Searcharxiv⌕ Search

arXiv subjects

Xiaodong Luo

Publications and source records attributed to Xiaodong Luo.

At least 55 records · Page 3Linked to original sources
arXiv2016

Efficient big data assimilation through sparse representation: A 3D benchmark case study in seismic history matching

In a previous work \citep{luo2016sparse2d_spej}, the authors proposed an ensemble-based 4D seismic history matching (SHM) framework, which has some relatively new ingredients, in terms of the type of seismic data in choice, the way to handle big seismic data and related data noise estimation, and the use of a recently developed iterative ensemble history matching algorithm. In seismic history matching, it is customary to use inverted seismic attributes, such as acoustic impedance, as the observed data. In doing so, extra uncertainties may arise during the inversion processes. The proposed SHM framework avoids such intermediate inversion processes by adopting amplitude versus angle (AVA) data. In addition, SHM typically involves assimilating a large amount of observed seismic attributes into reservoir models. To handle the big-data problem in SHM, the proposed framework adopts the following wavelet-based sparse representation procedure: First, a discrete wavelet transform is applied to observed seismic attributes. Then, uncertainty analysis is conducted in the wavelet domain to estimate noise in the resulting wavelet coefficients, and to calculate a corresponding threshold value. Wavelet coefficients above the threshold value, called leading wavelet coefficients hereafter, are used as the data for history matching. The retained leading wavelet coefficients preserve the most salient features of the observed seismic attributes, whereas rendering a substantially smaller data size. Finally, an iterative ensemble smoother is adopted to update reservoir models, in such a way that the leading wavelet coefficients of simulated seismic attributes better match those of observed seismic attributes. (The rest of the abstract was omitted for the length restriction.)

physics.data-an↗
arXiv2016

An Ensemble 4D Seismic History Matching Framework with Sparse Representation Based on Wavelet Multiresolution Analysis

In this work we propose an ensemble 4D seismic history matching framework for reservoir characterization. Compared to similar existing frameworks in reservoir engineering community, the proposed one consists of some relatively new ingredients, in terms of the type of seismic data in choice, wavelet multiresolution analysis for the chosen seismic data and related data noise estimation, and the use of recently developed iterative ensemble history matching algorithms. Typical seismic data used for history matching, such as acoustic impedance, are inverted quantities, whereas extra uncertainties may arise during the inversion processes. In the proposed framework we avoid such intermediate inversion processes. In addition, we also adopt wavelet-based sparse representation to reduce data size. Concretely, we use intercept and gradient attributes derived from amplitude versus angle (AVA) data, apply multilevel discrete wavelet transforms (DWT) to attribute data, and estimate noise level of resulting wavelet coefficients. We then select the wavelet coefficients above a certain threshold value, and history-match these leading wavelet coefficients using an iterative ensemble smoother. (The rest of the abstract is omitted for exceeding the limit of length)

physics.data-an↗
arXiv2016

Iterative ensemble smoother as an approximate solution to a regularized minimum-average-cost problem: theory and applications

The focus of this work is on an alternative implementation of the iterative ensemble smoother (iES). We show that iteration formulae similar to those used in \cite{chen2013-levenberg,emerick2012ensemble} can be derived by adopting a regularized Levenberg-Marquardt (RLM) algorithm \cite{jin2010regularized} to approximately solve a minimum-average-cost (MAC) problem. This not only leads to an alternative theoretical tool in understanding and analyzing the behaviour of the aforementioned iES, but also provides insights and guidelines for further developments of the smoothing algorithms. For illustration, we compare the performance of an implementation of the RLM-MAC algorithm to that of the approximate iES used in \cite{chen2013-levenberg} in three numerical examples: an initial condition estimation problem in a strongly nonlinear system, a facies estimation problem in a 2D reservoir and the history matching problem in the Brugge field case. In these three specific cases, the RLM-MAC algorithm exhibits comparable or even better performance, especially in the strongly nonlinear system.

