Theory and applications of the multiquadric-biharmonic method 20 years of discovery 1968–1988

Hardy, Rolland L.

doi:10.1016/0898-1221(90)90272-l

Cited by 765 publications

(320 citation statements)

References 43 publications

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“…Solutions to this Hermite problem with RBFs have been around since Hardy's introduction of the MQ method [28] (see also [29]). Other expositions on this and related Hermite-type RBF problems can be found, for example, in [30][31][32].…”

Section: Hermite Rbf Interpolationmentioning

confidence: 99%

Scattered node compact finite difference-type formulas generated from radial basis functions

Wright,

Fornberg

2006

Journal of Computational Physics

283

133

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Section: Hermite Rbf Interpolationmentioning

confidence: 99%

Scattered node compact finite difference-type formulas generated from radial basis functions

Wright,

Fornberg

2006

Journal of Computational Physics

283

133

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“…The coefficient matrixÂ can be related to the interpolation functions by an unknown matrix of constant coefficients B aŝ A = B · F. In this equation, F contains a set of predefined interpolation functions f j (z) of input parameters z. The choice of f j (z) can be arbitrary and in this study an inverse multiquadric radial function, a type of RBF (see [13] for a description), is chosen as interpolation function. Finally, an approximation of the output system response corresponding to an arbitrary set of input parameters is obtained by S a ⇡ˆ · B · F a .…”

Section: Pod-rbf and Nnmf-rbf Network For Fuzzy Datamentioning

confidence: 99%

Real-Time Fuzzy Analysis of Machine Driven Tunneling

Cao¹,

Freitag²,

Meschke³

2017

Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. Reliability assessment in mechanized tunneling requires to take into account limited information describing the local geology and the corresponding geotechnical parameters. The geotechnical data are often quite limited and generally not available in the form of precise models and parameter values. In this case, epistemic uncertainty should be considered within the reliability assessment. The concept of fuzzy numbers is applied to predict tunneling induced settlements in real-time. An advanced numerical simulation is utilized as forward model for the settlement prediction. However, to achieve real-time capabilities, surrogate models are required. Deterministic surrogate models can be used together with an ↵-cut optimization approach to compute fuzzy data. In this paper, a surrogate modeling strategy is introduced to directly process fuzzy input-output data. Within this approach, the time-consuming optimization procedure is replaced by a surrogate model to obtain the fuzzy settlement field prediction in realtime. The significant reduction in computation time maintaining similar prediction performance leads to potential applications in steering of mechanized tunneling processes.

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“…Applications of RBFs include bathymetry, topography, hydrology, mapping, geophysics, geology, image warping and medical imaging, and see [1,4,8,14,15,18,26]. Experience in a variety of applications has shown RBFs to be particularly well suited to scattered data interpolation problem.…”

Section: Introductionmentioning

confidence: 99%

Improvement Of The Multiquadric Quasi-interpolation Lw2

Sarboland¹,

Aminataei²

2014

J. Math. Computer Sci.

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In this paper, we improve the multiquadric (MQ) quasi-interpolation operator 2 . The operator 2 is based on inverse multiquadric radial basis function (IMQ-RBF) interpolation, and Wu and Schaback's MQ quasi-interpolation operator . In definition process of the quasi-interpolation 2 , the second derivative of function is used that approximated by center finite difference. In this paper, we use compact finite difference for approximation of the second derivative and increase accuracy of quasi-interpolation 2 . Numerical experiments demonstrate that the proposed MQ quasi-interpolation scheme is valid.

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Theory and applications of the multiquadric-biharmonic method 20 years of discovery 1968–1988

Cited by 765 publications

References 43 publications

Scattered node compact finite difference-type formulas generated from radial basis functions

Scattered node compact finite difference-type formulas generated from radial basis functions

Real-Time Fuzzy Analysis of Machine Driven Tunneling

Improvement Of The Multiquadric Quasi-interpolation Lw2

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