# Matthias FaesTechnische Universität Dortmund | TUD · Chair of Reliability Engineering

Matthias Faes

Professor

Developing methods to include data, uncertainty and numerical models to better predict mechanical behaviour.

## About

112

Publications

55,086

Reads

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985

Citations

Introduction

I work as a professor in Reliability Engineering at the TU Dortmund. My research is focused on inverse probabilistic and non-probabilistic methods for Uncertainty Quantification, the modelling of spatial and multi-variate uncertainty under scarce data using interval methods and the application of high-dimensional measurement techniques such as Digital Image Correlation. Recently, I also initiated works in the field of grey-box modelling.

Additional affiliations

November 2017 - February 2022

## Publications

Publications (112)

This paper introduces an improved version of a novel inverse approach for the indirect quantification of multivariate interval uncertainty for high dimensional models under scarce data availability. The method is compared to results obtained via the well-established probabilistic framework of Bayesian model updating via Transitional Markov Chain Mo...

This paper gives an overview of recent advances in the field of non-probabilistic uncertainty quantification. Both techniques for the forward propagation and inverse quantification of interval and fuzzy uncertainty are discussed. Also the modeling of spatial uncertainty in an interval and fuzzy context is discussed. An in depth discussion of a rece...

The accurate prediction of the dynamic behaviour of a complex component or system is often difficult due to uncertainty or scatter on the physical parameters in the underlying numerical models. Over the past years, several non-deterministic techniques have been developed to account for these model inaccuracies, supporting an objective assessment of...

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...

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...

The objective of this study is to estimate the, probably correlated, ligament material properties and attachment sites in a highly non-linear, musculoskeletal knee model based on kinematic data of a knee rig experiment for seven specific specimens. Bayesian parameter estimation is used to account for uncertainty in the limited experimental data by...

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 work proposes a methodology for the concurrent homogenization-based optimization of the type and the configuration of the microstructure of the structural domain, based on a list of pre-defined composite microstructures. The candidate microstructures are represented on this list by their homogenized mechanical properties, as predicted by means...

One of the key challenges of uncertainty analysis in model updating is the lack of experimental data. The definition of an appropriate uncertainty quantification metric, which is capable of measuring as sufficient as possible information from the limited and sparse experimental data, is significant for the outcome of model updating. This work is de...

Uncertainties existing in physical and engineering systems can be characterized by different kinds of mathematical models according to their respective features. However, efficient propagation of hybrid uncertainties via an expensive-to-evaluate computer simulator is still a computationally challenging task. In this contribution, estimation of resp...

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 investigation proposes a more general dashpot model with elastoplastic deformation and rough surface based on the fractal theory in allusion to the rough surface with fractal characteristic. Firstly, the rough surface of the contact body is depicted using the Weierstrass-Mandelbrot (W-M) function. The entire contact process of a single asperit...

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...

This paper introduces a novel method to create an interval field based on measurement data. Such interval fields are typically used to describe a spatially distributed non-deterministic quantity, e.g., Young's modulus. The interval field is based on a number of measurement points, i.e., control points, expended throughout the domain by a set of bas...

Typically, non-deterministic models of spatial or time dependent uncertainty are modelled using the well-established random field framework. However, while tailored for exactly these types of time and spatial variations, stochastic processes and random fields currently have only limited success in industrial engineering practice. This is mainly cau...

Research on stochastic processes in recent decades has pointed out that, in the context of modelling spatial or temporal uncertainties, auto-correlation functions that are differentiable at the origin have advantages over functions that are not differentiable. For instance, the non-differentiability of e.g., single exponential auto-correlation func...

Typically, non-deterministic models of spatial or time dependent uncertainty are modelled using the well-established random field framework. However, while tailored for exactly these types of time and spatial variations, stochastic processes and random fields currently have only limited success in industrial engineering practice. This is mainly cau...

Research on stochastic processes in recent decades has pointed out that, in the context of modelling spatial or temporal uncertainties, auto-correlation functions that are differentiable at the origin have advantages over functions that are not differentiable. For instance, the non-differentiability of e.g., single exponential auto-correlation func...

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...

This paper deals with lack-of-knowledge uncertainty in complex non-linear simulations on a component level, i.e., a crashbox during frontal impact of a vehicle. Specifically, the focus lies on using interval field techniques to model the uncertain boundary conditions during impact simulations. The uncertainty considered in this work is the unknown...

This paper presents a multilevel Quasi-Monte Carlo method for interval analysis, as a computationally efficient method for high-dimensional linear models. Interval analysis typically requires a global optimisation procedure to calculate the interval bounds on the output side of a computational model. The main issue of such a procedure is that it re...

Non-deterministic approaches that enable uncertainty analysis in numerical simulation have been studied extensively over the past decades. Non-deterministic models of spatial uncertainty are modeled in the well-established random field framework. This chapter focuses on the use of the more intuitive interval concept in the context of modeling spati...

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...

Research on stochastic processes in recent decades has pointed out that, in the context of modelling spatial or temporal uncertainties, auto-correlation functions that are differentiable at the origin have advantages over functions that are not differentiable. For instance, the non-differentiability of e.g., single exponential autocorrelation funct...