physics.data-an↗
arXiv2014

Ensemble Kalman filtering with a divided state-space strategy for coupled data assimilation problems

This study considers the data assimilation problem in coupled systems, which consists of two components (sub-systems) interacting with each other through certain coupling terms. A straightforward way to tackle the assimilation problem in such systems is to concatenate the states of the sub-systems into one augmented state vector, so that a standard ensemble Kalman filter (EnKF) can be directly applied. In this work we present a divided state-space estimation strategy, in which data assimilation is carried out with respect to each individual sub-system, involving quantities from the sub-system itself and correlated quantities from other coupled sub-systems. On top of the divided state-space estimation strategy, we also consider the possibility to run the sub-systems separately. Combining these two ideas, a few variants of the EnKF are derived. The introduction of these variants is mainly inspired by the current status and challenges in coupled data assimilation problems, and thus might be of interest from a practical point of view. Numerical experiments with a multi-scale Lorentz 96 model are conducted to evaluate the performance of these variants against that of the conventional EnKF. In addition, specific for coupled data assimilation problems, two prototypes of extensions of the presented methods are also developed in order to achieve a trade-off between efficiency and accuracy.

physics.ao-ph↗
arXiv2014

Toward an enhanced Bayesian estimation framework for multiphase flow soft-sensing

In this work the authors study the multiphase flow soft-sensing problem based on a previously established framework. There are three functional modules in this framework, namely, a transient well flow model that describes the response of certain physical variables in a well, for instance, temperature, velocity and pressure, to the flow rates entering and leaving the well zones; a Markov jump process that is designed to capture the potential abrupt changes in the flow rates; and an estimation method that is adopted to estimate the underlying flow rates based on the measurements from the physical sensors installed in the well. In the previous studies, the variances of the flow rates in the Markov jump process are chosen manually. To fill this gap, in the current work two automatic approaches are proposed in order to optimize the variance estimation. Through a numerical example, we show that, when the estimation framework is used in conjunction with these two proposed variance-estimation approaches, it can achieve reasonable performance in terms of matching both the measurements of the physical sensors and the true underlying flow rates.

stat.ME↗
arXiv2014

Ensemble Kalman filtering with residual nudging: an extension to state estimation problems with nonlinear observation operators

The ensemble Kalman filter (EnKF) is an efficient algorithm for many data assimilation problems. In certain circumstances, however, divergence of the EnKF might be spotted. In previous studies, the authors proposed an observation-space-based strategy, called residual nudging, to improve the stability of the EnKF when dealing with linear observation operators. The main idea behind residual nudging is to monitor and, if necessary, adjust the distances (misfits) between the real observations and the simulated ones of the state estimates, in the hope that by doing so one may be able to obtain better estimation accuracy. In the present study, residual nudging is extended and modified in order to handle nonlinear observation operators. Such extension and modification result in an iterative filtering framework that, under suitable conditions, is able to achieve the objective of residual nudging for data assimilation problems with nonlinear observation operators. The 40 dimensional Lorenz 96 model is used to illustrate the performance of the iterative filter. Numerical results show that, while a normal EnKF may diverge with nonlinear observation operators, the proposed iterative filter remains stable and leads to reasonable estimation accuracy under various experimental settings.

physics.ao-ph↗
arXiv2013

Covariance inflation in the ensemble Kalman filter: a residual nudging perspective and some implications

This note examines the influence of covariance inflation on the distance between the measured observation and the simulated (or predicted) observation with respect to the state estimate. In order for the aforementioned distance to be bounded in a certain interval, some sufficient conditions are derived, indicating that the covariance inflation factor should be bounded in a certain interval, and that the inflation bounds are related to the maximum and minimum eigenvalues of certain matrices. Implications of these analytic results are discussed, and a numerical experiment is presented to verify the validity of our analysis.

