A nonparametric test for stationarity based on local Fourier analysis

Basu, Prabahan; Rudoy, Daniel; Wolfe, Patrick J.

doi:10.1109/icassp.2009.4960256

Cited by 17 publications

(15 citation statements)

References 4 publications

(13 reference statements)

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“…Other attempts have nevertheless been made in this direction too by contrasting local properties with global ones [4], [8], but not necessarily properly phrased in terms of hypothesis testing. Among more recent approaches, we can mention those reported in [9], [10] which share some ideas with this work, but with the notable difference that they are basically model-based (whereas ours is not). Early works [11], [12] proposed a global test of stationarity based on approximate statistics of evolutionary spectra [ 13], which is performed as a two-step analysis of variance.…”

supporting

confidence: 56%

“…One difference between theoretical (secondorder) stationarity of random processes and operational stationarity that we study, and that aims at being consistent with the physical and time-frequency interpretation of what stationarity means, is that both situations where there is no change in time of second-order statistics (here at microscale), and situations where there is a regular repetition if the same feature (here at macroscale of observation) are considered as being stationary in its operational acceptance. They are moreover quantified in the sense that, when the null hypothesis of stationarity is rejected (middle diagram), both an index and a scale of nonstationarity can be defined according to ( 10) and (11). In the present case, the maximum value of INS is obtained for SNS = T h /T ≈ 0.2, in qualitative accordance with the 4 AM periods entering the observation window.…”

Section: F Illustrationmentioning

confidence: 99%

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Testing Stationarity With Surrogates: A Time-Frequency Approach

Borgnat

Flandrin

Honeiné

et al. 2010

IEEE Trans. Signal Process.

149

105

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Abstract-An operational framework is developed for testing stationarity relatively to an observation scale, in both stochastic and deterministic contexts. The proposed method is based on a comparison between global and local time-frequency features. The originality is to make use of a family of stationary surrogates for defining the null hypothesis of stationarity and to base on them two different statistical tests. The first one makes use of suitably chosen distances between local and global spectra, whereas the second one is implemented as a one-class classifier, the time-frequency features extracted from the surrogates being interpreted as a learning set for stationarity. The principle of the method and of its two variations is presented, and some results are shown on typical models of signals that can be thought of as stationary or nonstationary, depending on the observation scale used.

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supporting

confidence: 56%

Section: F Illustrationmentioning

confidence: 99%

Testing Stationarity With Surrogates: A Time-Frequency Approach

Borgnat

Flandrin

Honeiné

et al. 2010

IEEE Trans. Signal Process.

149

105

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“…(43) Instead, we show that (43) holds for all t ∈ supp (T na w r )which, together with (42), is sufficient to establish (41), and consequently our claimed result.…”

Section: Discussionmentioning

confidence: 58%

Superposition Frames for Adaptive Time-Frequency Analysis and Fast Reconstruction

Rudoy

Basu

Wolfe

2010

IEEE Trans. Signal Process.

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Abstract-In this article we introduce a broad family of adaptive, linear time-frequency representations termed superposition frames, and show that they admit desirable fast overlap-add reconstruction properties akin to standard short-time Fourier techniques. This approach stands in contrast to many adaptive time-frequency representations in the existing literature, which, while more flexible than standard fixed-resolution approaches, typically fail to provide for efficient reconstruction and often lack the regular structure necessary for precise frame-theoretic analysis. Our main technical contributions come through the development of properties which ensure that our superposition construction provides for a numerically stable, invertible signal representation. Our primary algorithmic contributions come via the introduction and discussion of specific signal adaptation criteria in deterministic and stochastic settings, based respectively on time-frequency concentration and nonstationarity detection. We conclude with a short speech enhancement example that serves to highlight potential applications of our approach.

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“…Two main questions may be identified in this regard, the first is on how to select the length of the period where it is considered that the structural parameters remain more or less constant; the second is on how to represent the variability in the parameters as a function of the EOCs. The selection of the period of pseudoconstant dynamics may be obtained empirically by means of stationarity tests, as described for example in Kay (2008), Basu et al (2009), andBorgnat et al (2010). On the other hand, the representation of the variability in the dynamics of the structure as an effect of the EOCs is the main problem addressed in this work, for which a Gaussian Process Regression approach is postulated, as shown in the remainder of this work.…”

Section: Limitations Of the Traditional Linear Regressive Modelsmentioning

confidence: 99%

Gaussian Process Time-Series Models for Structures under Operational Variability

Avendaño-Valencia

Chatzi

Koo

et al. 2017

Front. Built Environ.

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A wide range of vibrating structures are characterized by variable structural dynamics resulting from changes in environmental and operational conditions, posing challenges in their identification and associated condition assessment. To tackle this issue, the present contribution introduces a stochastic modeling methodology via Gaussian Process (GP) time-series models. In the presently introduced approach, the vibration response is represented by means of a random coefficient time-series model, whose coefficients comply with a GP regression on the environmental and operational parameters. The approach may be implemented in conjunction to any type of linear-in-the-parameters time-series model, ranging from simple AR models to more complex non-linear or nonstationary time-series models. The obtained GP time-series modeling approach provides an effective and compact global representation of the vibrational response of a structure under a wide span of environmental and operational conditions. The effectiveness of the postulated GP time-series models is demonstrated through two case studies: the first involves the identification of the vertical vibration response of the Humber bridge, evaluated over a period of three years; the second considers the long-term simulated vibration response of a wind turbine featuring non-stationary dynamics stemming from the rotor speed. In both cases, the variation of the average wind speed is the main driver of uncertainty, while, through application of the proposed GP time-series models, it is possible to track the resulting variation in modal quantities.

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A nonparametric test for stationarity based on local Fourier analysis

Cited by 17 publications

References 4 publications

Testing Stationarity With Surrogates: A Time-Frequency Approach

Testing Stationarity With Surrogates: A Time-Frequency Approach

Superposition Frames for Adaptive Time-Frequency Analysis and Fast Reconstruction

Gaussian Process Time-Series Models for Structures under Operational Variability

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