3,049 research outputs found

    Linear Amplification in Nonequilibrium Turbulent Boundary Layers

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    Resolvent analysis is applied to nonequilibrium incompressible adverse pressure gradient (APG) turbulent boundary layers (TBL) and hypersonic boundary layers with high temperature real gas effects, including chemical nonequilibrium. Resolvent analysis is an equation-based, scale-dependent decomposition of the Navier Stokes equations, linearized about a known mean flow field. The decomposition identifies the optimal response and forcing modes, ranked by their linear amplification. To treat the nonequilibrium APG TBL, a biglobal resolvent analysis approach is used to account for the streamwise and wall-normal inhomogeneities in the streamwise developing flow. For the hypersonic boundary layer in chemical nonequilibrium, the resolvent analysis is constructed using a parallel flow assumption, incorporating N₂, O₂, NO, N, and O as a mixture of chemically reacting gases. Biglobal resolvent analysis is first applied to the zero pressure gradient (ZPG) TBL. Scaling relationships are determined for the spanwise wavenumber and temporal frequency that admit self-similar resolvent modes in the inner layer, mesolayer, and outer layer regions of the ZPG TBL. The APG effects on the inner scaling of the biglobal modes are shown to diminish as their self-similarity improves with increased Reynolds number. An increase in APG strength is shown to increase the linear amplification of the large-scale biglobal modes in the outer region, similar to the energization of large scale modes observed in simulation. The linear amplification of these modes grows linearly with the APG history, measured as the streamwise averaged APG strength, and relates to a novel pressure-based velocity scale. Resolvent analysis is then used to identify the length scales most affected by the high-temperature gas effects in hypersonic TBLs. It is shown that the high-temperature gas effects primarily affect modes localized near the peak mean temperature. Due to the chemical nonequilibrium effects, the modes can be linearly amplified through changes in chemical concentration, which have non-negligible effects on the higher order modes. Correlations in the components of the small-scale resolvent modes agree qualitatively with similar correlations in simulation data. Finally, efficient strategies for resolvent analysis are presented. These include an algorithm to autonomously sample the large amplification regions using a Bayesian Optimization-like approach and a projection-based method to approximate resolvent analysis through a reduced eigenvalue problem, derived from calculus of variations.</p

    Algorithms and complexity for approximately counting hypergraph colourings and related problems

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    The past decade has witnessed advancements in designing efficient algorithms for approximating the number of solutions to constraint satisfaction problems (CSPs), especially in the local lemma regime. However, the phase transition for the computational tractability is not known. This thesis is dedicated to the prototypical problem of this kind of CSPs, the hypergraph colouring. Parameterised by the number of colours q, the arity of each hyperedge k, and the vertex maximum degree Δ, this problem falls into the regime of LovĂĄsz local lemma when Δ â‰Č qᔏ. In prior, however, fast approximate counting algorithms exist when Δ â‰Č qᔏ/Âł, and there is no known inapproximability result. In pursuit of this, our contribution is two-folded, stated as follows. ‱ When q, k ≄ 4 are evens and Δ ≄ 5·qᔏ/ÂČ, approximating the number of hypergraph colourings is NP-hard. ‱ When the input hypergraph is linear and Δ â‰Č qᔏ/ÂČ, a fast approximate counting algorithm does exist

    A probabilistic approach for acoustic emission based monitoring techniques: with application to structural health monitoring

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    It has been demonstrated that acoustic-emission (AE), inspection of structures can offer advantages over other types of monitoring techniques in the detection of damage; namely, an increased sensitivity to damage, as well as an ability to localise its source. There are, however, numerous challenges associated with the analysis of AE data. One issue is the high sampling frequencies required to capture AE activity. In just a few seconds, a recording can generate very high volumes of data, of which a significant portion may be of little interest for analysis. Identifying the individual AE events in a recorded time-series is therefore a necessary procedure for reducing the size of the dataset and projecting out the influence of background noise from the signal. In this paper, a state-of-the-art technique is presented that can automatically identify cluster the AE events from a probabilistic perspective. A nonparametric Bayesian approach, based on the Dirichlet process (DP), is employed to overcome some of the challenges associated with this task. Additionally, the developed model is applied for damage detection using AE data collected from an experimental setup. Two main sets of AE data are considered in this work: (1) from a journal bearing in operation, and (2) from an Airbus A320 main landing gear subjected to fatigue testing

    Semiparametric posterior corrections

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    We present a new approach to semiparametric inference using corrected posterior distributions. The method allows us to leverage the adaptivity, regularization and predictive power of nonparametric Bayesian procedures to estimate low-dimensional functionals of interest without being restricted by the holistic Bayesian formalism. Starting from a conventional nonparametric posterior, we target the functional of interest by transforming the entire distribution with a Bayesian bootstrap correction. We provide conditions for the resulting one-step posterior\textit{one-step posterior} to possess calibrated frequentist properties and specialize the results for several canonical examples: the integrated squared density, the mean of a missing-at-random outcome, and the average causal treatment effect on the treated. The procedure is computationally attractive, requiring only a simple, efficient post-processing step that can be attached onto any arbitrary posterior sampling algorithm. Using the ACIC 2016 causal data analysis competition, we illustrate that our approach can outperform the existing state-of-the-art through the propagation of Bayesian uncertainty.Comment: 53 page

    Classifier Calibration: A survey on how to assess and improve predicted class probabilities

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    This paper provides both an introduction to and a detailed overview of the principles and practice of classifier calibration. A well-calibrated classifier correctly quantifies the level of uncertainty or confidence associated with its instance-wise predictions. This is essential for critical applications, optimal decision making, cost-sensitive classification, and for some types of context change. Calibration research has a rich history which predates the birth of machine learning as an academic field by decades. However, a recent increase in the interest on calibration has led to new methods and the extension from binary to the multiclass setting. The space of options and issues to consider is large, and navigating it requires the right set of concepts and tools. We provide both introductory material and up-to-date technical details of the main concepts and methods, including proper scoring rules and other evaluation metrics, visualisation approaches, a comprehensive account of post-hoc calibration methods for binary and multiclass classification, and several advanced topics

    Subjective Crowd Disagreements for Subjective Data: Uncovering Meaningful CrowdOpinion with Population-level Learning

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    Human-annotated data plays a critical role in the fairness of AI systems, including those that deal with life-altering decisions or moderating human-created web/social media content. Conventionally, annotator disagreements are resolved before any learning takes place. However, researchers are increasingly identifying annotator disagreement as pervasive and meaningful. They also question the performance of a system when annotators disagree. Particularly when minority views are disregarded, especially among groups that may already be underrepresented in the annotator population. In this paper, we introduce \emph{CrowdOpinion}\footnote{Accepted for publication at ACL 2023}, an unsupervised learning based approach that uses language features and label distributions to pool similar items into larger samples of label distributions. We experiment with four generative and one density-based clustering method, applied to five linear combinations of label distributions and features. We use five publicly available benchmark datasets (with varying levels of annotator disagreements) from social media (Twitter, Gab, and Reddit). We also experiment in the wild using a dataset from Facebook, where annotations come from the platform itself by users reacting to posts. We evaluate \emph{CrowdOpinion} as a label distribution prediction task using KL-divergence and a single-label problem using accuracy measures.Comment: Accepted for Publication at ACL 202

    Asymptotics of stochastic learning in structured networks

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