Dependence of optimal structural weight on aerodynamic shape for a High Speed Civil Transport

Balabanov, Vladimir; Kaufman, Matthew; Knill, Duane L.; Haim, D.; Golovidov, Oleg; Giunta, Anthony A.; Haftka, Raphael T.; Grossman, Bernard; Mason, William H.; Watson, Layne T.

doi:10.2514/6.1996-4046

Cited by 37 publications

(56 citation statements)

References 13 publications

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“…Thus, the error at the N s design points is a function of coefficients vector (2) only. Since the RSA model coefficients vector b is an unbiased estimate of coefficients vector (1) , it is expected that the error in the prediction will be a function of coefficients in vector (2) , and this is indeed observed from Equation (12).…”

Section: Estimation Of Bias Error Boundsmentioning

confidence: 99%

“…The vector f(x) has two components: f (1) (x) is the vector of basis functions used in the RSA or fitting model, and f (2) (x) is the vector of additional basis functions which are missing in the linear regression model. Similarly, the coefficient vector can be written as a combination of the vectors (1) and (2) which represent the true coefficients associated with the basis functions vectors f (1) (x) and f (2) (x), respectively. That is,…”

Section: Estimation Of Bias Error Boundsmentioning

confidence: 99%

“…where y is the vector of observed responses at the data points, X (1) is the Gramian design matrix constructed using the basis functions corresponding to f (1) (x), and X (2) is constructed using the missing basis functions corresponding to f (2) (x). A Gramian design matrix in two variables (with monomial basis functions), when the RSA model is quadratic and the true response is cubic, is shown in Equation (4).…”

Section: Estimation Of Bias Error Boundsmentioning

confidence: 99%

“…A few examples are given as follows. Kaufman et al [1], Balabanov et al [2,3], Papila and Haftka [4,5],…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

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Generalized pointwise bias error bounds for response surface approximations

Goel

Haftka

Papila

et al. 2005

Numerical Meth Engineering

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SUMMARYThis paper proposes a generalized pointwise bias error bounds estimation method for polynomialbased response surface approximations when bias errors are substantial. A relaxation parameter is introduced to account for inconsistencies between the data and the assumed true model. The method is demonstrated with a polynomial example where the model is a quadratic polynomial while the true function is assumed to be cubic polynomial. The effect of relaxation parameter is studied. It is demonstrated that when bias errors dominate, the bias error bounds characterize the actual error field better than the standard error. The bias error bound estimates also help to identify regions in the design space where the accuracy of the response surface approximations is inadequate. It is demonstrated that this information can be utilized for adaptive sampling in order to improve accuracy in such regions.

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Section: Estimation Of Bias Error Boundsmentioning

confidence: 99%

Section: Estimation Of Bias Error Boundsmentioning

confidence: 99%

Section: Estimation Of Bias Error Boundsmentioning

confidence: 99%

“…A few examples are given as follows. Kaufman et al [1], Balabanov et al [2,3], Papila and Haftka [4,5],…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

See 2 more Smart Citations

Generalized pointwise bias error bounds for response surface approximations

Goel

Haftka

Papila

et al. 2005

Numerical Meth Engineering

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“…However, some other problems are starting to arise with metamodeling at this point in time, mainly that the response surfaces being used did not handle highly non-linear design spaces well, and had problems with high dimensionality 11,13 .…”

Section: A History Of Metamodelingmentioning

confidence: 99%

Development of an Integrated Gaussian Process Metamodeling Application for Engineering Design

Baukol¹

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Development of an Integrated Gaussian Process MetamodelingApplication for Engineering Design Collin Richard BaukolAs engineering technologies continue to grow and improve, the complexities in the engineering models which utilize these technologies also increase. This seemingly endless cycle of increased computational power and demand has sparked the need to create representative models, or metamodels, which accurately reflect these complex design spaces in a computationally efficient manner. As research into metamodeling and using advanced metamodeling techniques continues, it is important to remember design engineers who need to use these advancements. Even experienced engineers may not be well versed in the material and mathematical background that is currently required to generate and fully comprehend advanced complex metamodels. A metamodeling environment which utilizes an advanced metamodeling technique known as Gaussian Process is being developed to help bridge the gap that is currently growing between the research community and design engineers. This tool allows users to easily create, modify, query, and visually/numerically assess the quality of metamodels for a broad spectrum of design challenges.v ACKNOWLEDGEMENTSThe research that is presented in this thesis was made possible by a large number of people. These people include those that are directly connected to the research itself, those that stood by me even when times were tough, and everyone in between. Creating a thorough list of everyone who deserves thanking is beyond my grasp.

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