Due to factors related to manufacturing or construction processes, ageing, loading & boundary conditions, measurement errors, modeling assumptions/inefficiencies and numerous others, almost every engineering system is characterized by uncertainty. The propagation of uncertainty through the system gives rise to corresponding complexities in the simulation of structural response and behavior. Consequently, only a limited degree of confidence can be attributed in the behavior, reliability and safety of structural systems in particular throughout their life cycle. For this purpose, it is imperative to develop models and processes able to encompass the aforementioned uncertainties. 

This mini-symposium deals with uncertainty quantification and propagation methods applicable to the simulation of complex engineering systems. It covers theoretical and computational issues, applications in structural dynami cs, earthquake engineering, mechanical and aerospace engineering, as well as other related engineering disciplines. Topics relevant to the session include: dynamics of structural systems, structural health monitoring methods for damage and reliability prognosis, theoretical and experimental system identification for systems with uncertainty, uncertainty quantification in model selection and parameter estimation, stochastic simulation techniques for state estimation and model class selection, structural prognosis techniques, updating response and reliability predictions using data. Papers dealing with experimental investigation and verification of theories are especially welcomed.

Inherent complexity, randomness and lack of information in a wide range of phenomena of engineering interest have motivated the modelling and study of systems in presence of uncertainties. This poses a challenge for suitable mathematical modelling and efficient analysis tools. In this context, important
research has been devoted, in particular, to situations which involve limited information and data, model uncertainty, subjectivity and experience, imprecise measurements, etc. Probabilistic and nonprobabilistic methods as well as mixed concepts of imprecise probabilities have been developed and applied successfully. Depending on the available information and depending on the purpose of the analysis these concepts possess useful features, which are complementary rather than contradictory to one another. In addition, considerable progress in numerical efficiency has significantly increased their practical applicability in the recent past.

The objective of this mini-symposium is to present recent advances, theories, concepts, methods and techniques for a proper conceptual and numerical treatment of vague and imprecise information in the context of challenging engineering problems Further, it will provide a forum for fruitful exchange of
ideas and interaction among diverse technical and scientific disciplines such as aerospace, civil, marine, mechanical, electrical, and nuclear engineering, computer science and mathematics.

A non-exhaustive list includes generalized probabilistic and set-theoretical approaches and methods extending the traditional probabilistic approach, Bayesian techniques, efficient Monte Carlo simulation methods, signal processing techniques, smart sensing, system reliability assessment, decision making under uncertain data, as well as risk and hazard mitigation applications. Issues of numerical efficiency and applicability to industry-size problems are of particular interest.
Keywords: Imprecise probability, Monte Carlo method, Uncertainty Quantification, Risk Informed decision

Over the last few years, the development of multiscale methods in a stochastic setting for uncertainty quantification and reliability analysis of composite materials and structures, as well as the integration of stochastic methods into a multiscale framework are becoming an emerging research frontier. This Mini-Symposium aims at presenting recent advances in the field of multiscale analysis and design of random heterogeneous media. In this respect, topics of interest include but are not limited to:

• Random field modeling of heterogeneous media
• Efficient simulation of random microstructure/morphology
• Finite element solution of multiscale stochastic partial differential equations
• Stochastic finite element (SFE) analysis of composite materials and structures
• Methods for improving the efficiency of Monte Carlo simulation
• Efficient algorithms to accelerate the SFE solution of multiscale problems
• Large-scale applications

Engineering problems typically involve non-deterministic information in various forms and of variable nature. To ensure a faultless life of the products/systems and to provide decision margins, complex technological installations, engineering systems and components have to be designed to cope with risk and
uncertainty (e.g. extreme load conditions, inherently uncertain processes and human errors). Realistic consideration and treatment of uncertainties of variable nature and scale is a key issue in the development of robust engineering solutions. The solution of such problems rely on the availability of efficient
numerical methods. While new algorithms are still arising in different fields, Monte Carlo methods are now established and ready for applications in a real practical engineering setting, thanks to the advent of modern computer technology. In addition, considerable advancements in numerical efficiency have significantly increased their practical applicability in the recent past. Examples of new methods include Subset Simulation, Line Sampling, sparse-grid stochastic collocation methods, Bayesian nested sampling, variance reduction techniques (i.e. Latin hypercube, importance sampling), and new adaptive Monte Carlo and quasi-Monte Carlo methods.

