small number of simulation runs, but still provides valuable information to further implement the uncertainty and sensitivity analyses. The article also demonstrates how grid computing can be used to speed up the calculation for many independent EnergyPlus models by harnessing the processing power of idle desktop computers.

Metamodelling for Agent-Based Modelling: An Application for Posted Pricing Institutions

Agent-Based Modelling is gaining wider acceptance as a paradigm for social research. However, it still presents limitations in the management of the process to generate the simulations from the initial conceptual models. This makes it difficult to reuse the knowledge from available models and to adapt it to different hypotheses. This paper proposes the use of metamodels in order to define explicitly the core concepts of a problem domain and to differentiate the aspects involved in the process. A case study for posted pricing institutions shows how to define the related metamodel and use it to address alternative situations in these auctions. The case study drives the discussion on the advantages and limitations that metamodelling can bring to social simulation.

A grid-enabled asynchronous metamodel-assisted evolutionary algorithm for aerodynamic optimization

A Grid-enabled asynchronous metamodel-assisted evolutionary algorithm is presented and assessed on a number of aerodynamic shape optimization problems. An efficient way of implementing surrogate evaluation models or metamodels (artificial neural networks) in the context of an asynchronous evolutionary algorithm is proposed. The use of metamodels relies on the inexact pre-evaluation technique already successfully applied to synchronous (i.e. generation-based) evolutionary algorithms, which needs to be revisited so as to efficiently cooperate with the asynchronous search method. The so-created asynchronous metamodel-assisted evolutionary algorithm is further enabled for Grid Computing. The Grid deployment of the algorithm relies on three middleware layers: GridWay, Globus Toolkit and Condor. Single- and multi-objective CFD-based designs of isolated airfoils and compressor cascades are handled using the proposed algorithm and the gain in CPU cost is demonstrated.

Using subsystem linear regression metamodels in stochastic simulation

Abstract This article explores the use of metamodels as simulation building blocks. The metamodel replaces a part of the simulation model with a mathematical function that mimics the input–output behavior of that part, with respect to some measure of interest to the designer. The integration of metamodels as components of the simulation model simplifies the model and reduces the simulation time. Such use of the metamodels also gives the designer a better understanding of the behavior of those parts of the model, making the simulation model as a whole more intelligible. The metamodel-based simulation model building process is examined, step by step, and the designer options are explored. This process includes the identification of the metamodel candidates and the construction of the metamodels themselves. The assessment of the proposed approach includes the evaluation of the integration effort of the metamodel into the metamodel-based simulation model, and the accuracy of the output data when compared to the original system. A metamodel-based simulation model validation test, based on a simulation model validation test, is developed to ensure that the response conforms to the original simulation model. The proposed test comprises the cases when the simulation response variance varies with the experimental point and when it is constant. A message routing and processing example, with a fourth-degree polynomial regression metamodel, is used to illustrate the proposed procedure. An integrated simulation system is used to integrate the metamodel-based simulation model as well as the original simulation model.

Metamodeling: An Emerging Representation Paradigm for System-Level Design

The use of metamodeling in system design allows abstraction of concepts germane to a number of varying modeling domains, and provides the ability of exploiting meta-information for a variety of system design tasks such as analysis, verification, synthesis, and test generation. This article provides an overview of emerging metamodeling techniques and their applications.

Metamodeling for model- based system design

Metamodeling is defined, according to Wikipedia, as the construction of a collection of concepts within a certain domain. A model is an abstraction of phenomena in the real world; a metamodel is yet another abstraction that highlights the properties of the model itself. Metamodeling originated in the field of mathematical logic, and software engineering research has been very actively using this approach for model-driven software design. It has been increasingly used in electronic system design in recent years as a result of our never-ending need to move the abstraction level of design ever higher. Metamodeling tools and methodologies have recently been employed in creating design frameworks for SoCs. Some experts believe that there will be increasing use of metamodels for supporting automated system integration, system test generation, and verification because these models provide information that enable tools to efficiently explore system design alternatives as well as generate verification test benches.

