Barron J. Bichon

Efficient Global Reliability Analysis for Nonlinear Implicit Performance Functions

Many engineering applications are characterized by implicit response functions that are expensive to evaluate and sometimes nonlinear in their behavior, making reliability analysis difficult. This paper develops an efficient reliability analysis method that accurately characterizes the limit state throughout the random variable space. The method begins with a Gaussian process model built from a very small number of samples, and then adaptively chooses where to generate subsequent samples to ensure that the model is accurate in the vicinity of the limit state. The resulting Gaussian process model is then sampled using multimodal adaptive importance sampling to calculate the probability of exceeding (or failing to exceed) the response level of interest. By locating multiple points on or near the limit state, more complex and nonlinear limit states can be modeled, leading to more accurate probability integration. By concentrating the samples in the area where accuracy is important (i.e., in the vicinity of the limit state), only a small number of true function evaluations are required to build a quality surrogate model. The resulting method is both accurate for any arbitrarily shaped limit state and computationally efficient even for expensive response functions. This new method is applied to a collection of example problems including one that analyzes the reliability of a microelectromechanical system device that current available methods have difficulty solving either accurately or efficiently.

Efficient surrogate models for reliability analysis of systems with multiple failure modes

Despite many advances in the field of computational reliability analysis, the efficient estimation of the reliability of a system with multiple failure modes remains a persistent challenge. Various sampling and analytical methods are available, but they typically require accepting a tradeoff between accuracy and computational efficiency. In this work, a surrogate-based approach is presented that simultaneously addresses the issues of accuracy, efficiency, and unimportant failure modes. The method is based on the creation of Gaussian process surrogate models that are required to be locally accurate only in the regions of the component limit states that contribute to system failure. This approach to constructing surrogate models is demonstrated to be both an efficient and accurate method for system-level reliability analysis.

Multimodal Reliability Assessment for Complex Engineering Applications using Efficient Global Optimization

As engineering applications become increasingly complex, they are often characterized by implicit response functions that are both expensive to evaluate and nonlinear in their behavior. Reliability assessment given this type of response is dicult with available methods. Current reliability methods focus on the discovery of a single most probable point of failure, and then build a low-order approximation to the limit state at this point. This creates inaccuracies when applied to engineering applications for which the limit state has a higher degree of nonlinearity or is multimodal. Sampling methods, on the other hand, do not rely on an approximation to the shape of the limit state and are therefore generally more accurate when applied to problems with nonlinear limit states. However, sampling methods typically require a large number of response function evaluations, which can make their application infeasible for computationally expensive problems. This paper describes the application of ecient global optimization to reliability assessment to provide a method that eciently characterizes the limit state throughout the uncertain space. The method begins with a Gaussian process model built from a very small number of samples, and then intelligently chooses where to generate subsequent samples to ensure the model is accurate in the vicinity of the limit state. The resulting Gaussian process model is then sampled using multimodal adaptive importance sampling to calculate the probability of exceeding (or failing to exceed) the response level of interest. By locating multiple points on or near the limit state, more complex limit states can be modeled, leading to more accurate probability integration. By concentrating the samples in the area where accuracy is important (i.e. in the vicinity of the limit state), only a small number of true function evaluations are required to build a quality surrogate model. The resulting method is both accurate for any arbitrarily shaped limit state and computationally ecient even for expensive response functions. This new method is applied to a collection of example problems that currently available methods have diculty

Reliability-Based Design Optimization Using Efficient Global Reliability Analysis

Finding the optimal (lightest, least expensive, etc.) design for an engineered component that meets or exceeds a specified level of reliability is a problem of obvious interest across a wide spectrum of engineering fields. Various methods for this reliability-based design optimization problem have been proposed. Unfortunately, this problem is rarely solved in practice because, regardless of the method used, solving the problem is too expensive or the final solution is too inaccurate to ensure that the reliability constraint is actually satisfied. This is especially true for engineering applications involving expensive, implicit, and possibly nonlinear performance functions (such as large finite element models). The Efficient Global Reliability Analysis method was recently introduced to improve both the accuracy and efficiency of reliability analysis for this type of performance function. This paper explores how this new reliability analysis method can be used in a design optimization context to create a method of sufficient accuracy and efficiency to enable the use of reliability-based design optimization as a practical design tool.

