Showing papers by "Costas Papadimitriou published in 2016"

A hierarchical Bayesian framework for force field selection in molecular dynamics simulations.

Abstract: We present a hierarchical Bayesian framework for the selection of force fields in molecular dynamics (MD) simulations. The framework associates the variability of the optimal parameters of the MD potentials under different environmental conditions with the corresponding variability in experimental data. The high computational cost associated with the hierarchical Bayesian framework is reduced by orders of magnitude through a parallelized Transitional Markov Chain Monte Carlo method combined with the Laplace Asymptotic Approximation. The suitability of the hierarchical approach is demonstrated by performing MD simulations with prescribed parameters to obtain data for transport coefficients under different conditions, which are then used to infer and evaluate the parameters of the MD model. We demonstrate the selection of MD models based on experimental data and verify that the hierarchical model can accurately quantify the uncertainty across experiments; improve the posterior probability density function estimation of the parameters, thus, improve predictions on future experiments; identify the most plausible force field to describe the underlying structure of a given dataset. The framework and associated software are applicable to a wide range of nanoscale simulations associated with experimental data with a hierarchical structure.

Fusing heterogeneous data for the calibration of molecular dynamics force fields using hierarchical Bayesian models

Abstract: We propose a hierarchical Bayesian framework to systematically integrate heterogeneous data for the calibration of force fields in Molecular Dynamics (MD) simulations. Our approach enables the fusion of diverse experimental data sets of the physico-chemical properties of a system at different thermodynamic conditions. We demonstrate the value of this framework for the robust calibration of MD force-fields for water using experimental data of its diffusivity, radial distribution function, and density. In order to address the high computational cost associated with the hierarchical Bayesian models, we develop a novel surrogate model based on the empirical interpolation method. Further computational savings are achieved by implementing a highly parallel transitional Markov chain Monte Carlo technique. The present method bypasses possible subjective weightings of the experimental data in identifying MD force-field parameters.

Identification Methods for Structural Health Monitoring

Abstract: The papers in this volume provide an introduction to well known and established system identification methods for structural health monitoring and to more advanced, state-of-the-art tools, able to tackle the challenges associated with actual implementation. Starting with an overview on fundamental methods, introductory concepts are provided on the general framework of time and frequency domain, parametric and non-parametric methods, input-output or output only techniques. Cutting edge tools are introduced including, nonlinear system identification methods; Bayesian tools; and advanced modal identification techniques (such as the Kalman and particle filters, the fast Bayesian FFT method). Advanced computational tools for uncertainty quantification are discussed to provide a link between monitoring and structural integrity assessment. In addition, full scale applications and field deployments that illustrate the workings and effectiveness of the introduced monitoring schemes are demonstrated

Approximate Bayesian Computation for Granular and Molecular Dynamics Simulations

Abstract: The effective integration of models with data through Bayesian uncertainty quantification hinges on the formulation of a suitable likelihood function. In many cases such a likelihood may not be readily available or it may be difficult to compute. The Approximate Bayesian Computation (ABC) proposes the formulation of a likelihood function through the comparison between low dimensional summary statistics of the model predictions and corresponding statistics on the data. In this work we report a computationally efficient approach to the Bayesian updating of Molecular Dynamics (MD) models through ABC using a variant of the Subset Simulation method. We demonstrate that ABC can also be used for Bayesian updating of models with an explicitly defined likelihood function, and compare ABC-SubSim implementation and efficiency with the transitional Markov chain Monte Carlo (TMCMC). ABC-SubSim is then used in force-field identification of MD simulations. Furthermore, we examine the concept of relative entropy minimization for the calibration of force fields and exploit it within ABC. Using different approximate posterior formulations, we showcase that assuming Gaussian ensemble fluctuations of molecular systems quantities of interest can potentially lead to erroneous parameter identification.

Robust and Reliability-Based Structural Topology Optimization Using a Continuous Adjoint Method

Abstract: A unified framework for robust and reliability-based structural topology optimization, considering structural model and loading uncertainties, is presented using a continuous adjoint formulation. The topology optimization is formulated for objective functions related to uncertainty measures of the compliance or displacements of the structure. Uncertainty measures, such as mean, standard deviation, and level exceedance probability or failure probability, involve the estimation of multidimensional integrals over the uncertain parameter space. These integrals are evaluated using (1) sparse grid quadrature techniques for the mean and standard deviation and (2) the approximate first-order reliability method (FORM) for failure probability. A unified continuous adjoint formulation is presented for the different objective function formulations. Simplifications are proposed that result in increased computational efficiency and accuracy for special cases of uncertainties and structural performance measures....

Bayesian estimation of tension in bridge hangers using modal frequency measurements

Abstract: The tension of an arch bridge hanger is estimated using a number of experimentally identified modal frequencies. The hanger is connected through metallic plates to the bridge deck and arch. Two different categories of model classes are considered to simulate the vibrations of the hanger: an analytical model based on the Euler-Bernoulli beam theory, and a high-fidelity finite element (FE) model. A Bayesian parameter estimation and model selection method is used to discriminate between models, select the best model, and estimate the hanger tension and its uncertainty. It is demonstrated that the end plate connections and boundary conditions of the hanger due to the flexibility of the deck/arch significantly affect the estimate of the axial load and its uncertainty. A fixed-end high fidelity FE model of the hanger underestimates the hanger tension by more than 20% compared to a baseline FE model with flexible supports. Simplified beam models can give fairly accurate results, close to the ones obtained from the high fidelity FE model with flexible support conditions, provided that the concept of equivalent length is introduced and/or end rotational springs are included to simulate the flexibility of the hanger ends. The effect of the number of experimentally identified modal frequencies on the estimates of the hanger tension and its uncertainty is investigated.

Bayesian Uncertainty Quantification and Propagation (UQ+P): State-of-the-Art Tools for Linear and Nonlinear Structural Dynamics Models

Abstract: A Bayesian framework for uncertainty quantification and propagation in complex structural dynamics simulations using vibration measurements is presented. The framework covers uncertainty quantification techniques for parameter estimation and model selection, as well as uncertainty propagation techniques for robust prediction of output quantities of interest in reliability and safety of the structural systems analyzed. Bayesian computational tools such as asymptotic approximation and sampling algorithms are presented. The Bayesian framework and the computational tools are implemented for linear and nonlinear finite element models in structural dynamics using either identified modal frequencies, measured response time histories, or frequency response spectra. High performance computing techniques that drastically reduce the excessive computational demands that arise from the large number of system simulations are outlined. Identified modal properties from a full-scale bridge demonstrate the use of the proposed framework for parameter estimation of linear FE models.

A Bayesian Framework for Optimal Experimental Design in Structural Dynamics

Abstract: A Bayesian framework for optimal experimental design in structural dynamics is presented. The optimal design is based on an expected utility function that measures the value of the information arising from alternative experimental designs and takes into account the uncertainties in model parameters and model prediction error. The evaluation of the expected utility function requires a large number of structural model simulations. Asymptotic techniques are used to simplify the expected utility functions under small model prediction error uncertainties, providing insight into the optimal design and drastically reducing the computation effort involved in the evaluation of the multi-dimensional integrals that arise. The framework is demonstrated using the design of sensors for modal identification and is applied to the design of a small number of reference sensors for experiments involving multiple sensor configuration setups accomplished with reference and moving sensors. In contrast to previous formulations, the Bayesian optimal experimental design overcomes the problem of the ill-conditioned Fisher information matrix for small number of reference sensors by exploiting the information in the prior distribution.