1,045 research outputs found

    Learning model discrepancy: A Gaussian process and sampling-based approach

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    Predicting events in the real world with a computer model (simulator) is challenging. Every simulator, to varying extents, has model discrepancy, a mismatch between real world observations and the simulator (given the ‘true’ parameters are known). Model discrepancy occurs for various reasons, including simplified or missing physics in the simulator, numerical approximations that are required to compute the simulator outputs, and the fact that assumptions in the simulator are not generally applicable to all real world contexts. The existence of model discrepancy is problematic for the engineer as performing calibration of the simulator will lead to biased parameter estimates, and the resulting simulator is unlikely to accurately predict (or even be valid for) various contexts of interest. This paper proposes an approach for inferring model discrepancy that overcomes non-identifiability problems associated with jointly inferring the simulator parameters along with the model discrepancy. Instead, the proposed procedure seeks to identify model discrepancy given some parameter distribution, which could come from a ‘likelihood-free’ approach that considers the presence of model discrepancy during calibration, such as Bayesian history matching. In this case, model discrepancy is inferred whilst marginalising out the uncertain simulator outputs via a sampling-based approach, therefore better reflecting the ‘true’ uncertainty associated with the model discrepancy. Verification of the approach is performed before a demonstration on an experiential case study, comprising a representative five storey building structure

    Sparse Gaussian Process Emulators for surrogate design modelling

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    Efficient surrogate modelling of computer models (herein defined as simulators) becomes of increasing importance as more complex simulators and non-deterministic methods, such as Monte Carlo simulations, are utilised. This is especially true in large multidimensional design spaces. In order for these technologies to be feasible in an early design stage context, the surrogate model (oremulator) must create an accurate prediction of the simulator in the proposed design space. Gaussian Processes (GPs) are a powerful non-parametric Bayesian approach that can be used as emulators. The probabilistic framework means that predictive distributions are inferred, providing an understanding of the uncertainty introduced by replacing the simulator with an emulator, known as code uncertainty. An issue with GPs is that they have a computational complexity of O(N3) (where N is the number of data points), which can be reduced to O(NM2) by using various sparse approximations, calculated from a subset of inducing points (where M is the number of inducing points). This paper explores the use of sparse Gaussian process emulators as a computationally efficient method for creating surrogate models of structural dynamics simulators. Discussions on the performance of these methods are presented along with comments regarding key applications to the early design stage

    Spectral stability of noncharacteristic isentropic Navier-Stokes boundary layers

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    Building on work of Barker, Humpherys, Lafitte, Rudd, and Zumbrun in the shock wave case, we study stability of compressive, or "shock-like", boundary layers of the isentropic compressible Navier-Stokes equations with gamma-law pressure by a combination of asymptotic ODE estimates and numerical Evans function computations. Our results indicate stability for gamma in the interval [1, 3] for all compressive boundary-layers, independent of amplitude, save for inflow layers in the characteristic limit (not treated). Expansive inflow boundary-layers have been shown to be stable for all amplitudes by Matsumura and Nishihara using energy estimates. Besides the parameter of amplitude appearing in the shock case, the boundary-layer case features an additional parameter measuring displacement of the background profile, which greatly complicates the resulting case structure. Moreover, inflow boundary layers turn out to have quite delicate stability in both large-displacement and large-amplitude limits, necessitating the additional use of a mod-two stability index studied earlier by Serre and Zumbrun in order to decide stability

    Existence and stability of viscoelastic shock profiles

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    We investigate existence and stability of viscoelastic shock profiles for a class of planar models including the incompressible shear case studied by Antman and Malek-Madani. We establish that the resulting equations fall into the class of symmetrizable hyperbolic--parabolic systems, hence spectral stability implies linearized and nonlinear stability with sharp rates of decay. The new contributions are treatment of the compressible case, formulation of a rigorous nonlinear stability theory, including verification of stability of small-amplitude Lax shocks, and the systematic incorporation in our investigations of numerical Evans function computations determining stability of large-amplitude and or nonclassical type shock profiles.Comment: 43 pages, 12 figure