Typically, non-deterministic models of spatial or time dependent uncertainty are modelled using the well-established random field framework. However, while tailored for exactly these types of time and spatial variations, stochastic processes and random fields currently have only limited success in industrial engineering practice. This is mainly cau...

Interval analysis has proven to provide robust bounds on the performance of structures when there is only limited data available on the uncertainty. Calculating the interval bounds on the output side of a computational model typically involves a global optimisation algorithm or vertex analysis for monotonic models, where numerous model evaluations...

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...

Uncertainty quantification metrics have a critical position in inverse problems for dynamic systems as they quantify the discrepancy between numerically predicted samples and collected observations. Such metric plays its role by rewarding the samples for which the norm of this discrepancy is small and penalizing the samples otherwise. In this paper...

Objective:
This study proposes a computationally efficient method to quantify the effect of surgical inaccuracies on ligament strain in total knee arthroplasty (TKA). More specifically, this study describes a framework to determine the implant position and required surgical accuracy that results in a ligament balanced post-operative outcome with a...

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...

The consideration of imprecise probability in engineering analysis to account for missing, vague or incomplete data in the description of model uncertainties is a fast-growing field of research. Probability-boxes (p-boxes) are of particular interest in an engineering context, since they offer a mathematically straightforward description of imprecis...

Imprecise random fields consider both, aleatory and epistemic uncertainties. In this paper, spatially varying material parameters representing the constitutive parameters of a damage model for concrete are defined as imprecise random fields by assuming an interval valued correlation length. For each correlation length value, the corresponding rando...

The increasing complexity of modern engineering system has made the multi-source information fusion a necessary yet challenging task. In the context of reliability engineering, the information fusion process is either ineffective or less efficient as the aggregation error increases with respect to the collection of multiple dependent pieces of evid...

Interval fields have been introduced to model spatial uncertainty in Finite Element Models when the stochastic resolution of available data is too limited to build representative probabilistic models. However, current interval fields modelling techniques are according to the state-of-the-art limited in potential, as they homogenise the uncertain pa...

The consideration of imprecise probability in engineering analysis to account for missing, vague or incomplete data in the description of model uncertainties is a fast-growing field of research. Probability-boxes (p-boxes) are of particular interest in an engineering context, since they offer a mathematically straightforward description of imprecis...

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...

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...

This paper investigates the dependence of the functional life of additively manufactured plastic insert moulds on occurring shear stresses and temperatures during the injection moulding process. As a first step, a dedicated plastic insert is designed that allows for experimentally simulating different shear rates and thermal loads of the injected p...

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...

Today, in aerospace and automotive industries, structural components are more and more designed up to their functional limits, pursuing weight minimization without compromising the mechanical integrity. Especially in the aforementioned domains, the fracture behavior is of utmost importance in this respect. Yet, due to the complexity of the underlyi...

This paper introduces a novel method to model non-deterministic quantities based on experimental measurement data. The focus of this work is on quantities that vary over a continuous domain, e.g., material properties, time-dependent strain rate effects, or stress–strain curves. These quantities are modelled by means of the recently introduced conce...

Interval fields have been introduced to model spatial uncertainty in Finite Element Models when the stochastic resolution of available data is too limited to build representative probabilistic models. However, current interval fields modelling techniques are according to the state-of-the-art limited in potential, as they homogenise the uncertain pa...

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...

The consideration of imprecise probability in engineering analysis to account for missing, vague or imcomplete data in the description of model uncertainties is a currently fast growing field of research. Especially probability-boxes (p-boxes) are of interest in an engineering context since they offer a mathematically simple description of the deep...

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...

This paper presents an interval field approach to represent the complex interactions between adjacent components in car crash simulations. Typically, the design and optimization of individual components is made on a component-by-component scale under the assumption that these interactions are negligible. Since the mechanical behavior of these compo...

Interval fields have been introduced to model spatial uncertainty in Finite Element Models when the available data is insufficient to build representative probabilistic models. However, they are limited to modelling global non-stationary uncertainty and hence cannot model local non-stationary uncertainty. This is typically occurring in specific reg...

In an engineering context, design optimization is usually performed virtually using numerical models to approximate the underlying partial differential equations. However, valid criticism exists concerning such an approach, as more often than not, only partial or uninformative data are available to estimate the corresponding model parameters. As a...

This paper presents an objective comparison of random fields and interval fields to propagate spatial uncertainty, based on a finite element model of a lunar lander. The impulse based substructuring method is used to improve the analysis efficiency. The spatially uncertain input parameters are modeled by both random fields and interval fields. The...

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...

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 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...

Special issue in the ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems Part B: Mechanical Engineering on the topic of non-probabilistic and hybrid approaches for uncertainty quantification and reliability analysis.

This paper introduces a novel approach to model interval fields in high dimensional Finite Element models containing thousands of degrees of freedom. Typically, to simulate with interval fields in such high dimensional model spaces, a non-negligible computational cost has to be dedicated to the calculation of a combinatorial amount of distances in...