Geomechanical modeling of an extensional fault-propagation fold: Big Brushy Canyon monocline, Sierra Del Carmen, Texas

Field structural data from the Big Brushy Canyon monocline developed in Cretaceous strata of west Texas are combined with nonlinear finite element modeling to help bridge the gap between geometric, kinematic, and mechanical analysis techniques for understanding the deformation history of reservoir-scale geologic structures. The massive Santa Elena Limestone is offset along a steep normal fault, and fault displacement is accommodated upward by the folding of the Buda Limestone and Boquillas Formation and the thinning in the intervening Del Rio Clay. Mesostructures within competent Buda Limestone beds are concentrated in the monocline limb instead of the hinge and include bed-perpendicular veins that accommodate bed-parallel extension and bedding-plane slip surfaces that offset the veins and accommodate flexural slip. Finite element models were constructed to reproduce the monocline geometry and deformation distribution as well as to assess the effect of material properties and boundary conditions on structural evolution. The initial model configuration replicated the assumed predeformational geometry, included frictional sliding surfaces to allow for bedding-parallel slip, and used a displacement boundary condition at the base of the Santa Elena footwall to simulate fault motion. Geometry and strain evolution were tracked so that (1) fold shape, (2) cumulative extension, and (3) layer-parallel shear strain could be compared to field observations. Iterative model runs successfully matched field data and revealed the importance of benchmarking the model results against monocline geometry, layer-parallel extensional strain, and bedding slip in the natural example. Our results illustrate the potential use of this modeling approach whereby calibration is performed using available data and is followed by strain measurement throughout the model domain to aid in prediction of subseismic faults and fractures. This geomechanical modeling approach provides a powerful tool for site-specific subsurface deformation prediction in hydrocarbon reservoirs that incorporates details of the local mechanical stratigraphy and structural setting.

Bayesian Model Averaging for Reliability Analysis with Probability Distribution Model Form Uncertainty

rst specify probability distribution models for all of the input random variables. In practice, these models are often estimated based on observed data, and doing so introduces uncertainty because the true underlying probability distributions are unknown. Recent work has shown that this uncertainty can be addressed by quantifying the amount of uncertainty present in the estimated distribution model parameters. However, such an approach still assumes that the form of the probability distribution model is known. In this paper, we present an approach that makes use of Bayesian model averaging to quantify uncertainty associated with both distribution model parameters and distribution model form. The proposed approach is demonstrated for the reliability analysis of a bistable MEMS device; we make use of the Ecient Global Reliability Analysis method to eciently propagate the distribution uncertainty through the reliability analysis.

Applying EGRA to Reliability Analysis of Systems with Multiple Failure Modes

Despite many advances in the eld of computational reliability analysis, the e cient estimation of the reliability of a system with multiple failure modes remains a persistent challenge. Similar to component analysis, sampling methods may be applied, but at large computational expense. Further, these sampling methods require the evaluation of each component response function for each sample, when in reality some components may contribute little to system failure. To improve e ciency, analytical methods have also been proposed to extend the concept of the most probable point of failure from component to system analysis. Such methods are based on assumptions about the functional form of the component responses and how they combine together to form the system failure condition. The combination of these approximations can make these methods inaccurate, and they also do not address the issue of important versus unimportant failure modes. In this work, a surrogate-based approach is presented that simultaneously addresses the issues of accuracy, e ciency, and unimportant failure modes. The method is an extension of the E cient Global Reliability Analysis method, and it is based on the creation of Gaussian process surrogate models that are required to be locally accurate only in the regions of the component limit states that contribute to system failure. The method is demonstrated to be both more e cient and more accurate than existing methods for system-level reliability analysis.

