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Assessing the Effectiveness of Generalized Likelihood Ratio Test Detector Schemes in Seismic Event Detection and the Avoidance of Nontarget Signals

Cross-correlation techniques have played a long-standing and pivotal role in seismic event monitoring. However, the performance of correlation-based detectors is challenged by nuisance seismicity, or nontarget signals. Such detections are a problem when the mission is to automatically map events to the correct source region. Using aftershocks of the 2014 $M_w$ 6.0 South Napa, California, earthquake, we demonstrate the effectiveness of utilizing a dynamic correlation processor framework in a generalized likelihood ratio test (GLRT) detector configuration to minimize nontarget detections. A GLRT maximizes a detection statistic with respect to one or more unknown parameters. In this case, the detection statistic is a template signal match against the waveform in a window sliding over a data stream, and the unknown parameter is an index variable indicating group membership of the template event or events. Detected events are assigned to the event group that yields the largest detection statistic. In this work, our results show that a GLRT detector will outperform a suite of independently operating correlation and subspace detectors in terms of having a lower nontarget detection rate at a given missed detection rate. We also show that a GLRT detector composed of a few high-rank subspace detectors has a slightly higher nontarget detection rate, but a significantly lower missed detection rate, than a GLRT detector composed of many low-rank subspace detectors. The high-rank GLRT configuration produced impressive results even with marginal data (single channel, single station, and very low time bandwidth product), which bodes well for the utility of building efficient aftershock classification systems and global monitoring systems at larger scales. However, future work is required to assess performance at the regional scale and to assess the performance of the system at detecting target events not used in the detector template creation.

58 GEOSCIENCES↗

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↗

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

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. The underlying idea behind traditional indicators often revolves around tracking both cyclostationarity and abnormal impulses in the vibration signals without distinguishing the two. A recently proposed method to capture the rolling element bearing degradation lays out the groundwork for new indicator families utilizing 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 NREL 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. Furthermore, the new indicators are also tested with signals that carry multiple fault signatures. 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↗