Paul-Remo Wagner


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Wagner

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Paul-Remo

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0000-0003-4349-3784

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2016 - 2019112020 - 20229
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Publications 1 - 10 of 20
  • An adaptive algorithm based on spectral likelihood expansion for efficient Bayesian calibration
    Item type: Other Conference Item
    Wagner, Paul-Remo; Lataniotis, Christos; Marelli, Stefano; et al. (2019)
  • Stochastic Spectral Embedding in Forward and Inverse Uncertainty Quantification
    Item type: Doctoral Thesis
    Wagner, Paul-Remo (2021)
    Uncertainties are an important ingredient in the analysis of real-world systems by means of computational models. The scientific discipline that develops methods for modelling uncertainties in this context is called uncertainty quantification (UQ). Methods of this field are frequently grouped into forward and inverse UQ methods, where the former use information about the model input to quantify uncertainties in the model output, and the latter use information about the model output to indirectly quantify uncertainties in the model input. In this thesis we first give an overview of the current state-of-the-art in UQ by providing an in-depth literature review and introduction to the most widely used methods. For forward UQ we introduce techniques for uncertainty propagation, surrogate modelling, sensitivity analysis, and reliability analysis. For inverse UQ we present the powerful Bayesian inference framework, specifically in the context of model calibration. As a main methodological contribution we propose a new surrogate modelling technique called stochastic spectral embedding (SSE). Surrogate models enable many forward and inverse UQ analyses on high-fidelity computational models, by approximating the original model with a cheap-to-evaluate replacement model. This allows for repeated model evaluations that are necessary for many classes of UQ analyses. SSE is particularly powerful for approximating computational models with non-homogeneous complexity. This refers to models with outputs whose complexity strongly depends on the region of the input space that they are evaluated at. The technique consists of a series of local residual spectral expansions and, because it preserves the local spectral properties, enables the exact computation of the first two model output moments and variance-based Sobol' sensitivity indices. Applying SSE to likelihood functions typical of Bayesian inference, we show that it is possible to analytically compute many quantities of interest and effectively solve this type of inverse problem in a ``sampling-free'' manner. We call this approach stochastic spectral likelihood embedding (SSLE) and present it as a generalisation of the previously presented spectral likelihood expansion (SLE) technique. To improve the efficiency of this approach, we further introduce an adaptive experimental design enrichment scheme that predominantly evaluates the likelihood function in its informative regions. We then apply SSE to the limit-state function in reliability problems. By proposing modifications to its construction, this yields a powerful active-learning reliability method that we call stochastic spectral embedding-based reliability (SSER). We test this technique on a series of benchmark functions revealing its competitiveness with existing reliability methods. To disseminate advanced UQ techniques, we finally show two applications to complex engineering problems. The first problem studies a model for transient heat transfer in gypsum fire insulation boards that relies on temperature-dependent effective material properties (TEMPs). We propose a low-dimensional parametrisation and analyse the model with polynomial chaos expansions (PCE) and sensitivity analysis techniques. Using available measurements of the heat evolution, we also calibrate this model and validate our calibration against another set of measurements. In the second application we analyse a sediment transport model of a section of the Rhône river. We derive a probabilistic model for the uncertainties in the transport model input and construct a surrogate model. Using the latter we conduct a sensitivity analysis and show that only a small fraction of input parameters significantly influence the model output. Neglecting the unimportant parameter uncertainties, we calibrate the model using a measurement series of the riverbed height.
  • An active learning reliability algorithm based on local spectral residual expansions of the limit state function
    Item type: Other Conference Item
    Wagner, Paul-Remo; Marelli, Stefano; Papaioannou, Iason; et al. (2021)
    The assessment of structural reliability under uncertainties is a common problem in structural engineering. In a probabilistic setting, it is formalized by determining the failure probability of a system defined as the probability that the so-called limit-state function takes non-positive values. In recent years, considerable efforts have been devoted to developing algorithms that efficiently determine the failure probability. A powerful class of algorithms for reliability problems involving computationally demanding limit-state functions is the class of active learning reliability methods. These methods adaptively enhance an approximation of the limit state function resulting in considerable performance increase compared to more traditional stochastic simulation techniques. We recently proposed a new active learning reliability method based on the stochastic spectral embedding surrogate modeling technique [1]. It is based on adaptively constructing residual local spectral expansions in partitions of the parameter space with an adaptively enriched experimental design. The partitioning and enrichment rules exploit information about the local approximation accuracy and proximity to the limit state surface. In this contribution, we apply this technique to a reliability problem of a five story structural frame with 21 uncertain and mutually dependent input parameters. The frame is analyzed with the finite element method and has a reference failure probability in the order of 1e-6. With our proposed method, we consistently compute this failure probability with less than 200 evaluations of the original forward model.
