An adaptive design and interpolation technique for extracting highly nonlinear response surfaces from deterministic models

Shahsavani, Davood; Grimvall, Anders

doi:10.1016/j.ress.2008.10.013

Cited by 12 publications

(7 citation statements)

References 33 publications

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“…The polynomial response surface is easy to construct and, due to its smooth function characteristics, the optimization algorithm generally converges quickly, indicating its high efficiency. However, this method has poor accuracy in approximating highly nonlinear and irregular problems (Shahsavani and Grimvall, 2009).…”

Section: Combined Response Surface Methodologymentioning

confidence: 99%

A practical discrete sizing optimization methodology for the design of high-rise concrete buildings

Lou

Xiao

Wan

et al. 2022

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PurposeIn this article, a practical design methodology is proposed for discrete sizing optimization of high-rise concrete buildings with a focus on large-scale and real-life structures.Design/methodology/approachThis framework relies on a computationally efficient approximation of the constraint and objective functions using a radial basis function model with a linear tail, also called the combined response surface methodology (RSM) in this article. Considering both the code-stipulated constraints and other construction requirements, three sub-optimization problems were constructed based on the relaxation model of the original problem, and then the structural weight could be automatically minimized under multiple constraints and loading scenarios. After modulization, the obtained results could meet the discretization requirements. By integrating the commercially available ETABS, a dedicated optimization software program with an independent interface was developed and details for practical software development were also presented in this paper.FindingsThe proposed framework was used to optimize different high-rise concrete buildings, and case studies showed that material usage could be saved by up to 12.8% compared to the conventional design, and the over-limit constraints could be adjusted, which proved the feasibility and effectiveness.Originality/valueThis methodology can therefore be applied by engineers to explore the optimal distribution of dimensions for high-rise buildings and to reduce material usage for a more sustainable design.

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Section: Combined Response Surface Methodologymentioning

confidence: 99%

A practical discrete sizing optimization methodology for the design of high-rise concrete buildings

Lou

Xiao

Wan

et al. 2022

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“…Recently, efforts have been devoted to develop output-oriented adaptive design algorithms that iteratively collect samples in the guidance of existing model outputs (Ajdari & Mahlooji, 2014;Busby, 2009;Busby et al, 2007;Crombecq et al, 2011;Liu et al, 2017;Mackman & Allen, 2010;Shahsavani & Grimvall, 2009;Ulaganathan et al, 2016;van der Herten et al, 2015). These methods combine the exploitation metric for identifying the nonlinear regions with the exploration criterion for locating the unsampled areas to adaptively select informative new samples.…”

Section: Introductionmentioning

confidence: 99%

“…For example, Crombecq et al (2011), van der Herten et al (2015, and Ulaganathan et al (2016) used the gradient information at the samples to identify the nonlinear areas and the Voronoi tessellation decomposition to balance the exploration and exploitation. Busby (2009) and Shahsavani and Grimvall (2009) also employed the idea of domain decomposition for balancing the two criteria, but used cross validation and a roughness criterion to determine nonlinear regions, respectively. Mackman and Allen (2010) used the product of sample separation and the estimated Laplacian to achieve the compromise between the exploration and exploitation.…”

Section: Introductionmentioning

confidence: 99%

“…To our best knowledge, little effort has been spent in this research area. The most often used stopping criteria are that the collected sample size reaches a given amount or that the cross-validation errors drop below a given threshold (e.g., Ajdari & Mahlooji, 2014;Busby et al, 2007;Crevill en-Garc ıa et al, 2017;Crombecq et al, 2011;Deman et al, 2016;Eason & Cremaschi, 2014;Gan et al, 2015;Shahsavani & Grimvall, 2009;Zhan et al, 2013). The former is useful when limited computational resources are affordable, but the resulted surrogate may not achieve the desired approximation accuracy.…”

Section: Introductionmentioning

confidence: 99%

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A Taylor Expansion‐Based Adaptive Design Strategy for Global Surrogate Modeling With Applications in Groundwater Modeling

