Reliability assessment in structural dynamics B. Goller, H.J. Pradlwarter n , G.I. Schu¨ eller University of Innsbruck, Technikerstr. 13, 6020 Innsbruck, Austria article info Article history: Accepted 16 November 2012 Handling Editor: G. Degrande abstract This paper presents a brief survey of methods for efficient reliability analysis of dynamical systems. The importance of the consideration of uncertainties both with respect to loading characteristics and structural parameters and the therefore arising question about the reliability of a structure are thoroughly discussed. The adopted classification of the investigated approaches is application-based, i.e. the methods are divided according to their applicability to linear or non-linear systems, to deterministic or stochastic structural systems, to deterministic or stochastic loads and also to low- or high-dimensional problems. The approaches which will be discussed in the following are clearly only a small selection out of a vast amount of methods, where the selection is mainly based on recent approaches which were proposed in the last decade and which are applicable to large Finite Element models. Hence, this small selection is intended to give a short and concise overview of the state of the art which might also serve as an introduction into this topic. & 2013 Published by Elsevier Ltd. 1. Introduction When analyzing a dynamically excited structure, the determination of the probability of failure is a key issue because of the uncertainties in future loads and in modeling of the structure. The definition of failure of a system is usually based on the exceedance of a predefined threshold level. In many engineering problems, the design aims at not exceeding this given extreme value of a structural response. Hence, failure occurs when the threshold value is exceeded at its first time and this kind of analysis falls into the category of the first excursion problem [1–9]. Exceedances of thresholds are also used in many other disciplines: in steady state operational systems, the distribution of the first passage time to failure is of interest. In structural engineering, the estimation of so-called fragility curves gained much importance to assess the vulnerability of the infrastructure due to earthquakes. Fragility curves provide the probability of exceeding a prescribed level of damage for a wide range of ground motion intensity. Typically, the peak ground acceleration or spectral accelerations are used as a measure for the earthquake intensity. Many procedures have been proposed to estimate these fragility curves: empirical statistical methods, seismic code methods, nonlinear static analysis methods (pushover) and nonlinear dynamic analysis methods. In case the ground motion is described by a stochastic process compatible with the earthquake intensity measure, procedures as described herein which focus on the excursion probability in dynamics provide methods for quantifying fragility curves and might be applied to assess also low probabilities failure events. Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/jsvi Journal of Sound and Vibration 0022-460X/$ - see front matter & 2013 Published by Elsevier Ltd. http://dx.doi.org/10.1016/j.jsv.2012.11.021 n Corresponding author. E-mail address: Helmut.Pradlwarter@uibk.ac.at (H.J. Pradlwarter). Journal of Sound and Vibration 332 (2013) 2488–2499