Sezer Atamturktur

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.

Defect detection in concrete members

A rock pocket is a deficient volume within hardened concrete consisting of coarse aggregate and voids that reduce the overall stiffness of the concrete members. The leakage of wet concrete from the form, segregation, or insufficient consolidation during concrete placement may leave rock pockets in concrete construction. This study is concerned with the detection, location and quantification of internal defects, particularly rock pockets, in reinforced concrete members. This is achieved by coupling in situ vibration testing with finite element analysis through Bayesian inference. First, the importance of providing sufficient physical evidence while calibrating the finite element models is illustrated using simulated experiments. With simulated experiments, model calibration successfully detected not only the locations but also the severity of rock pocket defects. Then, the results of impact hammer tests, completed on a concrete beam defected with rock pockets are presented. The finite element model of the test beam is segmented, and the stiffness properties of these segments are independently calibrated with the help of Bayesian calibration techniques using varying amounts of experimental information. The success in detecting defects obtained using simulated experiments, was not observed when the procedure is applied to the scaled concrete beams tested under laboratory conditions. However, the cause(s) of the poor performance with real experiments can be attributed to several factors, each of which requires further evaluation. (Publication approved for unlimited, public release on November-4- 2009, Unclassified.)

Demonstrating Predictive Capability of Validated Wind Turbine Blade Models

Verification and Validation (V&V) activities provide a means by which credibility can be established for simulation models developed to predict the behavior of wind turbines. This paper discusses the use of validation activities in the development of finite element (FE) models for wind turbine blades. The nine-meter CX-100 wind turbine blade, developed at Sandia National Laboratories (SNL), is utilized in this study. The FE model is developed using design specifications for the geometry of the blade, and the rule of mixtures is applied to smear the cross section so that it can be represented using isotropic material properties. Experimental modal data from laboratory tests of the CX-100 blade at the National Renewable Energy Laboratory (NREL), is collected for a fixed-free boundary condition, in which the blade is bolted to a 20 t steel frame. The experimental modal data is collected in two configurations: (1) in the original fixed-free condition and, (2) with two masses attached to the blade at the 1.6 and 6.75 m stations. To mimic the second experimental configuration, the FE model is modified by incorporating point masses attached to the blade with springs. Calibration of the fixed-free and mass-added FE models is limited to use of the natural frequencies only. By exploring these different configurations of the wind turbine blade, credibility can be established regarding the ability of the FE model to predict the response to different loading conditions. Through the use of test-analysis correlation, the experimental data can be compared to model output and an assessment is given of the predictive capability of the model. (Publication approved for unlimited, public release on September 26, 2011, LA-UR-11-5490, Unclassified.)

Demonstrating the Improvement of Predictive Maturity of a Computational Model

We demonstrate an improvement of predictive capability brought to a non-linear material model using a combination of test data, sensitivity analysis, uncertainty quantification, and calibration. A model that captures increasingly complicated phenomena, such as plasticity, temperature and strain rate effects, is analyzed. Predictive maturity is defined, here, as the accuracy of the model to predict multiple Hopkinson bar experiments. A statistical discrepancy quantifies the systematic disagreement (bias) between measurements and predictions. Our hypothesis is that improving the predictive capability of a model should translate into better agreement between measurements and predictions. This agreement, in turn, should lead to a smaller discrepancy. We have recently proposed to use discrepancy and coverage, that is, the extent to which the physical experiments used for calibration populate the regime of applicability of the model, as basis to define a Predictive Maturity Index (PMI). It was shown that predictive maturity could be improved when additional physical tests are made available to increase coverage of the regime of applicability. This contribution illustrates how the PMI changes as “better” physics are implemented in the model. The application is the non-linear Preston-Tonks-Wallace (PTW) strength model applied to Beryllium metal. We demonstrate that our framework tracks the evolution of maturity of the PTW model. Robustness of the PMI with respect to the selection of coefficients needed in its definition is also studied. (Approved for unlimited, public release on April-01-2010, LA-UR-10-2003.)