Geological Stress State Calibration and Uncertainty Analysis

The stress state is an important controlling factor on the slip behavior of faults and fractures in the earth’s crust and hence on the productivity of faulted and fractured hydrocarbon reservoirs. Uncertain or poorly constrained estimates of stress states can lead to high risk both in drilling and production costs. Current methods for stress tensor estimation rely on slip vector field data, however, this information is not generally available from datasets that are commonly used in the oil and gas industry. This work presents an approach whereby predicted slip tendency is used as a proxy for fault displacement, which can easily be extracted from datasets routinely used by the oil and gas industry. In doing so, a calibration approach is developed in order to estimate the parameters governing the underlying stress state by calibrating slip tendency predicted by the 3DStress® software to match measured slip displacement. A Bayesian approach is employed, and several uncertainty sources are accounted for in the estimation process, including the impacts of limited data and correlated data taken from geologically similar measurement locations.

GAUSSIAN PROCESS RESPONSE SURFACE MODELING AND GLOBAL SENSITIVITY ANALYSIS USING NESSUS

NESSUS is a general-purpose software program for probabilistic analysis that includes state-of-the-art algorithms, flexible methods for interfacing with external numerical models, and a mature graphical user interface. NESSUS was originally developed for NASA under a long-term research and development program to develop methods and tools for reliability analysis of space shuttle main engine components. In the past few years, recent NESSUS development has focused on the incorporation of advanced response surface modeling and global sensitivity analysis methods. NESSUS now includes a variety of tools for building and analyzing Gaussian Process (GP) models. This includes general-purpose GP response surface models as well as the Efficient Global Reliability Analysis (EGRA) method, which uses adaptive sampling to target surrogate model accuracy in the vicinity of the limit state. In addition, several methods have been implemented into NESSUS for the calculation of variance-based sensitivity indices, including sampling-based methods and analytical solutions based on response surface models. This paper gives an overview of these recent enhancements. In particular, we introduce the NESSUS Response Surface Toolkit (RST), which is a recently released standalone software application included with NESSUS for building, visualizing, and assessing response surface models. 225 Available online at www.eccomasproceedia.org Eccomas Proceedia UNCECOMP (2017) 225-237 ©2017 The Authors. Published by Eccomas Proceedia. Peer-review under responsibility of the organizing committee of UNCECOMP 2017. doi: 10.7712/120217.5365.16997 John M. McFarland, John A. Dimeo, and Barron J. Bichon

Dynamic Modeling of Knee Mechanics

It is widely accepted that the mechanical environment within the knee, or more specifically, increased or altered stresses or strains generated within the cartilage, is a leading cause of knee osteoarthritis (OA). However, a significant unfulfilled technological challenge in musculoskeletal biomechanics and OA research has been determining the dynamic mechanical environment of the cartilage (and other components) resulting from routine and non-routine physical movements. There are two methods of investigating musculoskeletal joint mechanics that have been used to date: 1) forward and inverse multibody dynamic simulations of human movement and 2) detailed quasi-static finite element modeling of individual joints. The overwhelming majority of work has been focused on musculoskeletal multibody dynamics modeling. This method, in combination with experimental motion capture and analysis, has been integral to understanding torques, muscle and ligament forces, and reaction forces occurring at the joint during activities such as walking, running, squatting, and jumping as well as providing key insights into musculoskeletal motor control schemes. However, multibody dynamics simulations do not allow for the detailed continuum level analysis of the mechanical environment of the cartilage and other knee joint structures (meniscus, ligaments, and underlying bone) within the knee during physical activities. This is a critical technology gap that is required to understand the relationship between functional or injurious loading of the knee and cartilage degradation. We have developed a detailed neuromuscularly activated dynamic finite element model of the human lower body and have used this model to simultaneously determine the dynamic muscle forces, joint kinematics, contact forces, and detailed (e.g., continuum) stresses and strains within the knee (cartilage, meniscus, ligaments, and bone) during several increasingly complex neuromuscularly controlled and actuated lower limb movements. Motion at each joint is controlled explicitly via deformable cartilage-to-cartilage surface contact at each articular surface (rather than idealized as simple revolute or ball and socket joints). The major muscles activating the lower limb are explicitly modeled with Hill-type active force generating springs using anatomical muscle insertion points and geometric wrapping. Muscle activation dynamics were determined via a constrained optimization scheme to minimize muscle activation energy. Time histories of the mechanical environment of all soft tissues within the knee are determined for a simulated leg extension.Copyright