  • Calibrating fire insulation models through Bayesian Inference
    Item type: Presentation
    Wagner, Paul-Remo; Fahrni, Reto; Klippel, Michael; et al. (2017)
    We outline an approach for the calibration of a finite element model (FEM), describing the heat transfer in insulation when exposed to fire, by using a full Bayesian inference approach. The considered simplistic finite element model disregards many mechanisms taking place when the insulation is exposed to fire. In order to capture these effects, we resort to so-called temperature dependent effective material parameters. These parameters do not constitute any observable real world quantities, but are a mere modeling approach. Their calibration is required for applying the improved component additive method to determine the fire resistance of e.g. timber frame assemblies. Based on experiments carried out in recent years, these parameters had been typically calibrated by hand using trial and error approaches. To this end considerable resources were devoted to finding parameters that satisfactorily reproduced the observations. We herein propose a full Bayesian procedure, that allows the sought model parameters to be calculated in an efficient way. We distinguish two approaches, namely (1) a standard Bayesian parameter estimation approach and (2) a more involved hierarchical Bayesian modeling approach. The standard Bayesian approach is applicable to the case of single measurements, where a best fit considering measurement and modeling errors is sought. The hierarchical approach can be applied to cases where multiple measurements under differing experimental conditions are available, so as to capture the variability of effective material parameters across experiments. Bayesian inference is typically carried out using Markov Chain Monte Carlo (MCMC) simulations. These simulations, however, require a large number of model evaluations that in turn are computationally very expensive to execute. To circumvent these limitations, we use a surrogate modeling technique (polynomial chaos expansion). This surrogate model can be used in MCMC simulations instead of the actual forward model and helps reducing the computational burden to a feasible level.
  • Bayesian model inversion using stochastic spectral embedding
    Item type: Journal Article
    Wagner, Paul-Remo; Marelli, Stefano; Sudret, Bruno (2021)
    Journal of Computational Physics
    In this paper we propose a new sampling-free approach to solve Bayesian model inversion problems that is an extension of the previously proposed spectral likelihood expansions (SLE) method. Our approach, called stochastic spectral likelihood embedding (SSLE), uses the recently presented stochastic spectral embedding (SSE) method for local spectral expansion refinement to approximate the likelihood function at the core of Bayesian inversion problems. We show that, similar to SLE, this approach results in analytical expressions for key statistics of the Bayesian posterior distribution, such as evidence, posterior moments and posterior marginals, by direct post-processing of the expansion coefficients. Because SSLE and SSE rely on the direct approximation of the likelihood function, they are in a way independent of the computational/mathematical complexity of the forward model. We further enhance the efficiency of SSLE by introducing a likelihood specific adaptive sample enrichment scheme. To showcase the performance of the proposed SSLE, we solve three problems that exhibit different kinds of complexity in the likelihood function: multimodality, high posterior concentration and high nominal dimensionality. We demonstrate how SSLE significantly improves on SLE, and present it as a promising alternative to existing inversion frameworks.
  • Robust-to-uncertainties optimal design of seismic metamaterials
    Item type: Journal Article
    Wagner, Paul-Remo; Dertimanis, Vasilis; Chatzi, Eleni; et al. (2018)
    Journal of Engineering Mechanics
    Metamaterials, which draw their origin from a special class of structured (periodic) materials characterized by a dynamic filtering effect, have recently emerged as a prospective means for structural seismic protection. This paper explores such a periodic arrangement in the form of local adaptive resonators buried in the soil, serving as a seismic protection barrier. As a starting point, a simplistic representation is chosen herein that comprises chains of mass-in-mass unit cells. A robust-to-uncertainties optimization of such a chain, addressing uncertainties at the level of the excitation, the system properties and the model structure itself, is conducted. The optimization problem is formulated within the context of reliability assessment, where the objective function is the failure probability of the structure to be protected against seismic input. The problem is solved through adoption of the subset optimization algorithm enhanced through the simultaneous implementation of a stochastic approximation algorithm. It is demonstrated that not all parameters of the chain model require optimization, because the failure probability proves to be a monotonic function of a subset of the parameters. A primary objective herein lies in optimizing the internal unit-cell stiffness properties. It is further demonstrated that the effectiveness of the protection offered by the metamaterial is improved for spatially varying unit-cell properties. The optimization procedure is carried out in the frequency domain, with an example application confirming that a time domain optimization is expected to yield similar optimal configurations. A parametric study using a nonlinear model is also presented, offering a starting point for more refined future investigations.
