Random field modeling with insufficient data sets for probability analysis

2012 ◽  
Author(s):  
Zhimin Xi ◽  
Byung C. Jung ◽  
Byeng D. Youn
Keyword(s):  
Random Field ◽  
Probability Analysis ◽  
Data Sets ◽  
Insufficient Data ◽  
Field Modeling

Random Field Characterization With Insufficient Data Sets for Probability Analysis and Design

2011 ◽  
Author(s):  
Zhimin Xi ◽  
Byung C. Jung ◽  
Byeng D. Youn
Keyword(s):  
Random Field ◽  
Field Data ◽  
Lithium Ion ◽  
Probability Analysis ◽  
Statistical Dependence ◽  
Data Sets ◽  
Insufficient Data ◽  
Analysis And Design ◽  
Field Modeling ◽  
Engineering Problems

Random field is a generalization of a stochastic field, of which randomness can be characterized as a function of spatial variables. Examples of the random field can often be found as a geometry, material, and process variation in engineering products and processes. It has been widely acknowledged that consideration of the random field is quite significant to accurately predict variability in system performances. However, current approaches for characterizing the random field can only be applied to the situation with sufficient random field data sets and are not suitable to most engineering problems where the data sets are insufficient. The contribution of this paper is to model the random field based on the insufficient data sets such that sufficient data sets can be simulated or generated according to the random field modeling. Therefore, available random field characterization approaches and probability analysis methods can be used for probability analysis and design of many engineering problems with the lack of random field data sets. The proposed random field modeling is composed of two technical components including: 1) a Bayesian updating approach using the Markov Chain Monte Carlo (MCMC) method for modeling the random field based on available random field data sets; and 2) a Bayesian Copula dependence modeling approach for modeling statistical dependence of random field realizations at different measurement locations. Three examples including a mathematical problem, a heat generation problem of the Lithium-ion battery, and a refrigerator assembly problem are used to demonstrate the effectiveness of the proposed approach.

Random field modeling with insufficient field data for probability analysis and design

2014 ◽  
Vol 51 (3) ◽  
pp. 599-611 ◽  
Author(s):  
Zhimin Xi ◽  
Byeng D. Youn ◽  
Byung C. Jung ◽  
Joung Taek Yoon
Keyword(s):  
Random Field ◽  
Field Data ◽  
Probability Analysis ◽  
Analysis And Design ◽  
Field Modeling

scholarly journals Mobile Robotic Sensors for Environmental Monitoring using Gaussian Markov Random Field

Robotica ◽  
2020 ◽  
pp. 1-23
Author(s):  
Linh Nguyen ◽  
Sarath Kodagoda ◽  
Ravindra Ranasinghe ◽  
Gamini Dissanayake
Keyword(s):  
Random Field ◽  
Markov Random Field ◽  
Adaptive Sampling ◽  
Published Data ◽  
Data Sets ◽  
Independence Property ◽  
Gaussian Markov Random Field ◽  
Markov Random ◽  
Sampling Optimization ◽  
Robotic Sensors

SUMMARY This paper addresses the issue of monitoring spatial environmental phenomena of interest utilizing information collected by a network of mobile, wireless, and noisy sensors that can take discrete measurements as they navigate through the environment. It is proposed to employ Gaussian Markov random field (GMRF) represented on an irregular discrete lattice by using the stochastic partial differential equations method to model the physical spatial field. It then derives a GMRF-based approach to effectively predict the field at unmeasured locations, given available observations, in both centralized and distributed manners. Furthermore, a novel but efficient optimality criterion is then proposed to design centralized and distributed adaptive sampling strategies for the mobile robotic sensors to find the most informative sampling paths in taking future measurements. By taking advantage of conditional independence property in the GMRF, the adaptive sampling optimization problem is proven to be resolved in a deterministic time. The effectiveness of the proposed approach is compared and demonstrated using pre-published data sets with appealing results.

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