Non-destructive testing of aerospace structures: granularity and data mining approach

Osegueda, Roberto A; Kreinovich, Vladik; Potluri, L.; Alò, Richard A.

doi:10.1109/fuzz.2002.1005075

Cited by 12 publications

(11 citation statements)

References 6 publications

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“…Uncertainty about measurements that is appropriately characterized by intervals is called incertitude, and it arises naturally in a variety of circumstances Osegueda et al 2002). This section reviews eight sources from which the information is best represented by intervals, including plus-or-minus reports, significant digits, intermittent measurement, non-detects, censoring, data binning, missing data and gross ignorance.…”

Section: Where Do Interval Data Come From?mentioning

confidence: 99%

Experimental uncertainty estimation and statistics for data having interval uncertainty.

et al. 2007

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This report addresses the characterization of measurements that include epistemic uncertainties in the form of intervals. It reviews the application of basic descriptive statistics to data sets which contain intervals rather than exclusively point estimates. It describes algorithms to compute various means, the median and other percentiles, variance, interquartile range, moments, confidence limits, and other important statistics and summarizes the computability of these statistics as a function of sample size and characteristics of the intervals in the data (degree of overlap, size and regularity of widths, etc.). It also reviews the prospects for analyzing such data sets with the methods of inferential statistics such as outlier detection and regressions. The report explores the tradeoff between measurement precision and sample size in statistical results that are sensitive to both. It also argues that an approach based on interval statistics could be a reasonable alternative to current standard methods for evaluating, expressing and propagating measurement uncertainties. 4 AcknowledgmentsWe thank Roger Nelsen of Lewis and Clark University, Bill Huber of Quantitative Decisions, Gang Xiang, Jan Beck, Scott Starks and Luc Longpré of University of Texas at El Paso, Troy Tucker and David Myers of Applied Biomathematics, Chuck Haas of Drexel University, Arnold Neumaier of Universität Wien, and Jonathan Lucero and Cliff Joslyn of Los Alamos National Laboratory for their collaboration. We also thank Floyd Spencer and Steve Crowder for reviewing the report and giving advice that substantially improved it. Jason C. Cole of Consulting Measurement Group also offered helpful comments. Finally, we thank Tony O'Hagan of University of Sheffield for challenging us to say where intervals come from. The work described in this report was performed for Sandia National Laboratories under Contract Number 19094. William Oberkampf managed the project for Sandia. As always, the opinions expressed in this report and any mistakes it may harbor are solely those of the authors. This report will live electronically at http://www.ramas.com/intstats.pdf. Please send any corrections and suggestions for improvements to scott@ramas.com. the empty set  infinity, or simply a very large number  standard normal cumulative distribution function E the true scalar value of the arithmetic mean of measurands in a data set N sample size N(m, s) normal distribution with mean m and standard deviation s O(  ) on the order of P(  ) probability of R real line R* extended real line, i.e., R  {, } S N (X) the fraction of N values in a data set that are at or below the magnitude X Note on typography. Upper case letters are used to denote scalars and lower case letter are used for intervals. (The only major exception is that we still use lower case i, j, and k for integer indices.) For instance, the symbol E denotes the scalar value of the arithmetic mean of the measurands in a data set, even if we don't know its magnitude precisely. We might use ...

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Section: Where Do Interval Data Come From?mentioning

confidence: 99%

Experimental uncertainty estimation and statistics for data having interval uncertainty.

et al. 2007

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“…In contrast to the mean, variance, covariance, and correlation are, in general, nonmonotonic. It turns out that in general, computing the values of these characteristics under interval uncertainty is NP-hard [2,3,10,11]. This means, crudely speaking, that unless P=NP (which most computable scientists believe to be wrong), no feasible (i.e., no polynomial-time) algorithm is possible that would always compute the range of the corresponding characteristic under interval uncertainty.…”

Section: Need To Take Into Account Interval Uncertaintymentioning

confidence: 99%

“…Interval computations -in particular, interval computations of statistical characteristics -have many applications, in particular, engineering applications; see, e.g., [1,4,5,7,8,9,10,11,13].…”

Section: Need To Take Into Account Interval Uncertaintymentioning

confidence: 99%

Estimating correlation under interval uncertainty

Jalal-Kamali

Kreinovich

2013

Mechanical Systems and Signal Processing

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In many engineering situations, we are interested in finding the correlation ρ between different quantities x and y based on the values xi and yi of these quantities measured in different situations i. Measurements are never absolutely accurate; it is therefore necessary to take this inaccuracy into account when estimating the correlation ρ. Sometimes, we know the probabilities of different values of measurement errors, but in many cases, we only know the upper bounds ∆xi and ∆yi on the corresponding measurement errors. In such situations, after we get the measurement results xi and yi, the only information that we have about the actual (unknown) values xi and yi is that they belong to the corresponding intervals [ xi − ∆xi, xi + ∆xi] and [ yi − ∆yi, yi + ∆yi]. Different values from these intervals lead, in general, to different values of the correlation ρ. It is therefore desirable to find the range [ρ, ρ] of possible values of the correlation when xi and yi take values from the corresponding intervals. In general, the problem of computing this range is NP-hard. In this paper, we provide a feasible (= polynomial-time) algorithm for computing at least one of the endpoints of this interval: for computing ρ when ρ > 0 and for computing ρ when ρ < 0.

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“…In general, computing the range of the covariance C xy based on given intervals x i and y i is NP-hard [38].…”

Section: Covariancementioning

confidence: 99%

“…To detect an outlier, we must know the mean and standard deviation of the normal values -and these values can often only be measured with interval uncertainty (see, e.g., [38,39]). In other words, often, we know the result x of measuring the desired characteristic x, and we know the upper bound ∆ on the absolute value |∆x| of the measurement error ∆x def = x − x (this upper bound is provided by the manufacturer of the measuring instrument), but we have no information about the probability of different values ∆x ∈ [−∆, ∆].…”

mentioning

confidence: 99%

Fast Algorithms for Computing Statistics under Interval Uncertainty: An Overview

Kreinovich

Xiang

Advances in Soft Computing

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Abstract. In many engineering applications, we have to combine probabilistic and interval uncertainty. For example, in environmental analysis, we observe a pollution level x(t) in a lake at different moments of time t, and we would like to estimate standard statistical characteristics such as mean, variance, autocorrelation, correlation with other measurements. In environmental measurements, we often only measure the values with interval uncertainty. We must therefore modify the existing statistical algorithms to process such interval data.In this paper, we provide a survey of algorithms for computing various statistics under interval uncertainty and their computational complexity. The survey includes both known and new algorithms.

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Non-destructive testing of aerospace structures: granularity and data mining approach

Cited by 12 publications

References 6 publications

Experimental uncertainty estimation and statistics for data having interval uncertainty.

Experimental uncertainty estimation and statistics for data having interval uncertainty.

Estimating correlation under interval uncertainty

Fast Algorithms for Computing Statistics under Interval Uncertainty: An Overview

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