Metamodeling for the quantitative assessment of conceptual designs in an immersive virtual reality environment

The engineering design process has undergone extensive research in the area of detailed design. Many computer aided design (CAD) software packages have been developed from this research to provide an integral analysis tool for companies in the detailed design phase. However with the development of more complex technologies and systems, decisions made earlier in the design process have been crucial to product success. To help provide valuable information to assist these earlier decisions, tools have also been developed for conceptual design such as lightened CAD packages, concept elimination methods, and image processing software. Unfortunately, these tools have been proven ineffective based on the inability to provide a lower fidelity real-time analysis of each and every concept. By providing real-time analysis, engineers could spend more time evaluating every concept mathematically and base decisions on factual information instead of personal opinion. On a different note, companies continually undergo next generation development of their products. This continuous cycle of design iterations generates a stockpile of high fidelity analysis which we refer to as legacy data. Legacy data contains thousands of geometrical properties and analytical data used to assess the validity of previous designs. This data creates a vast amount of analytical engineering knowledge which can be harnessed to help evaluate the validity of future designs. Statistical approximations known as metamodels can be applied to summarize the general trends of the inputs and outputs of legacy dataset, and eliminate the need for recreating CAD analysis models for each concept. Metamodeling techniques cannot produce 100% accuracy, but at the conceptual design stage, 100% accuracy is not a necessity. This thesis presents an implementation scheme for incorporating Polynomial Response Surface (PRS) methods, Kriging Approximations, and Radial Basis Function Neural Networks (RBFNN) into conceptual design. A conceptual design software application, the Advanced Systems Design Suite (ASDS), has also been developed to incorporate these metamodeling techniques into assessment tools to evaluate conceptual design concepts in both a desktop and immersive virtual reality (VR) environment. The goal of the implementation scheme was to develop a strategy for constructing metamodels upon conceptual design datasets based upon their ability to perform under several conditions including various sample sizes, dataset linearity, interpolation within a domain, and extrapolation outside a domain. In order to develop the implementation scheme, two conceptual design datasets, wheel loading and stress analysis, were constructed due to a lack of available legacy data. The two datasets were setup using a design of experiments (DOE) to generate accurate sample points for the datasets. Once the DOE was formulated, digital prototypes were created in CAD software and the FEA test runs generated the responses of the DOE input parameters. The results of these FEA simulations generated the necessary conceptual design datasets required analyze the three metamodeling techniques. The performance results revealed that each metamodeling technique outperformed the others when tested again the various parameters. For instance, PRS metamodels performed very well when extrapolating outside its domain and with datasets consisting of more than 40 sample points. PRS metamodels require very setup and can be generated very quickly. If speed is the key consideration for metamodel construction, then PRS is the best option. Kriging metamodels showed the best performance with any non-linear dataset and large design space datasets exhibiting linear or non-linear behavior. Kriging metamodels are a very robust metamodeling technique especially when using a first-order global model on non-linear datasets. On the downside, Kriging metamodels require slightly more time to setup and construct than PRS metamodels. RBFNN metamodels performed well when interpolating within a large design space and on any sample size of linear datasets. However to reach performance levels of either PRS or Kriging, the ideal radius value must be determined prior to constructing the final model which took hours on small datasets. If the datasets consisted of thousands of design variables, constructing a RBFNN metamodel would take days to weeks to generate. However if construction time is not an issue, RBFNN metamodels outperform both PRS and Kriging techniques on linear datasets. This implementation scheme for incorporating metamodels into conceptual design provides a method for generating rapid assessment capabilities as an alternative to high fidelity analysis. Future work includes evaluating additional conceptual design datasets to create a more robust implementation scheme. More research will also be done in implementing additional types and varying setup parameters of both Kriging Approximations and Radial Basis Function Neural Networks

Automatic surrogate model type selection during the optimization of expensive black-box problems

The use of Surrogate Based Optimization (SBO) has become commonplace for optimizing expensive black-box simulation codes. A popular SBO method is the Efficient Global Optimization (EGO) approach. However, the performance of SBO methods critically depends on the quality of the guiding surrogate. In EGO the surrogate type is usually fixed to Kriging even though this may not be optimal for all problems. In this paper the authors propose to extend the well-known EGO method with an automatic surrogate model type selection framework that is able to dynamically select the best model type (including hybrid ensembles) depending on the data available so far. Hence, the expected improvement criterion will always be based on the best approximation available at each step of the optimization process. The approach is demonstrated on a structural optimization problem, i.e., reducing the stress on a truss-like structure. Results show that the proposed algorithm consequently finds better optimums than traditional kriging-based infill optimization

