Reliability Sensitivity Analysis of Dynamical Systems
The reliability sensitivity analysis of systems subjected to stochastic loading is considered in this chapter. In particular, the change that the probability of failure undergoes due to changes in the distribution parameters of the uncertain model paramet
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Reliability Sensitivity Analysis of Dynamical Systems
Abstract The reliability sensitivity analysis of systems subjected to stochastic loading is considered in this chapter. In particular, the change that the probability of failure undergoes due to changes in the distribution parameters of the uncertain model parameters is utilized as a sensitivity measure. A simulation-based approach that corresponds to a simple post-processing step of an advanced sampling-based reliability analysis is used to perform the sensitivity analysis. In particular, subset simulation, introduced in the previous chapter, is applied in the present formulation. The analysis does not require any additional system response evaluations. The feasibility and effectiveness of the approach is demonstrated on a finite element model of a bridge under stochastic ground excitation. The sensitivity analysis is carried out in a reduced space of generalized coordinates. The computational effort involved in the reliability sensitivity analysis of the reduced-order model is significantly decreased with respect to the corresponding analysis of the full finite element model. The reduction is accomplished without compromising the accuracy of the reliability sensitivity estimates.
5.1 Motivation The level of safety of a structure can be measured in terms of its reliability. Even though this information is essential, it is also important to analyze the sensitivity of the reliability estimates with respect to variations in model parameters [3, 8, 13, 18, 30]. In particular, the determination of the variation in the reliability (or equivalently in the failure probability) due to changes in model parameters can provide useful information. For example, it can be used to identify the most influential model parameters and provide an important insight on system failure for risk-based decision making, such as reliability-based characterization of system responses, robust control, reliability-based design optimization, etc. [2, 6, 15, 24, 26, 34]. The subject of reliability sensitivity has been addressed in a large number of contributions. In fact, many works based on standard approximate methods such as first- and second-order reliability methods and simulation-based methods have been studied in the literature. These methods are quite general, and they have proved to © Springer Nature Switzerland AG 2019 H. Jensen and C. Papadimitriou, Sub-structure Coupling for Dynamic Analysis, Lecture Notes in Applied and Computational Mechanics 89, https://doi.org/10.1007/978-3-030-12819-7_5
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5 Reliability Sensitivity Analysis of Dynamical Systems
be very effective in a large number of problems, but their range of application is somewhat limited in the context of complex dynamical systems. A representative list of these works is included in the Refs. [1, 3–5, 13, 16, 18, 20, 22, 27, 29].
5.2 Reliability Sensitivity Analysis Formulation As indicated in Sect. 4.1, the vector of uncertain parameters θ is characterized in a probabilistic manner by means of a joint probabi
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