Automatic Autocorrelation and Spectral Analysis

Broersen, P.M.T.

doi:10.1007/1-84628-329-9

Cited by 42 publications

(4 citation statements)

References 77 publications

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“…Thus, estimating the autocorrelation reduces to estimating the parameters of an AR model. However, because the "true" process order is unknown, a hierarchy of models with increasing order p are simultaneously estimated 9,10 . From these candidates, the best model is chosen using an information-theoretic, finite sampling model selection criterion 8 .…”

Section: A Sampling Errormentioning

confidence: 99%

“…Fitting such models to observed data has been studied extensively 3,4,[9][10][11]23 , and there are a number of available algorithms. Here, classical Burg recursion 3 is used to compute the parameters because it is less susceptible to round-off error accumulation than the more efficient recursive denominator variant 4,23 .…”

Section: A Sampling Errormentioning

confidence: 99%

“…In this approach, the autocorrelation of the data, which is not known a priori, must be estimated from the data, which presents its own challenges. Here, we follow the work of Broersen 9,10 and fit autoregressive models from which the autocorrelation function is then computed.…”

Section: Introductionmentioning

confidence: 99%

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Estimating uncertainties in statistics computed from direct numerical simulation

et al. 2014

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1 Rigorous assessment of uncertainty is crucial to the utility of DNS results. Uncertainties in the computed statistics arise from two sources: finite statistical sampling and the discretization of the Navier-Stokes equations. Due to the presence of nontrivial sampling error, standard techniques for estimating discretization error (such as Richardson extrapolation) fail or are unreliable. This work provides a systematic and unified approach for estimating these errors. First, a sampling error estimator that accounts for correlation in the input data is developed. Then, this sampling error estimate is used as part of a Bayesian extension of Richardson extrapolation in order to characterize the discretization error. These methods are tested using the Lorenz equations and are shown to perform well. These techniques are then used to investigate the sampling and discretization errors in the DNS of a wall-bounded turbulent flow atdomain sizes are investigated. For each case, a sequence of meshes was generated by first designing a "nominal" mesh using standard heuristics for wall-bounded sim-

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Section: A Sampling Errormentioning

confidence: 99%

Section: A Sampling Errormentioning

confidence: 99%

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Estimating uncertainties in statistics computed from direct numerical simulation

et al. 2014

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“…Due to the scaling factor, unbiased auto-correlation functions are indefinite and have statistical and numerical disadvantages for practical applications in power spectral density estimations. They may result in negative values of power, contradicting physical interpretation and prohibiting a representation in logarithmic scale [26,[28][29][30]. This was observed by us also for unbiased RR τ and the usage of a biased estimator (superscript * )…”

Section: Power Spectral Density Estimationmentioning

confidence: 64%

Recurrence Rate spectrograms for the classification of nonlinear and noisy signals

Hertrampf,

Oberst

2024

Phys. Scr.

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Time series analysis of real-world measurements is fundamental in naturalsciences and engineering, and machine learning has been recently of great assistance especiallyfor classification of signals and their understanding. Yet, the underlying system’s nonlinearresponse behaviour is often neglected. Recurrence Plot (RP) based Fourier-spectra constructedthrough τ-Recurrence Rate (RRτ) have shown the potential to reveal nonlinear traits otherwisehidden from conventional data processing. We report a so far disregarded eligibility forsignal classification of nonlinear time series by training RESnet-50 on spectrogram images,which allows recurrence-spectra to outcompete conventional Fourier analysis. To exemplify itsfunctioning, we employ a simple nonlinear physical flow of a continuous stirred tank reactor,able to exhibit exothermic, first order, irreversible, cubic autocatalytic chemical reactions, anda plethora of fast-slow dynamics. For dynamics with noise being ten times stronger than thesignal, the classification accuracy was up to ≈75 % compared to ≈17 % for the periodogram.We show that an increase in entropy only detected by the RRτ allows differentiation. Thisshows that RP power spectra, combined with off-the-shelf machine learning techniques, havethe potential to significantly improve the detection of nonlinear and noise contaminated signals.

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Low Cost Recurrent and Asymptotically Unbiased Estimators of Statistical Uncertainty on Averaged Fields for DNS and LES

Boxho,

Toulorge,

Rasquin

et al. 2024

Flow Turbulence Combust

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Automatic Autocorrelation and Spectral Analysis

Cited by 42 publications

References 77 publications

Estimating uncertainties in statistics computed from direct numerical simulation

Estimating uncertainties in statistics computed from direct numerical simulation

Recurrence Rate spectrograms for the classification of nonlinear and noisy signals

Low Cost Recurrent and Asymptotically Unbiased Estimators of Statistical Uncertainty on Averaged Fields for DNS and LES

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