A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms

This is the author accepted manuscript. The final version is available from Springer Verlag via the DOI in this record.Evolutionary algorithms are widely used for solving multiobjective optimization problems but are often criticized because of a large number of function evaluations needed. Approximations, especially function approximations, also referred to as surrogates or metamodels are commonly used in the literature to reduce the computation time. This paper presents a survey of 45 different recent algorithms proposed in the literature between 2008 and 2016 to handle computationally expensive multiobjective optimization problems. Several algorithms are discussed based on what kind of an approximation such as problem, function or fitness approximation they use. Most emphasis is given to function approximation-based algorithms. We also compare these algorithms based on different criteria such as metamodeling technique and evolutionary algorithm used, type and dimensions of the problem solved, handling constraints, training time and the type of evolution control. Furthermore, we identify and discuss some promising elements and major issues among algorithms in the literature related to using an approximation and numerical settings used. In addition, we discuss selecting an algorithm to solve a given computationally expensive multiobjective optimization problem based on the dimensions in both objective and decision spaces and the computation budget available.The research of Tinkle Chugh was funded by the COMAS Doctoral Program (at the University of Jyväskylä) and FiDiPro Project DeCoMo (funded by Tekes, the Finnish Funding Agency for Innovation), and the research of Dr. Karthik Sindhya was funded by SIMPRO project funded by Tekes as well as DeCoMo

An advanced cost estimation methodology for engineering systems

A mathematically advanced method for improving the fidelity of cost estimation for an engineering system is presented. In this method historical cost records can be expanded either through the use of local metamodels or by using an engineering build‐up model. In either case, the expanded data set is analyzed using principal component analysis (PCA) in order to identify the physical parameters, and the principal components (PCs) which demonstrate the highest correlation to the cost. A set of predictor variables, composed of the physical parameters and of the multipliers of the principal components which demonstrate the highest correlation to the cost, is developed. This new set of predictor variables is regressed, using the Kriging method, thus creating a cost estimation model with a high level of predictive capability and fidelity. The new methodology is used for analyzing a set of cost data available in the literature, and the new cost model is compared to results from a neural network based analysis and to a cost regression model. Further, a case study addressing the fabrication of a submarine pressure hull is developed in order to illustrate the new method. The results from the final regression model are presented and compared to results from other cost regression methods. The technical characteristics of the new novel general method are presented and discussed. © 2011 Wiley Periodicals, Inc. Syst EngPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90246/1/20192_ftp.pd

Data-driven model based design and analysis of antenna structures

Data-driven models, or metamodels, offer an efficient way to mimic the behaviour of computation-intensive simulators. Subsequently, the usage of such computationally cheap metamodels is indispensable in the design of contemporary antenna structures where computation-intensive simulations are often performed in a large scale. Although metamodels offer sufficient flexibility and speed, they often suffer from an exponential growth of required training samples as the dimensionality of the problem increases. In order to alleviate this issue, a Gaussian process based approach, known as Gradient-Enhanced Kriging (GEK), is proposed in this work to achieve cost-efficient modelling of antenna structures. The GEK approach incorporates adjoint-based sensitivity data in addition to function data obtained from electromagnetic simulations. The approach is illustrated using a dielectric resonator and an ultra-wideband antenna structures. The method demonstrates significant accuracy improvement with the less number of training samples over the Ordinary Kriging (OK) approach which utilises function data only. The discussed technique has been favourably compared with OK in terms of computational cost

Otimização eficiente global dirigida por metamodelos combinados : novos caminhos abertos pela aproximação por mínimos quadrados

Orientador: Alberto Luiz SerpaTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia MecânicaResumo: O presente trabalho representa a compilação dos resultados anteriores dessa pesquisa no campo de metamodelos combinados e otimização eficiente global (EGO), os quais foram sumetidos para publicação em periódicos especializados. Recentemente foi implementado nesse trabalho de doutorado o algoritmo LSEGO que é uma abordagem para conduzir algoritmos tipo EGO, baseando-se em metamodelos combinados através da aproximação por mínimos quadrados (metamodelos combinados LS). Através dos metamodelos combinados LS é possível estimar a incerteza da aproximação usando qualquer tipo de metamodelagem (e não somente do tipo kriging), permitindo estimar a função de expectativa de melhora para a função objetivo. Nos experimentos computacionais anteriores em problemas de otimização sem restrições, a abordagem LSEGO mostrou-se como uma alternativa viável para conduzir otimização eficiente global usando metamodelos combinados, sem se restringir a somente um ponto adicional por ciclo de otimização iterativa. Na presente tese o algoritmo LSEGO foi extendido de modo a tratar também problemas de otimização com restrições. Os resultados de testes numéricos com problemas analíticos e de referência e também em um estudo de caso de engenharia em escala industrial mostraram-se bastante promissores e competitivos em relação aos trabalhos similares encontrados na literaturaAbstract: In this work we review and compile the results of our previous research in the fields of ensemble of metamodels and efficient global optimization (EGO). Recently we implemented LSEGO that is an approach to drive EGO algorithms, based on LS (least squares) ensemble of metamodels. By means of LS ensemble of metamodels, it is possible to estimate the uncertainty of the prediction by using any kind of model (not only kriging) and provide an estimate for the expected improvement function. In previous numerical experiments with unconstrained optimization problems, LSEGO approach has shown to be a feasible alternative to drive efficient global optimization by using multiple or ensemble of metamodels, not restricted to kriging approximation or single infill point per optimization cycles. In the present work we extended the previous LSEGO algorithm to handle constrained optimization problems as well. Some numerical experiments were performed with analytical benchmark functions and also for industry scale engineering problems with competitive resultsDoutoradoMecanica dos Sólidos e Projeto MecanicoDoutor em Engenharia Mecânic