Extremes of Nonlinear Vibration: Comparing Models Based on Moments, L-Moments, and Maximum Entropy

Winterstein, Steven R.; MacKenzie, Cameron A.

doi:10.1115/1.4007050

Cited by 48 publications

(16 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…corresponding to a monotone transformation of xðuÞ, requiring dx=du > 0. Practically, this condition corresponds to (Kwon and Kareem, 2011;Winterstein and Mackenzie, 2011) γ e ! ð1:25γ 3 Þ 2 :…”

Section: Required Duration Of the Time Seriesmentioning

confidence: 99%

A de-mixing approach for the management of large negative peaks in wind tunnel data

Rigo

Andrianne

Denoël

2020

Journal of Wind Engineering and Industrial Aerodynamics

View full text Add to dashboard Cite

Large negative peak pressures commonly take place near the edges of buildings due to the presence of local corner vortices and impingement of shear layers. As a result, Probability Density Functions (PDF) of the measured pressure signals exhibit one or more components which contributes to the non-Gaussianity of the pressure loading. These mixed flows can be modeled with mixture models. Whenever several processes coexist, and when one of them is leading in the tail of the statistical distribution, it is natural to construct the extreme value model with only this process leading in the tail and not with the mixed observed pressures. In this paper, we propose a method that is based on the autocorrelation of the pressure coefficient to de-mix the measured signals. This information improves the de-mixing process where classical methods would struggle. Indeed, the two phenomena to be separated and identified might be characterized by significantly different timescales , which are not reflected in the PDF. In this paper, the large negative pressures measured on a flat roof are analyzed and decomposed into two elementary processes, namely, the flapping corner vortex and the turbulent flow detaching from the sharp upstream edges. This paper finally shows that an accurate decomposition of the recorded pressures into their underlying modes provides a more meaningful evaluation of extreme pressures.

show abstract

Section: Required Duration Of the Time Seriesmentioning

confidence: 99%

A de-mixing approach for the management of large negative peaks in wind tunnel data

Rigo

Andrianne

Denoël

2020

Journal of Wind Engineering and Industrial Aerodynamics

View full text Add to dashboard Cite

show abstract

“…This makes the ME PDF of little use for softening behaviors, which are common cases of interest in structural engineering. For further details and numerical examples, see Winterstein and Mackenzie …”

Section: Me Formalismmentioning

confidence: 99%

“…Thus, only the lower‐order moments are typically considered, but in such case, f ME ( x ) hardly models tails fatter than the Gaussian. Therefore, the tails of many distributions cannot be well fitted by the ME distribution with M ≤ 4. Furthermore, from a practical point of view, we do not have the true moments , but samples of data, from which the sample moments are derived. Depending on the size of the sample, the estimates of the higher‐order moments provide large statistical errors, which imply high bias in the estimate of the tails of the ME PDF.…”

Section: Introductionmentioning

confidence: 99%

Kernel density maximum entropy method with generalized moments for evaluating probability distributions, including tails, from a small sample of data