physics.ao-ph↗
arXiv2013

Efficient particle filtering through residual nudging

We introduce an auxiliary technique, called residual nudging, to the particle filter to enhance its performance in cases that it performs poorly. The main idea of residual nudging is to monitor, and if necessary, adjust the residual norm of a state estimate in the observation space so that it does not exceed a pre-specified threshold. We suggest a rule to choose the pre-specified threshold, and construct a state estimate accordingly to achieve this objective. Numerical experiments suggest that introducing residual nudging to a particle filter may (substantially) improve its performance, in terms of filter accuracy and/or stability against divergence, especially when the particle filter is implemented with a relatively small number of particles.

physics.ao-ph↗
arXiv2012

Ensemble Kalman filtering with residual nudging

Covariance inflation and localization are two important techniques that are used to improve the performance of the ensemble Kalman filter (EnKF) by (in effect) adjusting the sample covariances of the estimates in the state space. In this work an additional auxiliary technique, called residual nudging, is proposed to monitor and, if necessary, adjust the residual norms of state estimates in the observation space. In an EnKF with residual nudging, if the residual norm of an analysis is larger than a pre-specified value, then the analysis is replaced by a new one whose residual norm is no larger than a pre-specified value. Otherwise the analysis is considered as a reasonable estimate and no change is made. A rule for choosing the pre-specified value is suggested. Based on this rule, the corresponding new state estimates are explicitly derived in case of linear observations. Numerical experiments in the 40-dimensional Lorenz 96 model show that introducing residual nudging to an EnKF may improve its accuracy and/or enhance its stability against filter divergence, especially in the small ensemble scenario.

physics.ao-ph↗
arXiv2011

Particle Kalman Filtering: A Nonlinear Bayesian Framework for Ensemble Kalman Filters

This paper investigates an approximation scheme of the optimal nonlinear Bayesian filter based on the Gaussian mixture representation of the state probability distribution function. The resulting filter is similar to the particle filter, but is different from it in that, the standard weight-type correction in the particle filter is complemented by the Kalman-type correction with the associated covariance matrices in the Gaussian mixture. We show that this filter is an algorithm in between the Kalman filter and the particle filter, and therefore is referred to as the particle Kalman filter (PKF). In the PKF, the solution of a nonlinear filtering problem is expressed as the weighted average of an "ensemble of Kalman filters" operating in parallel. Running an ensemble of Kalman filters is, however, computationally prohibitive for realistic atmospheric and oceanic data assimilation problems. For this reason, we consider the construction of the PKF through an "ensemble" of ensemble Kalman filters (EnKFs) instead, and call the implementation the particle EnKF (PEnKF). We show that different types of the EnKFs can be considered as special cases of the PEnKF. Similar to the situation in the particle filter, we also introduce a re-sampling step to the PEnKF in order to reduce the risk of weights collapse and improve the performance of the filter. Numerical experiments with the strongly nonlinear Lorenz-96 model are presented and discussed.

physics.data-an↗
arXiv2011

Robust ensemble filtering and its relation to covariance inflation in the ensemble Kalman filter

We propose a robust ensemble filtering scheme based on the $H_{\infty}$ filtering theory. The optimal $H_{\infty}$ filter is derived by minimizing the supremum (or maximum) of a predefined cost function, a criterion different from the minimum variance used in the Kalman filter. By design, the $H_{\infty}$ filter is more robust than the Kalman filter, in the sense that the estimation error in the $H_{\infty}$ filter in general has a finite growth rate with respect to the uncertainties in assimilation, except for a special case that corresponds to the Kalman filter. The original form of the $H_{\infty}$ filter contains global constraints in time, which may be inconvenient for sequential data assimilation problems. Therefore we introduce a variant that solves some time-local constraints instead, and hence we call it the time-local $H_{\infty}$ filter (TLHF). By analogy to the ensemble Kalman filter (EnKF), we also propose the concept of ensemble time-local $H_{\infty}$ filter (EnTLHF). We outline the general form of the EnTLHF, and discuss some of its special cases. In particular, we show that an EnKF with certain covariance inflation is essentially an EnTLHF. In this sense, the EnTLHF provides a general framework for conducting covariance inflation in the EnKF-based methods. We use some numerical examples to assess the relative robustness of the TLHF/EnTLHF in comparison with the corresponding KF/EnKF method.

