Vadiraj Hombal

Discretization Error Estimation in Multidisciplinary Simulations

This paper proposesmethods to estimate the discretization error in the system output of coupledmultidisciplinary simulations. In such systems, the governing equations for each discipline are numerically solved by a different computational code, and each discipline has different mesh size parameters. A classic example of multidisciplinary analysis involves fluid–structure interaction, where the element sizes in fluid and structure meshes are typically different. The general case of three-dimensional steady-state problems is considered in the current paper, where mesh refinement is possible in all three spatial directions for each discipline. Two aspects of discretization error, which are of interest in multidisciplinary analysis, are considered: disciplinary mesh sizes and the mismatch of disciplinary meshes at the interface at which boundary conditions are exchanged. Two alternate representations for the discretization error for the previously specified generic case are presented: 1) ignoring mesh mismatch at the interface and 2) considering mesh mismatch at the interface. Polynomial, rational function, and Gaussian process error models are used to represent the discretization error. The proposed error models are illustrated using a threedimensional fluid–structure interaction problem of an aircraft wing.

Functional derivatives for uncertainty quantification and error estimation and reduction via optimal high-fidelity simulations

One of the most fundamental challenges in predictive modeling and simulation involving materials is quantifying and minimizing the errors that originate from the use of approximate constitutive laws (with uncertain parameters and/or model form). We propose to use functional derivatives of the quantity of interest (QoI) with respect to the input constitutive laws to quantify how the QoI depends on the entire input functions as opposed to its parameters as is common practice. This functional sensitivity can be used to (i) quantify the prediction uncertainty originating from uncertainties in the input functions; (ii) compute a first-order correction to the QoI when a more accurate constitutive law becomes available, and (iii) rank possible high-fidelity simulations in terms of the expected reduction in the error of the predicted QoI. We demonstrate the proposed approach with two examples involving solid mechanics where linear elasticity is used as the low-fidelity constitutive law and a materials model including non-linearities is used as the high-fidelity law. These examples show that functional uncertainty quantification not only provides an exact correction to the coarse prediction if the high-fidelity model is completely known but also a high-accuracy estimate of the correction with only a few evaluations of the high-fidelity model. The proposed approach is generally applicable and we foresee it will be useful to determine where and when high-fidelity information is required in predictive simulations.

Multiscale adaptive sampling in environmental robotics

Observation of spatially distributed oceanographic phenomena using sensor-enabled AUVs involves a trade-off between coverage and resolution. In this paper the performance of adaptive variation sensitive sample distributions in such a sensing task is evaluated under mission constraints such as finite measurement time and finite vehicle speed and compared to uniform sampling. The relative performance of the four algorithms considered is characterized in terms of localization of features in the test functions.

Concurrent Optimization of Mesh Refinement and Design Parameters in Multidisciplinary Design

accuracy in terms of discretization error. Further discussed are the challenges that a design-optimization setting poses to the estimation of discretization error and how the ‘optimum’ mesh-refinement assessment is, in fact, nested within the design-optimization problem. The paper puts forth two significant contributions for multidisciplinary design-optimization formulations: 1) investigation of the impact of the so-called design inputs to discretization error in multidisciplinary design optimization, and 2) development of a concurrent optimization framework for simultaneous mesh refinement and design parameter optimization for multidisciplinary systems. The proposed method is illustrated using a simplified aircraft wing-design problem. I. Introduction I

A new approach to estimate discretization error for multidisciplinary and multidirectional mesh refinement

Discretization error estimation in the system output of multidisciplinary simulations, where each disciplinary simulation has multidirectional mesh refinement, is considered in this paper. In such systems, the governing equations for each discipline are numerically solved by a different computational code, and each discipline has different mesh size parameters. The general case of three-dimensional steady state problems is considered in the current paper. Two aspects of discretization error, that are of interest in multidisciplinary analysis, are considered: disciplinary mesh sizes, and the mismatch of disciplinary meshes at the interface at which boundary conditions are exchanged. Two alternate representations for discretization error for the above specified generic case are presented: (1) ignoring mesh mismatch at the interface, and (2) considering mesh mismatch at the interface. Polynomial, rational function, and Gaussian process error models are used to represent the discretization error. The proposed error models are illustrated using a three-dimensional fluid-structure interaction problem of an aircraft wing using ANSYS multifield module.

Uncertainty Quantification In Non-planar Crack Growth Analysis

Due to the various uncertainties and errors inherent to non-planar fatigue crack growth analysis, uncertainty quantification is required to obtain a robust assessment of component reliability. Computational costs associated with high-fidelity 3-D finite element analyses(FEA) prohibit their recurrent use in further probabilistic life prediction analysis. This paper presents two approaches for the development of surrogate model based non-planar fatigue crack growth analysis that allow for a probabilistic assessment of the component life. The first approach employs a parameterized representation of the non-planar crack for use in crack growth analyses that account for uncertainty in crack growth. The proposed method employs two surrogate models: the first surrogate model uses 3-D fatigue crack growth analyses to capture the relationship between the applied load history and equivalent planar crack orientation, and the second surrogate model calculates the stress intensity factor as a function of crack size, crack orientation, and load magnitude. Individual predictions of the two surrogate models, as well as their combined predictions are verified for accuracy using full 3-D finite element simulations. Uncertainty quantification using the verified two-stage surrogate model is then demonstrated. The second approach employs a Principal Component Analysis based non-parametric crack shape representation that allows for construction of a surrogate model for non-planar crack growth with complex crack shapes. In addition to providing a more realistic representation of non-planar cracks, the proposed approach allows for modeling the effects of spatial and temporal discretization in 3-D FEA based non-planar crack growth analysis. The ability of the surrogate model to accurately predict the evolution of the crack growth over entire load histories is verified. Extension of the proposed surrogate model to account for the effects of spatial and temporal discretization is presented. The proposed approaches are illustrated through non-planar crack growth analysis in a cylindrical component that is similar to a rotorcraft mast.