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Uncertainty reduction strategies to enhance geotechnical site characterization: a case study of the red roof landslide in Wyoming

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Discover Geoscience 2024年第1期2卷 1-17页

作者： Oluwatuyi, Opeyemi E. Ng, Kam W. Wulff, Shaun S. Ree, Taylor Geotechnical Services Terracon Consultants Inc Cheyenne USA Department of Civil and Architectural Engineering and Construction Management University of Wyoming Laramie USA Department of Mathematics and Statistics University of Wyoming Laramie USA Wyoming Department of Transportation Cheyenne USA

This study presents a method for identifying strategic locations to drill additional boreholes by quantifying and reducing subsurface uncertainties in geotechnical site investigations. The case study is the Red Roof landslide site located near milepost 140 on US Highway 26/89 in Teton County, Wyoming. A landslide remediation report had recommended additional boreholes before completion of the project. Two primary sources of uncertainty in geomaterials, namely geological and ground, are evaluated to determine the locations for these additional boreholes. The study aims to enhance site characterization and improve the accuracy of geotechnical assessments by strategically selecting and drilling additional boreholes that will reduce these subsurface uncertainties. The method involves reviewing and collecting the available site investigation data. An extensive geostatistical simulation is conducted based on the available data to identify spatial locations at the site that have uncertain subsurface conditions. Data from the additional boreholes could be utilized in these areas to reduce the uncertainty. This approach aligns with the current multi-phasing of site investigation in engineering practice, where a preliminary investigation is conducted before a detailed investigation. The results show that the locations of additional boreholes identified using this method differ from the ones earlier recommended, showcasing the effectiveness of the methodology in this application. This study also provides insights into effective strategies for reducing uncertainties through strategic borehole placement in similar geotechnical investigations. By quantifying geological and ground uncertainties, the method enables informed decision-making for slope stability analysis and risk assessment, with implications for infrastructure stability and geohazard mitigation.

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CLASSIFICATION OF FIRN DATA VIA TOPOLOGICAL FEATURES

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arXiv 2025年

作者： Day, Sarah Dimino, Jesse Jester, Matt Keegan, Kaitlin Weighill, Thomas Department of Mathematics William & Mary WilliamsburgVA23185 United States Department of Mathematics CUNY College of Staten Island Staten IslandNY10314 United States Department of Mathematics and Statistics University of North Carolina at Greensboro GreensboroNC27412 United States Nevada Geosciences Department of Geological Sciences and Engineering University of Nevada Reno RenoNV89557 United States

In this paper we evaluate the performance of topological features for generalizable and robust classification of firn image data, with the broader goal of understanding the advantages, pitfalls, and trade-offs in topological featurization. Firn refers to layers of granular snow within glaciers that haven’t been compressed into ice. This compactification process imposes distinct topological and geometric structure on firn that varies with depth within the firn column, making topological data analysis (TDA) a natural choice for understanding the connection between depth and structure. We use two classes of topological features, sublevel set features and distance transform features, together with persistence curves, to predict sample depth from microCT images. A range of challenging training-test scenarios reveals that no one choice of method dominates in all categories, and uncoveres a web of trade-offs between accuracy, interpretability, and *** Codes 55N31, 68T45 Copyright © 2025, The Authors. All rights reserved.

关键词： Topology

Invited Paper: SNR Analysis of Differential Modulation for Distributed Massive MIMO Systems

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Invited Paper: SNR Analysis of Differential Modulation for D...

International Conference on Industrial and Information Systems, ICIIS

作者： Supuni Gunasekara Peter Smith Margreta Kuijper Rajitha Senanayake Department of Electrical and Electronic Engineering University of Melbourne Australia School of Mathematics and Statistics Victoria University of Wellington New Zealand

This paper focuses on non-coherent detection in distributed massive MIMO systems and characterizes the performance in terms of the received signal-to-noise ratio (SNR). We derive closed-form solutions for the cumulative distributive functions (CDF) of the received SNR for cooperative and non-cooperative differential detection. Outage probabilities (calculated through the CDFs of received SNR) offer a simpler alternative to symbol error probability (SEP) expressions, making them valuable in system control procedures. Moreover, the diversity order of both non-cooperative and cooperative systems is derived by characterizing their high SNR behavior.

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Comparative Analysis of Deep Learning Approaches for Predicting Thermomechanical Behavior of Shape Memory Polymers

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Comparative Analysis of Deep Learning Approaches for Predict...

