Modeling Uncertainty In Metric Space
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Modeling Uncertainty in Metric Space
Modeling uncertainty for future prediction requires drawing multiple posterior models. Such drawing within a Bayesian framework is dependent on the likelihood (data-model relationship) as well as prior distribution of the model variables, For the uncertainty assessment in the Earth models, we propose the framework of Modeling Uncertainty in Metric Space (MUMS) to achieve this in a general way. MUMS constructs a metric space where the models are represented exclusively by a distance correlated with or equal to the difference in their responses (application-tailored distance). In the framework of MUMS, various operations are available: projection of metric space by multi-dimensional scaling, model expansion by kernel Karhunen-Loeve expansion, generation of additional prior model by solving the pre-image problem, and generation of multiple posterior models by solving the post-image problem. We propose a robust solution for the pre-image problem: geologically constrained optimization, which utilizes the probability perturbation method from the solution of the fixed-point iteration algorithm. Additionally, we introduce a so-called post-image problem for obtaining the feature expansion of the ''true Earth'' by defining a distance as the difference in their responses. The combination of geologically constrained optimization and the post-image problem efficiently generates multiple posterior Earth models constrained to prior geologic information, hard data, and nonlinear time-dependent data. The proposed method provides a realistic uncertainty model for future prediction, compared with the result of the rejection sampler. We also propose a metric ensemble Kalman filter (Metric EnKF), which applies the ensemble Kalman filter (EnKF) to the parameterizations by the kernel KL expansion in metric space. Metric EnKF overcomes some critical limitations of EnKF: it preserves prior geologic information; it creates a stable and consistent filtering. However, the results of Metric EnKF applied to various cases including the Brugge field-scale synthetic reservoir show the same problem as with the EnKF in general, that is, it does not provide a realistic uncertainty model.
Modeling Uncertainty in Metric Space
Modeling uncertainty for future prediction requires drawing multiple posterior models. Such drawing within a Bayesian framework is dependent on the likelihood (data-model relationship) as well as prior distribution of the model variables, For the uncertainty assessment in the Earth models, we propose the framework of Modeling Uncertainty in Metric Space (MUMS) to achieve this in a general way. MUMS constructs a metric space where the models are represented exclusively by a distance correlated with or equal to the difference in their responses (application-tailored distance). In the framework of MUMS, various operations are available: projection of metric space by multi-dimensional scaling, model expansion by kernel Karhunen-Loeve expansion, generation of additional prior model by solving the pre-image problem, and generation of multiple posterior models by solving the post-image problem. We propose a robust solution for the pre-image problem: geologically constrained optimization, which utilizes the probability perturbation method from the solution of the fixed-point iteration algorithm. Additionally, we introduce a so-called post-image problem for obtaining the feature expansion of the ''true Earth'' by defining a distance as the difference in their responses. The combination of geologically constrained optimization and the post-image problem efficiently generates multiple posterior Earth models constrained to prior geologic information, hard data, and nonlinear time-dependent data. The proposed method provides a realistic uncertainty model for future prediction, compared with the result of the rejection sampler. We also propose a metric ensemble Kalman filter (Metric EnKF), which applies the ensemble Kalman filter (EnKF) to the parameterizations by the kernel KL expansion in metric space. Metric EnKF overcomes some critical limitations of EnKF: it preserves prior geologic information; it creates a stable and consistent filtering. However, the results of Metric EnKF applied to various cases including the Brugge field-scale synthetic reservoir show the same problem as with the EnKF in general, that is, it does not provide a realistic uncertainty model.
Advances in Soft Computing, Intelligent Robotics and Control
Author: János Fodor
language: en
Publisher: Springer Science & Business Media
Release Date: 2014-03-20
Soft computing, intelligent robotics and control are in the core interest of contemporary engineering. Essential characteristics of soft computing methods are the ability to handle vague information, to apply human-like reasoning, their learning capability and ease of application. Soft computing techniques are widely applied in the control of dynamic systems, including mobile robots. The present volume is a collection of 20 chapters written by respectable experts of the fields, addressing various theoretical and practical aspects in soft computing, intelligent robotics and control. The first part of the book concerns with issues of intelligent robotics, including robust xed point transformation design, experimental verification of the input-output feedback linearization of differentially driven mobile robot and applying kinematic synthesis to micro electro-mechanical systems design. The second part of the book is devoted to fundamental aspects of soft computing. This includes practical aspects of fuzzy rule interpolation, subjective weights based meta learning in multi criteria decision making, swarm-based heuristics for an area exploration and knowledge driven adaptive product representations. The last part addresses different problems, issues and methods of applied mathematics. This includes perturbation estimates for invariant subspaces of Hessenberg matrices, uncertainty and nonlinearity modelling by probabilistic metric spaces and comparison and visualization of the DNA of six primates.