Efficient multi-objective optimal design of water distribution networks on a budget of simulations using hybrid algorithms

The design of water distribution networks is a large-scale combinatorial, non-linear optimisation problem, involving many complex implicit constraint sets, such as nodal mass balance and energy conservation, which are commonly satisfied through the use of hydraulic network solvers. These problem properties have motivated several prior studies to use stochastic search optimisation, because these derivative-free global search algorithms have been shown to obtain higher quality solutions for large network design problems. Global stochastic search methods, however, require many iterations to be performed in order to achieve a satisfactory solution, and each iteration may involve running computationally expensive simulations. Recently, this problem has been compounded by the evident need to embrace more than a single measure of performance into the design process, since by nature multi-objective optimisation methods require even more iterations. The use of metamodels as surrogates for the expensive simulation functions has been investigated as a possible remedy to this problem. However, the identification of reliable surrogates is not always a viable alternative. Under these circumstances, methods that are capable of achieving a satisfactory level of performance with a limited number of function evaluations represent a valuable alternative. This paper represents a first step towards filling this gap. Two recently introduced multi-objective, hybrid algorithms, ParEGO and LEMMO, are tested on the design problem of a real medium-size network in Southern Italy, and a real large-size network in the UK under a scenario of a severely restricted number of function evaluations. The results obtained suggest that the use of both algorithms, in particular LEMMO, could be successfully extended to the efficient design of large-scale water distribution networks.

The use of metamodeling for VoIP over WiFi capacity evaluation [Transactions Letters

The increasing popularity of wireless fidelity (Wi-Fi) networks at home, in public areas and in the enterprise motivates extensive modeling and analysis of their performance measures, such as network capacity and quality of service (QoS) capabilities. Some of the easier performance problems can be solved by analytical modeling methods, but most of the complicated ones, involving several design parameters from multiple layers, can only be answered through simulation studies that are typically implicit and less suitable for design and optimization. Hence, we believe it is crucial to obtain explicit mathematic models, that are effective in representing system behavior and a basis for performance optimization. Here, we first advocate the application of formal empirical modeling techniques to performance studies of Wi-Fi networks, in order to find usable, if approximate, closed-form mathematical models. Subsequently, by applying these metamodeling techniques, we perform a case study with very useful results: our VoWiFi (voice over Wi-Fi) admission capacity metamodel gives a much tighter bound than those existing in the literature and leads to a more effective admission control scheme. Our work, therefore, points out a new direction for future performance studies of Wi-Fi networks.

Use of Metamodels in the Multi-Objective Optimization of Mechanical Structures with Uncertainties

In this paper, we propose a method which takes into account the propagation of uncertainties in the finite element models in a multi-objective optimization procedure. This method is based on the coupling of the Stochastic Response Surface Method (SRSM) and a genetic algorithm of NSGA type (Non-dominated Sorting Genetic Algorithm). The SRSM is based on the use of Stochastic Finite Element Method (SFEM) via the use of the perturbation method. Thus, we can avoid the use of Monte Carlo simulation, whose cost is prohibitive in the optimization problems, especially when the finite element models are large and with a considerable number of design parameters. The objective of this study is, on the one hand, to quantify efficaciously the effects of these uncertainties on the variability of responses which we wish to optimize, and on the other hand, to calculate solutions which are both optimal and robust resulting from the numerical simulation. At the end of a multi-objective optimization procedure, the space of optimal solutions is generally of a large dimension. The solutions obtained are practically non-exploitable by the designer. To facilitate this interpretation, a study of sensitivity a posteriori can be exploited in order to eliminate the non-significant design parameters. The use of the clusters resulting from the Self-Organizing Maps of Kohonen (SOM) is also suggested for a rational management of the design space. The importance of the methodology that we have used along with suggestions for its performances are highlighted by two numerical examples. The criterion of quality selected consists in obtaining the best compromise: the minimal computing time versus the maximum precision of results.

Information Mediation Using Metamodels

Information mediation is an approach used to resolve heterogeneity of online information sources. This article discusses the concept of information mediation and several related research projects that use a typical mediation model. The problems and issues with existing approaches are discussed. This article then proposes the use of metamodels as an advanced architecture for information mediation, where XML is a main driving force. The new architecture is partly established on the common warehouse metamodel (CWM), a standard adopted by the Object Management Group (OMG). Illustrative examples are presented in the article to describe and discuss the new architecture.