Mo¹,

Shi³

et al. 2017

Water Resources Research

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Global sensitivity analysis (GSA) and uncertainty quantification (UQ) for groundwater modeling are challenging because of the model complexity and significant computational requirements. To reduce the massive computational cost, a cheap‐to‐evaluate surrogate model is usually constructed to approximate and replace the expensive groundwater models in the GSA and UQ. Constructing an accurate surrogate requires actual model simulations on a number of parameter samples. Thus, a robust experimental design strategy is desired to locate informative samples so as to reduce the computational cost in surrogate construction and consequently to improve the efficiency in the GSA and UQ. In this study, we develop a Taylor expansion‐based adaptive design (TEAD) that aims to build an accurate global surrogate model with a small training sample size. TEAD defines a novel hybrid score function to search informative samples, and a robust stopping criterion to terminate the sample search that guarantees the resulted approximation errors satisfy the desired accuracy. The good performance of TEAD in building global surrogate models is demonstrated in seven analytical functions with different dimensionality and complexity in comparison to two widely used experimental design methods. The application of the TEAD‐based surrogate method in two groundwater models shows that the TEAD design can effectively improve the computational efficiency of GSA and UQ for groundwater modeling.

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“…Metamodels are typically constructed by examining the response of the simulator to a limited number of intelligently chosen parameter sets. Examples of metamodeling techniques include: kriging [ Sacks et al , 1989; Sakata et al , 2003; Simpson and Mistree , 2001], neural networks [ Behzadian et al , 2009; Papadrakakis et al , 1998], radial basis functions [ Hussain et al , 2002; Mugunthan et al , 2005; Mullur and Messac , 2006; Nakayama et al , 2002], multivariate adaptive regression splines [ Friedman , 1991; Jin et al , 2001], high‐dimensional model representation [ Rabitz et al , 1999; Sobol , 2003], treed Gaussian processes [ Gramacy and Lee , 2008], Gaussian emulator machines [ Shahsavani and Grimall , 2009], proper orthogonal decomposition [ Audouze et al , 2009], and others [ Myers and Montgomery , 2002; Wang , 2003].…”

Section: Introductionmentioning

confidence: 99%

Reducing the computational cost of automatic calibration through model preemption

Razavi

Tolson

Matott

et al. 2010

Water Resources Research

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[1] Computational budget is frequently a limiting factor in both uncertainty-based (e.g., through generalized likelihood uncertainty estimation (GLUE)) and optimization-based (e.g., through least squares minimization) calibration of computationally intensive environmental simulation models. This study introduces and formalizes the concept of simulation model preemption during automatic calibration. The proposed "model preemption" method terminates a simulation model early to save computational budget if it is recognized through intermediate simulation model results that a given solution (model parameter set) is so poor that it will not benefit the search strategy. The methodology proposed here is referred to as deterministic model preemption because it leads to exactly the same calibration result as when deterministic preemption is not applied. As such, deterministic preemption-enabled calibration algorithms which make no approximations to the mathematical simulation model are a simple alternative to the increasingly common and more complex approach of metamodeling for computationally constrained model calibration. Despite its simplicity, the deterministic model preemption concept is a promising concept that has yet to be formalized in the environmental simulation model automatic calibration literature. The model preemption concept can be applied to a subset of uncertainty-based and optimization-based automatic calibration strategies using a variety of different objective functions. Results across multiple calibration case studies demonstrate actual preemption computational savings ranging from 14% to 49%, 34% to 59%, and 52% to 96% for the dynamically dimensioned search, particle swarm optimization, and GLUE automatic calibration methods, respectively.

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An adaptive design and interpolation technique for extracting highly nonlinear response surfaces from deterministic models

Cited by 12 publications

References 33 publications

A practical discrete sizing optimization methodology for the design of high-rise concrete buildings

A practical discrete sizing optimization methodology for the design of high-rise concrete buildings

A Taylor Expansion‐Based Adaptive Design Strategy for Global Surrogate Modeling With Applications in Groundwater Modeling

Reducing the computational cost of automatic calibration through model preemption

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