    Foundations of population-based SHM, Part I : homogeneous populations and forms

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    In Structural Health Monitoring (SHM), measured data that correspond to an extensive set of operational and damage conditions (for a given structure) are rarely available. One potential solution considers that information might be transferred, in some sense, between similar systems. A population-based approach to SHM looks to both model and transfer this missing information, by considering data collected from groups of similar structures. Specifically, in this work, a framework is proposed to model a population of nominally-identical systems, such that (complete) datasets are only available from a subset of members. The SHM strategy defines a general model, referred to as the population form, which is used to monitor a homogeneous group of systems. First, the framework is demonstrated through applications to a simulated population, with one experimental (test-rig) member; the form is then adapted and applied to signals recorded from an operational wind farm

    Probabilistic inference for structural health monitoring: new modes of learning from data

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    In data-driven structural health monitoring (SHM), the signals recorded from systems in operation can be noisy and incomplete. Data corresponding to each of the operational, environmental, and damage states are rarely available a priori; furthermore, labeling to describe the measurements is often unavailable. In consequence, the algorithms used to implement SHM should be robust and adaptive while accommodating for missing information in the training data—such that new information can be included if it becomes available. By reviewing novel techniques for statistical learning (introduced in previous work), it is argued that probabilistic algorithms offer a natural solution to the modeling of SHM data in practice. In three case-studies, probabilistic methods are adapted for applications to SHM signals, including semisupervised learning, active learning, and multitask learning

    Ramsar Wetlands of International Importance–improving conservation outcomes

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    The Ramsar Convention (or the Convention on Wetlands), signed in 1971, was one of the first international conservation agreements, promoting global wise use of wetlands. It has three primary objectives: national designation and management of wetlands of international importance; general wise use of wetlands; and international cooperation. We examined lessons learnt for improving wetland conservation after Ramsar’s nearly five decades of operation. The number of wetlands in the Ramsar Site Network has grown over time (2,391 Ramsar Sites, 2.5 million km2, as at 2020-06-09) but unevenly around the world, with decreasing rate of growth in recent decades. Ramsar Sites are concentrated in countries with a high Gross Domestic Product and human pressure (e.g., western Europe) but, in contrast, Ramsar Sites with the largest wetland extent are in central-west Africa and South America. We identified three key challenges for improving effectiveness of the Ramsar Site Network: increasing number of sites and wetland area, improved representation (functional, geographical and biological); and effective management and reporting. Increasing the number of sites and area in the Ramsar network could benefit from targets, implemented at national scales. Knowledge of representativeness is inadequate, requiring analyses of functional ecotypes, geographical and biological representativeness. Finally, most countries have inadequate management planning and reporting on the ecological character of their Ramsar Sites, requiring more focused attention on a vision and objectives, with regular reporting of key indicators to guide management. There are increasing opportunities to rigorously track ecological character, utilizing new tools and available indicators (e.g., remote sensing). It is critical that the world protect its wetlands, with an effective Ramsar Convention or the Convention on Wetlands at the core

    Exact Occupation Time Distribution in a Non-Markovian Sequence and Its Relation to Spin Glass Models

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    We compute exactly the distribution of the occupation time in a discrete {\em non-Markovian} toy sequence which appears in various physical contexts such as the diffusion processes and Ising spin glass chains. The non-Markovian property makes the results nontrivial even for this toy sequence. The distribution is shown to have non-Gaussian tails characterized by a nontrivial large deviation function which is computed explicitly. An exact mapping of this sequence to an Ising spin glass chain via a gauge transformation raises an interesting new question for a generic finite sized spin glass model: at a given temperature, what is the distribution (over disorder) of the thermally averaged number of spins that are aligned to their local fields? We show that this distribution remains nontrivial even at infinite temperature and can be computed explicitly in few cases such as in the Sherrington-Kirkpatrick model with Gaussian disorder.Comment: 10 pages Revtex (two-column), 1 eps figure (included
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