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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Entropy-Infused Deep Learning Loss Function for Capturing Extreme Values in Wind Power Forecasting

Extreme scenarios in wind power generation occur with higher frequency and larger magnitude in the recent years due to the ever-increasing extreme meteorological factors. Accurate forecasting of the occurrence of extreme values in wind power generation is of great concern to ensure reliable power system operation. Recently, deep learning models have surged in popularity for wind power forecasting, with the mean squared error (MSE) loss function being commonly used. However, the MSE loss function, being sensitive to extreme values, disproportionately penalizes larger errors, cannot adequately capture the extreme values present in wind energy data, and novel loss functions have seldom been tailored for wind power forecasting. To this end, in this paper, we introduce a novel loss function specifically crafted to capture extreme values in wind power forecasting. The experimental results with four fundamental deep learning methods on open source wind power dataset validate that the new loss function is efficient and superior in all cases compared to MSE in capturing extreme values while maintaining forecasting performance.

17 WIND ENERGY↗
DOE OSTI2024

Extreme-value statistics in nonlinear optics

We show that, although nonlinear optics may give rise to a vast multitude of statistics, all these statistics converge, in their extreme-value limit, to one of a few universal extreme-value statistics. Specifically, in the class of polynomial nonlinearities, such as those found in the Kerr effect, weak-field harmonic generation, and multiphoton ionization, the statistics of the nonlinear-optical output converges, in the extreme-value limit, to the exponentially tailed, Gumbel distribution. Exponentially growing nonlinear signals, on the other hand, such as those induced by parametric instabilities and stimulated scattering, are shown to reach their extreme-value limits in the class of the Fréchet statistics, giving rise to extreme-value distributions (EVDs) with heavy, manifestly nonexponential tails, thus favoring extreme-event outcomes and rogue-wave buildup.

Zheltikov, Aleksei M. (ORCID:0000000291380576)↗
NASA NTRS1972

Bias and spread in extreme value theory measurements of probability of error

Extreme value theory is examined to explain the cause of the bias and spread in performance of communications systems characterized by low bit rates and high data reliability requirements, for cases in which underlying noise is Gaussian or perturbed Gaussian. Experimental verification is presented and procedures that minimize these effects are suggested. Even under these conditions, however, extreme value theory test results are not particularly more significant than bit error rate tests.

Smith, J. G.↗
DOE OSTI2024

Extreme Risk Mitigation in Reinforcement Learning using Extreme Value Theory

Risk-sensitive reinforcement learning (RL) has garnered significant attention in recent years due to the growing interest in deploying RL agents in real-world scenarios. A critical aspect of risk awareness involves modelling highly rare risk events (rewards) that could potentially lead to catastrophic outcomes. These infrequent occurrences present a formidable challenge for data-driven methods aiming to capture such risky events accurately. While risk-aware RL techniques do exist, they suffer from high variance estimation due to the inherent data scarcity. Our work proposes to enhance the resilience of RL agents when faced with very rare and risky events by focusing on refining the predictions of the extreme values predicted by the state-action value distribution. To achieve this, we formulate the extreme values of the state-action value function distribution as parameterized distributions, drawing inspiration from the principles of extreme value theory (EVT). We propose an extreme value theory based actor-critic approach, namely, Extreme Valued Actor-Critic (EVAC) which effectively addresses the issue of infrequent occurrence by leveraging EVT-based parameterization. Importantly, we theoretically demonstrate the advantages of employing these parameterized distributions in contrast to other risk-averse algorithms. Our evaluations show that the proposed method outperforms other risk averse RL algorithms on a diverse range of benchmark tasks, each encompassing distinct risk scenarios.

Wang, Yu↗
NASA NTRS2004

GPS FOM Chimney Analysis using Generalized Extreme Value Distribution

Many a time an objective of a statistical analysis is to estimate a limit value like 3-sigma 95% confidence upper limit from a data sample. The generalized Extreme Value Distribution method can be profitably employed in many situations for such an estimate. . .. It is well known that according to the Central Limit theorem the mean value of a large data set is normally distributed irrespective of the distribution of the data from which the mean value is derived. In a somewhat similar fashion it is observed that many times the extreme value of a data set has a distribution that can be formulated with a Generalized Distribution. In space shuttle entry with 3-string GPS navigation the Figure Of Merit (FOM) value gives a measure of GPS navigated state accuracy. A GPS navigated state with FOM of 6 or higher is deemed unacceptable and is said to form a FOM 6 or higher chimney. A FOM chimney is a period of time during which the FOM value stays higher than 5. A longer period of FOM of value 6 or higher causes navigated state to accumulate more error for a lack of state update. For an acceptable landing it is imperative that the state error remains low and hence at low altitude during entry GPS data of FOM greater than 5 must not last more than 138 seconds. I To test the GPS performAnce many entry test cases were simulated at the Avionics Development Laboratory. Only high value FoM chimneys are consequential. The extreme value statistical technique is applied to analyze high value FOM chimneys. The Maximum likelihood method is used to determine parameters that characterize the GEV distribution, and then the limit value statistics are estimated.

