Begell House Inc.
International Journal for Uncertainty Quantification
IJUQ
2152-5080
6
2
2016
PREFACE: FIRST QUEST CONFERENCE
vi-vii
Peng
Wang
School of Mathematics and Systems Science & International Research Institute for Multidisciplinary Science, Beihang University, Beijing 100191, China
Dongbin
Xiu
Ohio State University
Daniel M.
Tartakovsky
Department of Energy Resources Engineering, Stanford University, USA
EXPLOSIVE SYNCHRONIZATION OF COMBINATIONAL PHASES ON RANDOM MULTIPLEX NETWORKS
99-108
Guanying
Huo
LMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
Xin
Jiang
LMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
Lili
Ma
School of Statistics, Capital University of Economics and Business, Beijing 100070, China
Quantong
Guo
LMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
Yifang
Ma
School of Mathematical Science, Peking University, Beijing 100871, China
Meng
Li
LMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
Zhiming
Zheng
LMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
The coherent dynamics of a large ensemble of interconnected dynamical units can be characterized by the synchronization process of coupled oscillators. In many real situations, each unit, in the meantime, may exist in multilayer networks, where the composite state of the unit can be determined by the corresponding states on each layer. In this paper, a combinational phase is introduced to describe the joint action of several phases. The combinational phase is a linear superposition of the phase in each layer with a coupling parameter, in the same manner as the generation of voltage from electricity and resistance when applying the phaser method. We study the dynamics of combinational phases by applying the Kuramoto model on multiplex networks, in which the weight of each layer affecting the combinational phase is controlled by a coupling parameter. An abrupt transition is found to emerge in the synchronization of combinational phases by adjusting the coupling parameter. We also show that phases of oscillators in each single layer remain incoherent while the combinational ones are fully synchronized. Theoretical analysis of this explosive transition is studied on a multiplex network, of which one layer is a star network, and the other is a fully connected one. Our findings provide a first understanding of the explosive critical phenomena of combinational phases on multiplex networks.
INCORPORATING PRIOR KNOWLEDGE FOR QUANTIFYING AND REDUCING MODEL-FORM UNCERTAINTY IN RANS SIMULATIONS
109-126
Jianxun
Wang
Department of Aerospace and Ocean Engineering, Virginia Tech, Blacksburg, Virginia 24060, USA
Jin-Long
Wu
Department of Aerospace and Ocean Engineering, Virginia Tech, Blacksburg, Virginia 24060, USA
Heng
Xiao
Department of Aerospace and Ocean Engineering, Virginia Tech, Blacksburg, Virginia 24060, USA
Simulations based on Reynolds-averaged Navier-Stokes (RANS) models have been used to support high-consequence decisions related to turbulent flows. Apart from the deterministic model predictions, the decision makers are often equally concerned about the prediction confidence. Among the uncertainties in RANS simulations, the model-form uncertainty is an important or even a dominant source. Therefore, quantifying and reducing the model-form uncertainties in RANS simulations are of critical importance to make risk-informed decisions. Researchers in statistics communities have made efforts on this issue by considering numerical models as black boxes. However, this physics-neutral approach is not a most efficient use of data, and is not practical for most engineering problems. Recently, we proposed an open-box, Bayesian framework for quantifying and reducing model-form uncertainties in RANS simulations based on observation data and physics-prior knowledge. It can incorporate the information from the vast body of existing empirical knowledge with mathematical rigor, which enables a more efficient usage of data. In this work, we examine the merits of incorporating various types of prior knowledge in the uncertainties quantification and reduction in RANS simulations. The result demonstrates that informative physics-based prior knowledge plays an important role in improving the performance of model-form uncertainty reduction, particularly when the observation data are limited. Moreover, it suggests that the proposed Bayesian framework is an effective way to incorporate empirical knowledge from various sources of turbulence modeling.
UNCERTAINTY QUANTIFICATION TOWARDS FILTERING OPTIMIZATION IN SCENE MATCHING AIDED NAVIGATION SYSTEMS
127-140
Shengdi
Zhang
Department of Mathematics and Systems Science, College of Science, National University of Defense Technology, Changsha, Hunan, HN 731, People's Republic of China
Xiaojun
Duan
Department of Mathematics and Systems Science, College of Science, National University of Defense Technology, Changsha, Hunan, HN 731, People's Republic of China
Lijun
Peng
Department of Mathematics and Systems Science, College of Science, National University of Defense Technology, Changsha, Hunan, HN 731, People's Republic of China
There exist many uncertain sources for positioning process of scene matching aided navigation systems, and filter architecture and random parameters are considered mainly in this paper for the goal of trajectory optimization. In order to reduce the uncertainty of filter architecture, a practical scene matching optimization scheme is proposed, where fusion architecture and filtering parameters are both considered, in the circumstance of different sampling rates without transmission delay. The matching interval is determined by adjustment time of matching, matching points are settled from back to front, a cost function for the matching number is designed according to optimization criteria, and finally an appropriate matching number is determined by required mapping accuracy. The optimization scheme is validated by the simulation. On the other hand the filtering parameters are identified and validated by reducing parameter space in advance and local sensitivity analysis method. Simulation results illustrate that the systems are more sensitive for the measurement noise, which provides a theoretical basis for engineering applications.
