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stochastic gradient descent method with convex penalty for ill-posed problems in Banach spaces

INVERSE PROBLEMS 2025年第5期41卷 055003-055003页

作者： Gu, Ruixue Fu, Zhenwu Han, Bo Fu, Hongsun Dalian Maritime Univ Sch Sci Dalian 116026 Peoples R China Harbin Inst Technol Dept Math Harbin 150001 Heilongjiang Peoples R China

In this work, we investigate a stochastic gradient descent (SGD) method for solving inverse problems that can be written as systems of linear or nonlinear ill-posed equations in Banach spaces. The method uses only a randomly selected equation at each iteration and employs the convex function as the penalty term, and thus it is scalable to the problem size and has the ability to detect special features of solutions such as nonnegativity and piecewise constancy. To suppress the oscillation in iterates and reduce the semi-convergence of such methods, by incorporating the spirit of discrepancy principle, an adaptive strategy for choosing the step size is suggested. Under certain conditions, we establish the regularization results of the method under an a priori stopping rule. Further, we study an a posteriori stopping rule for SGD-theta method and show the finite iterations termination property. Several numerical simulations on computed tomography and schlieren imaging are provided to demonstrate the effectiveness of the method.

关键词： stochastic gradient descent method linear and nonlinear inverse problems system of ill-posed equations convex penalty convergence analysis tomography

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A stochastic gradient descent method for Computational Design of Random Rough Surfaces in Solar Cells

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Communications in Computational Physics 2023年第10期34卷 1361-1390页

作者： Qiang Li Gang Bao Yanzhao Cao Junshan Lin Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Department of Mathematics Zhejiang UniversityChina Department of Mathematics and Statistics Auburn UniversityAuburnAL 36849USA

In this work,we develop a stochastic gradient descent method for the computational optimal design of random rough surfaces in thin-film solar *** formulate the design problems as random PDE-constrained optimization problems and seek the optimal statistical parameters for the random *** optimizations at fixed frequency as well as at multiple frequencies and multiple incident angles are *** evaluate the gradient of the objective function,we derive the shape derivatives for the interfaces and apply the adjoint state method to perform the *** stochastic gradient descent method evaluates the gradient of the objective function only at a few samples for each iteration,which reduces the computational cost *** numerical experiments are conducted to illustrate the efficiency of the method and significant increases of the absorptance for the optimal random *** also examine the convergence of the stochastic gradient descent algorithm theoretically and prove that the numerical method is convergent under certain assumptions for the random interfaces.

关键词： Optimal design random rough surface solar cell Helmholtz equation stochastic gradient descent method

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An output-only structural condition assessment method for civil structures by the stochastic gradient descent method

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STRUCTURAL CONTROL & HEALTH MONITORING 2022年第12期29卷 e3132-e3132页

作者： Ni, Ping-He Ye, Xiao-Wei Ding, Yang Beijing Univ Technol Minist Educ Key Lab Urban Secur & Disaster Engn Beijing Peoples R China Zhejiang Univ Dept Civil Engn Hangzhou 310058 Peoples R China

The interesting to assess the condition of a structure with structural health monitoring data has gained many attentions. Most of the existing methods require the measurement at the force location. This paper presents a novel output-only condition assessment method that does not require measurement at the force location. The unknown structural damage indices and input force can be identified with the stochastic gradient descent method. The dynamic acceleration response sensitivities with respect to the unknown structural damage indices and input force are derived analytically. Both unknown damage indices and unknown input force can be identified by minimizing the discrepancy between the measured and calculated vibration data. Numerical studies on a two-dimensional truss and seven-floor frame and experimental studies on a steel frame structure are presented to verify the accuracy and efficiency of the proposed method. Results demonstrate that the damage severity, location, and unknown input force can be identified. Also, the measurement at the force location is not required. Furthermore, when 20% measurement noise is considered, the identified error is less than 5%.

关键词： condition assessment output-only stochastic gradient descent method structural health monitoring inverse problem

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Machine learning for computation of droop controller coefficients to improve the frequency nadir and ROCOF of a stand-alone microgrid

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International Journal of Information Technology (Singapore) 2025年第1期17卷 367-378页

作者： Nair, Swathy Manickavasagam, K. Rao, S. Nagaraja Faculty of Engineering & amp Technology Department of Electrical Engineering M S Ramaiah University of Applied Sciences Bangalore India Department of Electrical and Electronics Engineering Education National Institute of Technical Teachers’ Training and Research Bhopal India

