In order to make design decisions, engineers may seek to identify regions of the design domain that are acceptable in a computationally efficient manner. A design is typically considered acceptable if its reliability with respect to parametric uncertainty exceeds the designer’s desired level of confidence. Despite major advancements in reliability estimation and in design classification via decision boundary estimation, the current literature still lacks a design classification strategy that incorporates parametric uncertainty and desired design confidence. To address this gap, this works offers a novel interpretation of the acceptance region by defining the decision boundary as the hypersurface which isolates the designs that exceed a user-defined level of confidence given parametric uncertainty. This work addresses the construction of this novel decision boundary using computationally efficient algorithms that were developed for reliability analysis and decision boundary estimation. The proposed approach is verified on two physical examples from structural and thermal analysis using Support Vector Machines and Efficient Global Optimization-based contour estimation.
In this report we demonstrate some relatively simple and inexpensive methods to effectively account for various sources of epistemic lack-of-knowledge type uncertainty in inverse problems. The demonstration problem involves inverse estimation of six parameters of a bolted joint that attaches a kettlebell shaped object to a thick plate. The parameters are efficiently inverted in a modal-based model calibration using gradient-based optimization. Two material properties of the kettlebell are treated as uncertain to within given epistemic uncertainty bounds. We apply and test interval and sparse-sample probabilistic approaches to account for uncertainty in the estimated parameters (and various scalar functionals of the parameters as generic quantities of interest, QOIs) due to uncertainties in the material properties. We also investigate the error effects of limited numbers of vibration sensors (accelerometers) on the kettlebell and plate, and therefore abbreviated excitation/response information in the parameter inversions. We propose and demonstrate a Leave-K-Sensors-Out “cross-prediction” UQ approach to estimate related uncertainties on the parameters and QOI functionals. We indicate how uncertainties from material properties and limited sensors are treated in a combined manner. The economical combined UQ approach involves just three to five samples (i.e. three to five inverse simulations), with no added complication or error/uncertainty from use of surrogate models for affordability. Finally, we describe a related economical UQ approach for handling potential parameter solution non-uniqueness and numerical optimization related precision uncertainties in the estimated parameter values. Indicated further research is identified.
Many engineering design problems can be formulated as decisions between two possible options. This is the case, for example, when a quantity of interest must be maintained below or above some threshold. The threshold thereby determines which input parameters lead to which option, and creates a boundary between the two options known as the decision boundary. This report details a machine learning approach for estimating decision boundaries, based on support vector machines (SVMs), that is amenable to large scale computational simulations. Because it is computationally expensive to evaluate each training sample, the approach iteratively estimates the decision boundary in a manner that requires relatively few training samples to glean useful estimates. The approach is then demonstrated on three example problems from structural mechanics and heat transport.
The inverse methods team provides a set of tools for solving inverse problems in structural dynamics and thermal physics, and also sensor placement optimization via Optimal Experimental Design (OED). These methods are used for designing experiments, model calibration, and verfication/validation analysis of weapons systems. This document provides a user's guide to the input for the three apps that are supported for these methods. Details of input specifications, output options, and optimization parameters are included.