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作者： Shi, Zheng Lehigh University

学位级别：Ph.D., Doctor of Philosophy

This dissertation consists of 2 parts and 5 chapters. In Chapter 1, we present fundamental concepts, on which the works are based, and provide an overview of this dissertation. In Part I, we develop two novel adaptive algorithms to solve machine learning problems, derive their theoretical convergence, conduct numerical experiment on binary classification problems, and explore empirical merits of adopting both methods to solve machine learning problems in particular settings. In Part II, we develop deep neural networks to solve engineering application problems, analyze the challenges in training deep neural networks for these problems, propose to use second-order methods for training the networks, and conduct numerical experiment to evaluate the performance of the proposed methods. In Chapter 2, we present a first-order adaptive and implicit stochastic recursive gradient method to solve the Empirical Risk Minimization (ERM) or Finite-Sum problems in machine learning. This algorithm employs the outer-inner loop structure of classic stochastic recursive gradient method yet being developed as a fully adaptive algorithm without any hyper-parameter tuning. This algorithm adopts implicit approach to estimate the local geometry and dynamically determine the step-size at every iteration. With strongly convex Finite-Sum and convex component functions, it is guaranteed to converge linearly, and can produce a possibly faster convergence than classic stochastic recursive gradient method if local geometry permits. This algorithm can be easily implemented and is computationally efficient. In practice, compared with other state-of-art first-order methods with fine-tune hyper-parameters, this algorithm exhibits competitive empirical performance. In spite of being tune-free, this algorithm consistently outperforms its fine-tuned classic counterparts on an extensive set of problems and cases. In Chapter 3, we present a second-order doubly adaptive scaled algorithm to solve ERM or Fini

关键词： adaptive algorithm Deep learning First-order method Machine learning Optimization Second-order method

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adaptive Notch Filter Design for Flexible Modes of Guided Munitions 13

Adaptive Notch Filter Design for Flexible Modes of Guided Mu...

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13th IEEE International Conference on Mechanical and Intelligent Manufacturing Technologies (ICMIMT)

作者： Eser, Ahmet Oner Kurkcu, Burak Ayasun, Saffet Gazi Univ Dept Elect & Elect Engn Aselsan Inc Ankara Turkey Hacettepe Univ Dept Comp Engn Ankara Turkey Gazi Univ Dept Elect & Elect Engn Ankara Turkey

ISBN: (纸本)9781665484008

In this study, an adaptive notch filter design is proposed to prevent flexible mode oscillations caused by the wings' structure in air-to-surface missiles. The proposed filter detects oscillations and prevents vibrations by simply changing the filter coefficients. The algorithm first identifies any existing oscillations and then calculates the corresponding oscillation frequency by satisfying the stability conditions of the filter such that poles of the notch filter are located within the unit circle in the z-plane. With the designed algorithm, the notch filter can be easily integrated into real-time applications because of the low resource consumption and simple structure of filter.

关键词： notch filter adaptive algorithm flexible mode vibrations

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adaptive Rational Orthogonal Basis Functions for Identification of Continuous-Time Systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2021年第4期66卷 1809-1816页

作者： Mi, Wen Zheng, Wei Xing Univ Elect Sci & Technol China Sch Math Sci Chengdu 611731 Peoples R China Western Sydney Univ Sch Comp Data & Math Sci Sydney NSW 2751 Australia

In this article, we present two algorithms for identification of continuous-time linear time-invariant systems in frequency domain. These algorithms are constructed in terms of continuous rational orthogonal basis functions. First, a two-stage algorithm is developed through one-by-one selection of poles for the basis functions, and such consecutive selection is easy to realize. Next, a direct algorithm is proposed to select poles for the rational orthogonal basis functions. Different poles result in different bases and these selections guarantee that better approximations can be reached. For different systems, there are different sequences of poles selected for basis functions, which shows the adaptivity of the proposed algorithms. A numerical example is given to show that the proposed algorithms are useful. Also, in this example, comparison is made with the method that uses rational orthogonal basis functions in which all poles of the basis functions are true poles of the original system.

关键词： Frequency-domain analysis Approximation algorithms Mathematical model Linear systems Computational modeling Transfer functions adaptive algorithm frequency domain identification orthogonal basis rational function

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Accelerated system-reliability-based disaster resilience analysis for structural systems

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STRUCTURAL SAFETY 2024年 109卷

作者： Kim, Taeyong Yi, Sang-ri Ajou Univ Dept Civil Syst Engn Suwon South Korea Univ Calif Berkeley Dept Civil & Environm Engn Berkeley CA 94720 USA

