• Structural Engineering and Mechanics
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• v.52 no.1
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• pp.19-33
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• 2014

Structural robustness refers to the ability of a structure to avoid disproportionate consequences to the original cause. Currently attentions focus on the concepts of structural robustness, and discussions on methods of robustness based structural design are rare. Firstly, taking basis in robust $H_{\infty}$ control theory, structural robustness is assessed by $H_{\infty}$ norm of the system transfer function. Then using the SIMP material model, robustness based design of grid structures is formulated as a continuum topology optimization problem, where the relative density of each element and structural robustness are considered as the design variable and the optimization objective respectively. Generalized elitist genetic algorithm is used to solve the optimization problem. As examples, robustness configurations of plane stress model and the rectangular hyperbolic shell model were obtained by robustness based structural design. Finally, two models of single-layer grid structures were designed by conventional and robustness based method respectively. Different interference scenarios were simulated by static and impact experiments, and robustness of the models were analyzed and compared. The results show that the $H_{\infty}$ structural robustness index can indicate whether the structural response is proportional to the original cause. Robustness based structural design improves structural robustness effectively, and it can provide a conceptual design in the initial stage of structural design.

• Earthquakes and Structures
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• v.12 no.1
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• pp.47-54
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• 2017

Introduction of robustness index in the structure is done in three ways: deterministic robustness index, probabilistic robustness index, and risk-based robustness index. In past decades, there have been numerous researches to evaluate robustness index in both deterministic and probabilistic ways. In this research, by using a risk analysis, a risk-based robustness index has been defined for the structure. By creating scenarios in accordance with uncertainty parameters of critical and unexpected gas blast accident, a new method has been suggested for evaluating risk-based robustness index. Finally, a numerical example for the evaluation of risk-based robustness index of a four-storey reinforced concrete moment frame, designed and built based on Eurocode 8 code, has been presented with results showing a lower risk of robustness.

• Structural Engineering and Mechanics
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• v.56 no.6
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• pp.1063-1093
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• 2015

Structural robustness has become an important design variable. However, based on the existing definitions of structural robustness it is often difficult to analyse and evaluate structural robustness, and sometimes not efficient since they mix structural robustness with several other structural variables. This paper concerns the development of a new structural robustness definition, and structural robustness and structural fragility indices. The basis for the development of the new indices is the analysis of the damage energy of structural systems for a given hazard scenario and involves a criterion to define an "unavoidable collapse" state. Illustrative examples are given detailing the steps and calculations needed to obtain values for both the structural robustness and the structural fragility indices. Finally, this paper presents the main advantages of the newly proposed definition and indices for the structural risk analysis over existing traditional methods.

• Journal of Institute of Control, Robotics and Systems
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• v.1 no.2
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• pp.78-82
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• 1995

In this paper, we consider the robustness analysis problem in state space models with linear time invariant perturbations. Based upon the discrete-time Lyapunov approach, sufficient conditions are derived for the eigenvalues of perturbed matrix to be located in a circle, and robustness bounds on perturbations are obtained. Spaecially, for the case of a diagonalizable hermitian matrix the bound is given in terms of the nominal matrix without the solution of Lyapunov equation. This robustness analysis takes account not only of stability robustness but also of certain types of performance robustness. For two perturbation classes resulting bounds are shown to be improved over the existing ones. Examples given include comparison of the proposed analysis method with existing one.

• Structural Engineering and Mechanics
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• v.76 no.2
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• pp.193-205
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• 2020

The growing need for assuring efficient and sustainable investments in civil engineering structures has determined a renovated interest in the rational design of such structures from designers, clients and authorities. As a result, risk-informed decision-making methodologies are increasingly being used as a direct decision tool or as an upper-level layer from which performance-based approaches are then calibrated against. One of the most important and challenging aspects of today's structural design is to adequately handle the system-level effects, the known unknowns and the unknown unknowns. These aspects revolve around assessing and evaluating relevant damage scenarios, namely those involving unacceptable/intolerable damage levels. Hence, the importance of risk analysis of disproportionate collapse, and along with it of robustness. However, the way robustness has been used in modern design codes varies substantially, from simple provisions of prescriptive rules to complex risk analysis of the disproportionate collapse. As a result, implementing design for robustness is still very much a grey area and more so when it comes to defining means to quantify robustness. This paper revisits the most common robustness frameworks, highlighting their merits and limitations, and identifies one among them which is very promising as a way forward to solve the still open challenges.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.7
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• pp.794-799
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• 1999

