SICODYN Research Project: Variability and Uncertainty in Structural Dynamics

This work presents a method for uncertainty propagation that is consistent with the “building-block approach” in which components of a system are tested and validated individually instead of an integrated vehicle test and validation being performed. The approach gives a unified methodology for representing and quantifying uncertainty in a Hurty/Craig-Bampton component based on component test results and propagating the uncertainty in component models into system-level predictions. Uncertainty in the Hurty/Craig-Bampton representations is quantified using a new hybrid parametric variation approach based on Soize’s maximum entropy method. The proposed approach combines parametric and nonparametric uncertainty by treating the Hurty/Craig-Bampton fixed-interface eigenvalues as random variables and treating the corresponding mass and stiffness as random matrices. The proposed method offers several advantages over traditional approaches to uncertainty quantification in structural dynamics: the number of parametric random variables is relatively small compared to the usually large number of potential random finite element model parameters; therefore, time-consuming parametric sensitivity studies do not have to be performed. In addition, nonparametric model-form uncertainty is easily included using random matrix theory. The method requires the selection of dispersion values for the Hurty/Craig-Bampton fixed-interface eigenvalues and the corresponding mass and stiffness matrices. Test/analysis frequency error is used to identify the fixed-interface eigenvalue dispersions, and test/analysis cross-orthogonality is used to identify the Hurty/Craig-Bampton stiffness matrix dispersion value. Currently, the mass matrix dispersion is based on engineering judgment, past experience, and historical results. The proposed uncertainty quantification methodology is applied to the Space Launch System liftoff configuration. Robustness of the attitude control system is studied by propagating derived component uncertainty models into gain uncertainty in specific transfer functions relating engine inputs to rate sensors on the core stage, and frequency uncertainty for the fundamental bending and roll modes.

Robust uncertainty quantification in structural dynamics under scarse experimental modal data: A Bayesian-interval approach

Adaptive sub-interval perturbation-based computational strategy for epistemic uncertainty in structural dynamics with evidence theory

The Bayesian framework for hierarchical modeling is applied to quantify uncertainties, arising mainly due to manufacturing variability, for a group of identical structural components. Parameterized Gaussian models of uncertainties in structural model parameters are introduced that depend on a set of hyperparameters. Laplace methods of asymptotic approximation and, more accurate, stochastic simulation algorithms are used for estimating posterior joint and marginal distributions of structural model parameters and hyper-parameters. The posterior distribution of the hyperparameters is formulated as the product of as many multi-dimensional integrals as the number of structural components tested, with the dimension in each integral equal to the number of physical uncertain model parameters. Novel analytical approximations of these integrals are proposed that are shown to be computationally efficient, accurate and highly parallelized. A parallelized blocked Gibbs sampler is also proposed to efficiently generate samples simultaneously along the different uncertain parameter subspaces associated with the different number of structural component tested. Theoretical and computational developments are illustrated using simulated data for modal frequencies obtained from a number of identical bar structures.

The model-form uncertainty and the connection parameter uncertainty are difficult to separate in structural dynamics. In this paper, we study a model-form uncertainty substructure identification method. Through the precision evaluation of the hyper-model of the substructure, and the experimental modal analysis of the substructure, the method of identifying the model-form uncertainty in the overall structure is given. Through the experimental modal analysis of the connection substructure, the uncertainty quantification is conducted and the joints parameters of the structure are identified. Finally, the response error estimation of the overall structure is given by combining the uncertainty of model form and of parameters. By comparing with the response errors estimated of the overall experiment, the proposed method is validated. In this paper, using modal parameters and frequency response as the response feature. A general definition of validation metrics was conducted which related to frequency response function. By using a bolted frame the framework of model validation is illustrated and the validation of the method in this paper is proved.

Severe epistemic uncertainties not only can affect the prescription of parameters within a given model but also the choice of models we make to interpret and infer from experimental data. In this work, we incorporate experimental, parametric and model-form uncertainties in the calibration of a carbon nitridation model. The model-form uncertainties considered stem from the different modeling choices that are taken as valid representations of a set of plasma wind tunnel experiments. To this end, we define a Bayesian Model Averaging strategy where the marginal posteriors of the nitridation reaction efficiencies are weighted by the marginalized likelihoods of the experimental data for each proposed model. First, Bayes factors are computed to possibly discard invalid models. The baseline model, a thermal equilibrium stagnation line flow with nitridation as only surface reaction, performs as well as all the alternative models proposed, which range from adding surface recombination reactions to considering thermal non-equilibrium in the gas and gas-surface interface. The presence of nitrogen recombination reactions is shown to broaden the support of the nitridation marginal posteriors considerably, allowing it to take on larger values. Lastly, a Bayesian model averaged Arrhenius law for the nitridation efficiencies is computed for a range of surface temperatures.