A non‐stationary covariance‐based Kriging method for metamodelling in engineering design

AbstractMetamodels are widely used to facilitate the analysis and optimization of engineering systems that involve computationally expensive simulations. Kriging is a metamodelling technique that is well known for its ability to build surrogate models of responses with non‐linear behaviour. However, the assumption of a stationary covariance structure underlying Kriging does not hold in situations where the level of smoothness of a response varies significantly. Although non‐stationary Gaussian process models have been studied for years in statistics and geostatistics communities, this has largely been for physical experimental data in relatively low dimensions. In this paper, the non‐stationary covariance structure is incorporated into Kriging modelling for computer simulations. To represent the non‐stationary covariance structure, we adopt a non‐linear mapping approach based on parameterized density functions. To avoid over‐parameterizing for the high dimension problems typical of engineering design, we propose a modified version of the non‐linear map approach, with a sparser, yet flexible, parameterization. The effectiveness of the proposed method is demonstrated through both mathematical and engineering examples. The robustness of the method is verified by testing multiple functions under various sampling settings. We also demonstrate that our method is effective in quantifying prediction uncertainty associated with the use of metamodels. Copyright © 2006 John Wiley & Sons, Ltd.

Meta-modeling framework: A new approach to manage meta-modelbase and modeling knowledge

In this era of digital revolution models are considered an important organizational resource. This demands a new approach in managing the repository of models for decision makers. This study presents a framework for meta-modeling of knowledge. The study proposes a generalized method for meta-modelbase management to use, store, and manage modeling knowledge. Further, to illustrate the application of the meta-modeling framework, we present the design and development of MetaSimModel – a knowledge-based decision support environment to organize, manage, use, and reuse modeling knowledge of simulation models in a flexible manufacturing environment. This study illustrates the use of meta-models (models that store knowledge about other models) to represent models. The ability to construct larger, composite models from reusable, pre-fabricated components plays an important role in improving productivity in a modeling environment.

On the use of metamodel-assisted, multi-objective evolutionary algorithms

This article is concerned with the optimal use of metamodels in the context of multi-objective evolutionary algorithms which are based on computationally expensive function evaluations. The goal is to capture Pareto fronts of optimal solutions with the minimum computational cost. In each generation during the evolution, the metamodels act as filters that distinguish the most promising individuals, which will solely undergo exact and costly evaluations. By means of the so-called inexact pre-evaluation phase, based on continuously updated local metamodels, most of the non-promising individuals are put aside without aggravating the overall cost. The gain achieved through this technique is amazing in single-objective problems. However, with more than one objective, noticeable performance degradation occurs. This article scrutinizes the role of metamodels in multi-objective evolutionary algorithms and proposes ways to overcome expected weaknesses and improve their performance. Minimization of mathematical functions as well as aerodynamic shape optimization problems are used for demonstration purposes.

Update strategies for kriging models used in variable fidelity optimization

Many optimization methods for simulation-based design rely on the sequential use of metamodels to reduce the associated computational burden. In particular, kriging models are frequently used in variable fidelity optimization. Nevertheless, such methods may become computationally inefficient when solving problems with large numbers of design variables and/or sampled data points due to the expensive process of optimizing the kriging model parameters in each iteration. One solution to this problem would be to replace the kriging models with traditional Taylor series response surface models. Kriging models, however, were shown to provide good approximations of computer simulations that incorporate larger amounts of data, resulting in better global accuracy. In this paper, a metamodel update management scheme (MUMS) is proposed to reduce the cost of using kriging models sequentially by updating the kriging model parameters only when they produce a poor approximation. The scheme uses the trust region ratio (TR-MUMS), which is a ratio that compares the approximation to the true model. Two demonstration problems are used to evaluate the proposed method: an internal combustion engine sizing problem and a control-augmented structural design problem. The results indicate that the TR-MUMS approach is very effective; on the demonstration problems, it reduced the number of likelihood evaluations by three orders of magnitude compared to using a global optimizer to find the kriging parameters in every iteration. It was also found that in trust region-based method, the kriging model parameters need not be updated using a global optimizer—local methods perform just as well in terms of providing a good approximation without affecting the overall convergence rate, which, in turn, results in a faster execution time.

Vers des patrons de métamodélisation. Structuration de métamodèles par séparation des préoccupations

In regard to the increase of metamodeling technique use in software engineering, means have to be proposed in order to improve the definition and use of metamodels. This article discusses our proposal to achieve this goal through the separation of concerns and the use of metamodeling patterns. These patterns are aimed at structuring the definition of metamodels thus providing specific modeling means suited to the requirements of application domains. In addition, using the separation of concerns permits the saving of the definitions of concern concepts thus the sharing (and even standardization) of concern metamodels. This discussion is applied to the definition of a metamodel dedicated to the definition and use of component-based software architectures.