IEEE Southeastcon

作者： Khan Raqib Mahmud Lingxiao Wang Jinyuan Chen Xiyuan Liu Sunzid Hassan Department of Computer Science Louisiana Tech University Ruston USA Department of Electrical Engineering Louisiana Tech University Ruston USA Department of Mathematics and Statistics Louisiana Tech University Ruston USA

ISBN: (数字)9798331504847

ISBN: (纸本)9798331504854

Thermomechanical constitutive modeling is crucial for understanding and designing shape memory polymers (SMPs) for advanced engineering applications. Traditional approaches are often time-consuming and computationally expensive which requires the development of more efficient and accurate methods. In this paper, we propose a Transformer-based deep learning model to predict the thermomechanical behavior of semicrys-talline two-way shape memory polymers (2W-SMPs) under thermomechanical cycles. By leveraging its ability to capture complex, time-dependent patterns, the framework accurately models the intricate relationships between polymer strain, time, temperature, and stress. A comparative analysis with other deep learning models demonstrates that the Transformer excels in accuracy and robustness by capturing intricate dependencies and non-linearities in the data. The test results demonstrate that our proposed Transformer model achieved a root mean squared error (RMSE) of 0.3365, outperforms the traditional deep learning models such as the feedforward neural network (FNN), convolutional neural network (CNN), and long short-term memory (LSTM) models which achieved RMSE values of 6.78, 17.35, and 13.85, respectively. This study highlights the potential of the Transformer model as a powerful tool for predicting material behavior and reducing the time and resources required for constitutive modeling.

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$L_{\infty}$ Bounds for Transient Growth in Repetitive and Iterative Learning Control Systems

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$L_{\infty}$ Bounds for Transient Growth in Repetitive and I...

American Control Conference (ACC)

作者： Douglas A. Bristow John R. Singler Department of Mechanical and Aerospace Engineering Missouri University of Science and Technology Rolla MO USA Department of Mathematics and Statistics Missouri University of Science and Technology Rolla MO USA

ISBN: (数字)9798350382655

ISBN: (纸本)9798350382662

This paper revisits the problem of large transient growth in Iterative Learning Control (ILC) and Repetitive Process Control (RPC) systems. In ILC and RPC problems a process is repeated iteratively, with new control calculations occurring in between each iteration. Large transient growth refers to the propensity of some control algorithms to grow error exponentially before eventually converging. While robust monotonic convergence algorithms (in which monotonic convergence is guaranteed usually in exchange for a small loss in performance) have largely eliminated the concern for large transient growth in ILC, similar results cannot always be obtained in RPC. The emergence of additive manufacturing processes as an important RPC problem, in which each iteration is a layer of deposition, encourages the revisit to large transient growth. Using time-bounded convolution operations, we show here new results for bounding large transient growth with causal ILC and RPC systems. The results show surprising new insights, such as guaranteed convergence, an exponential relationship between peak transient growth and time-length of the iteration, and faster than exponential convergence. The so-called $\lambda$ -norm, classically used in ILC analysis, is reconsidered with respect to the new results.

关键词： Convolution Process control Writing Three-dimensional printing Transient analysis Convergence Iterative learning control

Forecasting density-valued functional panel data

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arXiv 2024年

作者： Jiménez-Varón, Cristian F. Sun, Ying Shang, Han Lin Department of Mathematics University of York Department of Physics and Mathematics Universidad Autónoma de Manizales Colombia CEMSE Division Statistics Program King Abdullah University of Science and Technology Saudi Arabia Department of Actuarial Studies and Business Analytics Macquarie University Australia Department of Mathematics University of York Heslington YorkYO10 5DD United Kingdom

We introduce a statistical method for modeling and forecasting functional panel data represented by multiple densities. Density functions are nonnegative and have a constrained integral and thus do not constitute a linear vector space. We implement a center log-ratio transformation to transform densities into unconstrained functions. These functions exhibit cross-sectional correlation and temporal dependence. Via a functional analysis of variance decomposition, we decompose the unconstrained functional panel data into a deterministic trend component and a time-varying residual component. To produce forecasts for the time-varying component, a functional time series forecasting method, based on the estimation of the long-run covariance, is implemented. By combining the forecasts of the time-varying residual component with the deterministic trend component, we obtain h-step-ahead forecast curves for multiple populations. Illustrated by age- and sex-specific life-table death counts in the United States, we apply our proposed method to generate forecasts of the life-table death counts for 51 states. © 2024, CC BY.

