System reliability is usefully applied to assess the performance of individual structures and portfolios of structures. In many instances, one is interested in knowing the probability that m failures have occurred among n components in a system, or that at least m failures have occurred among n components. Examples include structural failure modes within a single infrastructure or building, buildings

We suggest in this paper two new random walk based stochastic algorithms for solving high-dimensional PDEs for domains with complicated geometrical structure. The first one, a Random Walk on Spheres (RWS) algorithm is developed for solving systems of coupled drift–diffusion–reaction equations where the random walk is living both on randomly sampled spheres and inside the relevant balls. The second

The concrete properties inherently fluctuate even using the same manufacturing process. A Legendre polynomial based micromechanical framework is proposed to investigate the inherent randomness of the concrete’s elastic behavior. The three-phase composite model is employed to represent the concrete material at microscale level. The volume fractions of different constituents are reached using a simplified

A renewed methodology for simulating two-spatial dimensional stochastic wind field is addressed in the present study. First, the concept of cross wavenumber spectral density (WSD) function is defined on the basis of power spectral density (PSD) function and spatial coherence function to characterize the spatial variability of the stochastic wind field in the two-spatial dimensions. Then, the hybrid

Seismic fragilities are the probability that structural response of a system overcomes specified limit values for given seismic intensity measures. These curves are frequently defined as functions of single/multiple ordinates of the pseudo-acceleration response spectrum. Recently it was reported that this approach can lead to inaccurate estimation of the structural performance for complex non-linear

A finite element (FE) model is developed for a curved cable-stayed footbridge located in Terni (Umbria Region, Central Italy) which accounts for uncertainties in geometry, material properties, and boundary conditions as well as limited knowledge on the behavior of connections and other components. Ambient vibration tests (AVTs) are carried out to identify the main dynamic parameters which are used

Isogeometric analysis which extends the finite element method through the usage of B-splines has become well established in engineering analysis and design procedures. In this paper, this concept is considered in context with the methodology of polynomial chaos as applied to computational stochastic mechanics. In this regard it is noted that many random processes used in several applications can be

The robust geotechnical design (RGD), which aims to ensure a design that is robust against variations in the input variables, is receiving wider attention and acceptance in the past few years. In this paper, the authors proposed the sensitivity of reliability index (SRI) to evaluate the feasibility robustness of the design, resulting in a modified RGD approach. The performance of the proposed approach

In this paper the estimation of masonry characteristics by means of thermographic images, enhanced by sampling Kantorovich algorithm, is taken into account. In particular, the convergence of the Statistical Volume Element (SVE) to the Representative Volume Element (RVE) is analyzed. It is found that the enhancement, obtained by the proposed procedure, allows a faster convergence of SVE to RVE and a

The assessment of structural capacity against collapse is conducive to the optimal design of new structures as well as checking the safety of existing structures. However, the evaluation cannot be typically carried out by means of destructive tests on prototype or reduced scale structures. In this regard, the numerical models that adequately represent the prototype structures can be alternatively used

In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconceptions in the Bayesian framework since it is robust with respect to the modeling assumptions and the observed data. Rather, this issue has deep roots in users’ inability to develop

Nonlinear vibrations due to combined deterministic and stochastic loads are investigated through a novel linearization scheme. The steady-state motion is expressed as a sum of an ensemble mean (deterministic) part and a zero-mean stochastic part. Further, harmonic averaging is used to account for the mean response, while statistical linearization is used to determine the standard deviation of the random

The moment equations technique together with modified cumulant-neglect closure techniques is developed for a non-linear dynamic system subjected to a random train of impulses driven by an Erlang renewal counting process. The original non-Markov problem is converted into a Markov one by recasting the excitation process with the aid of an auxiliary, pure-jump stochastic process characterized by a Markov

In this work, the performance of non-gradient as well as gradient-enhanced versions of two different classes of surrogate modeling approaches, polynomial least squares regression and kernel based radial basis function interpolation, are compared in the context of a composite mechanics problem. Sequential space filling random designs are used for selecting the training points. The primary goal is to

Motivated by practical needs to reduce data transmission payloads in wireless sensors for vibration-based monitoring of engineering structures, this paper proposes a novel approach for identifying resonant frequencies of white-noise excited structures using acceleration measurements acquired at rates significantly below the Nyquist rate. The approach adopts the deterministic co-prime sub-Nyquist sampling

The present study addresses the analysis of structures with uncertain properties modelled as random variables characterized by imprecise Probability Density Functions (PDFs), namely PDFs with interval basic parameters (mean-value, variance, etc.). Due to imprecision in the probabilistic model, the statistics of the response and the failure probability are described by interval quantities. An efficient

The focus of the present investigation is on the introduction of uncertainty directly in reduced order models of the nonlinear geometric response of structures following maximum entropy concepts. While the approach was formulated and preliminary validated in an earlier paper, its broad application to a variety of structures based on their finite element models from commercial software was impeded by

The Wiener path integral (WPI) approximate semi-analytical technique for determining the joint response probability density function (PDF) of stochastically excited nonlinear oscillators is generalized herein to account for systems with singular diffusion matrices. Indicative examples include (but are not limited to) systems with only some of their degrees-of-freedom excited, hysteresis modeling via

This paper is concerned with the hydraulic performance assessment of large scale water distribution networks in presence of uncertainty. In particular, the associate connectivity detection problem is examined in detail. For this purpose, a Bayesian system identification methodology is combined with an efficient hydraulic simulation model. A number of hydraulic model classes are defined as potential

The exact joint response transition probability density function (PDF) of linear multi-degree-of-freedom oscillators under Gaussian white noise is derived in closed-form based on the Wiener path integral (WPI) technique. Specifically, in the majority of practical implementations of the WPI technique, only the first couple of terms are retained in the functional expansion of the path integral related

The Fokker–Planck–Kolmogorov (FPK) equation, as a well investigated partial differential equation, is of great significance to stochastic dynamics due to its theoretical rigor and exactness. However, practical difficulties with the FPK method are encountered when analysis of multi-degree-of-freedom (MDOF) systems with arbitrary nonlinearity is required. In the present paper, a cell renormalized method

While the concept of structural monitoring has been around for a number of decades, it remains under-exploited in practice. A main driver for this shortcoming lies in the difficulty to robustly and autonomously interpret the information that is extracted from dynamic data. This hindrance in properly deciphering the collected information may be attributed to the uncertainty that is inherent in i) the

In this paper, the active learning Kriging model (ALK), which has been studied extensively in recent years, has been expanded by combining with the directional importance sampling (DIS) method. The directional sampling method can reduce the dimensionality of the variable space by random sampling or interpolation in the direction of vector diameter, which can improve the efficiency of reliability analysis

A popular peaks-over-threshold (PoT) method of Extreme Value Theory to quantify the probabilities of rare events is examined here on data generated from a nonlinear random oscillator model, describing a qualitative behavior of rolling of a ship in irregular seas. The restoring force in the oscillator model has a softening shape associated with the ship rolling application, and the response is also

In this study the non-linear hereditariness of knee tendons and ligaments is framed in the context of stochastic mechanics. Without losing the possibility of generalization, this work was focused on knee Anterior Cruciate Ligament (ACL) and the tendons used in its surgical reconstruction. The proposed constitutive equations of fibrous tissues involves three material parameters for the creep tests and