Extreme Quantile Estimation and Uncertainty Quantification with Stochastic Simulation Models
Pan, Qiyun
2019
Abstract
With the fast development of computing power over the last few decades, simulation models become increasingly popular in many applications when running actual experiments are expensive or even impossible. In particular, this dissertation considers stochastic simulation models that generate random outputs with multiple simulation runs at the same input. In order to fully reflect high level uncertainties in reality, modern simulation models tend to embed a large number of random variables for generating stochastic outputs. Thus, stochastic simulation models have been employed in many applications including wind energy. One important use of the simulation models is to analyze extreme events for complex systems. However, heavy computational requirement for running stochastic simulation models brings great challenges in the system reliability analysis. A system failure is often defined as an event where the system response exceeds a certain threshold level. Mathematically the threshold level, when it is associated with a small failure probability, refers to the extreme quantile of the random response. This dissertation aims to provide computationally efficient methods to estimate the extreme quantile for random responses and quantify the estimation uncertainty via stochastic simulation. This dissertation consists of three main chapters, including (a) a variance reduction method for extreme quantile estimation using stochastic simulation models, (b) uncertainty quantification for the extreme quantile estimation with the variance reduction method, (c) an adaptive variance reduction method for the extreme quantile estimation. First, we propose using importance sampling combined with order statistics to estimate extreme quantiles via stochastic simulation models. Importance sampling has been known as one of the most powerful variance reduction techniques. The proposed method reduces the computational burden significantly while achieving much better estimation accuracy, compared with existing methods. We present our method with a wind turbine case study for estimating extreme load responses. Second, to quantify the uncertainty of the extreme quantile estimation with stochastic simulation models, we build confidence intervals for the extreme quantile. We consider multiple approaches, including theoretical approach, batching-based approaches, bootstrapping and Jackknife. We validate asymptotic properties for extreme quantile estimator and show that the quantile estimator is asymptotically normal following the central limit theorem. The immediate result is a theoretically valid confidence interval in an explicit form. Building on the theoretical validity of the quantile estimator, confidence intervals using three batching-based approaches, namely, batching, sectioning and sectioning-batching, are presented. We present numerical results to compare the confidence interval estimation performance of all studied methods. Lastly, we develop a new adaptive importance sampling method for estimating extreme quantiles using stochastic simulation models in a more computationally efficient way. In our first study, we employ importance sampling to estimate extreme quantile with stochastic simulation model and show its computational advantage over alternative methods. However, a good choice of the importance sampling density relies on information about the unknown extreme quantile. Faced with this challenge, we develop an adaptive method that refines the importance sampling density parameter toward the unknown target quantile along the iterations. The proposed adaptive scheme allows us to use the simulation outcomes obtained in previous iterations for steering the simulation process to focus on important input areas. We prove consistency properties of the proposed method and show that our approach can achieve variance reduction over crude Monte Carlo sampling. We demonstrate its estimation efficiency through both numerical examples and wind turbine case study.Subjects
extreme quantile estimation, importance sampling, uncertainty quantification, adaptive algorithm
Types
Thesis
Metadata
Show full item recordCollections
Remediation of Harmful Language
The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.
Accessibility
If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.