This presentation will provide a summary of the research and applications of structural dynamics model validation at Los Alamos National Laboratory. In this context model validation refers to the assessment of confidence in the usefulness of computational structural dynamics predictions for a particular application. The presentation will cover the problem definition, objectives, and motivation for studying model validation. Current paradigms for the model validation problem will also be presented. Supporting technologies such as uncertainty quantification, global sensitivity analysis, metamodeling, parameter updating, and design of experiments will be discussed, along with their role in the model validation process. The usefulness of model validation results for the computational modeling of system-level structural dynamics will be demonstrated. Examples of model validation techniques applied to transient structural dynamics problems of interest will be shown.

Ensemble-based uncertainty quantification and decomposition of probabilistic surrogate models using Bayesian neural networks

This paper puts privacy cybersecurity protection into framework of an Internet of Things industrial environment (IIoT) and analyzes on two tools’ groups in particular: (1) Standards and technical norms specifically designed to be applied in industrial environments, and (2) assessment tools for cybersecurity of Intermet of Things (IoT) devices usable in industrial infrastructures and environments. These case studies show the cybersecurity challenges and concerns triggered by these limited technologies and how they are addressed by regulations, standards, and technical mechanisms. The goal of these case studies is to illustrate how regulation and technologies attempt to protect the cybersecurity interests in industrial contexts. Finally, the case studies aim to generate an understanding of challenges and how standards and technology address cybersecurity issues in these industrial contexts.

We describe the application of a validation and uncertainty quantification methodology to multiphase computational fluid dynamics modeling, demonstrating the methodology with simulations of a pilot-scale circulating fluidized bed. The overall pressure drop is used as the quantity of interest (QoI); the solids circulation rate and the superficial gas velocity are chosen as the uncertain input quantities. The uncertainty in the QoI, caused by uncertainties in input parameters, surrogate model, spatial discretization, and time averaging, is calculated, and the model form uncertainty is estimated by comparing simulation results with experimental data. The spatial discretization error was determined to be the most dominant source of uncertainty, but the applicability of the method used to calculate that uncertainty needs to be further investigated. The results of the analysis are expressed as a probability box (p-box) plot. A p-box similarly constructed for predictive simulations will give the design engineer information about the confidence in the predicted values.

This paper gives a broad overview of a complete framework for assessing the predictive uncertainty of scientific computing applications. The framework is complete in the sense that it treats both types of uncertainty (aleatory and epistemic) and inco rporates uncertainty due to the form of the model and any numerical approximations used. Aleatory (or random) uncertainties in model inputs are treated using cumulative distribution functions, while epistemic (lack of knowledge) uncertainties are treated a s intervals. Approaches for propagating both types of uncertainties through the model to the system response quantities of interest are discussed. Numerical approximation errors (due to discretization, iteration, and round off) are estimated using verifica tion techniques, and the conversion of these errors into epistemic uncertainties is discussed. Model form uncertainties are quantified using model validation procedures, which include a comparison of model predictions to experimental data and then extrapolation of this uncertainty structure to points in the application domain where experimental data do not exist. Finally, methods for conveying the total predictive uncertainty to decision makers are presented.