Ott, Rick↗
NASA NTRS1992

Extreme value statistics analysis of fracture strengths of a sintered silicon nitride failing from pores

Statistical analysis and correlation between pore-size distribution and fracture strength distribution using the theory of extreme-value statistics is presented for a sintered silicon nitride. The pore-size distribution on a polished surface of this material was characterized, using an automatic optical image analyzer. The distribution measured on the two-dimensional plane surface was transformed to a population (volume) distribution, using the Schwartz-Saltykov diameter method. The population pore-size distribution and the distribution of the pore size at the fracture origin were correllated by extreme-value statistics. Fracture strength distribution was then predicted from the extreme-value pore-size distribution, usin a linear elastic fracture mechanics model of annular crack around pore and the fracture toughness of the ceramic. The predicted strength distribution was in good agreement with strength measurements in bending. In particular, the extreme-value statistics analysis explained the nonlinear trend in the linearized Weibull plot of measured strengths without postulating a lower-bound strength.

Chao, Luen-Yuan↗
NASA NTRS1950

The application of the statistical theory of extreme values to gust-load problems

An analysis is presented which indicates that the statistical theory of extreme values is applicable to the problems of predicting the frequency of encountering the larger gust loads and gust velocities for both specific test conditions as well as commercial transport operations. The extreme-value theory provides an analytic form for the distributions of maximum values of gust load and velocity. Methods of fitting the distribution are given along with a method of estimating the reliability of the predictions. The theory of extreme values is applied to available load data from commercial transport operations. The results indicate that the estimates of the frequency of encountering the larger loads are more consistent with the data and more reliable than those obtained in previous analyses. (author)

Press, Harry↗
NASA NTRS1997

A New Approach to Extreme Value Estimation Applicable to a Wide Variety of Random Variables

Designing reliable structures requires an estimate of the maximum and minimum values (i.e., strength and load) that may be encountered in service. Yet designs based on very extreme values (to insure safety) can result in extra material usage and hence, uneconomic systems. In aerospace applications, severe over-design cannot be tolerated making it almost mandatory to design closer to the assumed limits of the design random variables. The issue then is predicting extreme values that are practical, i.e. neither too conservative or non-conservative. Obtaining design values by employing safety factors is well known to often result in overly conservative designs and. Safety factor values have historically been selected rather arbitrarily, often lacking a sound rational basis. To answer the question of how safe a design needs to be has lead design theorists to probabilistic and statistical methods. The so-called three-sigma approach is one such method and has been described as the first step in utilizing information about the data dispersion. However, this method is based on the assumption that the random variable is dispersed symmetrically about the mean and is essentially limited to normally distributed random variables. Use of this method can therefore result in unsafe or overly conservative design allowables if the common assumption of normality is incorrect.

Holland, Frederic A., Jr.↗
NASA NTRS1992

Bivariate extreme value distributions

In certain engineering applications, such as those occurring in the analyses of ascent structural loads for the Space Transportation System (STS), some of the load variables have a lower bound of zero. Thus, the need for practical models of bivariate extreme value probability distribution functions with lower limits was identified. We discuss the Gumbel models and present practical forms of bivariate extreme probability distributions of Weibull and Frechet types with two parameters. Bivariate extreme value probability distribution functions can be expressed in terms of the marginal extremel distributions and a 'dependence' function subject to certain analytical conditions. Properties of such bivariate extreme distributions, sums and differences of paired extremals, as well as the corresponding forms of conditional distributions, are discussed. Practical estimation techniques are also given.

Elshamy, M.↗
NASA NTRS2020

Comparison of Extreme Value Distributions for Electrostatic Discharge Magnitudes in Spacecraft Charging Tests

Electrostatic Discharge (ESD) induced by the accumulation of charge in the space environment is known to cause spacecraft anomalies and failures. While it is critical to estimate the worst-case expected ESD, sensitive radar instruments can be impacted by high rates of occurrence of very small ESD. To estimate the correct extreme behavior, it is important to select the correct extreme value distribution for extrapolation of test results limited in time and sensitivity. Quantile-quantile (Q-Q) analysis is used to compare electron beam-induced ESD test data to several statistical distributions used in the published literature. The best-fit distribution is shown to vary from between tests on different materials; however, it is clear that power law distributions are not good approximations for low amplitude events. Q-Q analysis is a convenient graphical method for evaluating multiple theoretical extreme-value distributions simultaneously.

Kim, Wousik↗
DOE OSTI2025

Misclassification in Workers’ Telecommuting Frequency Choices Using a Generalized Extreme Value Model

Telecommuting frequency is a response variable collected in travel surveys and is, therefore, prone to errors leading to mismeasurements or misclassification. Misclassification of explanatory variables is a common risk when using statistical modeling techniques. We define “misclassification” as a response reported or recorded in the wrong category; for example, a variable is recorded as a 1 when it should be 0. Here, in this context, this study aims to develop a statistical model to analyze telecommuting data which accounts for potential misclassification errors by building on existing literature in econometrics. The empirical analysis was undertaken using the 2017 National Household Travel Survey (NHTS) and the general extreme value (GEV) models available in the literature. Specifically, the frequency of telecommuting days was analyzed using the negative binomial (NB) model recast as the multinomial logit (MNL) model. By nature—and consistent with other studies—NHTS data are prone to errors that can be classified as intentional or unintentional misinformation provided by the person being interviewed. Ignoring these errors while modeling telecommuting frequencies using standard discrete count models can result in biased parameter estimates. The misclassification parameter was calculated for both over-reporting and under-reporting scenarios. The misclassification errors can be as high as 14% over-reported and 10% under-reported, particularly for the neighboring values. Statistical fit comparison between the models shows that models that ignore misclassification have worse data fit and biased parameter estimates with significant policy implications.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