Browsing by Subject "Measurement errors"
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Item Adaptive Reliability Analysis of Reinforced Concrete Bridges Using Nondestructive Testing(2011-08-08) Huang, QindanThere has been increasing interest in evaluating the performance of existing reinforced concrete (RC) bridges just after natural disasters or man-made events especially when the defects are invisible, or in quantifying the improvement after rehabilitations. In order to obtain an accurate assessment of the reliability of a RC bridge, it is critical to incorporate information about its current structural properties, which reflects the possible aging and deterioration. This dissertation proposes to develop an adaptive reliability analysis of RC bridges incorporating the damage detection information obtained from nondestructive testing (NDT). In this study, seismic fragility is used to describe the reliability of a structure withstanding future seismic demand. It is defined as the conditional probability that a seismic demand quantity attains or exceeds a specified capacity level for given values of earthquake intensity. The dissertation first develops a probabilistic capacity model for RC columns and the capacity model can be used when the flexural stiffness decays nonuniformly over a column height. Then, a general methodology to construct probabilistic seismic demand models for RC highway bridges with one single-column bent is presented. Next, a combination of global and local NDT methods is proposed to identify in-place structural properties. The global NDT uses the dynamic responses of a structure to assess its global/equivalent structural properties and detect potential damage locations. The local NDT uses local measurements to identify the local characteristics of the structure. Measurement and modeling errors are considered in the application of the NDT methods and the analysis of the NDT data. Then, the information obtained from NDT is used in the probabilistic capacity and demand models to estimate the seismic fragility of the bridge. As an illustration, the proposed probabilistic framework is applied to a reinforced concrete bridge with a one-column bent. The result of the illustration shows that the proposed framework can successfully provide the up-to-date structural properties and accurate fragility estimates.Item Bayesian Semiparametric Density Deconvolution and Regression in the Presence of Measurement Errors(2014-06-24) Sarkar, AbhraAlthough the literature on measurement error problems is quite extensive, solutions to even the most fundamental measurement error problems like density deconvolution and regression with errors-in-covariates are available only under numerous simplifying and unrealistic assumptions. This dissertation demonstrates that Bayesian methods, by accommodating measurement errors through natural hierarchies, can provide a very powerful framework for solving these important measurement errors problems under more realistic scenarios. However, the very presence of measurement errors often renders techniques that are successful in measurement error free scenarios inefficient, numerically unstable, computationally challenging or intractable. Additionally, measurement error problems often have unique features that compound modeling and computational challenges. In this dissertation, we develop novel Bayesian semiparametric approaches that cater to these unique challenges of measurement error problems and allow us to break free from many restrictive parametric assumptions of previously existing approaches. In this dissertation, we first consider the problem of univariate density deconvolution when replicated proxies are available for each unknown value of the variable of interest. Existing deconvolution methods often make restrictive and unrealistic assumptions about the density of interest and the distribution of measurement errors, e.g., normality and homoscedasticity and thus independence from the variable of interest. We relax these assumptions and develop robust and efficient deconvolution approaches based on Dirichlet process mixture models and mixtures of B-splines in the presence of conditionally heteroscedastic measurement errors. We then extend the methodology to nonlinear univariate regression with errors-in-covariates problems when the densities of the covariate, the regression errors and the measurement errors are all unknown, and the regression and the measurement errors are conditionally heteroscedastic. The final section of this dissertation is devoted to the development of flexible multivariate density deconvolution approaches. The methods available in the existing sparse literature all assume the measurement error density to be fully specified. In contrast, we develop multivariate deconvolution approaches for scenarios when the measurement error density is unknown but replicated proxies are available for each subject. We consider scenarios when the measurement errors are distributed independently from the vector valued variable of interest as well as scenarios when they are conditionally heteroscedastic. To meet the significantly harder modeling and computational challenges of the multivariate problem, we exploit properties of finite mixture models, multivariate normal kernels, latent factor models and exchangeable priors in many novel ways. We provide theoretical results showing the flexibility of the proposed models. In simulation experiments, the proposed semiparametric methods vastly outperform previously existing approaches. Our methods also significantly outperform theoretically more flexible possible nonparametric alternatives even when the true data generating process closely conformed to these alternatives. The methods automatically encompass a variety of simplified parametric scenarios as special cases and often outperform their competitors even in those special scenarios for which the competitors were specifically designed. We illustrate practical usefulness of the proposed methodology by successfully applying the methods to problems in nutritional epidemiology. The methods can be readily adapted and applied to similar problems from other areas of applied research. The methods also provide the foundation for many interesting extensions and analyses.Item Linear estimation for data with error ellipses(2012-05) Amen, Sally Kathleen; Powers, Daniel A.; Robinson, Edward L.When scientists collect data to be analyzed, regardless of what quantities are being measured, there are inevitably errors in the measurements. In cases where two independent variables are measured with errors, many existing techniques can produce an estimated least-squares linear fit to the data, taking into consideration the size of the errors in both variables. Yet some experiments yield data that do not only contain errors in both variables, but also a non-zero covariance between the errors. In such situations, the experiment results in measurements with error ellipses with tilts specified by the covariance terms. Following an approach suggested by Dr. Edward Robinson, Professor of Astronomy at the University of Texas at Austin, this report describes a methodology that finds the estimates of linear regression parameters, as well as an estimated covariance matrix, for a dataset with tilted error ellipses. Contained in an appendix is the R code for a program that produces these estimates according to the methodology. This report describes the results of the program run on a dataset of measurements of the surface brightness and Sérsic index of galaxies in the Virgo cluster.