• Computational Structural Engineering : An International Journal
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• v.1 no.2
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• pp.81-87
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• 2001

A framework for reliability analysis of structural components and systems under conditions of statistical and model uncertainty is presented. The Bayesian parameter estimation method is used to derive the posterior distribution of model parameters reflecting epistemic uncertainties. Point, predictive and bound estimates of reliability accounting for parameter uncertainties are derived. The bounds estimates explicitly reflect the effect of epistemic uncertainties on the reliability measure. These developments are enhance-ments of second-moment uncertainty analysis methods developed by A. H-S. Ang and others three decades ago.

• Structural Engineering and Mechanics
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• v.27 no.3
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• pp.263-276
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• 2007

This paper presents a fuzzy finite element model for the analysis of structures in the presence of multiple uncertainties. A new methodology to evaluate the cumulative effect of multiple uncertainties on structural response is developed in the present work. This is done by modifying Muhanna's approach for handling single uncertainty. Uncertainty in load and material properties is defined by triangular membership functions with equal spread about the crisp value. Structural response is obtained in terms of fuzzy interval displacements and rotations. The results are further post-processed to obtain interval values of bending moment, shear force and axial forces. Membership functions are constructed to depict the uncertainty in structural response. Sensitivity analysis is performed to evaluate the relative sensitivity of displacements and forces to uncertainty in structural parameters. The present work demonstrates the effectiveness of fuzzy finite element model in establishing sharp bounds to the uncertain structural response in the presence of multiple uncertainties.

• Structural Engineering and Mechanics
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• v.29 no.5
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• pp.469-488
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• 2008

Finite element methods have often been used for structural analyses of various mechanical problems. When finite element analyses are utilized to resolve mechanical systems, numerical uncertainties in the initial data such as structural parameters and loading conditions may result in uncertainties in the structural responses. Therefore the initial data have to be as accurate as possible in order to obtain reliable structural analysis results. The typical finite element method may not properly represent discrete systems when using uncertain data, since all input data of material properties and applied loads are defined by nominal values. An interval finite element analysis, which uses the interval arithmetic as introduced by Moore (1966) is proposed as a non-stochastic method in this study and serves a new numerical tool for evaluating the uncertainties of the initial data in structural analyses. According to this method, the element stiffness matrix includes interval terms of the lower and upper bounds of the structural parameters, and interval change functions are devised. Numerical uncertainties in the initial data are described as a tolerance error and tree graphs of uncertain data are constructed by numerical uncertainty combinations of each parameter. The structural responses calculated by all uncertainty cases can be easily estimated so that structural safety can be included in the design. Numerical applications of truss and frame structures demonstrate the efficiency of the present method with respect to numerical analyses of structural uncertainties.

• Architectural research
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• v.8 no.2
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• pp.27-36
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• 2006

Structural uncertainties are generally modeled using probabilistic approaches in order to quantify uncertainties in behaviors of structures. This uncertainty results from the uncertainties of structural parameters. Monte Carlo methods have been usually carried out for analyses of uncertainty problems where no analytical expression is available for the forward relationship between data and model parameters. In such cases any direct mathematical treatment is impossible, however the forward relation materializes itself as an algorithm allowing data to be calculated for any given model. This study addresses a new method which is utilized as a basis for the uncertainty estimates of structural responses. It applies double uniform random numbers (i.e. DURN technique) to conventional Monte Carlo algorithm. In DURN method, the scenarios of uncertainties are sequentially selected and executed in its simulation. Numerical examples demonstrate the beneficial effect that the technique can increase uncertainty degree of structural properties with maintaining structural stability and safety up to the limit point of a breakdown of structural systems.

• Structural Engineering and Mechanics
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• v.36 no.1
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• pp.79-94
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• 2010

This study shows how uncertainties of data like material properties quantitatively have an influence on structural topology optimization results for dynamic problems, here such as both optimal topology and shape. In general, the data uncertainties may result in uncertainties of structural behaviors like deflection or stress in structural analyses. Therefore optimization solutions naturally depend on the uncertainties in structural behaviors, since structural behaviors estimated by the structural analysis method like FEM need to execute optimization procedures. In order to quantitatively estimate the effect of data uncertainties on topology optimization solutions of dynamic problems, a so-called interval analysis is utilized in this study, and it is a well-known non-stochastic approach for uncertainty estimate. Topology optimization is realized by using a typical SIMP method, and for dynamic problems the optimization seeks to maximize the first-order eigenfrequency subject to a given material limit like a volume. Numerical applications topologically optimizing dynamic wall structures with varied supports are studied to verify the non-stochastic interval analysis is also suitable to estimate topology optimization results with dynamic problems.

