# Marcos ValdebenitoTechnische Universität Dortmund | TUD · Chair of Reliability Engineering

Marcos Valdebenito

Doctor of Engineering

## About

104

Publications

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1,383

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Introduction

## Publications

Publications (104)

First-passage probability estimation of high-dimensional nonlinear stochastic dynamic
systems is a significant task to be solved in many science and engineering fields, but
remains still an open challenge. The present paper develops a novel approach, termed
‘fractional moments-based mixture distribution’, to address such challenge. This
approach is...

Numerical methods play a dominant role in structural reliability analysis, and the goal has long been to produce a failure probability estimate with a desired level of accuracy using a minimum number of performance function evaluations. In the present study, we attempt to offer a Bayesian perspective on the failure probability integral estimation,...

This study proposes a novel sensitivity index to provide essential insights into numerical models whose inputs are characterized by intervals. Based on the interval model and its normalized form, the interval processes are introduced to define a new sensitivity index. The index can represent the individual or joint influence of the interval inputs...

In this paper, we propose a method to bound the first excursion probability of uncertain linear systems subjected to Gaussian loading. Specifically, a case is considered, where the structural behaviour is affected by both interval and random variables. Further, the structure is subjected to a Gaussian stochastic process load, and it is of interest...

This paper presents a highly efficient and effective approach to bound the first excursion probability of linear stochastic FE models subjected to imprecise Gaussian excitations. In previous work, some of the authors proposed a highly efficient approach based on the operator norm framework to bound such first excursion probabilities without having...

Probabilistic engineering computation involves two groups of models, i.e., the probability model for characterizing the randomness of input variables, and the physic model (usually described as a set of PDEs) for describing the behavior of a physic system. The probabilistic analysis aims at propagating the probability models through the physic one,...

This paper presents an approach for estimating second-order statistics of the buckling load of structural systems subject to randomness. The proposed approach is based on sampling and it exploits the correlation existing between buckling loads calculated by means of linearized and nonlinear buckling analysis under the framework provided by control...

Various numerical methods have been extensively studied and used for reliability analysis over the past several decades. However, how to understand the effect of numerical uncertainty (i.e., numerical error due to the discretization of the performance function) on the failure probability is still a challenging issue. The active learning probabilist...

This contribution focuses on reliability-based design and optimum design sensitivity of linear dynamical structural systems subject to Gaussian excitation. Directional Importance Sampling (DIS) is implemented for reliability assessment, which allows to obtain first-order derivatives of the failure probabilities as a byproduct of the sampling proces...

This paper is concerned with approximating the scalar response of a complex computational model subjected to multiple input interval variables. Such task is formulated as finding both the global minimum and maximum of a computationally expensive black-box function over a prescribed hyper-rectangle. On this basis, a novel non-intrusive method, calle...

In stochastic dynamics, it is indispensable to model environmental processes in order to design structures safely or to determine the reliability of existing structures. Wind loads or earthquakes are examples of these environmental processes and may be described by stochastic processes. Such a process can be characterised by means of the power spec...

Existing ensemble-learning methods for reliability analysis are usually developed by combining ensemble-learning with a learning function. A commonly used strategy is to construct the initial training set and the test set in advance. The training set is used to train the initial ensemble model, while the test set is adopted to allocate weight facto...

In practical engineering, experimental data is not fully in line with the true system response due to various uncertain factors, e.g., parameter imprecision, model uncertainty, and measurement errors. In the presence of mixed sources of aleatory and epistemic uncertainty, stochastic model updating is a powerful tool for model validation and paramet...

Constructed facilities should be robust with respect to the loss of load-bearing elements due to abnormal events. Yet, strengthening structures to withstand such damage has a significant impact on construction costs. Strengthening costs should be justified by the threat and should result in smaller expected costs of progressive collapse. In regular...

Engineering structures are sometimes subject to extreme loading events like vehicle impact, gas explosions, fire or terrorist bombing. These events are characterized by very small probabilities of occurrence, but large effects on design loads. Extreme loading events are also characterized by large uncertainty: impact load changes significantly with...

This paper presents a highly efficient approach for bounding the responses and probability of failure of nonlinear models subjected to imprecisely defined stochastic \red{Gaussian} loads.
Typically, such computations involve solving a nested double loop problem, where the propagation of the aleatory uncertainty has to be performed for each realizat...

An efficient procedure is proposed to estimate the failure probability function (FPF) with respect to design variables, which correspond to distribution parameters of basic structural random variables. The proposed procedure is based on the concept of an augmented reliability problem, which assumes the design variables as uncertain by assigning a p...

Line sampling is an efficient sampling-based simulation approach for reliability analysis of complex engineering structures and systems. It is particularly suitable for estimating the probability of occurrence of rare events for problems involving a large number of uncertain parameters and moderately nonlinear behavior. The basis of line sampling c...

An efficient framework is proposed for reliability-based design optimization (RBDO) of structural systems. The RBDO problem is expressed in terms of the minimization of the failure probability with respect to design variables which correspond to distribution parameters of random variables, e.g. mean or standard deviation. Generally, this problem is...

