Dynamic response of a beam to a random train of moving forces moving with the same velocity is considered. Unlike a widely used Poisson process model, a more adequate Erlang renewal process is used as a process driving the train of forces. Normal-mode approach is used to convert the problem into that of a renewal driven train of general pulses. Consequently the modal responses are the filtered renewal

In the stochastic dynamic analysis, the probability density evolution method (PDEM) provides an optional way to capture the complete probability distribution of the stochastic response of general nonlinear systems. In the PDEM, the key point is to solve the generalized probability density evolution equation (GDEE), which governs the evolution of the joint probability density function (PDF) of the response

An enrichment scheme based upon the Neumann expansion method is proposed to augment the deterministic coefficient vectors associated with the polynomial chaos expansion method. The proposed approach relies upon a split of the random variables into two statistically independent sets. The principal variability of the system is captured by propagating a limited number of random variables through a low-ordered

This work is devoted to constructing a stochastic analysis model for train-track interaction. The fundamentals of the modelling framework in the establishment of the dynamic model, simulation of system uncertainties and randomness propagation process have been properly illustrated and unified in detail. For modelling train-track interaction, a matrix representation method is developed to depict the

An analytical method for determining stochastic response and survival probability of nonlinear oscillators endowed with fractional element and subjected to evolutionary excitation is developed in this paper. This is achieved by the variational formulation of the recently developed analytical Wiener path integral (WPI) technique. Specifically, the stochastic average/linearization treatment of the fractional-order

A new idea of two-scale random field is presented by taking the mechanical behaviors of quasi-brittle materials as an example. In this way, the random fluctuation of material damage at the micro-meso-scale and the spatial correlation of mechanical properties at the macro-scale are both well described by the random distribution of fracture strain. Moreover, it is proved that by introducing a transform

High temperature design methods rely on constitutive models for inelastic deformation and failure typically calibrated against the mean of experimental data without considering the associated scatter. Variability may arise from the experimental data acquisition process, from heat-to-heat material property variations, or both and need to be accurately captured to predict parameter bounds leading to

The problem of reducing the level of vibrations in various constructions has been considered for many years. This is an important element of analyzing the technical condition of buildings and the comfort of users. Various ways and means of preventing unacceptable vibrations are known and the search for an optimal absorber is still ongoing. Different kinds of vibration absorbers are applied for reducing

A method is developed for propagation of model parameter uncertainties into frequency response functions based on a modal representation of the equations of motion. Individual local surrogate models of the eigenfrequencies and residue matrix elements for each mode are trained to build a global surrogate model. The computational cost of the global surrogate model is reduced in three steps. First, modes

Calculation of probability of exceedance for nonstationary non-Gaussian responses remains a great challenge to researchers in the field of structural reliability. In this paper, an analytical solution is proposed for calculating the mean upcrossing rate (MCR) of the non-stationary non-Gaussian responses by approximating the displacement and velocity responses with the bivariate vector translation process

A new model is proposed to represent and simulate Gaussian/non-Gaussian stochastic processes. In the proposed model, stochastic harmonic function (SHF) is extended to represent multivariate Gaussian process firstly. Compared with the conventional spectral representation method (SRM), the SHF based model requires much fewer variables and Cholesky decompositions. Then, SHF based model is further extended

This work presents a framework for predicting the unknown probability distributions of input parameters, starting from scarce experimental measurements of other input parameters and the Quantity of Interest (QoI), as well as a computational model of the system. This problem is relevant to aeronautics, an example being the calculation of the material properties of carbon fibre composites, which are

Generally, in designing nonlinear energy sink (NES), only uncertainties in the ground motion parameters are considered and the unconditional expected mean of the performance metric is minimized. However, such an approach has two major limitations. First, ignoring the uncertainties in the system parameters can result in an inefficient design of the NES. Second, only minimizing the unconditional mean

Metamodel-based method is a wise reliability analysis technique because it uses the metamodel to substitute the actual limit state function under the predefined accuracy. Adaptive Kriging (AK) is a famous metamodel in reliability analysis for its flexibility and efficiency. AK combined with the importance sampling (IS) method abbreviate as AK–IS can extremely reduce the size of candidate sampling pool

In this paper, an efficient and explicit technique is proposed for transforming correlated non-normal random variables into independent standard normal variables based on the three-parameter (3P) lognormal distribution. In contrast with the classic Nataf transformation, the derived equivalent correlation coefficient in non-orthogonal standard normal space of the proposed transformation is expressed

This paper explores the applicability of variability response functions to nonlinear soil–structure interaction problems, focusing on the impacts of spatially variable soil properties on foundation reliability regarding the settlement response. An estimation scheme is proposed to obtain the response functions, which involves a periodic function to approximate the relationship between foundation response

This paper introduces a generalized 3rd-order Spectral Representation Method for the simulation of multi-dimensional random fields and ergodic multi-variate stochastic processes with asymmetric non-linearities. The formula for the simulation of general d-dimensional random fields is presented and the method is applied to simulate 2D and 3D random fields. The differences between samples generated by

Traditionally, the main structural system of tall buildings is designed iteratively to resist extreme wind loads, which provides safe, but typically suboptimal building systems. Topology optimization provides a general approach to obtain optimal material layout to carry the required load within specified design constraints. The wind loading on a structure is typically modeled as an equivalent static

The reliability analysis of high-dimensional stochastic dynamical systems subjected to random excitations has long been one of the major challenges in civil and various engineering fields. Despite great efforts, no satisfactory method with high efficiency and accuracy has been available as yet for high-dimensional systems even when they are linear systems, not to mention generic nonlinear systems.

This paper is a sequel to papers studying the continuum approach to the high-cycle fatigue model of Ottosen et al. First, we study the estimation of fatigue limit and statistical characteristics of the estimates. We have two cases. Either the fatigue limit is a material constant or it is a random variable. Finally, we derive approximate distributions for the parameter estimators of the fatigue model

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

Abstract 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

By adopting a Multilevel Monte Carlo (MLMC) framework, we show 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 thousands typically needed in classical Monte Carlo analyses. We introduce the MLMC method, compare its theoretical complexity with classical Monte Carlo, and give a simple-to-implement

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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

The present work provides a profound analytical 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 parameters

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract Integral equations of the type in Bernard and Shipley (1972) are used to calculate approximately the distribution of the first time T a 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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: S F ( t , ω ) = t 2 λ e − 2 γ ( ω ) t Φ ( ω ) . The proposed Laplace-frequency method also

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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

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 misconception in the Bayesian framework since it is absolutely robust with respect to the modeling assumptions and the observed data. Rather, this issue has deep roots in users' inability

Abstract 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

Abstract 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

Abstract 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