Load Frequency Control (LFC) is vital to keep up the nominal frequency in power systems. LFC initiates control actions to bring back the grid frequency to the desired level when it varies from the nominal value. Addition or removal of load causes deviation in frequency of the power system. This is taken care by inertia present in conventional generators. Inverter based renewable power systems accommodated with Distributed Generators (DGs) have less inertia when compared to conventional synchronous generator based power system. Less inertia in DGs have to be handled by inverter controllers to minimize the frequency deviation. Designing of droop controller for DGs necessitates the determination of proper coefficients for the controller. This research discusses a machine learning methodology that use the stochastic gradient descent (SGD) algorithm to compute the droop coefficients. The controller designed using these coefficients is incorporated to ameliorate the system voltage and frequency profile. The droop coefficients computed using SGD are implemented in the controller and tested in a stand-alone microgrid system powered by solar photovoltaic panel. The droop coefficients assumed as + 0.05 in the conventional controller are replaced with the coefficients determined using the proposed machine learning techniques. The results shows that the Rate of Change of Frequency (RoCoF) and frequency nadir of the system has been improved when compared with conventional droop controller. © Bharati Vidyapeeth's Institute of Computer Applications and Management 2024.

关键词： Droop controller Frequency nadir Machine learning RoCoF Stand-alone microgrid stochastic gradient descent method

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Learning-Based Opportunistic Spectrum Access with Adaptive Hopping Transmission Strategy

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2012年第11期11卷 3957-3967页

作者： Derakhshani, Mahsa Tho Le-Ngoc McGill Univ Dept Elect & Comp Engn Montreal PQ H3A 0E9 Canada

This paper presents an adaptive hopping transmission strategy for secondary users (SUs) to access temporarily idle frequency-slots of a licensed frequency band in consideration of the random return of primary users (PUs), aiming to maximize the overall SU throughput. A SU dynamically hops over multiple idle frequency-slots, each with an adaptive activity factor to avoid high-risk data loss due to possible PU return. SU activity factor optimization problems are formulated to develop the optimal opportunistic spectrum access (OSA) algorithms for SUs based on the Lagrange dual decomposition method. Subsequently, a fully distributed learning-based OSA algorithm is developed in which each SU independently adapts its activity factors to the optimal values over time by learning other SUs' behavior from locally available information. The convergence and convergence rate that characterize its asymptotic behavior and efficiency are analyzed. It is shown that the proposed learning-based OSA algorithm converges with probability of 1 to the optimal solution. Illustrative results confirm its effectiveness and performance gain as compared to existing OSA schemes.

关键词： Opportunistic spectrum access hopping transmission dual optimization learning-based algorithm stochastic gradient descent method

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Space-time blind equalisation in impulsive noise

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IET SIGNAL PROCESSING 2009年第6期3卷 445-458页

作者： Li, S. Qiu, T. Sh. Zhang, Sh. F. Dalian Univ Technol Sch Elect & Informat Engn Dalian 116026 Peoples R China Dalian Univ Technol Coll Informat Engn Dalian 116024 Peoples R China

The presence of non-Gaussian impulsive noise in wireless system can degrade the performance of existing equalisers and signal detectors. The problem of blind source separation and equalisation for multiple-input/multiple-output (MIMO) channels under heavy-tailed impulsive noise environment is studied. A generalised multi-user constant modulus (CM) cost function is proposed by employing the fractional lower order CM property of the equaliser input signals as well as the fractional lower order cross-correlations between them. The associated adaptive blind equalisation algorithm based on a stochastic gradient descent method is defined as fractional lower order multi-user constant modulus algorithm (FMU_CMA), which is able to mitigate impulsive channel noise while recovering all input signals simultaneously. The steady-state mean-square error (MSE) performance of the FMU_CMA is studied in a noise-free environment;the approximate expression is derived based on the energy-preserving relation and the Taylor series expansion. Simulation studies are undertaken to support the analysis with CM and non-CM signal.

关键词： Electromagnetic compatibility and interference impulse noise energy-preserving relation signal detection signal detectors blind equalisers stochastic processes Other topics in statistics wireless channels MIMO channel wireless system Signal detection gradient methods fractional lower order cross-correlation stochastic gradient descent method steady-state mean-square error performance multiple-input multiple-output channel mean square error methods generalised multiuser constant modulus cost function impulsive channel noise mitigation space-time blind equalisation nonGaussian impulsive noise Interpolation and function approximation (numerical analysis) Radio links and equipment Communication channel equalisation and identification Taylor series expansion radio networks blind source separation MIMO communication interference suppression

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Adaptive identification of non-Gaussian/non-stationary glint noise

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 1999年第12期E82A卷 2783-2792页

作者： Wu, WR Wu, KG Natl Chiao Tung Univ Dept Commun Engn Hsinchu Taiwan Natl Chiao Tung Univ Dept Comp Sci & Informat Engn Hsinchu 30050 Taiwan

