In perspective of global approximation, this study presents a numerical method for the generalized density evolution equation (GDEE) based on spectral collocation. A sequential matrix exponential solution based on the Chebyshev collocation points is derived in consideration of the coefficient or velocity term of GDEE being constant in each time step, then the numerical procedure could be successively

By adopting a Multilevel Monte Carlo (MLMC) framework, this paper shows that only a handful of costly fine scale computations are needed to accurately estimate statistics of the failure of a composite structure, as opposed to the many thousands typically needed in classical Monte Carlo analyses. The paper introduces the MLMC method and provides an extension called MLMC with selective refinement to

In this paper, the reliability assessment of magnetorheological (MR) dampers in reducing structures’ seismic responses is studied. Two passive and semi-active control scenarios are considered and discussed. For semi-active control scenario, the Lyapunov control algorithm is used. In order to minimize the structure’s responses under a given earthquake excitation, an unconstrained optimization problem

A hypothetical seismic site is constructed for which the probability law of the seismic ground acceleration process X(t) is specified. Since the seismic hazard is known, the performance of the incremental dynamic analysis- (IDA) and multiple stripe analysis- (MSA) based fragilities, which are used extensively in Earthquake Engineering, can be assessed without ambiguity. It is shown that the IDA- and

A novel algorithm is proposed for simulating univariate non-Gaussian nonstationary processes (NNP) with the specified evolutionary power spectral density (EPSD)/nonstationary auto-correlation function (NACF) and first four-order time-varying marginal moments (TVMMs). The sample realizations of the target NNP are generated as the outputs from a specific time-varying auto-regressive (TVAR) model via

In this paper, a new computational framework based on the topology derivative concept is presented for evaluating stochastic topological sensitivities of complex systems. The proposed framework, designed for dealing with high dimensional random inputs, dovetails a polynomial dimensional decomposition (PDD) of multivariate stochastic response functions and deterministic topology derivatives. On one

The paper proposes an approach to model the geometrical uncertainty in case of curves in space. After highlighting the importance of the geometrical uncertainty in various fields of mechanics, the random set of “irregular or imperfect curves” is analysed in the natural or intrinsic reference system by the formulas of Serret–Frenet. It is shown that the Riccati’s random differential operator, in complex

Wind loads on structures are commonly described as stationary phenomena that occur in neutral atmospheric conditions at the synoptic scale with velocity profiles in equilibrium with the atmospheric boundary layer. Nevertheless, structural systems can be also affected by thunderstorm outflows, which are non-stationary local phenomena at the mesoscale that occur in convective conditions with totally

This paper focuses on issues related to Validation, i.e., determining for a computational tool that predicts the motions of a vessel in extreme seas if the theory and the code that implements the theory accurately models the relevant physical problem of interest. The challenge of this validation is the fact that the excitation process – waves – are stochastic and that as a consequence, the responses

This paper is a first attempt to develop a numerical technique to analyze the sensitivity and the propagation of uncertainty through a system with stochastic processes having independent increments as input. Similar to Sobol’ indices for random variables, a meta-model based on Chaos expansions is used and it is shown to be well suited to address such problems. New global sensitivity indices are also

Sensitivity analysis plays an important role in reliability evaluation, structural optimization and structural design, etc. The local sensitivity, i.e., the partial derivative of the quantity of interest in terms of parameters or basic variables, is inadequate when the basic variables are random in nature. Therefore, global sensitivity such as the Sobol’ indices based on the decomposition of variance

The present work provides a profound analytical treatment and numerical analysis of the material properties of SFRC on the mesoscale as well as the resulting correlation structure taking into account the probabilistic characteristics of the fiber geometry. This is done by calculating the engineering constants using the analytical framework given by Tandon and Weng as well as Halpin and Tsai. The input

