Bounding the first excursion probability of linear structures subjected to imprecise stochastic loading

This paper presents a highly efficient and accurate approach to determine the bounds on the first excursion probability of a linear structure that is subjected to an imprecise stochastic load. Traditionally, determining these bounds involves solving a double loop problem, where the aleatory uncertainty has to be fully propagated for each realization of the epistemic uncertainty or vice versa. When considering realistic structures such as buildings, whose numerical models often contain thousands of degrees of freedom, such approach becomes quickly computationally intractable. In this paper, we introduce an approach to decouple this propagation by applying operator norm theory. In practice, the method determines those epistemic parameter values that yield the bounds on the probability of failure, given the epistemic uncertainty. The probability of failure, conditional on those epistemic parameters, is then computed using the recently introduced framework of Directional Importance Sampling. Two case studies involving a modulated Clough-Penzien spectrum are included to illustrate the efficiency and exactness of the proposed approach

Resilience Assessment under Imprecise Probability

Resilience analysis of civil structures and infrastructure systems is a powerful approach to quantifying an object's ability to prepare for, recover from, and adapt to disruptive events. The resilience is typically measured probabilistically by the integration of the time-variant performance function, which is by nature a stochastic process as it is affected by many uncertain factors such as hazard occurrences and posthazard recoveries. Resilience evaluation could be challenging in many cases with imprecise probability information on the time-variant performance function. In this paper, a novel method for the assessment of imprecise resilience is presented, which deals with resilience problems with nonprobabilistic performance function. The proposed method, producing lower and upper bounds for imprecise resilience, has benefited from that for imprecise reliability as documented in the literature, motivated by the similarity between reliability and resilience. Two types of stochastic processes, namely log-Gamma and lognormal processes, are employed to model the performance function, with which the explicit form of resilience is derived. Moreover, for a planning horizon within which the hazards may occur for multiple times, the incompletely informed performance function results in "time-dependent imprecise resilience,"which is dependent on the duration of the service period (e.g., life cycle) and can also be handled by applying the proposed method. Through examining the time-dependent resilience of a strip foundation in a coastal area subjected to groundwater intrusion in a changing climate, the applicability of the proposed resilience bounding method is demonstrated. The impact of imprecise probability information on resilience is quantified through sensitivity analysis

Structural reliability analysis using imprecise evolutionary power spectral density functions

Abstract Buildings and structures in many regions of the world are exposed to environmental factors that can cause damage or failure, making it essential to model these factors accurately in engineering. Stochastic dynamics are crucial for modelling environmental processes, such as earthquake ground motions and wind loads, which can be characterised by a power spectral density (PSD) function that determines the dominant frequencies and corresponding amplitudes of the process. However, when generating a load model described by a PSD function, uncertainties in the processes must be taken into account, which makes a reliable estimation of the PSD function challenging, especially with only limited data available. This study employs the recently developed imprecise PSD function by using a radial basis function network to optimise data-enclosing bounds that produce an interval-valued PSD function. With this approach, a data set in the frequency domain can be bounded for uncertainty quantification. The method described in this work consists of optimising best-case and worst-case PSD functions within the bounds, which are transformed into a separable evolutionary PSD function. The reliability of structures is determined by an upper and lower failure probability, taking into account the present uncertainties. Advanced interval propagation schemes are linked to the imprecise PSD function to determine the failure probabilities efficiently. The method is illustrated by means of three numerical examples.</jats:p

Developmental and evolutionary significance of the zygomatic bone

International audienc

Structural reliability analysis with extremely small failure probabilities: A quasi-Bayesian active learning method

The concept of Bayesian active learning has recently been introduced from machine learning to structural reliability analysis. Although several specific methods have been successfully developed, significant efforts are still needed to fully exploit their potential and to address existing challenges. This work proposes a quasi-Bayesian active learning method, called ‘Quasi-Bayesian Active Learning Cubature’, for structural reliability analysis with extremely small failure probabilities. The method is established based on a cleaver use of the Bayesian failure probability inference framework. To reduce the computational burden associated with the exact posterior variance of the failure probability, we propose a quasi posterior variance instead. Then, two critical elements for Bayesian active learning, namely the stopping criterion and the learning function, are developed subsequently. The stopping criterion is defined based on the quasi posterior coefficient of variation of the failure probability, whose numerical solution scheme is also tailored. The learning function is extracted from the quasi posterior variance, with the introduction of an additional parameter that allows multi-point selection and hence parallel distributed processing. By testing on four numerical examples, it is empirically shown that the proposed method can assess extremely small failure probabilities with desired accuracy and efficiency