This mini-symposium aims at bringing together researchers, academics and practician engineers, providing a forum for discussion on theoretical and practical issues in the development and application of simulation-based uncertainty quantification and reliability analysis. Contributions to theory development,
applications, and implementation in engineering practice, are welcome. The issues of numerical efficiency and applicability to industry-size problems are of particular interest. This mini-symposium is organized under the auspices of the Committee on Probability and Statistics in Physical Sciences of the Bernoulli Society.

Keywords: Simulation methods, Monte Carlo, Uncertainty Quantification, Risk

Structural reliability methods and more generally, methods that aim at taking into account model- and parameters uncertainty have received much attention in the mechanical, civil, and aerospace engineering communities over the past two decades. Some well-known methods such as FORM/SORM for reliability analysis, spectral methods for stochastic finite element analysis, global sensitivity analysis (Sobol’ indices), etc. are nowadays applied in an industrial context, e.g. nuclear, aerospace, and automotive industries, among others.

However, accurate computational models (e.g., finite element analysis) of complex structures or systems are often costly. A single run of the model may last minutes to hours, even on powerful computers. In order to use these models for reliability analysis and reliability-based design optimization, which require repeated calls to the computational code, it is necessary to develop a substitute that may be evaluated thousands to millions of times at low cost: these substitutes are referred to as meta- models or surrogate models.

The aim of this mini-symposium is to confront various kinds of meta-modeling techniques in the context of uncertainty propagation including classical response surfaces, polynomial chaos expansions, Kriging, support vector regression, neural networks, low-rank tensor approximations, etc. Papers that present new methodology developments as well as large scale industrial applications that make use of surrogate models are welcome.

The awareness of the role of uncertainty in virtually all fields of applied sciences has grown steadily over the past decade. Including uncertainty quantification (UQ) in predictive models is a technical challenge that fostered the development of techniques such as probabilistic/non-probabilistic modelling of the sources of uncertainty, surrogate modelling, sensitivity analysis, model calibration, robust optimization, etc. The deployment and further diffusion of such techniques, however, is closely related to the availability of proper software that can be incorporated by researchers and practitioners into their own workflows.

This mini-symposium aims at bringing together leading and innovative players in the international uncertainty quantification software scene so as to foster discussions and exchange of ideas between developers and perspective users. Contributions are welcome on the following topics: non-intrusive UQ techniques, surrogate modelling, HPC in UQ, general-purpose UQ software and case studies and applications to real-scale industrial problems.

Non-probabilistic approaches like interval and fuzzy techniques are becoming increasingly popular in the context of modelling for engineering applications. These methods are capable of handling limited data, and are often considered to be very appropriate in an engineering context when a full probabilistic quantification of the model uncertainty is not available, or alternatively, when a full probabilistic quantification of the analysis result is not required. This mini-symposium focuses on the application of these techniques for the representation of uncertainty in typical engineering modelling activities. Researchers focusing on the application of interval and fuzzy techniques in numerical modelling for engineering applications, ranging from uncertainty propagation methodologies, inverse identification and quantification techniques to optimization under uncertainty are invited to submit an abstract to this mini-symposium.

In computational science and engineering, numerical models of physical systems are constructed with aim at reproducing experimental observations. The parameters of the numerical models are determined by combining information from different sources such as direct measurements of the parameters or the system behavior, expert knowledge, categorical data and information from literature. In probability theory, the process of combining information to learn model parameters is formalized in the concept of Bayesian updating. Thereby, the prior probability distribution of the model parameters is updated with new data to a posterior distribution. The derived distribution can be further used for forward uncertainty propagation and reliability assessment of the system performance.

This mini-symposium aims to attract papers that address either methodological developments or novel applications on Bayesian analysis of numerical models. Individual relevant topics include: Markov chain Monte Carlo methods; sequential Montel Carlo methods; Taylor series approximations to the posterior; Kriging/Gaussian process models; conjugate priors and Gibbs sampling; approximate Bayesian computation; structural identification; reliability updating; updating in the presence of spatial/time variability; updating of meta-models; applications that investigate the influence of prior considerations on the analysis results; definition of the likelihood function; representation of model errors; optimal experimental design.

