François M. Hemez

Uncertainty and Sensitivity Analysis of Damage Identification Results Obtained Using Finite Element Model Updating

A full-scale seven-story reinforced concrete shear wall building structure was tested on the UCSD- NEES shake table in the period October 2005-January 2006. The shake table tests were designed so as to damage the building progressively through several historical seis- mic motions reproduced on the shake table. A sensitivity- based finite element (FE) model updating method was used to identify damage in the building. The estimation uncertainty in the damage identification results was ob- served to be significant, which motivated the authors to perform, through numerical simulation, an uncertainty analysis on a set of damage identification results. This study investigates systematically the performance of FE model updating for damage identification. The dam- aged structure is simulated numerically through a change in stiffness in selected regions of a FE model of the shear wall test structure. The uncertainty of the identified damage (location and extent) due to variability of five input factors is quantified through analysis-of-variance

Improved Damage Location Accuracy Using Strain Energy-Based Mode Selection Criteria

A method is presented for selecting the subset of identified structural vibration modes to be used in finite element model correlation for structural damage detection. The method is hased on a ranking of the modes using measured modal strain energy and is a function of only the measured modal parameters. It is shown that a mode selection strategy based on maximum modal strain energy produces more accurate update results than a strategy based on minimum frequency. Strategies that use the strain energy stored by modes in both the undamaged and damaged structural configuration are considered. It is demonstrated that more accurate results are obtained when the modes are selected using the maximum strain energy stored in the damaged structural configuration. The mode selection techniques are applied to the results of a damage detection experiment on a suspended truss structure that has a large amount of localized modal behavior.

Overview of Uncertainty Assessment for Structural Health Monitoring

ABSTRACT Uncertainty quantification is an emergent field in engineering mechanics that makes use of statistical sampling, hypothesis testing and input-output effect analysis to characterize the effect that parametric and non-parametric uncertainty has on physical experiment or numerical simulation output. This publication overviews a project at Los Alamos National Laboratory that aims at developing a methodology for quantifying uncertainty and assessing the total predictability of structural dynamics simulations. The propagation of parametric variability through numerical simulations is discussed. Uncertainty assessment is also a critical component of model validation, where the total error between physical observation and model prediction must be characterized. The purpose of model validation is to assess the extent to which a model is an appropriate representation of reality, given the purpose intended for the numerical simulation and its domain of applicability. The discussion is illustrated with component-level and system-level validation experiments that feature the response of nonlinear models to impulse excitation sources. This publication is unclassified; it has been approved for unlimited, public release (number LA-UR-01-3828).

A Coupled Approach to Developing Damage Prognosis Solutions

Funding for the Los Alamos Damage Prognosis Initiative is being provided by the Department of Energy through Laboratory Directed Research Development. In addition to the authors, the Damage Prognosis research team includes Los Alamos staff members Matt Bement, Irene Beyerlein, Norm Hunter, Cheng Liu, Brett Nadler, and Jeni Wait. Los Alamos graduate research assistants Tim Fasel, Jan Goethals and Trevor Tippetts, and. Professor Dan Inman and graduate student David Allen at Virginia Tech.

UNCERTAINTY QUANTIFICATION OF SIMULATION CODES BASED ON EXPERIMENTAL DATA

We present an approach for assessing the uncertainties in simulation code outputs in which one focuses on the physics submodels incorporated into the code. Through a Bayesian analysis of a hierarchy of experiments that explore various aspects of the physics submodels, one can infer the sources of uncertainty, and quantify them. As an example of this approach, we describe an effort to describe the plastic-flow characteristics of a high-strength steel by combining data from basic material tests with an analysis of Taylor impact experiments. A thorough analysis of the material-characterization experiments is described, which necessarily includes the systematic uncertainties that arise form sample-to sample variations in the plastic behaviour of the specimens. The Taylor experiments can only be understood by means of a simulation code. We describe how this analysis can be done and how the results can be combined with the results of analyses of data from simpler materialcharacterization experiments.

Robustness, fidelity and prediction-looseness of models

Assessment of the credibility of a mathematical or numerical model of a complex system must combine three components: (i) the fidelity of the model to test data, e.g. as quantified by a mean-squared error; (ii) the robustness, of model fidelity, to lack of understanding of the underlying processes; and (iii) the prediction-looseness of the model. ‘Prediction-looseness’ is the range of predictions of models that are equivalent in terms of fidelity. The main result of this paper asserts that fidelity, robustness and prediction-looseness are mutually antagonistic. A change in the model that enhances one of these attributes will cause deterioration of another. In particular, increasing the fidelity to test data will decrease the robustness to imperfect understanding of the process. Likewise, increasing the robustness will increase the predictive looseness. The conclusion is that focusing only on fidelity-to-data is not a sound decision-making strategy for model building and validation. A better strategy is to explore the trade-offs between robustness-to-uncertainty, fidelity to data and tightness of predictions. Our analysis is based on info-gap models of uncertainty, which can be applied to cases of severe uncertainty and lack of knowledge.