关键词： Spatio-temporal data

LOW-RANK BAYESIAN MATRIX COMPLETION VIA GEODESIC HAMILTONIAN MONTE CARLO ON STIEFEL MANIFOLDS

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arXiv 2024年

作者： Cui, Tiangang Gorodetsky, Alex A. School of Mathematics and Statistics University of Sydney NSW2006 Australia Department of Aerospace Engineering University of Michigan Ann ArborMI48109 United States

We present a new sampling-based approach for enabling efficient computation of low-rank Bayesian matrix completion and quantifying the associated uncertainty. Firstly, we design a new prior model based on the singular-value-decomposition (SVD) parametrization of low-rank matrices. Our prior is analogous to the seminal nuclear-norm regularization used in non-Bayesian setting and enforces orthogonality in the factor matrices by constraining them to Stiefel manifolds. Then, we design a geodesic Hamiltonian Monte Carlo (-within-Gibbs) algorithm for generating posterior samples of the SVD factor matrices. We demonstrate that our approach resolves the sampling difficulties encountered by standard Gibbs samplers for the common two-matrix factorization used in matrix completion. More importantly, the geodesic Hamiltonian sampler allows for sampling in cases with more general likelihoods than the typical Gaussian likelihood and Gaussian prior assumptions adopted in most of the existing Bayesian matrix completion literature. We demonstrate an applications of our approach to fit the categorical data of a mice protein dataset and the MovieLens recommendation problem. Numerical examples demonstrate superior sampling performance, including better mixing and faster convergence to a stationary distribution. Moreover, they demonstrate improved accuracy on the two real-world benchmark problems we *** Codes 65F55, 62F15, 15A83 Copyright © 2024, The Authors. All rights reserved.

关键词： Singular value decomposition

Learning-Based Tracking Control of Unknown Robot Systems with Online Parameter Estimation

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Learning-Based Tracking Control of Unknown Robot Systems wit...

American Control Conference (ACC)

作者： Zhinan Peng Chen Chen Rui Luo Jingting Zhang Hong Cheng Bijoy Kumar Ghosh School of Automation Engineering University of Electronic Science and Technology of China Chengdu China Department of Mathematics and Statistics Texas Tech University Lubbock TX USA

ISBN: (数字)9798350382655

ISBN: (纸本)9798350382662

This paper proposes a novel learning-based optimal control approach for the tracking control problem of a robot manipulator, which is allowed to have uncertainty in the model parameters. We first employ neural network technique to design an identifier for the system parameters estimation. Then, an optimal tracking controller is proposed with a critic network. A novel online weight adaptation law is designed with the dynamic regression extension and mixing technique, for updating both the unknown parameters and the critic network's weight during the control process. With such setup, our approach can develop an important capability of relaxing the persistent excitation condition, leading to improved parameter-convergence accuracy and control applicability, which can be distinguished from the existing methods that use gradient-descent based weight adaptation laws. Rigorous theoretical analysis is conducted based on the Lyapunov stability theory and demonstrates the the uniform ultimate boundedness stability of the closed-loop systems. Effectiveness of the proposed method is validated through simulation study by using a two degree-of-freedom robot system.

关键词： Adaptation models Parameter estimation Uncertainty Optimal control Process control Artificial neural networks Stability analysis

DEEP NEURAL NETWORK SOLUTIONS FOR OSCILLATORY FREDHOLM INTEGRAL EQUATIONS

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arXiv 2024年

作者： Jiang, Jie Xu, Yuesheng School of Computer Science and Engineering Sun Yat-sen University Guangzhou China Department of Mathematics and Statistics Old Dominion University Norfolk United States

We studied the use of deep neural networks (DNNs) in the numerical solution of the oscillatory Fredholm integral equation of the second kind. It is known that the solution of the equation exhibits certain oscillatory behaviors due to the oscillation of the kernel. It was pointed out recently that standard DNNs favour low frequency functions, and as a result, they often produce poor approximation for functions containing high frequency components. We addressed this issue in this study. We first developed a numerical method for solving the equation with DNNs as an approximate solution by designing a numerical quadrature that tailors to computing oscillatory integrals involving DNNs. We proved that the error of the DNN approximate solution of the equation is bounded by the training loss and the quadrature error. We then proposed a multi-grade deep learning (MGDL) model to overcome the spectral bias issue of neural networks. Numerical experiments demonstrate that the MGDL model is effective in extracting multiscale information of the oscillatory solution and overcoming the spectral bias issue from which a standard DNN model suffers. Copyright © 2024, The Authors. All rights reserved.

关键词： Deep neural networks