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Statistical damage detection method for frame structures using a confidence interval

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Earthquake Engineering and Engineering Vibration 2010年第1期9卷 133-140页

作者： Li Weiming,Zhu Hongping~(++),Luo Hanbin~(++) and Xia Yong~(++) School of Civil Engineering and Mechanics,Huazhong University of Science and Technology,Wuhan 430074,China ~+PhD Candidate ++ Professor School of Civil Engineering and Mechanics Huazhong University of Science and Technology Wuhan China

A novel damage detection method is applied to a 3-story frame structure, to obtain statistical quantification control criterion of the existence, location and identification of damage. The mean, standard deviation, and exponentially weighted moving average （EWMA） are applied to detect damage information according to statistical process control （SPC） theory. It is concluded that the detection is insignificant with the mean and EWMA because the structural response is not independent and is not a normal distribution. On the other hand, the damage information is detected well with the standard deviation because the influence of the data distribution is not pronounced with this parameter. A suitable moderate confidence level is explored for more significant damage location and quantification detection, and the impact of noise is investigated to illustrate the robustness of the method.

关键词： damage detection standard deviation statistical method confidence interval noise

Empirical Likelihood Ratio confidence interval for Positively Associated Series

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Acta Mathematicae Applicatae Sinica 2007年第2期23卷 245-254页

作者： Jun-jian Zhang College of Applied Sciences Beijing University of Technology Beijing 100022 China College of Mathematics Guangxi Normal University Guilin 541004 China

Empirical likelihood is discussed by using the blockwise technique for strongly stationary, positively associated random variables. Our results show that the statistics is asymptotically chi-square distributed and the... 详细信息

关键词： Empirical likelihood positive association blockwise confidence interval

Deep learning-based evaluation of factor of safety with confidence interval for tunnel deformation in spatially variable soil

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Journal of Rock Mechanics and Geotechnical Engineering 2021年第6期13卷 1358-1367页

作者： Jinzhang Zhang Kok Kwang Phoon Dongming Zhang Hongwei Huang Chong Tang Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education Tongji UniversityShanghai200092China Department of Geotechnical Engineering Tongji UniversityShanghai200092China Department of Civil and Environmental Engineering National University of Singapore117576Singapore Singapore University of Technology and Design 487372Singapore

The random finite difference method(RFDM) is a popular approach to quantitatively evaluate the influence of inherent spatial variability of soil on the deformation of embedded ***,the high computational cost is an ongoing challenge for its application in complex *** address this limitation,a deep learning-based method for efficient prediction of tunnel deformation in spatially variable soil is *** proposed method uses one-dimensional convolutional neural network(CNN) to identify the pattern between random field input and factor of safety of tunnel deformation *** mean squared error and correlation coefficient of the CNN model applied to the newly untrained dataset was less than 0.02 and larger than 0.96,*** means that the trained CNN model can replace RFDM analysis for Monte Carlo simulations with a small but sufficient number of random field samples(about 40 samples for each case in this study).It is well known that the machine learning or deep learning model has a common limitation that the confidence of predicted result is unknown and only a deterministic outcome is *** calls for an approach to gauge the model’s confidence *** is achieved by applying dropout to all layers of the original model to retrain the model and using the dropout technique when performing *** excellent agreement between the CNN model prediction and the RFDM calculated results demonstrated that the proposed deep learning-based method has potential for tunnel performance analysis in spatially variable soils.

关键词： Deep learning Convolutional neural network(CNN) Tunnel safety confidence interval Random field

Bootstrap generated confidence interval for time averaged measure

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International Journal of Modeling, Simulation, and Scientific Computing 2015年第3期6卷 107-115页

作者： Jinsoo Park Haneul Lee Yun Bae Kim School of Management and Administration Yong In University YonginRepublic of Korea School of Engineering Sungkyunkwan University SuwonRepublic of Korea

In the simulation output analysis,there are some measures that should be calculated by time average concept such as the mean queue ***,the confidence interval of those measures might be required for statistical *** this situation,the traditional method that utilizes the central limit theorem(CLT)is inapplicable if the output data set has autocorrelation *** bootstrap is one of the most suitable methods which can reflect the autocorrelated phenomena in statistical ***,the confidence interval for a time averaged measure having autocorrelation structure can also be calculated by the bootstrap *** study introduces the method that constructs these confidence intervals applying the *** bootstraps proposed are the threshold bootstrap(TB),the moving block bootstrap(MBB)and stationary bootstrap(SB).Finally,some numerical examples will be provided for verification.