Key words: Uncertainty quantification, reduced order models, low-rank

Computational Models with uncertain resp. probabilistic elements as they occur in uncertainty quantification and Bayesian updating lead to high-dimensional problems and require a high computational effort. This motivates the desire to employ reduced order models (ROMs) and low-dimensional representations of high-dimensional functions in order to reduce the computational demands. This minisymposium will be devoted to the interplay of the computational demands from the envisaged uncertainty computation and the requirements which stem from the underlying physical model. This includes approaches which merely try to approximate some output of the computational model – a quantity of interest – using structured approximations (such as sparsity or low-rank) and many different paradigms for their construction (interpolation, statistical learning, etc). Also included are approaches which first try to approximate the state of the system in a reduced form, where the governing physical equations are satisfied in some weak sense for all realisations, and from this representation of the state derive approximations of the quantity of interest. Possible applications are uncertainty quantification, estimation of rare events, Bayesian updating, stochastic control and optimisation.

A key ingredient of uncertainty quantification methods is the modeling of spatial and temporal correlations that capture crucial dependencies in the available data.  This task is often based on the standard frameworks of spatial statistics or of Gaussian process regression.  The application of such methods usually requires a number of simplifying assumptions (e.g., statistical normality, temporal and spatial stationarity, space-time separability) which are not necessarily true in practice. This session will aim to explore new developments that enhance the scope and applicability of the existing models.  The main focus of the session will thus be on topics such as non-Gaussian joint dependence models for variables that do not conform to the standard joint normal assumption, the formulation of cross-covariance functions for multivariate problems (e.g., co-kriging), the development of novel non-stationary (in space and/or time) covariance functions, and the derivation of physically motivated, non-separable space-time covariance functions such as those that can be obtained from the solution of stochastic partial differential equations.  Other topics that also expand the standard framework of space-time uncertainty characterization will also be considered.

Heterogeneous materials, e.g. soil and composites, demonstrate enormous variability in their underlying micro-structure. Rapid simulation tools are required to accommodate uncertainty quantification and facilitate response prediction and design in challenging real life applications. Multiscale methods have been recognized as fundamental tools for studying the overall constitutive behavior, as well as the damage and failure processes in particular, of heterogeneous or multi-phase structures. Over the recent years, a number of intriguing multiscale computational approaches has been introduced including homogenization methods, multiscale finite element methods, as well as mesh-free and particle methods.

This mini-symposium will form a platform for idea exchange and knowledge dissemination concerning the latest developments in the field of uncertainty quantification within a multiscale setting, with a particular interest on recent advances in the simulation of inelastic processes and brittle/ductile damage. It aims at establishing a discussion forum for advanced multiscale computational techniques and at identifying associated research challenges. Topics relevant to the mini-symposium include, but are not limited to, implementations and algorithmic solutions for multiscale analysis of:

- Micro-mechanical constitutive behaviour
- Brittle and ductile damage processes
- Predictive multiscale modelling
- Verification and validation of multiscale methods

Contributions pertaining to the implementation of such methods on real-life applications are especially welcomed.

Computational multiscale modelling and homogenization of heterogeneous materials often requires the solution of stochastic problems including different types of uncertainties (aleatoric and/or epistemic).  These uncertainties may for example result from randomness in the material’s geometric microstructure and/or lack of sufficient knowledge of the material’s constitutive behavior and properties. As examples, the exact values of the material parameters, the material’s composition, e.g. the volume fraction of inclusions, the exact geometry of the microstructure and the bonding quality between different material phases are often not deterministic and/or not exactly known. Uncertainties are typically considered at the microscale, however, they may also result from loading and boundary conditions at meso- and/or macroscales.  

This MS is intended to foster development and interaction in the area of computational stochastic multiscale modelling. Thus novel computational contributions to different stochastic simulation techniques with wide application to multiscale and multiphysics problems are invited. These problem classes may e.g. cover stochastic and heterogeneous elasticity, plasticity, generic rheology, heat conduction, magneto- and electro-statics, etc., and their various couplings. Thereby possible stochastic multiscale simulation techniques may typically build on (but are certainly not restricted to) e.g.:

Stochastic FEM
Monte-Carlo Simulation
Stochastic Collocation
Perturbation Methods
Direct Numerical Simulation