Non-stationary glint noise is often observed in a radar tracking system. The distribution of glint noise is non-Gaussian anti heavy-tailed. Conventional recursive identification algorithms use the stochastic approximation (SA) method. However, the SP, method converges slowly and is invalid for nonstationary noise. This paper proposes an adaptive algorithm, which uses the stochastic gradient descent (SGD) method, to overcome th(:se problems. The SGD method retains the simple structure of the SA method and is suitable for real-world implementation. Convergence behavior of the SGD method is analyzed and closed-form expressions for sufficient step size bounds are derived. Since noise data are usually not available in practice, we then propose a noise extraction scheme. Combining the SGD method, we I:an perform on-line adaptive noise identification directly from radar measurements. Simulation results show that the performance of the SGD method is comparable to that of the maximum-likelihood (ML) method. Also, the noise extraction scheme is effective that the identification results from the radar measurements are close to those from pure glint noise data.

关键词： non-Gaussian noise non-stationary noise glint noise Gaussian mixture Gaussian and Laplacian mixture target tracking stochastic gradient descent method

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Artificial Intelligence Neural Network Approach to Self Tuning of a Discrete-Time PID Control System 9

Artificial Intelligence Neural Network Approach to Self Tuni...

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9th International Conference on Systems and Control (ICSC)

作者： Pal, Amit Kumar Nestorovic, Tamara Ruhr Univ Bochum Res Grp Mech Adapt Syst MAS Bochum Germany

ISBN: (纸本)9781665407823

Due to their efficiency in standard control problems, proportional-integral-derivative (PID) controllers are widely used in industrial control systems. Although this controller has been established as a control standard, tuning of its parameters and finding their optimal combination still represents a challenge, particularly under changing operating conditions, where control designer cannot rely on the invariance of the plant model. Tuning of the proportional, integral and derivative gain of a PID controller represents an optimization task, for which we propose in this work a solution based on artificial intelligence (AI) approach using radial basis (RB) function for activation of neural networks (NN) which adapt the controller gains and learn the plant model in order to account for the controller influence on the control outcome. The controller is implemented in a discrete-time system which enables real-time learning and implementation. The effectiveness of the proposed controller is tested on a benchmark example of a discrete-time model of a cantilever beam, obtained through the subspace model identification.

关键词： radial basis function based neural networks discrete-time self tuning PID controller stochastic gradient descent method

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Fractional gradient descent method for Spiking Neural Networks 2

Fractional Gradient Descent Method for Spiking Neural Networ...

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2nd Conference on Fully Actuated System Theory and Applications (CFASTA)

作者： Yang, Honggang Chen, Jiejie Jiang, Ping Xu, Mengfei Zhao, Haiming Hubei Normal Univ Coll Comp & Informat Engn Huangshi 435000 Peoples R China Hubei PolyTech Univ Sch Comp Huangshi 435000 Peoples R China

ISBN: (纸本)9798350332162

A fractional-order gradient descent method applicable to spiking neural networks(SNNs) is proposed for the problem of difficulty in training SNNs using stochastic gradient descent method. The method is an improvement of the location of the gradient backpropagation calculation in the training of SNNs and the output form of the last layer in the structure, respectively, and the convergence is proved using the fractional-order difference expression under the Griinwald-Letnikov definition. The test results on both pure SNN and CNN2SNN models simultaneously show that the method can effectively reduce the number of sample cycle inputs and thus the training time without reducing the accuracy.

关键词： Spiking Neural Networks stochastic gradient descent method Fractional Order Difference

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Laguerre Polynomials and gradient descent Approach for Linear Quadratic Optimal Control 7

Laguerre Polynomials and Gradient Descent Approach for Linea...

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7th International Conference on Electrical and Electronics Engineering (ICEEE)

作者： Jaber, Halah Frye, Michael Univ Incarnate Word Autonomous Vehicle Syst Lab Dept Engn San Antonio TX 78209 USA

ISBN: (纸本)9781728167886

This paper presents a computational approach for solving linear time invariant quadratic optimal control system problem. The proposed approach is classified as a direct method, which is utilized by applying state and control parametrization using a finite length of Laguerre polynomials as a basis function with unknown parameters. In addition, the stochastic gradient descent approach was used to estimate the optimal parameters. Furthermore, this paper provides numerical examples to demonstrate the proficiency of the proposed method. The results of this study showed that using the direct method along with the stochastic gradient descent techniques were effective in solving the linear time invariant quadratic optimal control system problem.

关键词： Laguerre polynomials control parametrization stochastic gradient descent method optimal control

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