physics.data-an↗
arXiv2010

Scaled unscented transform Gaussian sum filter: theory and application

In this work we consider the state estimation problem in nonlinear/non-Gaussian systems. We introduce a framework, called the scaled unscented transform Gaussian sum filter (SUT-GSF), which combines two ideas: the scaled unscented Kalman filter (SUKF) based on the concept of scaled unscented transform (SUT), and the Gaussian mixture model (GMM). The SUT is used to approximate the mean and covariance of a Gaussian random variable which is transformed by a nonlinear function, while the GMM is adopted to approximate the probability density function (pdf) of a random variable through a set of Gaussian distributions. With these two tools, a framework can be set up to assimilate nonlinear systems in a recursive way. Within this framework, one can treat a nonlinear stochastic system as a mixture model of a set of sub-systems, each of which takes the form of a nonlinear system driven by a known Gaussian random process. Then, for each sub-system, one applies the SUKF to estimate the mean and covariance of the underlying Gaussian random variable transformed by the nonlinear governing equations of the sub-system. Incorporating the estimations of the sub-systems into the GMM gives an explicit (approximate) form of the pdf, which can be regarded as a "complete" solution to the state estimation problem, as all of the statistical information of interest can be obtained from the explicit form of the pdf ... This work is on the construction of the Gaussian sum filter based on the scaled unscented transform.

physics.data-an↗
arXiv2007

Asymptotically pivotal statistic for surrogate testing with extended hypothesis

The method of surrogate data provides a framework for testing observed data against a hierarchy of alternative hypotheses. The aim of applying this method is to exclude the possibility that the data are consistent with simple linear explanations before seeking complex nonlinear causes. However, in recent time the method has attracted considerable criticism, largely as a result of ambiguity about the formation of the underlying null hypotheses, or about the power of the chosen statistic. In this communication we show that by employing a special family of ranks statistics these problems can be avoided and the method of surrogate data placed of a firm statistical foundation.

nlin.CD↗
arXiv2006

Exact nonparametric inference for detection of nonlinear determinism

We propose an exact nonparametric inference scheme for the detection of nonlinear determinism. The essential fact utilized in our scheme is that, for a linear stochastic process with jointly symmetric innovations, its ordinary least square (OLS) linear prediction error is symmetric about zero. Based on this viewpoint, a class of linear signed rank statistics, e.g. the Wilcoxon signed rank statistic, can be derived with the known null distributions from the prediction error. Thus one of the advantages of our scheme is that, it can provide exact confidence levels for our null hypothesis tests. Furthermore, the exactness is applicable for finite samples with arbitrary length. We demonstrate the test power of this statistic through several examples.

nlin.CD↗
arXiv2006

Surrogate data method applied to nonlinear time series

The surrogate data method is widely applied as a data dependent technique to test observed time series against a barrage of hypotheses. However, often the hypotheses one is able to address are not those of greatest interest, particularly for system known to be nonlinear. In the review we focus on techniques which overcome this shortcoming. We summarize a number of recently developed surrogate data methods. While our review of surrogate methods is not exhaustive, we do focus on methods which may be applied to experimental, and potentially nonlinear, data. In each case, the hypothesis being tested is one of the interests to the experimental scientist.

nlin.CD↗
arXiv2005

Optimal phase space projection for noise reduction

In this communication we will re-examine the widely studied technique of phase space projection. By imposing a time domain constraint (TDC) on the residual noise, we deduce a more general version of the optimal projector, which includes those appearing in previous literature as subcases but does not assume the independence between the clean signal and the noise. As an application, we will apply this technique for noise reduction. Numerical results show that our algorithm has succeeded in augmenting the signal-to-noise ratio (SNR) for simulated data from the Rössler system and experimental speech record.

nlin.CD↗