Chanyoung Park

Reliability-Based Structural Design of Aircraft Together with Future Tests

Traditional optimization changes variables that are available in the design stage to optimize objectives, such as aircraft structural reliability. However, there are many post-design measures, such as tests and structural health monitoring that reduce uncertainty and further improve the reliability. In this paper, a new reliability-based design framework that can include post-design uncertainty reduction variables is proposed. Among many post-design variables, this paper focuses on the number of coupon tests and the number of structural element tests. Uncertainty in the failure stress prediction, variability due to the finite number of coupon tests, and uncertainties in geometry and service conditions are studied in detail. The Bayesian technique is used to update the failure stress distribution based on results of the element tests. Tradeoff plots of the number of tests, weight and probability of failure in certification and in service are generated, and finally reliability-based design of future tests together with aircraft structure is performed for minimum lifecycle cost.

Modeling the Effect of Structural Tests on Uncertainty in Estimated Failure Stress

This paper investigates the effects of the number of coupon and element tests on uncertainty in element failure stress. In aircraft structural design, failure stress is first obtained from coupon tests, which is then used in predicting failure stress of structural element under combined loads. The mean and standard deviation of failure stress are expressed as a distribution due to errors in failure theory and variability due to finite number of coupon tests. This paper focuses on identifying the effect of the number of coupon and element tests on the distribution of failure stress of structural element. This paper assumes isotropic properties and the failure stress of structural element is assumed to be predicted by a failure theory (e.g. Von Mises), and initial distribution of this failure stress reflects uncertainties. Bayesian updating is used to reduce the uncertainties in the initial failure stress distribution by using element tests. The relation between the number of tests and the level of uncertainties is presented for a simple test case.

Function Prediction at One Inaccessible Point using Converging Lines

The focus of this paper is a strategy for making a prediction at a point where a function cannot be evaluated. The key idea is to take advantage of the fact that prediction is needed at one point and not in the entire domain. This paper explores the possibility of predicting a multidimensional function using multiple one-dimensional lines converging on the inaccessible point. The multidimensional approximation is thus transformed into several one-dimensional approximations, which provide multiple estimates at the inaccessible point. The Kriging model is adopted in this paper for the one-dimensional approximation, estimating not only the function value but also the uncertainty of the estimate at the inaccessible point. Bayesian inference is then used to combine multiple predictions along lines. We evaluated the numerical performance of the proposed approach using eight-dimensional and 100-dimensional functions in order to illustrate the usefulness of the method for mitigating the curse of dimensionality in surrogate-based predictions. Finally, we applied the method of converging lines to approximate a twodimensional drag coefficient function. The method of converging lines proved to be more accurate, robust, and reliable than a multidimensional Kriging surrogate for single-point prediction. [DOI: 10.1115/1.4036130]

Function Extrapolation of Noisy Data using Converging Lines

This paper is focused on extrapolating noisy data to a single inaccessible point using the method of converging lines. Matrix multiplication computation time, which is a twodimensional unimodal and monotonic function of matrix dimensions, was adopted as a test problem. Using the method of converging lines, multi-dimensional extrapolation was first transformed into series of one-dimensional extrapolation towards one point. Onedimensional extrapolation results at the extrapolation point were combined using Bayes method. One-dimensional long-range extrapolation was then performed differently depending on the noise level of the data. For low noise levels, the data pattern was clear using logarithmic transformation and standard polynomial regression was used for fitting it. For significant noise levels, ridge regression was used to reduce overfitting. This paper proposes a new scheme to determine the ridge parameter by minimizing prediction error at training samples. This scheme was evaluated based on manufactured data.

Validation, Uncertainty Quantification and Uncertainty Reduction for a Shock Tube Simulation

While we rely on simulations to predict the response of complex systems, we recognize that the models that underlie these simulations are never perfect. Comparison of simulations with experiments is an important tool for exposing limitations of models, and providing insights into which models need improvement. However, errors in numerical model and uncertainties in experiments can obscure the true discrepancies between predictions and physical reality, and therefore need to be reduced. In order to expose model deficiencies it is important to assess the magnitude of these uncertainties and reduce them until modeling errors become apparent. In this paper we describe an effort to reduce numerical model errors and expose physics model errors for shock tube simulations of a shock wave hitting a curtain of particles. The experiment was designed to explore models of particle interactions with the flow, and was performed initially with a flux calculation model known as AUSM+. Uncertainties in experimental conditions were propagated into simulations output with the aid of the method of converging lines, which generates simulations along multiple lines converging to a single point in input space. This approach exposed noisy behavior of the simulations that appeared to be numerical in nature. However, discrepancies between lines and negative pressures and temperatures at some points indicated modeling deficiencies. When the flux calculation model was corrected to a better numerical model known as AUSM+up, the numerical noise was greatly reduced and the discrepancy between lines eliminated, thus showing that modeling errors can produce noise that wrongly appears as numerical in nature. Another curiosity of the present study was that when the numerical model was improved, the discrepancy between simulations and experiments increased, pointing to cancelling modeling errors in the original simulations.