SOFTWARE RELIABILITY GROWTH MODEL WITH TEMPORAL CORRELATION IN A NETWORK ENVIRONMENT
141-156
Jiajun
Xu
School of Computer Science and Engineering, Beihang University, Beijing 100191, China
Shuzhen
Yao
School of Computer Science and Engineering, Beihang University, Beijing 100191, China
Shunkun
Yang
School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
Peng
Wang
School of Mathematics and Systems Science & International Research Institute for Multidisciplinary Science, Beihang University, Beijing 100191, China
Increasingly software systems are developed to provide great flexibility to customers but also introduce great uncertainty for system development. The uncertain behavior of fault-detection rate has irregular fluctuation and is described as a Markovian stochastic processes (white noise). However, in many cases the white noise idealization is insufficient, and real fluctuations are always correlated and correlated fluctuations (or colored noise) are non-Markovian stochastic processes. We develop a new model to quantify the uncertainties within non-homogeneous Poisson process (NHPP) in the noisy environment. Based on a stochastic model of the software fault detection process, the environmental uncertainties collectively are treated as a noise of arbitrary distribution and correlation structure. Based on the stochastic model, the analytical solution can be derived. To validate our model, we consider five particular scenarios with distinct environmental uncertainty. Experimental comparisons with existing methods demonstrate that the new framework shows a closer fitting to actual data and exhibits a more accurately predictive power.
CONSTRUCTION OF EVIDENCE BODIES FROM UNCERTAIN OBSERVATIONS
157-165
Liang
Zhao
School of Information Engineering, Southwest University of Science and Technology,
MianYang, 621010, China
Zhanping
Yang
Institute of Electronic Engineering, China Academy of Engineering Physics, MianYang,
621900, China
Longyuan
Xiao
Institute of Electronic Engineering, China Academy of Engineering Physics, MianYang,
621900, China
The construction of evidence bodies is a key issue when the evidence theory is applied in uncertainty quantification. The existing approaches proposed for this topic are usually too subjective to obtain rational evidence bodies in the situation of uncertain observations. This paper introduces a repeated kernel-density-estimation based approach for constructing evidence bodies from uncertain observations. The typical uncertain observations-limited point measurements together with interval measurements are considered in this paper. Using kernel density estimation with a loop, a family of probability distribution about the given observations is obtained, the probability box characterized by the bounds of the probability distribution family is discretized to evidence bodies by an outer discretization method. The approach also considers the uncertainty in the distribution assumption during the kernel density estimation. A numerical example is used to demonstrate the proposed approach.
UNCERTAINTY QUANTIFICATION OF SCIENTIFIC PROPOSAL EVALUATIONS
167-173
Xiaofeng
Shi
School of Mathematics and System Science, Beihang University, Beijing, China
Peng
Wang
School of Mathematics and Systems Science & International Research Institute for Multidisciplinary Science, Beihang University, Beijing 100191, China
Dongbin
Xiu
Mathematics and Scientific Computing and Imaging (SCI) Institute, The University of Utah, Utah, USA
Peer review is an integral part of safeguarding the fairness of scientific proposal evaluations, but it is also subject to uncertainty, such as reviewer's bias and potential discussion under the table, termed "DaZhaoHu" in Chinese. In this paper, we present a mathematical framework to model the peer review process. Through sensitivity analysis, we numerically demonstrate that the number of proposals has greater impact on overall fairness.
SEQUENTIAL SPARSITY ITERATIVE OPTIMAL DESIGN MODEL FOR CALIBRATION OF COMPLEX SYSTEMS WITH EPISTEMIC UNCERTAINTY
175-193
Weifeng
Li
Institution of Systems Science and Mathematics, Naval Aeronautical and Astronautical University, Yantai, Shandong, 264001, People's Republic of China
Xiaojun
Duan
Department of Mathematics and Systems Science, College of Science, National University of Defense Technology, Changsha, Hunan, HN 731, People's Republic of China
Chang
Li
College of Science, National University of Defense Technology, Changsha, Hunan, 410073, People's Republic of China
As for the experimental optimal design of some complex systems, it is difficult to obtain the accurate response model between the performance index and influence factors. But in some cases the prior information could provide a clue to construct the possible response model. An effective model calibration method is presented here based on the typical uncertainty quantification framework. In order to solve this epistemic uncertainty, some kinds of prior information about the system are utilized to obtain model-oriented basis functions, then a corresponding redundant regression model is designed to describe the internal response relationship. Through analyzing the influences of experimental costs, sampling sequences, and spatial positions of different experiment points, we define a sequential sparsity iterative optimal design model integrated with costs and spatio-temporal weights for experimental design. Based on sparse component analysis theory, calibration of a regression model with different stages is transformed into a sparse reconstruction problem. The conclusions from theoretical inferences as well as simulation results of the combined trigonometric polynomial function model and radar measurement model show that the parameter estimation error of the regression model is smaller, which demonstrates that the above-mentioned model is more efficient and comprehensive for its consideration of the weights for different influence factors and its consistence with practical experimental regulations.