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Results for “generalized likelihood ratio test”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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Bearing Fault Detection on Wind Turbine Gearbox Vibrations Using Generalized Likelihood Ratio-Based Indicators

Studies in condition monitoring literature often aim to detect rolling element bearing faults because they have one of the biggest shares among defects in turbo machinery. Accordingly, several prognosis and diagnosis methods have been devised to identify fault signatures from vibration signals. A recently proposed method to capture the rolling element bearing degradation provides the groundwork for new indicator families utilizing the generalized likelihood ratio test. This novel approach exploits the cyclostationarity and the impulsiveness of vibration signals independently in order to estimate the most suitable indicators for a given fault. However, the method has yet to be tested on complex experimental vibration signals such as those of a wind turbine gearbox. In this study, the approach is applied to the National Renewable Energy Laboratory Wind Turbine Gearbox Condition Monitoring Round Robin Study data set for bearing fault detection purposes. The data set is measured on an experimental test rig of a wind turbine gearbox; hence the complexity of the vibration signals is similar to a real case. The outcome demonstrates that the proposed method is capable of distinguishing between healthy and damaged vibration signals measured on a complex wind turbine gearbox.

condition monitoring↗

Statistical Significance Testing for Mixed Priors: A Combined Bayesian and Frequentist Analysis

In many hypothesis testing applications, we have mixed priors, with well-motivated informative priors for some parameters but not for others. The Bayesian methodology uses the Bayes factor and is helpful for the informative priors, as it incorporates Occam’s razor via the multiplicity or trials factor in the look-elsewhere effect. However, if the prior is not known completely, the frequentist hypothesis test via the false-positive rate is a better approach, as it is less sensitive to the prior choice. We argue that when only partial prior information is available, it is best to combine the two methodologies by using the Bayes factor as a test statistic in the frequentist analysis. We show that the standard frequentist maximum likelihood-ratio test statistic corresponds to the Bayes factor with a non-informative Jeffrey’s prior. We also show that mixed priors increase the statistical power in frequentist analyses over the maximum likelihood test statistic. We develop an analytic formalism that does not require expensive simulations and generalize Wilks’ theorem beyond its usual regime of validity. In specific limits, the formalism reproduces existing expressions, such as the p-value of linear models and periodograms. We apply the formalism to an example of exoplanet transits, where multiplicity can be more than 10 7 . We show that our analytic expressions reproduce the $p$-values derived from numerical simulations. We offer an interpretation of our formalism based on the statistical mechanics. We introduce the counting of states in a continuous parameter space using the uncertainty volume as the quantum of the state. We show that both the $p$-value and Bayes factor can be expressed as an energy versus entropy competition.

97 MATHEMATICS AND COMPUTING↗

Constraining cosmological parameters using the pairwise kinematic Sunyaev-Zel’dovich effect with CMB-S4 and future galaxy cluster surveys

We present a forecast of the pairwise kinematic Sunyaev-Zel’dovich (kSZ) measurement that will be achievable with the future CMB-S4 experiment. CMB-S4 is the next stage for ground-based cosmic microwave background experiments, with a planned wide-area survey that will observe approximately 50% of the sky. We construct a simulated sample of galaxy clusters that have been optically selected in a Legacy Survey of Space and Time–like survey and have spectroscopic redshifts. For this cluster sample, assuming the likelihood is Gaussian, we predict that CMB-S4 will reject the null hypothesis of zero pairwise kSZ signal at 36⁢𝜎. We estimate the effects of systematic uncertainties such as scatter in the mass-richness scaling relation and cluster miscentering. We find that these effects can reduce the signal-to-noise ratio of the CMB-S4 pairwise kSZ measurement by 20%. We explore the constraining power of the measured kSZ signal in combination with measurements of the galaxy clusters’ thermal SZ emission on two extensions to the standard cosmological model. The first extension allows the dark energy equation of state 𝑤 to vary. We find the CMB-S4 pairwise kSZ measurement yields a modest reduction in the uncertainty on 𝑤 by a factor of 1.36 over the Planck’s 2018 uncertainty. The second extension tests general relativity by varying the growth index 𝛾. In conclusion, we find that CMB-S4’s pairwise kSZ measurement will yield a 28⁢𝜎 constraint on 𝛾 and strongly constrain alternative theories of gravity.

79 ASTRONOMY AND ASTROPHYSICS↗