Data assimilation using bayesian filters and B-spline geological models

This paper proposes a new approach to problems of data assimilation, also known as history matching, of oilfield production data by adjustment of the location and sharpness of patterns of geological facies. Traditionally, this problem has been addressed using gradient based approaches with a level set parameterization of the geology. Gradient-based methods are robust, but computationally demanding with real-world reservoir problems and insufficient for reservoir management uncertainty assessment. Recently, the ensemble filter approach has been used to tackle this problem because of its high efficiency from the standpoint of implementation, computational cost, and performance. Incorporation of level set parameterization in this approach could further deal with the lack of differentiability with respect to facies type, but its practical implementation is based on some assumptions that are not easily satisfied in real problems. In this work, we propose to describe the geometry of the permeability field using B-spline curves. This transforms history matching of the discrete facies type to the estimation of continuous B-spline control points. As filtering scheme, we use the ensemble square-root filter (EnSRF). The efficacy of the EnSRF with the B-spline parameterization is investigated through three numerical experiments, in which the reservoir contains a curved channel, a disconnected channel or a 2-dimensional closed feature. It is found that the application of the proposed method to the problem of adjusting facies edges to match production data is relatively straightforward and provides statistical estimates of the distribution of geological facies and of the state of the reservoir

Multi-Scale 3D Scene Flow from Binocular Stereo Sequences

Scene flow methods estimate the three-dimensional motion field for points in the world, using multi-camera video data. Such methods combine multi-view reconstruction with motion estimation. This paper describes an alternative formulation for dense scene flow estimation that provides reliable results using only two cameras by fusing stereo and optical flow estimation into a single coherent framework. Internally, the proposed algorithm generates probability distributions for optical flow and disparity. Taking into account the uncertainty in the intermediate stages allows for more reliable estimation of the 3D scene flow than previous methods allow. To handle the aperture problems inherent in the estimation of optical flow and disparity, a multi-scale method along with a novel region-based technique is used within a regularized solution. This combined approach both preserves discontinuities and prevents over-regularization – two problems commonly associated with the basic multi-scale approaches. Experiments with synthetic and real test data demonstrate the strength of the proposed approach.National Science Foundation (CNS-0202067, IIS-0208876); Office of Naval Research (N00014-03-1-0108

Data-driven Soft Sensors in the Process Industry

In the last two decades Soft Sensors established themselves as a valuable alternative to the traditional means for the acquisition of critical process variables, process monitoring and other tasks which are related to process control. This paper discusses characteristics of the process industry data which are critical for the development of data-driven Soft Sensors. These characteristics are common to a large number of process industry fields, like the chemical industry, bioprocess industry, steel industry, etc. The focus of this work is put on the data-driven Soft Sensors because of their growing popularity, already demonstrated usefulness and huge, though yet not completely realised, potential. A comprehensive selection of case studies covering the three most important Soft Sensor application fields, a general introduction to the most popular Soft Sensor modelling techniques as well as a discussion of some open issues in the Soft Sensor development and maintenance and their possible solutions are the main contributions of this work

Optimization as a design strategy. Considerations based on building simulation-assisted experiments about problem decomposition

In this article the most fundamental decomposition-based optimization method - block coordinate search, based on the sequential decomposition of problems in subproblems - and building performance simulation programs are used to reason about a building design process at micro-urban scale and strategies are defined to make the search more efficient. Cyclic overlapping block coordinate search is here considered in its double nature of optimization method and surrogate model (and metaphore) of a sequential design process. Heuristic indicators apt to support the design of search structures suited to that method are developed from building-simulation-assisted computational experiments, aimed to choose the form and position of a small building in a plot. Those indicators link the sharing of structure between subspaces ("commonality") to recursive recombination, measured as freshness of the search wake and novelty of the search moves. The aim of these indicators is to measure the relative effectiveness of decomposition-based design moves and create efficient block searches. Implications of a possible use of these indicators in genetic algorithms are also highlighted.Comment: 48 pages. 12 figures, 3 table