The dangers of sparse sampling for the quantification of margin and uncertainty

Abstract Activities such as global sensitivity analysis, statistical effect screening, uncertainty propagation, or model calibration have become integral to the Verification and Validation (V&V) of numerical models and computer simulations. One of the goals of V&V is to assess prediction accuracy and uncertainty, which feeds directly into reliability analysis or the Quantification of Margin and Uncertainty (QMU) of engineered systems. Because these analyses involve multiple runs of a computer code, they can rapidly become computationally expensive. An alternative to Monte Carlo-like sampling is to combine a design of computer experiments to meta-modeling, and replace the potentially expensive computer simulation by a fast-running emulator. The surrogate can then be used to estimate sensitivities, propagate uncertainty, and calibrate model parameters at a fraction of the cost it would take to wrap a sampling algorithm or optimization solver around the physics-based code. Doing so, however, offers the risk to develop an incorrect emulator that erroneously approximates the “true-but-unknown” sensitivities of the physics-based code. We demonstrate the extent to which this occurs when Gaussian Process Modeling (GPM) emulators are trained in high-dimensional spaces using too-sparsely populated designs-of-experiments. Our illustration analyzes a variant of the Rosenbrock function in which several effects are made statistically insignificant while others are strongly coupled, therefore, mimicking a situation that is often encountered in practice. In this example, using a combination of GPM emulator and design-of-experiments leads to an incorrect approximation of the function. A mathematical proof of the origin of the problem is proposed. The adverse effects that too-sparsely populated designs may produce are discussed for the coverage of the design space, estimation of sensitivities, and calibration of parameters. This work attempts to raise awareness to the potential dangers of not allocating enough resources when exploring a design space to develop fast-running emulators.

Calibration under uncertainty for finite element models of masonry monuments

Historical unreinforced masonry buildings often include features such as load bearing unreinforced masonry vaults and their supporting framework of piers, fill, buttresses, and walls. The masonry vaults of such buildings are among the most vulnerable structural components and certainly among the most challenging to analyze. The versatility of finite element (FE) analyses in incorporating various constitutive laws, as well as practically all geometric configurations, has resulted in the widespread use of the FE method for the analysis of complex unreinforced masonry structures over the last three decades. However, an FE model is only as accurate as its input parameters, and there are two fundamental challenges while defining FE model input parameters: (1) material properties and (2) support conditions. The difficulties in defining these two aspects of the FE model arise from the lack of knowledge in the common engineering understanding of masonry behavior. As a result, engineers are unable to define these FE model input parameters with certainty, and, inevitably, uncertainties are introduced to the FE model.

Use of Response Surface Metamodels for Identification of Stiffness and Damping Coefficients in a Simple Dynamic System

Metamodels have been used with success in many areas of engineering for decades but only recently in the field of structural dynamics. A metamodel is a fast running surrogate that is typically used to aid an analyst or test engineer in the fast and efficient exploration of the design space. Response surface metamodels are used in this work to perform parameter identification of a simple five degree of freedom system, motivated by their low training requirements and ease of use. In structural dynamics applications, response surface metamodels have been utilized in a forward sense, for activities such as sensitivity analysis or uncertainty quantification. In this study a polynomial response surface model is developed, relating system parameters to measurable output features. Once this relationship is established, the response surface is used in an inverse sense to identify system parameters from measured output features. A design of experiments is utilized to choose points, representing a fraction of the full design space of interest, for fitting the response surface metamodel. Two parameters commonly used to characterize damage in a structural system, stiffness and damping, are identified. First changes are identified and located with success in a linear 5DOF system. Then parameter identification is attempted with a nonlinear 5DOF system and limited success is achieved. This work will demonstrate that use of response surface metamodels in an inverse sense shows promise for use in system parameter identification for both linear and weakly nonlinear systems and that the method has potential for use in damage identification applications.

OVERVIEW OF STRUCTURAL DYNAMICS MODEL VALIDATION ACTIVITIES AT LOS ALAMOS NATIONAL LABORATORY

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.