Methods for expected value of information analysis in complex health economic models: developments on the health economics of interferon-beta and glatiramer acetate for multiple sclerosis.

To develop methods for performing expected value of perfect information (EVPI) analysis in computationally expensive models and to report on the developments on the health economics of interferon-beta and glatiramer acetate in the management of multiple sclerosis (MS) using this methodological framework. Electronic databases and Internet resources, reference lists of relevant articles. A methodological framework was developed for undertaking EVPI analysis for complex models. The framework identifies conditions whereby EVPI may be calculated numerically, where the one-level algorithm sufficiently approximates the two-level algorithm, and whereby metamodelling techniques may accurately approximate the original simulation model. Metamodelling techniques, including linear regression, neural networks and Gaussian processes (GP), were systematically reviewed and critically appraised. Linear regression metamodelling, GP metamodelling and the one-level EVPI approximation were used to estimate partial EVPIs using the ScHARR MS cost-effectiveness model. The review of metamodelling approaches suggested that in general the simpler techniques such as linear regression may be easier to implement, as they require little specialist expertise although may provide only limited predictive accuracy. More complex methods such as Gaussian process metamodelling and neural networks tend to use less-restrictive assumptions concerning the relationship between the model inputs and net benefits, and therefore may permit greater accuracy in estimating EVPIs. Assuming independent treatment efficacy, the 'per patient' EVPI for all uncertainty parameters within the ScHARR MS model is 8855 British pounds. This leads to a population EVPI of 86,208,936 British pounds, which represents the upper estimate for the overall EVPI over 10 years. Assuming all treatment efficacies are perfectly correlated, the overall per patient EVPI is 4271 British pounds. This leads to a population EVPI of 41,581,273 British pounds, which represents the lower estimate for the overall EVPI over 10 years. The partial EVPI analysis, undertaken using both the linear regression metamodel and Gaussian process metamodel clearly, suggests that further research is indicated on the long-term impact of these therapies on disease progression, the proportion of patients dropping off therapy and the relationship between the EDSS, quality of life and costs of care. The applied methodology points towards using more sophisticated metamodelling approaches in order to obtain greater accuracy in EVPI estimation. Programming requirements, software availability and statistical accuracy should be considered when choosing between metamodelling techniques. Simpler, more accessible techniques are open to greater predictive error, whilst sophisticated methodologies may enhance accuracy within non-linear models, but are considerably more difficult to implement and may require specialist expertise. These techniques have been applied in only a limited number of cases hence their suitability for use in EVPI analysis has not yet been demonstrated. A number of areas requiring further research have been highlighted. Further clinical research is required concerning the relationship between the EDSS, costs of care and health outcomes, the rates at which patients drop off therapy and in particular the impact of disease-modifying therapies on the progression of MS. Further methodological research is indicated concerning the inclusion of epidemiological population parameters within the sensitivity analysis; the development of criteria for selecting a metamodelling approach; the application of metamodelling techniques within health economic models and in the specific application to EVI analyses; and the use of metamodelling for EVSI and ENBS analysis.

Metamodeling Approach to Optimization of Steady-State Flowsheet Simulations: Model Generation

Steady-state flowsheet simulations can be too complex to be amenable to direct optimization. An indirect route involves data collection from the simulation and fitting of less complex surrogates: metamodels, which are more readily optimized. The use of metamodels allows the optimization to proceed while requiring only a small number of solutions to be obtained from the simulation. This paper describes a general methodology for optimization of process simulations via metamodeling. Implementation issues surrounding the data collection and model generation phases of the methodology are identified. Examples of effective techniques are given.

Optimization and Validation of Steady-State Flowsheet Simulation Metamodels

The use of metamodels allows the optimization of steady-state flowsheet simulations to proceed while requiring only a small number of solutions to be obtained from the simulation. This paper presents the techniques needed to optimize the metamodel forms described by Palmer and Realff. Through a case study, we exemplify characteristics of the solution process and demonstrate the strength of the metamodeling approach. The operating cost of an ammonia synthesis plant is optimized over six input variables using a total of only 32 solutions of the plant simulation as data for the metamodels.