The state of materials and accordingly the properties of structures are changing over the period of use, which may influence the reliability and quality of the structure during its life-time. Therefore, identification of the model parameters of the system is a topic which has attracted attention in the content of structural health monitoring. The parameters of a constitutive model are usually identified

In this paper we discuss the accuracy of probability of failure sensitivity analysis with sampling-based schemes. Three approaches commonly employed in literature are discussed: the Weak sensitivity analysis, the Direct employment of finite difference schemes and the Common Random Variable approach. Theoretical estimates for the bias, the coefficient of variation and the mean square error for each

A method is developed for the explicit identification of solid-void interfaces in a Bayesian framework using a statistically efficient gradient based Markov Chain Monte Carlo (MCMC) algorithm called Hamiltonian Monte Carlo (HMC). The elastodynamic inversion is carried out in a Finite Element discretized domain considering parameterized representations of the actual interface between the elastic solid

The efficiency of existing stochastic analysis method depends on the discretization of the random variables domain. The number theoretical method has been proposed to discretize the random variable space and solve the generalized density evolution equation via sampling strategy. This method traditionally involves hyper-ball sieving (HS) algorithm to sample the representative point set. However, the

Integral equations of the type in Bernard and Shipley (1972) are used to calculate approximately the distribution of the first time Ta that a Gaussian process X(t) crosses a threshold a from below, referred as the first passage time. These equations involve kernels which are currently calculated numerically from multidimensional integrals. It is shown that Slepian models can be used to calculate efficiently

This paper addresses the determination of the closed-form solutions of redundantly constrained stochastic frames in terms of the probability density function (PDF). The full characterization of any response random variable of the structures, that are characterized by spatially random deformability (or its inverse, the stiffness), has been identified through the application of the force method and the

The stochastic response of frictionally damped strongly non-linear elastic impact oscillator subjected to white noise excitation and its stochastic bifurcation are considered. By the stochastic averaging method based on generalized harmonic function, one can obtain the stationary probability density function of this system. The effects of system parameters on the responses are investigated and the

A review of theoretical concepts and diverse applications of sparse representations and compressive sampling (CS) approaches in engineering mechanics problems is provided from a broad perspective. First, following a presentation of well-established CS concepts and optimization algorithms, attention is directed to currently emerging tools and techniques for enhancing solution sparsity and for exploiting

Nonlinear fluid viscous dampers have been widely used in energy-dissipating structures due to their stable and high dissipation capacity and low maintenance cost. However, the literature on stochastic optimization of nonlinear viscous dampers under nonstationary excitations is limited. This paper is devoted to the stochastic response and sensitivity analysis of large-scale energy-dissipating structures

In order to overcome the disadvantages of traditional deterministic models, a probabilistic bond strength model of reinforcement bar in concrete was presented. According to the partly cracked thick-walled cylinder model, a deterministic bond strength model of reinforcement bar in concrete was developed first by taking into account the influences of various important factors. Then the analytical expression

Bayesian linear regression (BLR) based demand prediction models are proposed for efficient seismic fragility analysis (SFA) of structures utilizing limited numbers of nonlinear time history analyses results. In doing so, two different BLR models i.e. one based on the classical Bayesian least squares regression and another based on the sparse Bayesian learning using Relevance Vector Machine are explored

Optimal control for improving the stability and reliability of nonlinear stochastic dynamical systems is of great significance for enhancing system performances. However, it has not been adequately investigated because the evaluation indicators for stability (e.g. maximal Lyapunov exponent) and for reliability (e.g. mean first-passage time) cannot be explicitly expressed as the functions of system

This article develops a Laplace-frequency method to derive the exact closed-form solution for the response evolutionary power spectral density (EPSD) of a simple oscillator subjected to an evolutionary stochastic process characterized by a particular kind of time–frequency (t,ω) non-separable EPSD: SF(t,ω)=t2λe−2γ(ω)tΦ(ω). The proposed Laplace-frequency method also gains insightful physics for the