This study deals with robustness bounds estimation for uncertain linear systems with structured perturbations where the eigenvalues of the perturbed systems are guaranteed to stay in a prescribed region. Based upon the Lyapunov approach, new theorems to estimate allowable perturbation parameter bounds are derived. The theorems are referred to as the zero-order or first-order asymmetric robustness measure depending on the order of the P matrix in the sense of Taylor series expansion of perturbed Lyapunov equation. It is proven that Gao's theorem for the estimation of stability robustness bounds is a special case of proposed zero-order asymmetric robustness measure for eigenvalue assignment. Robustness bounds of perturbed parameters measured by the proposed techniques are asymmetric around the origin and less conservative than those of conventional methods. Numerical examples are given to illustrate proposed methods.

• International Journal of High-Rise Buildings
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• v.9 no.2
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• pp.127-154
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• 2020

Disproportionate collapse triggered by local structural failure may cause huge casualties and economic losses, being one of the most critical civil engineering incidents. It is generally recognized that ensuring robustness of a structure, defined as its insensitivity to local failure, is the most acceptable and effective method to arrest disproportionate collapse. To date, the concept of robustness in its definition and quantification is still an issue of controversy. This paper presents a detailed review on about 50 quantitative measures of robustness for building structures, being classified into structural attribute-based and structural performance-based measures (deterministic and probabilistic). The definition of robustness is first described and distinguished from that of collapse resistance, vulnerability and redundancy. The review shows that deterministic measures predominate in quantifying structural robustness by comparing the structural responses of an intact and damaged structure. The attribute-based measures based on structural topology and stiffness are only applicable to elastic state of simple structural forms while the probabilistic measures receive growing interest by accounting for uncertainties in abnormal events, local failure, structural system and failure-induced consequences, which can be used for decision-making tools. There is still a lack of generalized quantifications of robustness, which should be derived based on the definition and design objectives and on the response of a structure to local damage as well as the associated consequences of collapse. Critical issues and recommendations for future design and research on quantification of robustness are provided from the views of column removal scenarios, types of structures, regularity of structural layouts, collapse modes, numerical methods, multiple hazards, degrees of robustness, partial damage of components, acceptable design criteria.

• Earthquakes and Structures
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• v.3 no.6
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• pp.805-820
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• 2012

An enhanced and efficient methodology is proposed for evaluating the robustness of an uncertain structure with passive dampers. Although the structural performance for seismic loads is an important design criterion in earthquake-prone countries, the structural parameters such as storey stiffnesses and damping coefficients of passive dampers are uncertain due to various factors or sources, e.g. initial manufacturing errors, material deterioration, temperature dependence. The concept of robust building design under such uncertain structural-parameter environment may be one of the most challenging issues to be tackled recently. By applying the proposed method of interval analysis and robustness evaluation for predicting the response variability accurately, the robustness of a passively controlled structure can be evaluated efficiently in terms of the so-called robustness function. An application is presented of the robustness function to the design and evaluation of passive damper systems.

• International journal of steel structures
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• v.18 no.5
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• pp.1710-1722
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• 2018

Investigating remained damages from terrible earthquakes, it could be concluded that some events including explosion because of defect and failure in the building mechanical facilities or caused by gas leak, firing, aftershocks, etc., which are occurred during or a few time after the earthquake, will increase the effects of damages. In this paper, by introducing a complete risk analysis which included direct and indirect risks for earthquake (the main shock) and aftershock, the corresponding robustness index was created that called as "robustness index sequential critical events risk-based". One of the main properties of the intended robustness index is using progressive collapse percentage in its evaluation. Then, in a numerical example for a 4-storey moment resisting steel frame structure, a method is presented for obtaining all effective parameters in robustness index evaluation based on the intended risk and at last its results were reported.

• Journal of the Korean Statistical Society
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• v.27 no.3
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• pp.331-348
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• 1998

In this paper, we have proposed some robust Bayes estimators using ML-II priors as well as certain empirical Bayes estimators in estimating the finite population mean in the presence of auxiliary information. These estimators are compared with the classical ratio estimator and a subjective Bayes estimator utilizing the auxiliary information in terms of "posterior robustness" and "procedure robustness" Also, we have addressed the issue of choice of sampling design from a robust Bayesian viewpoint.