Resilience has emerged as a crucial concept for evaluating structural performance under disasters because of its ability to extend beyond traditional risk assessments, accounting for a system's ability to minimize disruptions and maintain functionality during recovery. To facilitate the holistic understanding of resilience performance in structural systems, a system-reliability-based disaster resilience analysis framework was developed. The framework describes resilience using three criteria: reliability (beta), redundancy (pi), and recoverability (gamma), and the system's internal resilience is evaluated by inspecting the characteristics of reliability and redundancy for different possible progressive failure modes. However, the practical application of this framework has been limited to complex structures with numerous sub-components, as it becomes intractable to evaluate the performances for all possible initial disruption scenarios. To bridge the gap between the theory and practical use, especially for evaluating reliability and redundancy, this study centers on the idea that the computational burden can be substantially alleviated by focusing on initial disruption scenarios that are practically significant. To achieve this research goal, we propose three methods to efficiently eliminate insignificant scenarios: the sequential search method, the n-ball sampling method, and the surrogate model-based adaptive sampling algorithm. Three numerical examples, including buildings and a bridge, are introduced to prove the applicability and efficiency of the proposed approaches. The findings of this study are expected to offer practical solutions to the challenges of assessing resilience performance in complex structural systems.

关键词： Disaster resilience Structural reliability Resilience criteria Surrogate model adaptive algorithm Deep learning

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A MULTIRESOLUTION adaptive WAVELET METHOD FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

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INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING 2021年第2期19卷 29-37页

作者： Harnish, C. Dalessandro, L. Matous, K. Livescu, D. Univ Notre Dame Dept Aerosp & Mech Engn Notre Dame IN 46556 USA Indiana Univ Dept Intelligent Syst Engn Bloomington IN 47405 USA Los Alamos Natl Lab Comp & Computat Sci Div Los Alamos NM 87545 USA

The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to solve partial differential equations (PDEs) with features evolving on a wide range of spatial and temporal scales. To meet these challenges, we present a multiresolution wavelet algorithm to solve PDEs with significant data compression and explicit error control. We discretize in space by projecting fields and spatial derivative operators onto wavelet basis functions. We provide error estimates for the wavelet representation of fields and their derivatives. Then, our estimates are used to construct a sparse multiresolution discretization which guarantees the prescribed accuracy. Additionally, we embed a predictor-corrector procedure within the temporal integration to dynamically adapt the computational grid and maintain the accuracy of the solution of the PDE as it evolves. We present examples to highlight the accuracy and adaptivity of our approach.

关键词： multiresolution analysis wavelets adaptive algorithm nonlinear PDEs data compression

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An enriched Galerkin-characteristics finite element method for convection-dominated and transport problems

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APPLIED NUMERICAL MATHEMATICS 2021年 167卷 119-142页

作者： Ouardghi, Abdelouahed El-Amrani, Mofdi Seaid, Mohammed Univ Mohammed VI Polytech Int Water Res Inst Benguerir Morocco Abdelmalek Essaadi Univ Math & Applicat Lab FST Tangier Morocco Univ Durham Dept Engn South Rd Durham DH1 3LE England

We propose an enriched Galerkin-characteristics finite element method for numerical solution of convection-dominated problems. The method uses the modified method of characteristics for the integration of the total derivative in time, combined with the finite element method for the spatial discretization on unstructured grids. The L-2-projection method is implemented for the evaluation of numerical solutions by tracking the departure points from the integration points in each element. In the present study, a family of quadrature rules are used to enrich the approximation of integrals in the L-2-projection method. The use of quadrature rules as an enrichment procedure allows for spatial discretizations on coarse fixed meshes and no need to introduce time-dependent enrichments. This procedure offers a very great advantage over the conventional Galerkin-characteristics finite element method since the same governing matrix representation can be used during the entire time steeping process. We also propose a multilevel adaptive procedure in the enriched Galerkin-characteristics finite element method by monitoring the gradient of the solution in the computational domain during its advection. In comparison with the traditional finite element analysis with h-, p- and hp-version refinements, the present approach is much simpler, more robust and efficient, and it yields more accurate solutions for a fixed number of degrees of freedom without refining the mesh. To examine the performance of the proposed method we solve several test examples for convectiondiffusion problems. Comparison to the conventional Galerkin-characteristics finite element method is also carried out in the present work. The aim of such enriched method compared to the classical finite element method is to solve the time-dependent convection-dominated problems efficiently and with an appropriate level of accuracy. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： Enriched finite elements Galerkin-characteristics method Convection-diffusion equations L-2-projection adaptive algorithm

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Quaternary splitting algorithm in group testing

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2021年第1期41卷 73-79页

作者： Lu, Jinn Fu, Hung-Lin Natl Chiao Tung Univ Dept Appl Math Hsinchu 30010 Taiwan

In Classical group testing, one is given a population of n items N which contains some defective d items inside. A group test (pool) is a test on a subset of N. Under the circumstance of no errors, a test is negative if the testing pool contains no defective items and the test is positive if the testing pool contains at least one defective item but we don't know which one. The goal is to find all defectives by using as less tests as possible, mainly to minimize the number of tests (in the worst case situation). Let M(d, n) denote the minimum number of tests in the worst case situation where vertical bar N vertical bar = n and d is the number of defectives. In this paper, we focus on estimating M(d, n) and obtain a better result than known ones in various cases of d and n.

