Browsing by Author "Hu, Zhangli"

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    Photoelectron Sheath near the Lunar Surface: Fully Kinetic Modeling and Uncertainty Quantification Analysis
    (American Institute of Aeronautics and Astronautics, 2020-01-05) Zhao, Jianxun; Wei, Xinpeng; Hu, Zhangli; He, Xiaoming; Han, Daoru; Hu, Zhen; Du, Xiaoping; Mechanical and Energy Engineering, School of Engineering and Technology
    This paper considers plasma charging on the lunar surface with a focus on photoelectron sheath. The plasma species includes ambient solar wind (protons and electrons) and photoelectrons emitted from the illuminated lunar surface. This work is motivated by the high computational cost associated with uncertainty quantification (UQ) analysis of plasma simulations using high-fidelity fully kinetic models. In this paper, we study the photoelectron sheath near the lunar surface with a focus on effects of variables of uncertainty (such as the ambient electron density or photoelectron temperature) on the plasma environment. A fully kinetic 3-D finite-difference (FD) particle-in-cell (PIC) code is utilized to simulate the plasma interaction near the lunar surface and the resulting photoelectron sheath. For the uncertainty quantification analysis, this PIC code is treated as a black box providing high-fidelity quantities of interest, which are also used to construct efficient reduced-order models to perform UQ analysis. A 1-D configuration is first studied to demonstrate the procedure and capability of the UQ analysis. The rest of the paper is organized as follows. Section III presents the analytic and numerical solutions of the 1-D photoelectron sheath. Verification and validation of the FD-PIC code for photoelectron sheath solution is shown. Section IV describes the Kriging model and the uncertainty quantification approach. Section V discusses the UQ analysis of the 1-D photoelectron sheath. The conclusion is given in Section VI.
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    Second Order Reliability Method for Time-Dependent Reliability Analysis Using Sequential Efficient Global Optimization
    (ASME, 2019-11) Hu, Zhangli; Du, Xiaoping; Mechanical and Energy Engineering, School of Engineering and Technology
    Reliability depends on time if the associated limit-state function includes time. A time-dependent reliability problem can be converted into a time-independent reliability problem by using the extreme value of the limit-state function. Then the first order reliability method can be used but it may produce a large error since the extreme limit-state function is usually highly nonlinear. This study proposes a new reliability method so that the second order reliability method can be applied to time-dependent reliability analysis for higher accuracy while maintaining high efficiency. The method employs sequential efficient global optimization to transform the time-dependent reliability analysis into the time-independent problem. The Hessian approximation and envelope theorem are used to obtain the second order information of the extreme limit-state function. Then the second order saddlepoint approximation is use to evaluate the reliability. The accuracy and efficiency of the proposed method are verified through numerical examples.
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    Second-order reliability methods: a review and comparative study
    (Springer Nature, 2021) Hu, Zhangli; Mansour, Rami; Olsson, Mårten; Du, Xiaoping; Mechanical and Energy Engineering, Purdue School of Engineering and Technology
    Second-order reliability methods are commonly used for the computation of reliability, defined as the probability of satisfying an intended function in the presence of uncertainties. These methods can achieve highly accurate reliability predictions owing to a second-order approximation of the limit-state function around the Most Probable Point of failure. Although numerous formulations have been developed, the lack of full-scale comparative studies has led to a dubiety regarding the selection of a suitable method for a specific reliability analysis problem. In this study, the performance of commonly used second-order reliability methods is assessed based on the problem scale, curvatures at the Most Probable Point of failure, first-order reliability index, and limit-state contour. The assessment is based on three performance metrics: capability, accuracy, and robustness. The capability is a measure of the ability of a method to compute feasible probabilities, i.e., probabilities between 0 and 1. The accuracy and robustness are quantified based on the mean and standard deviation of relative errors with respect to exact reliabilities, respectively. This study not only provides a review of classical and novel second-order reliability methods, but also gives an insight on the selection of an appropriate reliability method for a given engineering application.
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    Time-Dependent System Reliability Analysis With Second-Order Reliability Method
    (American Society of Mechanical Engineers, 2020) Wu, Hao; Hu, Zhangli; Du, Xiaoping; Mechanical and Energy Engineering, School of Engineering and Technology
    System reliability is quantified by the probability that a system performs its intended function in a period of time without failures. System reliability can be predicted if all the limit-state functions of the components of the system are available, and such a prediction is usually time consuming. This work develops a time-dependent system reliability method that is extended from the component time-dependent reliability method using the envelope method and second-order reliability method. The proposed method is efficient and is intended for series systems with limit-state functions whose input variables include random variables and time. The component reliability is estimated by the second-order component reliability method with an improve envelope approach, which produces a component reliability index. The covariance between component responses is estimated with the first-order approximations, which are available from the second-order approximations of the component reliability analysis. Then, the joint distribution of all the component responses is approximated by a multivariate normal distribution with its mean vector being component reliability indexes and covariance being those between component responses. The proposed method is demonstrated and evaluated by three examples.