Local Smoothness of Graph Signals

Daković, Miloš; Stanković, Ljubiša; Sejdić, Ervin

doi:10.1155/2019/3208569

Cited by 27 publications

(20 citation statements)

References 21 publications

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“…The proposed modal-to-graph mapping is inspired by the idea to move the smooth modal pattern of modal shapes into the smoothness assumption (i.e. smooth changes between connected vertices) [41] inherent in graph signals. This similarity led to the formalization of the modal shape smoothness λ p defined as…”

Section: Gsp Cluster-based Modal Analysismentioning

confidence: 99%

Cluster-Based Vibration Analysis of Structures With GSP

Zonzini

Girolami

Marchi

et al. 2021

IEEE Trans. Ind. Electron.

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This work describes a divide-and-conquer strategy suited for vibration monitoring applications. Based on a low-cost embedded network of Micro-ElectroMechanical (MEMS) accelerometers, the proposed architecture strives to reduce both power consumption and computational resources. Moreover, it eases the sensor deployment on large structures by exploiting a novel clustering scheme which consists of unconventional and non-overlapped sensing configurations. Signal processing techniques for inter and intra-cluster data assembly are introduced to allow for a full-scale assessment of the structural integrity. More specifically, the capability of graph signal processing is adopted for the first time in vibrationbased monitoring scenarios to capture the spatial relationship between acceleration data. The experimental validation, conducted on a steel beam perturbed with additive mass, revealed high accuracy in damage detection tasks. Deviations in spectral content and mode shape envelopes were correctly revealed regardless of environmental factors and operational uncertainties. Furthermore, an additional key advantage of the implemented architecture relies on its compliance with blind modal investigations, an approach which favors the implementation of autonomous smart monitoring systems.

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Section: Gsp Cluster-based Modal Analysismentioning

confidence: 99%

Cluster-Based Vibration Analysis of Structures With GSP

Zonzini

Girolami

Marchi

et al. 2021

IEEE Trans. Ind. Electron.

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“…The local smoothness can be defined for a vertex n. It will be denoted by λ(n). This parameter corresponds to the classical time-varying (instantaneous) frequency, ω(t), defined at an time-instant t, in the form [28]…”

Section: Undirected Circular Graphmentioning

confidence: 99%

“…• Sine window is obtained as the square root of the raised cosine window in (28). Obviously, this window will satisfy (31).…”

Section: Frame Decomposition-wola Conditionmentioning

confidence: 99%

“…In order to present the Chebyshev polynomial approximation in more detail, and give the exact values of the approximation coefficients we further reduced the approximation order to (M − 1) = 5. Then we used this order to calculate the approximations of the bandpass functions, H k (λ), for every k in the case of the raised cosine form, given in (28), with K = 10 bands. The resulting approximation coefficients, h i,k , which are used in the vertex-domain implementation, defined by (39), are shown in Table 1.…”

Section: Chebyshev Polynomialmentioning

confidence: 99%

“…Hamming window can be used in the same way as in (28). The only difference is that the Hamming windows sum-up to 1.08 in the overlapping interval, meaning that the result should be divided by this constant.…”

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confidence: 99%

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From Time–Frequency to Vertex–Frequency and Back

et al. 2021

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The paper presents an analysis and overview of vertex–frequency analysis, an emerging area in graph signal processing. A strong formal link of this area to classical time–frequency analysis is provided. Vertex–frequency localization-based approaches to analyzing signals on the graph emerged as a response to challenges of analysis of big data on irregular domains. Graph signals are either localized in the vertex domain before the spectral analysis is performed or are localized in the spectral domain prior to the inverse graph Fourier transform is applied. The latter approach is the spectral form of the vertex–frequency analysis, and it will be considered in this paper since the spectral domain for signal localization is well ordered and thus simpler for application to the graph signals. The localized graph Fourier transform is defined based on its counterpart, the short-time Fourier transform, in classical signal analysis. We consider various spectral window forms based on which these transforms can tackle the localized signal behavior. Conditions for the signal reconstruction, known as the overlap-and-add (OLA) and weighted overlap-and-add (WOLA) methods, are also considered. Since the graphs can be very large, the realizations of vertex–frequency representations using polynomial form localization have a particular significance. These forms use only very localized vertex domains, and do not require either the graph Fourier transform or the inverse graph Fourier transform, are computationally efficient. These kinds of implementations are then applied to classical time–frequency analysis since their simplicity can be very attractive for the implementation in the case of large time-domain signals. Spectral varying forms of the localization functions are presented as well. These spectral varying forms are related to the wavelet transform. For completeness, the inversion and signal reconstruction are discussed as well. The presented theory is illustrated and demonstrated on numerical examples.

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