Arun K. Subramaniyan

Improving High-Dimensional Physics Models Through Bayesian Calibration With Uncertain Data

We address the problem of calibrating model parameters in computational models to match uncertain and limited experimental data using a Bayesian framework. We employ a modified version of the Bayesian calibration framework proposed by Kennedy and O’Hagan [15], to perform calibration of large dimensional industrial problems. Results for two nonlinear industrial problems with 15 and 100 calibration parameters are presented. The unique advantages of the Bayesian framework are presented along with a discussion on the challenges in calibrating large number of parameters with uncertain and limited data.Copyright

Multimodal Particle Swarm Optimization: Enhancements and Applications

Optimization problems with multiple optima (local or global) are called multimodal problems. Many real world problems are multimodal and challenging to solve as compared to unimodal problems due to the possibility of premature convergence to a local optimum solution and possibly requiring a higher number of function evaluations. A multimodal optimization algorithm provides multiple solutions, thus a better understanding of the design space at minimal additional computational cost. The goal of multimodal particle swarm optimizer (MPSO) is to converge to multiple local and global optima with a reasonable number of function evaluations. The modifications to PSO include reduction in the personal best weight and an additional step to replace the global best with a group best in the PSO procedure. The modifications only allow a user defined number of particles (m ) to converge to a solution and relocate the particles if more than m particles converge to a solution. The relocation is active or inactive based on a predefined set of rules. MPSO is demonstrated on several optimization problems such as benchmark problems from the literature, spring design, and sequential sampling.

Calibrating Transient Models With Multiple Responses Using Bayesian Inverse Techniques

Several engineering applications of high interest to turbomachinery involve transient models with multiple outputs. Thus, the ability to calibrate transient models with multiple correlated outputs is critical for enabling predictive models for design and analysis of turbomachinery. When the number of calibration parameters becomes large along with limited knowledge about those parameters (large uncertainty), traditional deterministic methods like least squares don’t yield reasonable parameter estimates. We employ the Bayesian calibration framework, proposed by Kennedy and O’Hagan [1], to perform calibration of industrial scale transient problems. The focus of this article is on Bayesian calibration of models with multiple transient outputs. The methodology is demonstrated with two problems with transient outputs. The advantages of using a Bayesian framework are highlighted. Specific challenges related to Bayesian calibration of transient responses are discussed along with potential solutions.Copyright

Hybrid Bayesian Solution to NASA Langley Research Center Multidisciplinary Uncertainty Quantification Challenge

This paper presents a hybrid Bayesian solution to the multidisciplinary uncertainty quantification challenge posed by NASA Langley Research Center. The hybrid approach builds probabilistic models of the outputs by combining the simulations and “experimental” observations provided by NASA. The proposed method is a synergy between Gaussian process surrogate modeling and Bayesian principles, and the resulting tool allows construction of surrogate models, parameter calibration, and variance-based global sensitivity analysis. Besides Sobol indices, a cumulative-density-function-based sensitivity to the probability of failure is also explored. Particle swarm optimization has been used in conjunction with the Gaussian process surrogates to find extreme values of both the mean value of the worst-case requirement function and the failure probability. The capability of the proposed techniques is demonstrated on the four subproblems of uncertainty characterization, sensitivity analysis, uncertainty propagation, and ...

Challenges in Uncertainty, Calibration, Validation and Predictability of Engineering Analysis Models

Model calibration, validation, prediction and uncertainty quantification have progressed remarkably in the past decade. However, many issues remain. This paper attempts to provide answers to the key questions: 1) how far have we gone? 2) what technical challenges remain? and 3) what are the future directions for this work? Based on a comprehensive literature review from academic, industrial and government research and experience gained at the General Electric (GE) Company, the paper will summarize the advancements of methods and the application of these methods to calibration, validation, prediction and uncertainty quantification. The latest research and application thrusts in the field will emphasize the extension of the Bayesian framework to validation of engineering analysis models. Closing remarks will offer insight into possible technical solutions to the challenges and future research directions.Copyright