ObjectiveWe present a mathematical framework for non-parametric estimation of the force of infection, together with statistical upper and lower confidence bands. The resulting estimates allow to assess how well simpler models, such as SEIR, fit the observed time series of incidence data.IntroductionUncertainty Quantification (UQ), the ability to quantify the impact of sample-to-sample variations and model misspecification on predictions and forecasts, is a critical aspect of disease surveillance. While quantifying the impact of stochastic uncertainty in the data is well understood, quantifying the impact of model misspecification is significantly harder. For the latter, one needs a "universal model" to which more restrictive parametric models are compared too.MethodsThis talk presents a useful modeling framework for time series of incidence data from contagious diseases that enables one to identify and quantify the impact of model form uncertainty. Specifically, we propose to focus on estimating the timedependent force of infection. The latter is a universal parameters for all contagious disease model. Using a machine learning technique for estimating monotone functions, i.e., isotonic regression and its variants, one can estimate the force ofinfection without addtional assumptions. We note that most contagious disease model do satisfy this monotonicity assumption, due to a combination of factors: depletion of susceptibles, implementation of mitigation strategies, behavior change, etc. Comparing the resulting "non-parametric" estimate with parametric estimates, obtained by fitting an SEIR for example, can reveal model deficiencies and help quantify model form uncertainties.Finally, we discuss how ideas from "strict bound theory" can be used to develop upper and lower uncertainty bands for force of infection that acknowledge the intrinsic stochasticity in the data.ResultsWe demonstrate the application of the methodology to weekly Influenza Like Illness (ILI) incidence data from France andcompare the results to fitted SIR and SEIR models. This comparison can be seen as a nonparametric goodness of fit test, providing one with tools to do simple model selection.ConclusionsWe present a novel and flexible model to statistically describe the force of infection as a function of time. Comparing the fit to incidence data of that model with the fit of simpler parametric models enables the quantification of model form uncertainty and associated model selection.

Uncertainty quantification (UQ) and propagation are critical to the computational assessment of structural components and systems. In this work, we discuss the practical challenges of implementing uncertainty quantification for high-dimensional computational structural investigations, specifically identifying four major challenges: (1) Computational cost; (2) Integration of engineering expertise; (3) Quantification of epistemic and model-form uncertainties; and (4) Need for V&V, standards, and automation. To address these challenges, we propose an approach that is straightforward for analysts to implement, mathematically rigorous, exploits analysts' subject matter expertise, and is readily automated. The proposed approach utilizes the Latinized partially stratified sampling (LPSS) method to conduct small sample Monte Carlo simulations. A simplified model is employed and analyst expertise is leveraged to cheaply investigate the best LPSS design for the structural model. Convergence results from the simplified model are then used to design an efficient LPSS-based uncertainty study for the high-fidelity computational model investigation. The methodology is carried out to investigate the buckling strength of a typical marine stiffened plate structure with material variability and geometric imperfections.

The reliability of the mercury spallation target is mission-critical for the neutron science program of the spallation neutron source at the Oak Ridge National Laboratory. We present an inverse uncertainty quantification (UQ) study using the Bayesian framework for the mercury equation of state model parameters, with the assistance of polynomial chaos expansion surrogate models. By leveraging high-fidelity structural mechanics simulations and real measured strain data, the inverse UQ results reveal a tight posterior distribution for the tensile cutoff threshold, the mercury density, and the mercury speed of sound. The updated distributions do not necessarily represent the nominal mercury physical properties, but the ones that fit the strain data and the solid mechanics model we have used, and can be explained by three reasons. First, the limitations of the computer model or what is known as the “model-form uncertainty” that would result from numerical methods and physical approximations. Second, is the biases and errors in the experimental data. Third, is the mercury cavitation damage that also contributes to the change in mercury behavior. Consequently, the mercury equation of state model parameters try to compensate for these effects to improve fitness to the real data. The mercury target simulations using the posterior parametric values result in an excellent agreement with 88% average accuracy compared to experimental data, 6% average increase compared to reference parameters, with some sensors experiencing an increase of more than 25%. With a more accurate strain response predicted by the calibrated simulations, the component fatigue analysis can utilize the comprehensive strain history data to evaluate the target vessel’s lifetime closer to its real limit, saving tremendous target cost and improving the design of future targets as well.

The Duffing oscillator remains a key benchmark in nonlinear systems analysis and poses interesting challenges in nonlinear structural identification. The use of particle methods or sequential Monte Carlo (SMC) is becoming a more common approach for tackling these nonlinear dynamical systems, within structural dynamics and beyond. This paper demonstrates the use of a tailored SMC algorithm within a Markov Chain Monte Carlo (MCMC) scheme to allow inference over the latent states and parameters of the Duffing oscillator in a Bayesian manner. This approach to system identification offers a statistically more rigorous treatment of the problem than the common state-augmentation methods where the parameters of the model are included as additional latent states. It is shown how recent advances in particle MCMC methods, namely the particle Gibbs with ancestor sampling (PG-AS) algorithm is capable of performing efficient Bayesian inference, even in cases where little is known about the system parameters a priori. The advantage of this Bayesian approach is the quantification of uncertainty, not only in the system parameters but also in the states of the model (displacement and velocity) even in the presence of measurement noise.