Variance-based sensitivity indices play an important role in scientific computation and data mining, thus the significance of developing numerical methods for efficient and reliable estimation of these sensitivity indices based on (expensive) computer simulators and/or data cannot be emphasized too much. In this article, the estimation of these sen...

This paper presents a highly efficient and effective approach to bound the responses and probability of failure of linear systems where the model parameters are subjected to combinations of epistemic and aleatory uncertainty. These combinations can take the form of imprecise probabilities or hybrid uncertainties. Typically, such computations involv...

This contribution focuses on evaluating the sensitivity associated with first excursion probabilities of linear structural systems subject to stochastic Gaussian loading. The sensitivity measure considered is the partial derivative of the probability with respect to parameters that affect the structural response, such as dimensions of structural el...

This contribution proposes an approach for the assessment of the failure probability associated with a particular class of series systems. The type of systems considered involves components whose response is linear with respect to a number of Gaussian random variables. Component failure occurs whenever this response exceeds prescribed deterministic...

Structural performance is affected by deterioration processes and external loads. Both effects may change over time, posing a challenge for conducting reliability analysis. In such context, this contribution aims at assessing the reliability of structures where some of its parameters are modeled as random variables, possibly including deterioration...

Imprecise probability allows quantifying the level of safety of a system taking into account the effect of both aleatory and epistemic uncertainty. The practical estimation of an imprecise probability is usually quite demanding from a numerical viewpoint, as it is necessary to propagate separately both types of uncertainty, leading in practical cas...

This contribution proposes a strategy for performing fuzzy analysis of linear static systems applying alpha-level optimization. In order to decrease numerical costs, full system analyses are replaced by a reduced order model that projects the equilibrium equations to a small-dimensional space. The basis associated with the reduced order model is co...

published version available at: https://authors.elsevier.com/a/1bdRW39%7Et0VLw3. Efficient propagation of imprecise probability models is one of the most important, yet challenging tasks, for uncertainty quantification in many areas and engineering practices, especially when the involved epistemic uncertainty is substantial due to the extreme lack...

This paper presents an efficient approach to compute the bounds on the reliability of a structure subjected to uncertain parameters described by means of imprecise probabilities. These imprecise probabilities arise from epistemic uncertainty in the definition of the hyper-parameters of a set of random variables that describe aleatory uncertainty in...

Line Sampling (LS) has been widely recognized as one of the most appealing stochastic simulation algorithms for rare event analysis, but when applying it to many real-world engineering problems, improvement of the algorithm with higher efficiency is still required. This paper aims to improve both the efficiency and accuracy of LS by active learning...

Reliability-based optimization (RBO) offers the possibility of finding an optimal design for a system according to a prescribed criterion while explicitly taking into account the effects of uncertainty. However, due to the necessity of solving simultaneously a reliability problem nested in an optimization procedure, the corresponding computational...

Published version available at https://authors.elsevier.com/a/1bcOfAQEIt1QG. The efficient estimation of the failure probability function of rare failure events is a challenging task in the structural safety analysis when the input variables are characterized by imprecise probability models due to insufficient information on these variables. The re...

The decision to design a frame structure to bridge over a column lost due to accidental loading has obvious impacts on construction costs. Moreover, not all structures are potential targets of hazards likely leading to column loss events. In this context, we propose a formulation for risk-based cost-benefit analysis of design for load bridging over...

In engineering analysis, numerical models are being increasingly used for the approximation of the real-life behavior of components and structures. In this context, a designer is often faced with uncertain and inherently variable model quantities, which are respectively represented by epistemic and aleatory uncertainties. To ensure interpretability...

This paper presents a highly efficient and accurate approach to determine the bounds on the first excursion probability of a linear oscillator 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 realizati...

Real-time hybrid simulation (RTHS) is an experimental technique for structural testing, where a critical element is studied in the laboratory, and the rest of the structure is represented through numerical simulations. The boundary conditions on the physical specimen are imposed by a transfer system (i.e., actuators), and it is essential to minimiz...

This contribution presents a highly efficient and effective approach to bound the reliability of linear structures subjected to combinations of epistemic and aleatory uncertainty. These combinations can take the form of imprecise probabilities (e.g., stochastic quantities with imprecisely defined hyper-parameters) or hybrid uncertainties (combinati...

The reliability-based design of structural dynamic systems under stochastic excitation is presented. The design problem is formulated in terms of the global minimization of the system failure probability. The corresponding optimization problem is solved by an effective stochastic simulation scheme based on the transitional Markov chain Monte Carlo...

Reliability-based optimization (RBO) offers the possibility of finding the best design for a system according to a prescribed criterion while explicitly taking into account the effects of uncertainty. Although the importance and usefulness of RBO is undisputed, it is rarely applied to practical problems, as the associated numerical efforts are usua...

This work presents a general framework for performing reliability analyses of involved structural models equipped with friction-based devices under stochastic excitation. An experimentally validated model that takes into account main sources of performance degradation that these devices experience during seismic events is considered. To deal with t...

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 realizatio...