Biased landscapes for random Constraint Satisfaction Problems

The typical complexity of Constraint Satisfaction Problems (CSPs) can be investigated by means of random ensembles of instances. The latter exhibit many threshold phenomena besides their satisfiability phase transition, in particular a clustering or dynamic phase transition (related to the tree reconstruction problem) at which their typical solutions shatter into disconnected components. In this paper we study the evolution of this phenomenon under a bias that breaks the uniformity among solutions of one CSP instance, concentrating on the bicoloring of k-uniform random hypergraphs. We show that for small k the clustering transition can be delayed in this way to higher density of constraints, and that this strategy has a positive impact on the performances of Simulated Annealing algorithms. We characterize the modest gain that can be expected in the large k limit from the simple implementation of the biasing idea studied here. This paper contains also a contribution of a more methodological nature, made of a review and extension of the methods to determine numerically the discontinuous dynamic transition threshold.Comment: 32 pages, 16 figure

Highly accurate optic flow computation with theoretically justified warping

In this paper, we suggest a variational model for optic flow computation based on non-linearised and higher order constancy assumptions. Besides the common grey value constancy assumption, also gradient constancy, as well as the constancy of the Hessian and the Laplacian are proposed. Since the model strictly refrains from a linearisation of these assumptions, it is also capable to deal with large displacements. For the minimisation of the rather complex energy functional, we present an efficient numerical scheme employing two nested fixed point iterations. Following a coarse-to-fine strategy it turns out that there is a theoretical foundation of so-called warping techniques hitherto justified only on an experimental basis. Since our algorithm consists of the integration of various concepts, ranging from different constancy assumptions to numerical implementation issues, a detailed account of the effect of each of these concepts is included in the experimental section. The superior performance of the proposed method shows up by significantly smaller estimation errors when compared to previous techniques. Further experiments also confirm excellent robustness under noise and insensitivity to parameter variations

The diffuse Nitsche method: Dirichlet constraints on phase-field boundaries

We explore diffuse formulations of Nitsche's method for consistently imposing Dirichlet boundary conditions on phase-field approximations of sharp domains. Leveraging the properties of the phase-field gradient, we derive the variational formulation of the diffuse Nitsche method by transferring all integrals associated with the Dirichlet boundary from a geometrically sharp surface format in the standard Nitsche method to a geometrically diffuse volumetric format. We also derive conditions for the stability of the discrete system and formulate a diffuse local eigenvalue problem, from which the stabilization parameter can be estimated automatically in each element. We advertise metastable phase-field solutions of the Allen-Cahn problem for transferring complex imaging data into diffuse geometric models. In particular, we discuss the use of mixed meshes, that is, an adaptively refined mesh for the phase-field in the diffuse boundary region and a uniform mesh for the representation of the physics-based solution fields. We illustrate accuracy and convergence properties of the diffuse Nitsche method and demonstrate its advantages over diffuse penalty-type methods. In the context of imaging based analysis, we show that the diffuse Nitsche method achieves the same accuracy as the standard Nitsche method with sharp surfaces, if the inherent length scales, i.e., the interface width of the phase-field, the voxel spacing and the mesh size, are properly related. We demonstrate the flexibility of the new method by analyzing stresses in a human vertebral body

Linear State Models for Volatility Estimation and Prediction

This report covers the important topic of stochastic volatility modelling with an emphasis on linear state models. The approach taken focuses on comparing models based on their ability to fit the data and their forecasting performance. To this end several parsimonious stochastic volatility models are estimated using realised volatility, a volatility proxy from high frequency stock price data. The results indicate that a hidden state space model performs the best among the realised volatility-based models under consideration. For the state space model different sampling intervals are compared based on in-sample prediction performance. The comparisons are partly based on the multi-period prediction results that are derived in this report