Use Of Extreme Value Statistics Research Articles

Process qualification of laser powder bed fusion based on processing-defect structure-fatigue properties in Ti-6Al-4V

The aim of this manuscript is to give a compact overview of the results that illustrate the applicability of processing-structure-property relationships in the increasingly important context of 3D printing of metals. A process qualification approach based on the physics-based understanding of defect formation in laser powder bed fusion (L-PBF) additive manufacturing (AM) is investigated for an aerospace-grade titanium alloy (Ti-6Al-4V). A physically interpretable qualification approach is critical for enabling L-PBF part certification for structure-critical applications. This approach relies on systematic experimentation, characterization, testing, and data analysis tasks including design of experiments varying power and velocity to generate varying defect populations, process window development based on defect structure, high throughput fatigue testing, and fractography, 2D porosity characterization, and use of extreme value statistics to develop a porosity metric that, in turn, could have predictive power for the variation in fatigue performance. Results from four-point bend fatigue tests demonstrate that a process window can be defined based on this key mechanical property. This relatively high throughput approach can, in turn, support a reduced set of round bar fatigue tests typically used for qualification. Overall, the proposed ecosystem for process qualification of L-PBF AM shows promise and is expected to apply to other materials and powder bed fusion AM technologies. • A delineated process window for L-PBF printing with Ti-6Al-4V was identified for both porosity and fatigue in power and velocity space with all other variables fixed, which is in good agreement with previous work. • There is a distinct increase in porosity as one moves into the keyhole range (low speed, high power) or towards lack-of-fusion (high speed, low power). • Extreme value analysis (EVA) is found to be beneficial in quantifying pore sizes and frequencies. • The fatigue life measured in 4-point bend fatigue mirrors the variations in porosity, i.e., the fatigue life decreases as porosity increases and is maximal within the process window. • 4-point bend fatigue is found to be practical for screening printed material quality.

A Nearest Neighbor Open-Set Classifier based on Excesses of Distance Ratios

This article proposes an open-set recognition model that is based on the use of extreme value statistics. For this purpose, a distance ratio is introduced that expresses how dissimilar a target point is from the known classes by considering the ratio of distances locally around the target point. It is shown that the class of generalized Pareto distributions with bounded support can be used to model the peaks of the distance ratio above a high threshold. The resulting distribution provides a probabilistic framework to perform open-set recognition. Furthermore, we describe a numerical procedure to estimate the hyperparameters of our model. This procedure is based on a new objective function that considers both the fit of the generalized Pareto distribution and the misclassification error of the known classes. Our method is applied to three image datasets and an audio dataset showing that it outperforms similar open-set recognition and anomaly detection methods. Supplementary materials for this article are available online.

A Note on the Estimation of the Maximum Possible Earthquake Magnitude Based on Extreme Value Theory for the Groningen Gas Field

ABSTRACT Extreme value statistics is a popular and frequently used tool to model the occurrence of large earthquakes. The problem of poor statistics arising from rare events is addressed by taking advantage of the validity of general statistical properties in asymptotic regimes. In this note, I argue that the use of extreme value statistics for the purpose of practically modeling the tail of the frequency–magnitude distribution of earthquakes can produce biased and thus misleading results because it is unknown to what degree the tail of the true distribution is sampled by data. Using synthetic data allows to quantify this bias in detail. The implicit assumption that the true Mmax is close to the maximum observed magnitude Mmax,observed restricts the class of the potential models a priori to those with Mmax=Mmax,observed+ΔM with an increment ΔM≈0.5…1.2. This corresponds to the simple heuristic method suggested by Wheeler (2009) and labeled “Mmax equals Mobs plus an increment.” The incomplete consideration of the entire model family for the frequency–magnitude distribution neglects, however, the scenario of a large so far unobserved earthquake.

The Use of Extreme Value Statistics to Characterize Blood Glucose Curves and Patient Level Risk Assessment of Patients With Type I Diabetes.