关键词： Simulation output analysis confidence interval time averaged measure bootstrap

confidence interval Estimation of the Correlation in the Presence of Non-Detects

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Open Journal of Statistics 2021年第3期11卷 463-475页

作者： Courtney E. McCracken Stephen W. Looney Center for Research and Evaluation Kaiser Permanente Georgia Atlanta USA Department of Population Health Sciences Augusta University Augusta USA

This article deals with correlating two variables that have values that fall below the known limit of detection (LOD) of the measuring device;these values are known as non-detects (NDs). We use simulation to compare several methods for estimating the association between two such variables. The most commonly used method, simple substitution, consists of replacing each ND with some representative value such as LOD/2. Spearman’s correlation, in which all NDs are assumed to be tied at some value just smaller than the LOD, is also used. We evaluate each method under several scenarios, including small to moderate sample size, moderate to large censoring proportions, extreme imbalance in censoring proportions, and non-bivariate normal (BVN) data. In this article, we focus on the coverage probability of 95% confidence intervals obtained using each method. confidence intervals using a maximum likelihood approach based on the assumption of BVN data have acceptable performance under most scenarios, even with non-BVN data. intervals based on Spearman’s coefficient also perform well under many conditions. The methods are illustrated using real data taken from the biomarker literature.

关键词： confidence interval Coverage Probability Left Censoring Limit of Detection Maximum Likelihood Spearman Correlation

confidence intervalS FOR NONPARAMETRIC REGRESSION FUNCTIONS WITH MISSING DATA： MULTIPLE DESIGN CASE

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Journal of Systems Science & Complexity 2011年第6期24卷 1204-1217页

作者： Qingzhu LEI Yongsong QIN School of Mathematical Sciences Guangxi Normal University Guilin 541004 China

This paper considers two estimators of θ= g（x） in a nonparametric regression model Y = g（x）＋ ε（x∈ （0, 1）p） with missing responses： Imputation and inverse probability weighted esti- mators. Asymptotic normality of the two estimators is established, which is used to construct normal approximation based confidence intervals on θ.

关键词： confidence interval missing at random nonparametric regression normal approximation.

Constructing confidence intervals of extreme rainfall quantiles using Bayesian,bootstrap,and profile likelihood approaches

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Science China(Technological Sciences) 2016年第4期59卷 573-585页

作者： CHEN Si LI YaXing SHIN JiYae KIM TaeWoong department of civil and environmental engineering hanyang universitySeoul 133-791Korea department of electronics&communication engineering hanyang universityAnsan 426-791Korea department of civil and environmental engineering hanyang universityAnsan 426-791Korea

Hydrological risk is highly dependent on the occurrence of extreme *** fact has led to a wide range of studies on the estimation and uncertainty analysis of the *** most cases,confidence intervals(CIs)are constructed to represent the uncertainty of the *** the accuracy of CIs depends on the asymptotic normality of the data and is questionable with limited observations in practice,a Bayesian highest posterior density(HPD)interval,bootstrap percentile interval,and profile likelihood(PL)interval have been introduced to analyze the uncertainty that does not depend on the normality ***,comparison studies to investigate their performances in terms of the accuracy and uncertainty of the estimates are *** addition,the strengths,weakness,and conditions necessary for performing each method also must be ***,in this study,test experiments with simulations from varying parent distributions and different sample sizes were ***,applications to the annual maximum rainfall(AMR)time series data in South Korea were *** districts with 38-year(1973–2010)AMR observations were fitted by the three aforementioned methods in the *** both the experimental and application results,the Bayesian method is found to provide the lowest uncertainty of the design level while the PL estimates generally have the highest accuracy but also the largest *** bootstrap estimates are usually inferior to the other two methods,but can perform adequately when the distribution model is not heavy-tailed and the sample size is *** distribution tail behavior and the sample size are clearly found to affect the estimation accuracy and *** study presents a comparative result,which can help researchers make decisions in the context of assessing extreme rainfall uncertainties.

关键词： Bayesian bootstrap profile likelihood confidence interval frequency analysis

Semi-empirical Likelihood confidence intervals for the Differences of Quantiles with Missing Data

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Acta Mathematica Sinica,English Series 2009年第5期25卷 845-854页

作者： Yong Song QIN Jun Chao ZHANG School of Mathematical Sciences Guangxi Normal University Guilin 541004 P. R. China Department of Mathematics Harbin University Harbin 150086 P. R. China

Detecting population （group） differences is useful in many applications, such as medical research. In this paper, we explore the probabilistic theory for identifying the quantile differences .between two populations. Suppose that there are two populations x and y with missing data on both of them, where x is nonparametric and y is parametric. We are interested in constructing confidence intervals on the quantile differences of x and y. Random hot deck imputation is used to fill in missing data. Semi-empirical likelihood confidence intervals on the differences are constructed.

关键词： empirical likelihood confidence interval quantile missing data hot deck imputation

Empirical Likelihood confidence intervals for the Differences of Quantiles with Missing Data

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Acta Mathematicae Applicatae Sinica 2009年第1期25卷 105-116页

作者： Yong-song Qin Yong-jiang Qian School of Mathematical Sciences Guangxi Normal University Guilin Guangxi 541004 China

Suppose that there are two nonparametric populations x and y with missing data on both of them. We are interested in constructing confidence intervals on the quantile differences of x and y. Random imputation is used.... 详细信息

关键词： Empirical likelihood confidence interval quantile missing data imputation