The efficiency of the probability density evolution method (PDEM) is improved in this paper by embedding the Kullback–Leibler (K–L) relative sensitivity in the response analysis of a stochastic dynamic system. The response reliability obtained and the probability density function of the response peaks are used for ranking to get a reduced set of random variables for the PDEM analysis. The need of complicated

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

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

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

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 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 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

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

Investigations of wave propagation in composite materials have been used both to experimentally measure material properties and to validate material property model characterizations. For continuous fiber reinforced composites, these characterizations often have relied on a bulk description of the effective behavior of a Representative Volume Element (RVE) and assumed ideal conditions of transverse

A multilevel moving particles method is developed for the estimation of failure probabilities that are computed from numerical approximations of the performance function. The algorithm balances the statistical error of the estimate and the approximation error. This is achieved by computing a telescoping sum of estimates for the difference in the number of moves at subsequent levels of the approximation

This paper is concerned with aircraft aeroelastic interactions and the propagation of parametric uncertainties in numerical simulations using high-fidelity fluid flow solvers. More specifically, the influence of variable operational and structural parameters (random inputs) on the drag performance and deformation (outputs) of a flexible wing in transonic regime, is assessed. Because of the complexity

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

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

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

This paper proposes an efficient approach for estimating reliably the second order statistics of the response of continua excited by combinations of harmonic and random loads. The problem is relevant in several engineering applications, where, for instance, the harmonic load is influenced by significant noise that cannot be neglected when computing the response statistics. The considered problems pertain

It is nowadays widely acknowledged that optimal structural design should be robust with respect to the uncertainties in loads and material parameters. However, there are several alternatives to consider such uncertainties in structural optimization problems. This paper presents a comprehensive comparison between the results of three different approaches to topology optimization under uncertain loading

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 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 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

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

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

Nowadays stochastic ground motion models used for the seismic analysis and design of structures take into account the soil deposit only, disregarding the presence of existing buildings nearby. However, it is well known that ground motion in urban environment is modified by the presence of buildings, mainly due to the radiation energy emitted from a vibrating structure in the soil that alters the seismic

Models involving stochastic diffusion equations are utilized for describing the evolution of a number of natural phenomena and are widely discussed in the open literature. In recent years, these models have been revisited in light of experimental observations in which “anomalous” diffusion processes were identified, such as in the propagation of acoustic waves in random media. In this context, a critical

Various natural phenomena are described by anomalous diffusion processes. Notable examples relate to the study of diffusion of tracers in particles in turbulent flows, or in the propagation of acoustic waves. In this context, the governing equations involve a fractional Laplacian operator, which replaces the classical Laplacian, and may involve nonlinear terms. This leads to problems described by fractional

In this study, a lifecycle operational reliability assessment framework for water distribution networks (WDNs) is proposed on the basis of the probability density evolution method (PDEM). The occurrence models of daily accidents are fitted using the maintenance data provided by a local water administration sector. For a given accident, two types of accidents (e.g., leaks and bursts) are distinguished

Performance evaluation and reliability assessment of real-world structures under earthquakes is of paramount importance. Generally, different mechanical property parameters of a structure are usually not independent, nor completely dependent, but partly dependent or correlated. Therefore, how to reasonably characterize such partial dependency and whether such partial dependency real matters in the

Soil parameters are spatially random variables. Thus, the spatial correlation relationship, besides the mean and variance, of a specific soil site is needed for any realistic stochastic modeling. In this regard, an improved autocorrelation model involving a linear, an exponential and cosine terms, named linear-exponential-cosine (LNCS), is adopted here to capture the spatial properties of the soil

The scope of this paper is to evaluate different approaches for the prediction of the probability of failure of uncertain railway bridges subjected to high-speed trains. The peak acceleration of a bridge, which is commonly the governing response quantity for dynamic bridge design and failure, depends strongly on the type of train and the train speed. Since in many cases the critical speeds related