Characterizing blood glucose curves and providing precise patient level risk assessment of hyperglycemia using extreme value statistics and comparing these assessments with traditional indicators of glycemic variability which are not designed to specifically capture the risk of hyperglycemia. One year return level (blood glucose level exceeded exactly once every year on average) and probability of exceeding and expected time spent above certain thresholds (600 and 400 mg/dL) per year were calculated. As a comparison, traditional metrics for glycemic variability were determined too. The effect of body mass index on extremes was also investigated using non-stationary models. Metrics were calculated on a dataset containing 170.8 patient-years of measurements of 226 patients. Nine high-risk patients were identified with the novel metrics: their estimated time spent above 600 mg/dL per year were above 2 hours. These patients were at moderate risk according to the traditional metrics. Higher body mass index was associated with more extreme glucose levels. Through these estimates it is possible to assess each patient's individual clinical risk of hyperglycemia even beyond the observed blood glucose levels and detection limits. Additionally, it allows the assessment of the impact of clinical characteristics and treatments on blood glucose control in a novel, mathematically well-founded and potentially clinically more useful way than the already existing indicators.

FAS-Compatible Synthetic Signals for Equivalent-Linear Site Response Analyses

An alternative approach to generate the seismic input for equivalent-linear (EQL) site response analyses is proposed. The proposed approach encompasses the strengths from current time histories (THs) and random vibration theory (RVT) methods. It consists of the generation of synthetic signals in the time domain (analogous to the TH method) that are constructed to have a Fourier amplitude spectrum (FAS) compatible with the design response spectrum (analogous to the RVT method). Through this approach, the use of extreme value statistics (used in RVT and known to overestimate amplification functions) is avoided. Moreover, the need to develop an appropriate suite of realistic acceleration series, which is the most challenging and time-consuming part of the TH-based approach, is also circumvented. The methodology is evaluated through a comprehensive analysis that includes different site conditions, input spectral shapes, duration scenarios, levels of inelastic demand, and number of synthetic signals used.

Use of Extreme Value Statistics to Assess the Performance Implications of Cascaded ROADMs

The performance implications of passband impairments and bandwidth narrowing caused by the cascading of optical filters are investigated using a 100 Gb/s dual polarization, quadrature-phase-shift-keyed (DP QPSK) transceiver. The overall responses for cascades of filters are emulated using the combination of a programmable optical filter and variable bandwidth optical filter. The statistical variations in the responses for a cascade are addressed by considering 1000 realizations that result from randomly selected responses for each of the individual filters. To determine the impact on system margins, a methodology based on extreme value statistics is presented. The signal-to-noise ratios (SNRs) that correspond to real-time estimates of the pre-forward error correction bit error ratio (pre-FEC BER) are quantified in terms of the probability that the minimum of $n$ observations of the SNR is less than a specified value (maximum pre-FEC BER exceeds a specified value). This approach improves the reliability of predicting the impact of cascaded filtering on system performance by removing the uncertainty about the underlying statistical distribution of the SNR.

One-class classification of point patterns of extremes

Novelty detection or one-class classification starts from a model describing some type of 'normal behaviour' and aims to classify deviations from this model as being either novelties or anomalies. In this paper the problem of novelty detection for point patterns S = {x1,...,xk} ⊂ Rd is treated where examples of anomalies are very sparse, or even absent. The latter complicates the tuning of hyperparameters in models commonly used for novelty detection, such as one-class support vector machines and hidden Markov models. To this end, the use of extreme value statistics is introduced to estimate explicitly a model for the abnormal class by means of extrapolation from a statistical model X for the normal class. We show how multiple types of information obtained from any available extreme instances of S can be combined to reduce the high false-alarm rate that is typically encountered when classes are strongly imbalanced, as often occurs in the one-class setting (whereby 'abnormal' data are often scarce). The approach is illustrated using simulated data and then a real-life application is used as an exemplar, whereby accelerometry data from epileptic seizures are analysed - these are known to be extreme and rare with respect to normal accelerometer data.

PHP33 The Use of Extreme Value Statistics in Assessing Long Decision Times in Public Funding of Medicines with New Molecules or Therapeutic Indications

PHP33 The Use of Extreme Value Statistics in Assessing Long Decision Times in Public Funding of Medicines with New Molecules or Therapeutic Indications

Exact extreme value statistics and the halo mass function

ABSTRACT Motivated by observations that suggest the presence of extremely massive clusters at uncomfortably high redshifts for the standard cosmological model to explain, we develop a theoretical framework for the study of the most massive haloes, e.g. the most massive cluster found in a given volume, based on extreme value statistics (EVS). We proceed from the exact distribution of the extreme values drawn from a known underlying distribution, rather than relying on asymptotic theory (which is independent of the underlying form), arguing that the former is much more likely to furnish robust statistical results. We illustrate this argument with a discussion of the use of extreme value statistics as a probe of primordial non-Gaussianity.