Function Extrapolation at One Inaccessible Point Using Converging Lines

Focus of this paper is on the prediction accuracy of multidimensional functions at an inaccessible point. The paper explores the possibility of extrapolating a high-dimensional function using multiple one-dimensional converging lines. The main idea is to select samples along lines towards the inaccessible point. Multi-dimensional extrapolation is thus transformed into a series of one-dimensional extrapolations that provide multiple estimates at the inaccessible point. We demonstrate the performance of converging lines using Kriging to extrapolate a two-dimensional drag coefficient function. Post-processing of extrapolation results from different lines based on Bayesian theory is proposed to combine the multiple predictions. Selection of lines is also discussed. The method of converging lines proves to be more robust and reliable than two-dimensional Kriging surrogate for the example.Copyright

Multi-fidelity Surrogate Modeling for Application/Architecture Co-design

The HPC community has been using abstract, representative applications and architecture models to enable faster co-design cycles. While developers often qualitatively verify the correlation of the application abstractions to the parent application, it is equally important to quantify this correlation to understand how the co-design results translate to the parent application. In this paper, we propose a multi-fidelity surrogate (MFS) approach which combines data samples of low-fidelity (LF) models (representative apps and architecture simulation) with a few samples of a high-fidelity (HF) model (parent app). The application of MFS is demonstrated using a multi-physics simulation application and its proxy-app, skeleton-app, and simulation models. Our results show that RMSE between predictions of MFS and the baseline HF models was 4%, which is significantly better than using either LF or HF data alone, demonstrating that MFS is a promising approach for predicting the parent application performance while staying within a computational budget.

Confidence Interval of Bayesian Network and Global Sensitivity Analysis

A Bayesian network represents a causal relationship among random variables using conditional probabilities. Because of limited resources and sampling uncertainty, the estimated probabilities have both aleatory randomness and epistemic uncertainty. In this paper, two approaches are used to estimate the confidence intervals of component- and system-level probabilities. The first approach uses an analytical method, where a normal distribution is assumed for the component- and system-level probabilities. Another approach is the bootstrap method, which uses resampling to build a distribution of the probabilities. Global sensitivity is analyzed as well to identify the component-level probability that most significantly affects the uncertainty in the system level. It is shown that the confidence intervals of system probability can be effectively narrowed by reducing sampling uncertainty in the most significant component.

Anomaly Detection Using Groups of Simulations

Simulations can produce results that violate our understandings of the physical governing equations or that do not agree with common sense; these results are usually termed outliers or anomalies. This paper presents a sampling-based approach to identify these anomaly conditions and detect outliers based on comparison to multiple simulation results. The proposed sampling approach has two sampling steps, sampling of results in the input domain and sampling along lines in an input subdomain of interest. Anomalies are identified through iteratively reweighted least squares (IRLS) and cross validation (CV) using data from the samplings. This approach allows anomalies to be observed that may not be found by comparing individual simulations. The proposed approach is used to detect anomalies in predictions of the interaction of a planar shock wave with a dense particle curtain and the outliers were used to identify weaknesses in the simulation code. New simulation results indicate that the anomalies were removed.

Modeling the Contribution of Accident Investigation to Aircraft Safety

Although accident investigation has significantly contributed to safety and reliability improvement of airplanes over decades, its contribution has not been quantified and compared to that of other safety measures. In this paper, a cost effectiveness measure is proposed in terms of the cost and the number of likely future accidents in similar aircraft which could potentially be prevented by the investigation. We concluded that a crucial role of an investigation is to distinguish accidents caused by errors (such as failure to consider a failure mode) a rare combination of circumstances, such as an extremely strong gust hitting a damaged plane on its way to the repair depot. Errors are common to a large number of airplanes and the same accident is likely to happen to other airplanes, while a rare event is unlikely to happen again. We first analyzed past accidents in order to shed light on a key factor—the probability of reoccurrence of an accident. Then, we introduced a concept of cost effectiveness measurement, cost per life saved, and threshold of cost effectiveness. Past accidents with different types of cause were selected as examples, and we examined how the probability of reoccurrence affects cost effectiveness. Finally, we performed a comparison in cost effectiveness between accident investigation and structural design change intended to reduce the probability of failure due to fatigue of a fuselage panel. We found that for the example the safety improvement implemented by the accident investigation was clearly more cost effective.