This paper presents a highly efficient and effective approach to bound the responses and probability of failure of linear models subjected to combinations of epistemic and aleatory uncertainty.
These combinations can take the form of imprecise probabilities or hybrid uncertainties.
Typically, such computations involve solving a nested double loop...

The non-intrusive imprecise stochastic simulation (NISS) is a general framework for the propagation of imprecise probability models and analysis of reliability. The most appealing character of this methodology framework is that, being a pure simulation method, only one precise stochastic simulation is needed for implementing the method, and the req...

The non-intrusive imprecise stochastic simulation (NISS) is a general framework for the propagation of imprecise probability models and analysis of reliability. The most appealing character of this methodology framework is that, being a pure simulation method, only one precise stochastic simulation is needed for implementing the method, and the req...

Reliability-based optimization (RBO) offers the possibility of finding the best design for a system according to a prescribed criterion while explicitly taking into account the effects of uncertainty. Although the importance and usefulness of RBO is undisputed, it is rarely applied to practical problems, as the associated numerical efforts are usua...

Fuzzy probability offers a framework for taking into account the effects of both aleatoric and epistemic uncertainty on the performance of a system, quantifying its level of safety, for example, in terms of a fuzzy failure probability. However, the practical application of fuzzy probability is often challenging due to increased numerical efforts ar...

This paper presents a highly efficient and accurate approach to determine the bounds on the first excursion probability of a linear oscillator 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 realizati...

This contribution addresses the estimation of first excursion probabilities of linear structural systems subject to stochastic Gaussian loading by means of simulation. This probability is estimated by combining existing knowledge on the geometry of the associated failure domain with Directional Importance Sampling. In this way, the space associated...

This paper presents a framework for probability sensitivity estimation of a class of problems involving linear stochastic finite element models. The sensitivity measure consists of the derivative of the failure probability with respect to the statistics of the underlying random field associated with the model. The framework is formulated as a post-...

An efficient formulation for uncertainty propagation analysis of complex structural models is presented. The formulation is based on parametric reduced-order models. Fixed-interface normal modes and interface modes are approximated in terms of a set of support points in the uncertain parameter space. The potential time-consuming step of computing t...

Uncertainty characterization and propagation through computational models are the two key basic problems in risk and reliability analysis of structures and systems. Commonly used methods are mostly based on precise probability models, which are effective for characterizing the aleatory uncertainty. In real-world applications, the available data of...

Non-intrusive Imprecise Stochastic Simulation (NISS) is a recently developed general methodological framework for efficiently propagating the imprecise probability models and for estimating the resultant failure probability functions and bounds. Due to the simplicity, high efficiency, stability and good convergence, it has been proved to be one of...

This contribution investigates the application of reduced order models for approximating the response of a class of uncertain linear systems. The basis associated with the reduced model is generated based on the results of a single analysis of the system plus a sensitivity analysis. The aforementioned strategy is applied in combination with control...

RESUMEN La caracterización de la respuesta de sistemas estructurales sometidos a excitaciones dinámicas es altamente compleja. Esto se debe a que, por un lado, los modelos numéricos que permiten calcular la respuesta son cada vez más complejos y su implementación requiere un esfuerzo computacional elevado. Por otro lado, existe un alto nivel de inc...

Esta contribución propone una estrategia numérica para estimar las estadísticas de segundo orden de la respuesta de sistemas estructurales lineales y estáticos cuyas propiedades y/o cargas son inciertas. La estrategia propuesta combina dos elementos: una representación aproximada de la respuesta estructural mediante una base reducida y la aplicació...

This contribution presents a framework for calculating a sensitivity measure for problems of computational stochastic mechanics. More specifically, the sensitivity measure considered is the derivative of the failure probability with respect to parameters of the probability distributions (e.g. mean value, standard deviation) associated with the rand...

A comprehensive physical domain-based formulation of reduced-order models based on dominant and residual normal modes and interface reduction is presented. The dynamic behavior of the substructures is characterized by the dominant fixed interface normal modes and by the static contribution of higher order modes. Interface reduction is accomplished...

Esta contribución presenta una técnica numéricamente eficiente para estimar los índices de Sobol' para una clase particular de sistemas estructurales. La técnica propuesta se basa en los conceptos de subestructuración, base reducida y remuestreo. La aplicación de esta técnica se ilustra mediante un problema que involucra el modelo de un diente huma...

This contribution presents an approach for performing approximate fuzzy structural analysis of linear static systems. The proposed approach is based on an approximate representation of the structural displacement (which is constructed using intervening variables) and is capable of dealing with uncertainty present in both structural parameters and l...

This contribution proposes a strategy for estimating first excursion probabilities for linear dynamical systems involving uncertain structural parameters subject to Gaussian excitation. The proposed approach is based on Importance Sampling. The novel contribution of this paper is the introduction of an Importance Sampling density function related t...

This contribution presents an approach for performing fuzzy structural analysis of linear structures subject to static loading where uncertainties are present in both material properties and loadings. The responses of interest are displacements of the structure. The proposed approach is based on a non-linear approximation of these responses. This n...