Analysis of laser-induced breakdown spectroscopy spectra: The case for extreme value statistics

In most instances, laser-induced breakdown spectroscopy (LIBS) spectra are obtained through analog accumulation of multiple shots in the spectrometer CCD. The average acquired in the CCD at a given wavelength is assumed to be a good representation of the population mean, which in turn is implicitly regarded to be the best estimator for the central value of the distribution of the spectrum at the same wavelength. Multiple analog accumulated spectra are taken and then in turn averaged wavelength-by-wavelength to represent the final spectrum. In this paper, the statistics of single-shot and analog accumulated LIBS spectra of both solids and liquids were examined to evaluate whether the spectrum averaging approach is statistically defensible. At a given wavelength, LIBS spectra are typically drawn from a Frechet extreme value distribution, and hence the mean of an ensemble of LIBS spectra is not necessarily an optimal summary statistic. Under circumstances that are broadly general, the sample mean for LIBS data is statistically inconsistent and the central limit theorem does not apply. This result appears to be due to very high shot-to-shot plasma variability in which a very small number of spectra are high in intensity while the majority are very weak, yielding the extreme value form of the distribution. The extreme value behavior persists when individual shots are analog accumulated. An optimal estimator in a well-defined sense for the spectral average at a given wavelength follows from the maximum likelihood method for the extreme value distribution. Example spectra taken with both an Echelle and a Czerny–Turner spectrometer are processed with this scheme to create smooth, high signal-to-noise summary spectra. Plasma imaging was used in an attempt to visually understand the observed variability and to validate the use of extreme value statistics. The data processing approach presented in this paper is statistically reliable and should be used for accurate comparisons of LIBS spectra instead of arithmetic averaging on either complete or censored data sets.

3D statistical parametric mapping of EEG source spectra by means of variable resolution electromagnetic tomography (VARETA).

This article describes a new method for 3D QEEG tomography in the frequency domain. A variant of Statistical Parametric Mapping is presented for source log spectra. Sources are estimated by means of a Discrete Spline EEG inverse solution known as Variable Resolution Electromagnetic Tomography (VARETA). Anatomical constraints are incorporated by the use of the Montreal Neurological Institute (MNI) probabilistic brain atlas. Efficient methods are developed for frequency domain VARETA in order to estimate the source spectra for the set of 10(3)-10(5) voxels that comprise an EEG/MEG inverse solution. High resolution source Z spectra are then defined with respect to the age dependent mean and standard deviations of each voxel, which are summarized as regression equations calculated from the Cuban EEG normative database. The statistical issues involved are addressed by the use of extreme value statistics. Examples are shown that illustrate the potential clinical utility of the methods herein developed.

Statistics for modeling heavy tailed distributions in geology : Part II. Applications

In this paper, we present three diverse types of applications of extreme value statistics in geology, namely: earthquakes magnitudes, diamond values, and impact crater size distribution on terrestrial planets. Each of these applications has a different perspective toward tail modeling, yet many of these phenomena exhibit heavy or long tails which can be modeled by power laws. It is shown that the estimation of important tail characteristics, such as the extreme value index, is directly linked to the interpretation of the underlying geological process. Only the most extreme data are useful for studying such phenomena, so thresholds must be selected above which the data become power laws. In the case of earthquake magnitudes, we investigate the use of extreme value statistics in predicting large events on the global scale and for shallow intracontinental earthquakes in Asia. Large differences are found between estimates obtained from extreme value statistics and the usually applied standard statistical techniques. In the case of diamond deposits, we investigate the impact of the most precious stones in the global valuation of primary deposits. It is shown that in the case of Pareto-type behavior, the expected value of few extreme stones in the entire deposit has considerable influence on the global valuation. In the case of impact crater distributions, we study the difference between craters distributions on Earth and Mars and distributions occurring on other planets or satellites within the solar system. A striking result is that all planets display the same distributional tail except for Earth and Mars. In a concluding account, we demonstrate the apparent loghyperbolic variation in all of the above-mentioned examples.

Some critical remarks on the use of extreme-value statistics in climatology

Conventional statistical methods for the description of extreme events do not meet all mathematical conditions with respect to the analysis of meteorological parameters. Examples are presented illustrating the problems of using conventional extreme-value statistics. Inter alia, non-stationarity, extrapolation and estimation of the errors are discussed. Some ideas on how to solve these problems are presented, e.g. by the use of marginal distributions, spline functions and the estimation of the magnitude of non-stationarity.