Probabilistic Validation of Complex Engineering Simulations With Sparse Data

The challenges of validating expensive simulations with very sparse experimental data are addressed in this article. The effects of uncertainties in simulations and test data and their impact on validation are highlighted using several examples. Bayesian methods for calibration and tool validation are presented as the primary techniques for performing probabilistic validation. The applicability of the methods to complex engineering problems is discussed. The effect of prior assumptions on calibration and validation are explained through simple illustrative examples. Guidelines for planning simulations and experiments for validation are also provided.Copyright

A Comparative Study on Accuracy and Efficiency of Metamodels for Large Industrial Datasets

This paper provides a comparative study on accuracy and efficiency of metamodels constructed from large datasets. Two examples inspired by large industrial applications are used to identify the best metamodeling technique. Artificial Neural Networks, Radial Basis Functions, Gaussian Process and Nonlinear regression are used to build metamodels. The examples used showcase a broad range of industrial applications in aircraft engines and gas turbines. Although Radial Basis Functions and Gaussian Process models are robust for small data sets, their high computational cost for large datasets reduces their practical application. ANN models are found to perform optimally when large number of training points are readily available and the accuracy requirements are high.Copyright

Reduced order modeling for clearance control in turbomachinery

Finite element models (FEMs) are extensively used in the design optimization of utility scale steam turbines. As an example, by simulating multiple startup scenarios of steam power plants, engineers can obtain turbine designs that minimize material utilization and at the same time avoid the damaging effects of large thermal stresses or rubs between rotating and stationary parts. Unfortunately, FEMs are computationally expensive and only a limited amount of simulations can be afforded to get the final design. For this reason, numerous model reduction techniques have been developed to reduce the size of the original model without a significant loss of accuracy. When the models are nonlinear, as is the case for steam turbine FEMs, model reduction techniques are relatively scarce and their effectiveness becomes application dependent. Although there is an abundant literature on model reduction for nonlinear systems, many of these techniques become impractical when applied to a realistic industrial problem. This paper focuses in a class of nonlinear FEM characteristic of thermo-elastic problems with large temperature excursions. A brief overview of popular model reduction techniques is presented along with a detailed description of the computational challenges faced when applying them to a realistic problem. The main contribution of this work is a set of modifications to existing methods to increase their computational efficiency. The methodology is demonstrated on a steam turbine model, achieving a model size reduction by four orders of magnitude with only 5% loss of accuracy with respect to the full order FEMs. These practical implementations enable the calculation of multiple additional design scenarios.

Variance Based Global Sensitivity Analysis for Uncorrelated and Correlated Inputs With Gaussian Processes

Methods for efficient variance based global sensitivity analysis of complex high-dimensional problems are presented and compared. Variance decomposition methods rank inputs according to Sobol indices which can be computationally expensive to evaluate. Main and interaction effect Sobol indices can be computed efficiently in the Kennedy & O’Hagan framework with Gaussian Processes (GPs). These methods use the High Dimensional Model Representation (HDMR) concept for variance decomposition which presents a unique model representation when inputs are uncorrelated. However, when the inputs are correlated, multiple model representations may be possible leading to ambiguous sensitivity ranking with Sobol indices. In this work we present the effect of input correlation on sensitivity analysis and discuss the methods presented by Li & Rabitz in the context of Kennedy & O’ Hagan framework with GPs. Results are demonstrated on simulated and real problems for correlated and uncorrelated inputs and demonstrate the utility of variance decomposition methods for sensitivity analysis.Copyright

Probabilistic Optimization of Two-Phase Flow Using Bayesian Models

Gas-liquid two-phase flows are encountered in a variety of applications such as turbo-machinery flows, gas-turbines, ram-jet and scram-jets, automotive engines and aircraft engines. Designing systems to control such flows is enormously challenging owing to the addition of new non-dimensional groups that characterize the two-phase flow system compared to a single-phase flow. Additionally, two-phase flows can exhibit non-linear hydrodynamic instabilities that determine the overall behavior of the system.In this study, we choose a generic two-phase flow configuration that exhibits known complexities in realistic two-phase flow systems. The goal of the study is to optimize the geometry of the two-phase flow configuration with minimal computational cost. We propose a probabilistic approach to model the stochastic system and optimize the two-phase flow system under uncertain inputs. The potential benefits of the approach are highlighted along with future directions for using probabilistic design techniques to optimize two-phase flow systems.Copyright