Thermal problem solution using a surrogate model clustering technique

Brandyberry, Mark

doi:10.1016/j.cma.2007.05.029

Cited by 18 publications

(6 citation statements)

References 7 publications

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“…Several different approaches [20,[26][27][28][29][30][31] have been developed and presented in the literature on the thermal challenge problem as a result from the Sandia Validation workshop. We find these methods differ in how they utilize three different data sources (MPC, EN and AC data), the model updating formulations (e.g.…”

Section: Bayesian Approaches To the Thermal Challenge Problemmentioning

confidence: 99%

A Better Understanding of Model Updating Strategies in Validating Engineering Models

Xiong¹,

Chen²,

Tsui

2008

49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference &Amp;lt;br> 16th AIAA/ASME/AHS Ada

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Our objective in this work is to provide a better understanding of the various model updating strategies that utilize mathematical means to update a computer model based on both physical and computer observations. We examine different model updating formulations, e.g. calibration and bias-correction, as well as different solution methods. Traditional approaches to calibration treat certain computer model parameters as fixed over the physical experiment, but unknown, and the objective is to infer values for the so-called calibration parameters that provide a better match between the physical and computer data. In many practical applications, however, certain computer model parameters vary from trial to trial over the physical experiment, in which case there is no single calibrated value for a parameter. We pay particular attention to this situation and develop a maximum likelihood estimation (MLE) approach for estimating the distributional properties of the randomly varying parameters which, in a sense, calibrates them to provide the best agreement between physical and computer observations. Furthermore, we employ the newly developed u-pooling method (by Ferson et al.) as a validation metric to assess the accuracy of an updated model over a region of interest. Using the benchmark thermal challenge problem as an example, we study several possible model updating formulations using the proposed methodology. The effectiveness of the various formulations is examined. The benefits and limitations of using the MLE method versus a Bayesian approach are presented. Our study also provides insights into the potential benefits and limitations of using model updating for improving the predictive capability of a model.

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Section: Bayesian Approaches To the Thermal Challenge Problemmentioning

confidence: 99%

A Better Understanding of Model Updating Strategies in Validating Engineering Models

Xiong¹,

Chen²,

Tsui

2008

49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference &Amp;lt;br> 16th AIAA/ASME/AHS Ada

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“…Details of the challenge problem are found in Dowding et al 57 and in Storm. 58 Table 5 summarizes the results of the validation assessment along with twosample t-test results to compare with the work by Brandyberry 59 on the same challenge problem. The table indicates that the combined interval approach reached the same conclusions as the two-sample test.…”

Section: Methodology Applied To An Engineering Challenge Problemmentioning

confidence: 99%

“…Consider the parameter configuration q = 1500 and L = 0:0191, which represents the center point for the experimental region defined by the ensemble validation data. The two-sample t-test used by Brandyberry 59 cannot validate at this design point because no experimental data exists for a comparison of sample means. The regression-based statistical intervals utilize the OLS response surface at the desired configuration for an assessment of model validity.…”

Section: Methodology Applied To An Engineering Challenge Problemmentioning

confidence: 99%

Point-wise model validation over experimental regions using regression confidence and tolerance intervals with Bayesian relaxations

et al. 2019

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As systems grow more complex, so does our propensity to use computers to emulate complex real-world systems. Often these real-world systems possess dynamic response behavior over the operational domain of input parameter configurations. This domain is referred to as the design space or experimental region. It is critical we ensure that computer models which emulate such dynamic behavior be validated over the full design space. This paper presents a dual-interval validation methodology. Confidence intervals and tolerance intervals are developed based on a system response surface function. Model samples are compared to each interval to develop a complete model validation conclusion. The methodology is described, its robustness to noise and model lack-of-fit examined, and then it is applied to a well-established engineering validation challenge problem.

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“…Most research in model validation deals with the quantification of model uncertainty for one or two specified design configurations (Higdon et al 2008a;Liu et al 2008;Rutherford 2008;Hill and Dowding 2008;Ferson et al 2008;Brandyberry 2008). The literature on RBDO incorporating model uncertainty is even scarcer.…”

Section: Literature Surveymentioning

confidence: 99%

Model uncertainty approximation using a copula-based approach for reliability based design optimization

Peng

Yang

2016

Struct Multidisc Optim

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Reliability-based design optimization (RBDO) has been widely used to design engineering products with minimum cost function while meeting reliability constraints. Although uncertainties, such as aleatory uncertainty and epistemic uncertainty, have been well considered in RBDO, they are mainly considered for model input parameters. Model uncertainty, i.e., the uncertainty of model bias indicating the inherent model inadequacy for representing the real physical system, is typically overlooked in RBDO. This paper addresses model uncertainty approximation in a product design space and further integrates the model uncertainty into RBDO. In particular, a copula-based bias modeling approach is proposed and results are demonstrated by two vehicle design problems.

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Thermal problem solution using a surrogate model clustering technique

Cited by 18 publications

References 7 publications

A Better Understanding of Model Updating Strategies in Validating Engineering Models

A Better Understanding of Model Updating Strategies in Validating Engineering Models

Point-wise model validation over experimental regions using regression confidence and tolerance intervals with Bayesian relaxations

Model uncertainty approximation using a copula-based approach for reliability based design optimization

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