Numerical analysis on effects of deep foundation excavation to adjacent buildings

Xu, Bu; Yan, Qin; Ding, Wenqi; Tang, Zhendong

doi:10.1201/b17064-26

Cited by 1 publication

(4 citation statements)

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Mentioning

Contrasting

Order By: Relevance

“…By writing the H 2,ω -norm of the error of approximation, it appears that Sylvester equations appears in a similar way as in the H 2 problem Xu and Zeng (2011). Indeed,…”

Section: Frequency Limited Tsiamentioning

confidence: 98%

“…Tangential First-order optimality conditions introduced in Gallivan et al (2004) can also be achieved through the algorithm presented in Xu and Zeng (2011). It is based on the fact that solving AX + XΓ + BR T = 0 (5a) A T Y + Y Γ + C T L = 0 (5b) for X, Y ∈ R n×r with Γ ∈ R r×r , L ∈ R ny×r and R ∈ R r×nu , and constructing the reduced-order model such that :…”

Section: Two-sided Iteration Algorithmmentioning

confidence: 99%

“…where S(ω) andŜ(ω) are given by equation 10with the matrices A andÂ, respectively. Using these Sylvester equations (see Algorithm 2) instead of those used in the H 2 case in Xu and Zeng (2011) enables to improve the efficiency of the algorithm in terms of H 2,ω -norm. As for the TSIA, this algorithm requires good initial projectors, for instance, the projectors givent by the ISTIA can be used.…”

Section: Frequency Limited Tsiamentioning

confidence: 99%

“…Frequency-limited reduction of the aircraft model (r = 12) for varying ω tions equivalent to those appearing in the TSIA(Xu and Zeng (2011)). …”

mentioning

confidence: 99%

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H2 optimal and frequency limited approximation methods for large-scale LTI dynamical systems

Vuillemin¹,

Poussot-Vassal²,

Alazard³

2013

IFAC Proceedings Volumes

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Model order reduction over a bounded frequency range is more adapted than the standard H 2 approximation whenever the entire frequential behaviour of the large-scale model is not needed or not accurately known. However most of the methods that enable to reduce a model on a limited frequency range are based on the use of weights. Yet their determination is often an issue for engineers. That is why, in this paper, two weight-free model approximation algorithms are proposed. They are based on recent algorithms that achieve local H 2 optimal model reduction (see Gugercin (2007), Van Dooren et al. (2008) and Gugercin et al. (2008)). The proposed algorithms efficiency are validated both on a standard benchmark and on an industrial use case.

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“…By writing the H 2,ω -norm of the error of approximation, it appears that Sylvester equations appears in a similar way as in the H 2 problem Xu and Zeng (2011). Indeed,…”

Section: Frequency Limited Tsiamentioning

confidence: 98%

Section: Two-sided Iteration Algorithmmentioning

confidence: 99%

Section: Frequency Limited Tsiamentioning

confidence: 99%

“…Frequency-limited reduction of the aircraft model (r = 12) for varying ω tions equivalent to those appearing in the TSIA(Xu and Zeng (2011)). …”

mentioning

confidence: 99%

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