  • Estimating failure probabilities using an adaptive variant of stochastic spectral embedding
    Item type: Report
    Wagner, Paul-Remo; Papaioannou, Iason; Marelli, Stefano; et al. (2022)
    RSUQ-Report
    Reliability analysis aims to assess the probability of structural failure. The main difficulties in computing this quantity lie in its inherently low value, which causes most simulation methods to require a large number of expensive model evaluations. To alleviate the associated computational burden, practitioners today increasingly resort to active learning methods to train a surrogate model that is then used in lieu of the original model for computing the failure probability. In this contribution, we apply an adaptive variant of the recently proposed stochastic spectral embedding (SSE) surrogate modelling technique to solve reliability analysis problems. SSE creates a sequence of polynomial chaos expansions by splitting and refining subdomains of the input space. We propose here modified refinement and splitting criteria that can generate an efficient surrogate model with increased accuracy near the limit state surface. The performance of the algorithm is showcased on two reliability problems from the literature.
  • Rare event estimation using stochastic spectral embedding
    Item type: Journal Article
    Wagner, Paul-Remo; Marelli, Stefano; Papaioannou, Iason; et al. (2022)
    Structural Safety
    Estimating the probability of rare failure events is an essential step in the reliability assessment of engineering systems. Computing this failure probability for complex non-linear systems is challenging, and has recently spurred the development of active-learning reliability methods. These methods approximate the limit-state function (LSF) using surrogate models trained with a sequentially enriched set of model evaluations. A recently proposed method called stochastic spectral embedding (SSE) aims to improve the local approximation accuracy of global, spectral surrogate modelling techniques by sequentially embedding local residual expansions in subdomains of the input space. In this work we apply SSE to the LSF, giving rise to a stochastic spectral embedding-based reliability (SSER) method. The resulting partition of the input space decomposes the failure probability into a set of easy-to-compute conditional failure probabilities. We propose a set of modifications that tailor the algorithm to efficiently solve rare event estimation problems. These modifications include specialized refinement domain selection, partitioning and enrichment strategies. We showcase the algorithm performance on four benchmark problems of various dimensionality and complexity in the LSF.
  • Bayesian calibration and sensitivity analysis of heat transfer models for fire insulation panels
    Item type: Journal Article
    Wagner, Paul-Remo; Fahrni, Reto; Klippel, Michael; et al. (2020)
    Engineering Structures
    A common approach to assess the performance of fire insulation panels is the component additive method (CAM). The parameters of the CAM are based on the temperature-dependent thermal material properties of the panels. These material properties can be derived by calibrating finite element heat transfer models using experimentally measured temperature records. In the past, the calibration of the material properties was done manually by trial and error approaches, which was inefficient and prone to error. In this contribution, the calibration problem is reformulated in a probabilistic setting and solved using the Bayesian model calibration framework. This not only gives a set of best-fit parameters but also confidence bounds on the latter. To make this framework feasible, the procedure is accelerated through the use of advanced surrogate modelling techniques: polynomial chaos expansions combined with principal component analysis. This surrogate modelling technique additionally allows one to conduct a variance-based sensitivity analysis at no additional cost by giving access to the Sobol' indices. The calibration is finally validated by using the calibrated material properties to predict the temperature development in different experimental setups.
  • Surrogate models for uncertainty quantification and design optimization
    Item type: Other Conference Item
    Sudret, Bruno; Mai, Chu V.; Marelli, Stefano; et al. (2019)
    Nowadays computational models are used in virtually all fields of applied sciences and engineering to predict the behaviour of complex natural or man-made systems. Also known as simulators, they allow the engineer to assess the performance of a system in-silico, and then optimize its design or operating. Realistic models (e.g. finite element models) usually feature tens of parameters and are costly to run, even when taking full advantage of the available computer power. In parallel, the more complex the system, the more uncertainty in its governing parameters, environmental and operating conditions. In this respect, uncertainty quantification methods used to solve reliability, sensitivity or optimal design problems may require thousands to millions of model runs when using brute force techniques such as Monte Carlo simulation, which is not affordable with high-fidelity simulators. In contrast, surrogate models allow one to tackle the problem by constructing an accurate approximation of the simulator’s response from a limited number of runs at selected values (the so-called experimental design) and some learning algorithm. In this lecture, two types of efficient surrogate models will be presented in details, namely polynomial chaos expansions (including sparse approaches for high-dimensional problems) and Kriging (a.k.a. Gaussian process modelling). Recent extensions to dynamics and supervised learning will be addressed. Various applications in sensitivity and reliability analysis as well as model calibration (Bayesian inversion) and reliability-based design optimization will be shown as an illustration.
Publications 1 - 10 of 20