Approximating Cfree Space Topology by Constructing Vietoris-Rips Complex

AbstractIt is shown that for the Cesàro means (C, α) with α > - 1, and for a certain class of more general Nörlund means, summability of the series σan implies uniform summability of the series σan zn in a Stolz angle at z = 1.If B is a normal matrix and (B) denotes the series summability field with the usual Banach space topology, then the vectors {ek} (ek = {0,0,..., 1,0,...}) are said to form a Toplitz basis for (B) relative to a method H if H — Σakek = a for each a = {ak}ε(B). It is shown for example that the above relation holds for B = (C,α), α> − 1 , and H = Abel method; also for B = (C,α) and H = (C,β) with 0 ≤ α ≤ β.Applications are made to theorems on summability factors.

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PC Tendon Damage Detection Based on Change of Phase Space Topology

Journal of Advanced Concrete Technology ◽

10.3151/jact.16.416 ◽

2018 ◽

Vol 16 (8) ◽

pp. 416-428 ◽

Cited By ~ 1

Author(s):

Porjan Tuttipongsawat ◽

Eiichi Sasaki ◽

Keigo Suzuki ◽

Takuya Kuroda ◽

Kazuo Takase ◽

...

Keyword(s):

Phase Space ◽

Damage Detection ◽

Space Topology ◽

Phase Space Topology

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Structural interrogation using phase space topology of the wind-induced responses

Journal of Vibration and Control ◽

10.1177/1077546317701661 ◽

2017 ◽

Vol 24 (14) ◽

pp. 3148-3172

Author(s):

Riya C George ◽

Sudib K Mishra

Keyword(s):

Phase Space ◽

Structural Damage ◽

Model Building ◽

Chaotic Signal ◽

Experimental Investigations ◽

Damage Scenarios ◽

Space Topology ◽

Frame Building ◽

Low Dimensional ◽

Phase Space Topology

The applicability of the phase space interrogation (PSI) methodology for structural health monitoring (SHM) is limited on account of the fact that the structure needs to be excited by a low dimensional chaotic signal. The present study demonstrates that the phase space interrogation can still be applied to structures subjected to ambient/moderate wind excitations. Key to this extension is the relative low dimensionality of the wind-induced structural responses, amenable to phase space embedding by virtue of Takens’ embedding theorem. The so-formed pseudo-attractor is shown to sufficiently reflect the changes in system dynamics induced by structural damage(s). A widely employed damage feature, namely, the changes in phase space topology (CPST) is subsequently employed to the reconstructed attractor to link it with the presence, severity, as well as localization of damage(s). The CPST is established as a legitimate damage-sensitive feature by studying its variability with alternative damage scenarios in a multistoried frame building subjected to wind excitations. The performance of the methodology is demonstrated under different degrees of noise contamination in the measured responses as well as varying intensity of wind speed. The statistical robustness of the procedure is also assessed. The numerical findings are supported by the evidence from a limited number of experimental investigations carried out on a model building with inflicted damage scenarios. The wind loadings for the tests are simulated using a wind tunnel testing facility. Finally, a simple analysis is presented that establish the viability of the phase space analysis analytically.

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