关键词： Group testing adaptive algorithm Quaternary splitting

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Model-Independent Containment Control for Dynamic Multiple Euler-Lagrange Systems With Disturbances and Uncertainties

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IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING 2021年第4期8卷 3443-3452页

作者： Su, Housheng Zhang, Liren Huazhong Univ Sci & Technol Sch Artificial Intelligence & Automat Wuhan 430074 Peoples R China Huazhong Univ Sci & Technol Educ Minist China Key Lab Image Proc & Intelligent Control Wuhan 430074 Peoples R China

This article studies the model-independent distributed containment control problem for multiple Euler-Lagrange systems (MELSs) considering external disturbances and system uncertainties. First, we design a virtual network and propose a controller for all virtual nodes moving to the convex hull formed by all leaders. Then, we propose an adaptive tracking algorithm which combines a continuous robust integral of the sign of the error (RISE) feedback element and a neural network-based (NN-based) feedforward element to guarantee that each follower semi-globally asymptotically track the state of the corresponding virtual node. Apart from this, a smooth projection algorithm is ulitized to ensure that training values of NN weight matrices are bounded. Hence, the MELSs can achieve containment control. Furthermore, criteria for addressing the above model-independent containment control problem are given by the theoretical derivation. Finally, the correctness of the presented model-independent containment control method is checked out by a numerical simulation.

关键词： Uncertainty Artificial neural networks Linear systems Trajectory Stability analysis Process control Observers Multiple Euler-Lagrange systems containment control adaptive algorithm neural network RISE feedback

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adaptive Event-Triggered Strategy for Economic Dispatch in Uncertain Communication Networks

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IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS 2021年第4期8卷 1881-1891页

作者： Wan, Ying Long, Cheng Deng, Ruilong Wen, Guanghui Yu, Xinghuo Southeast Univ Sch Math Nanjing 210096 Peoples R China Southeast Univ Minist Educ Key Lab Measurement & Control Complex Syst Engn S Nanjing Peoples R China Nanyang Technol Univ Sch Comp Sci & Engn Singapore 639798 Singapore Zhejiang Univ Coll Control Sci & Engn Hangzhou 310027 Peoples R China Zhejiang Univ Sch Cyber Sci & Technol Hangzhou 310027 Peoples R China RMIT Univ Sch Engn Melbourne Vic 3001 Australia

This article investigates the economic dispatch problem in a smart grid with the event-triggered framework under uncertain communication networks. Unlike most of the existing works on economic dispatch, where the distributed consensus-based algorithms are conducted continuously or periodically, the event-triggered mechanism is employed for saving communication resources. For uncertainties, whose upper bounds may be even more significant than nominal weights, we design a general framework for the distributed event-triggered algorithm and an adaptive law for adjusting the coupling weights. The upper bounds of the communication uncertainties are not required in the design, and the adaptive tuning of coupling weights is proved to be able to compensate for the adverse effects caused by uncertainties in the consensus-seeking phase. Noteworthy, the design of event-triggered parameters is independent of the communication topology, which makes the proposed algorithm fully distributed. We also prove that the Zeno triggering of the event-triggered algorithms does not exist. Finally, a case study with the communication network represented by the random multiradius geographical graph is conducted to verify the effectiveness of the derived algorithms.

关键词： adaptive algorithm economic dispatch event-triggered control smart grid uncertain communication network

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Distributed Resource Allocation Over Directed Graphs via Continuous-Time algorithms

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2021年第2期51卷 1097-1106页

作者： Zhu, Yanan Ren, Wei Yu, Wenwu Wen, Guanghui Southeast Univ Sch Math Jiangsu Prov Key Lab Networked Collect Intelligen Nanjing 210096 Peoples R China Univ Calif Riverside Dept Elect & Comp Engn Riverside CA 95251 USA RMIT Univ Sch Engn Melbourne Vic 3000 Australia

This paper investigates the resource allocation problem for a group of agents communicating over a strongly connected directed graph, where the total objective function of the problem is composted of the sum of the local objective functions incurred by the agents. With local convex sets, we first design a continuous-time projection algorithm over a strongly connected and weight-balanced directed graph. Our convergence analysis indicates that when the local objective functions are strongly convex, the output state of the projection algorithm could asymptotically converge to the optimal solution of the resource allocation problem. In particular, when the projection operation is not involved, we show the exponential convergence at the equilibrium point of the algorithm. Second, we propose an adaptive continuous-time gradient algorithm over a strongly connected and weight-unbalanced directed graph for the reduced case without local convex sets. In this case, we prove that the adaptive algorithm converges exponentially to the optimal solution of the considered problem, where the local objective functions and their gradients satisfy strong convexity and Lipachitz conditions, respectively. Numerical simulations illustrate the performance of our algorithms.

关键词： adaptive algorithm directed graphs projection algorithm resource allocation

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