Alibrandi

Mosalam

2017

Numerical Meth Engineering

View full text Add to dashboard Cite

In this paper, a novel method to determine the distribution of a random variable from a sample of data is presented. The approach is called generalized kernel density maximum entropy method, because it adopts a kernel density representation of the target distribution, while its free parameters are determined through the principle of maximum entropy (ME). Here, the ME solution is determined by assuming that the available information is represented from generalized moments, which include as their subsets the power and the fractional ones. The proposed method has several important features: (1) applicable to distributions with any kind of support, (2) computational efficiency because the ME solution is simply obtained as a set of systems of linear equations, (3) good tradeoff between bias and variance, and (4) good estimates of the tails of the distribution, in the presence of samples of small size. Moreover, the joint application of generalized kernel density maximum entropy with a bootstrap resampling allows to define credible bounds of the target distribution. The method is first benchmarked through an example of stochastic dynamic analysis. Subsequently, it is used to evaluate the seismic fragility functions of a reinforced concrete frame, from the knowledge of a small set of available ground motions. /journal/nme other quantities derived from the data. The first general representations for a PDF have adopted Hermite polynomials, eg, A-type and C-type Gram Charlier series and the Edgeworth series expansion. 3,4 An improvement is represented by the model proposed by Winterstein, 5 and it is largely applied in engineering.The choice of the distribution type is an open issue, from a conceptual and practical point of view. In the presence of limited information (sample of small size and/or lower-order moments), in the most general case, there is no theoretical justification to prefer one distribution over another. In such case, an attractive technique is based on the principle of maximum entropy (ME). [6][7][8] The ME distribution represents the least biased distribution given the available information. However, the application of the ME principle, as typically adopted in literature, has some practical and theoretical limitations.If the power moments represent the available information, then the ME PDF f ME (x) may require a large number M of moments (M ≥ 4) to accurately describe the tails of the distribution. However, the moment problem is an ill-posed problem. 9 Thus, for large M, the entropy maximization algorithm experiences numerical instability. Moreover, at the tails, the ME distribution oscillates because of the nonmonotonic nature of the polynomial embedded in the f ME (x). Thus, only the lower-order moments are typically considered, but in such case, f ME (x) hardly models tails fatter than the Gaussian. Therefore, the tails of many distributions cannot be well fitted by the ME distribution with M ≤ 4. 10 Furthermore, from a practical point of view, we do not have the true moments, but samples of data, f...

show abstract

“…Subsequently, the scale parameter can be calculated with the following equation derived from Eqs. (15) and 24:…”

Section: Parameter Estimationmentioning

confidence: 99%

“…In most cases, the sampling variability of the parameter values determined from the two alternative methods of moments was much less than that of the conventional method of moments. Winterstein and MacKenzie [15] improved the four-moment Hermite model by using L-moments rather than conventional moments to estimate the extreme response statistics of nonlinear wind and wave loads on offshore structures. L-moments are defined as linear combinations of the overall statistics for the whole sample data.…”

Section: Introductionmentioning

confidence: 99%

LH-moment estimation for statistical analysis on the wave crest distributions of a deepwater spar platform model test

et al. 2017

View full text Add to dashboard Cite

The design of fixed and compliant offshore platforms requires the reliable estimation of extreme values with small probabilities of exceedance based on an appropriate probability distribution. The Weibull distribution is commonly utilised for the statistical analysis of wave crests, including near-field wave run-ups. The parameters are estimated empirically from experimental or onsite measurements. In this paper, the data set of wave crests from a Spar model test was statistically analysed by using the method of LH-moments for parameter estimation of the Weibull distribution. The root-mean-square errors (RMSEs) and the error of LH-kurtosis were used to examine the goodness-of-fit. The results for the first four LH-moments, the estimated parameters, and the probability distributions showed that the level of the LH-moments has a significant influence. At higher levels, the estimation results gave a more focused representation of the upper part of the wave crest distributions, which indicates consistency with the intention of the method of LH-moments. The low tail RMSE values of less than 2.5% demonstrated that a Weibull distribution model estimated by using high-level LH-moments can accurately represent the probability distribution of large extreme wave crests for incident waves, wave run-ups, and moon pool waves. Goodness-of-fit test on the basis of comparison of sampling LH-kurtosis and theoretical LH-kurtosis was recommended as a procedure for selecting an optimum level

show abstract

Extremes of Nonlinear Vibration: Comparing Models Based on Moments, L-Moments, and Maximum Entropy

Cited by 48 publications

References 11 publications

A de-mixing approach for the management of large negative peaks in wind tunnel data

A de-mixing approach for the management of large negative peaks in wind tunnel data

Kernel density maximum entropy method with generalized moments for evaluating probability distributions, including tails, from a small sample of data

LH-moment estimation for statistical analysis on the wave crest distributions of a deepwater spar platform model test

Contact Info

Product

Resources

About