• Structural Engineering and Mechanics
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• v.63 no.6
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• pp.779-788
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• 2017

System identification and damage detection for structural health monitoring have received considerable attention. Various time domain analysis methodologies based on measured vibration data of structures have been proposed. Among them, recursive least-squares estimation of structural parameters which is also known as parametric Kalman filter (PKF) approach has been studied. However, the conventional PKF requires that all the external excitations (inputs) be available. On the other hand, structural uncertainties are inevitable for civil infrastructures, it is necessary to develop approaches for probabilistic damage detection of structures. In this paper, a parametric Kalman filter with unknown inputs (PKF-UI) is proposed for the simultaneous identification of structural parameters and the unmeasured external inputs. Analytical recursive formulations of the proposed PKF-UI are derived based on the conventional PKF. Two scenarios of linear observation equations and nonlinear observation equations are discussed, respectively. Such a straightforward derivation of PKF-UI is not available in the literature. Then, the proposed PKF-UI is utilized for probabilistic damage detection of structures by considering the uncertainties of structural parameters. Structural damage index and the damage probability are derived from the statistical values of the identified structural parameters of intact and damaged structure. Some numerical examples are used to validate the proposed method.

• Structural Engineering and Mechanics
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• v.21 no.5
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• pp.507-518
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• 2005

In the shear-lag analysis of structures deterministic procedure is insufficient to provide complete information. Probabilistic analysis is a holistic approach for analyzing shear-lag effects considering uncertainties in structural parameters. This paper proposes an efficient and accurate algorithm to analyze shear-lag effects of structures with parameter uncertainties. The proposed algorithm integrated the advantages of the response surface method (RSM), finite element method (FEM) and Monte Carlo simulation (MCS). Uncertainties in the structural parameters can be taken into account in this algorithm. The algorithm is verified using independently generated finite element data. The proposed algorithm is then used to analyze the shear-lag effects of a simply supported beam with parameter uncertainties. The results show that the proposed algorithm based on the central composite design is the most promising one in view of its accuracy and efficiency. Finally, a parametric study was conducted to investigate the effect of each of the random variables on the statistical moment of structural stress response.

• Structural Engineering and Mechanics
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• v.8 no.5
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• pp.477-490
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• 1999

The uncertainties associated with structural parameters and dynamic loading are identified and discussed. Structural parametric uncertainties are treated as random variables and dynamic wind load is simulated as a random process. Dynamic wind-induced responses of structures with parametric uncertainties are investigated by using stochastic finite element method. The formulas for structural dynamic reliability analysis considering the randomness of structural resistance and loading are proposed. Two numerical examples of high-rise structures are presented to illustrate the proposed methodology. The calculated results demonstrate that the variation in structural parameters indeed influences the dynamic response and the first passage probability evaluation of structures.

• Proceedings of the Korea Concrete Institute Conference
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• 2003.05a
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• pp.181-186
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• 2003

There are many uncertainties in structural failures or structures, so probabilistic failure cause assessment should be performed in order to consider the uncertainties. However, in many cases of forensic engineering, the failure cause assessments are performed by deterministic approach though number of uncertainties are existed in the failures or structures. Thus, deterministic approach may have possibility for leading to unreasonable and unrealistic failure cause assessment due to ignorance of the uncertainties. Therefore, probabilistic approach is needed to complement the shortcoming of deterministic approach and to perform the more reasonable and realistic failure cause assessment. In this study, reliability-based failure cause assessment (reliability based forensic engineering) is performed, which can incorporate uncertainties in failures and structures. For more practical application, the modified ETA technique is proposed, which automatically generates the defected structural model, performs structural analysis and reliability analysis, and calculates the failure probabilities of the failure events and the occurrence probabilities of the failure scenarios. Also, for more precise reliability analysis, uncertainties are estimated more reasonably by using bayesian approach based on the experimental laboratory testing data in forensic report.

• Smart Structures and Systems
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• v.20 no.2
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• pp.207-217
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• 2017

Because of the inevitable uncertainties such as structural parameters, external excitations and measurement noises, the effects of uncertainties should be taken into consideration in structural damage detection. In this paper, two probabilistic structural damage detection approaches are proposed to account for the underlying uncertainties in structural parameters and external excitation. The first approach adopts the statistical moment-based structural damage detection (SMBDD) algorithm together with the sensitivity analysis of the damage vector to the uncertain parameters. The approach takes the advantage of the strength SMBDD, so it is robust to measurement noise. However, it requests the number of measured responses is not less than that of unknown structural parameters. To reduce the number of measurements requested by the SMBDD algorithm, another probabilistic structural damage detection approach is proposed. It is based on the integration of structural damage detection using temporal moments in each time segment of measured response time history with the sensitivity analysis of the damage vector to the uncertain parameters. In both approaches, probability distribution of damage vector is estimated from those of uncertain parameters based on stochastic finite element model updating and probabilistic propagation. By comparing the two probability distribution characteristics for the undamaged and damaged models, probability of damage existence and damage extent at structural element level can be detected. Some numerical examples are used to demonstrate the performances of the two proposed approaches, respectively.