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L唱M算法 1

人工神经网络 1

优化算法 1

短期负荷预测 1

结构化稀疏学习；算法；应用 1

贝叶斯正则化算法 1

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Adaptive simulation of wave propagation problems including dislocation sources and random media

Hassan YOUSEFI, Jamshid FARJOODI, Iradj MAHMOUDZADEH KANI

《结构与土木工程前沿（英文）》 2019年第13卷第5期页码 1054-1081 doi: 10.1007/s11709-019-0536-4

摘要： An adaptive Tikhonov regularization is integrated with an h-adaptive grid-based scheme for simulation of elastodynamic problems, involving seismic sources with discontinuous solutions and random media. The Tikhonov method is adapted by a newly-proposed detector based on the MINMOD limiters and the grids are adapted by the multiresolution analysis (MRA) via interpolation wavelets. Hence, both small and large magnitude physical waves are preserved by the adaptive estimations on non-uniform grids. Due to developing of non-dissipative spurious oscillations, numerical stability is guaranteed by the Tikhonov regularization acting as a post-processor on irregular grids. To preserve waves of small magnitudes, an adaptive regularization is utilized: using of smaller amount of smoothing for small magnitude waves. This adaptive smoothing guarantees also solution stability without over smoothing phenomenon in stochastic media. Proper distinguishing between noise and small physical waves are challenging due to existence of spurious oscillations in numerical simulations. This identification is performed in this study by the MINMOD limiter based algorithm. Finally, efficiency of the proposed concept is verified by: 1) three benchmarks of one-dimensional (1-D) wave propagation problems; 2) P-SV point sources and rupturing line-source including a bounded fault zone with stochastic material properties.

关键词： adaptive wavelet adaptive smoothing discontinuous solutions stochastic media spurious oscillations Tikhonov regularization minmod limiter

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A regularization scheme for explicit level-set XFEM topology optimization

Markus J. GEISS, Jorge L. BARRERA, Narasimha BODDETI, Kurt MAUTE

《机械工程前沿（英文）》 2019年第14卷第2期页码 153-170 doi: 10.1007/s11465-019-0533-2

摘要： Regularization of the level-set (LS) field is a critical part of LS-based topology optimization (TO) approaches. Traditionally this is achieved by advancing the LS field through the solution of a Hamilton-Jacobi equation combined with a reinitialization scheme. This approach, however, may limit the maximum step size and introduces discontinuities in the design process. Alternatively, energy functionals and intermediate LS value penalizations have been proposed. This paper introduces a novel LS regularization approach based on a signed distance field (SDF) which is applicable to explicit LS-based TO. The SDF is obtained using the heat method (HM) and is reconstructed for every design in the optimization process. The governing equations of the HM, as well as the ones describing the physical response of the system of interest, are discretized by the extended finite element method (XFEM). Numerical examples for problems modeled by linear elasticity, nonlinear hyperelasticity and the incompressible Navier-Stokes equations in two and three dimensions are presented to show the applicability of the proposed scheme to a broad range of design optimization problems.

关键词： level-set regularization explicit level-sets XFEM CutFEM topology optimization heat method signed distance field nonlinear structural mechanics fluid mechanics

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Non-convex sparse optimization-based impact force identification with limited vibration measurements

《机械工程前沿（英文）》 2023年第18卷第3期 doi: 10.1007/s11465-023-0762-2

摘要： Impact force identification is important for structure health monitoring especially in applications involving composite structures. Different from the traditional direct measurement method, the impact force identification technique is more cost effective and feasible because it only requires a few sensors to capture the system response and infer the information about the applied forces. This technique enables the acquisition of impact locations and time histories of forces, aiding in the rapid assessment of potentially damaged areas and the extent of the damage. As a typical inverse problem, impact force reconstruction and localization is a challenging task, which has led to the development of numerous methods aimed at obtaining stable solutions. The classical

ℓ 2

regularization method often struggles to generate sparse solutions. When solving the under-determined problem,

ℓ 2

regularization often identifies false forces in non-loaded regions, interfering with the accurate identification of the true impact locations. The popular

ℓ 1

sparse regularization, while promoting sparsity, underestimates the amplitude of impact forces, resulting in biased estimations. To alleviate such limitations, a novel non-convex sparse regularization method that uses the non-convex

ℓ 1 − 2

penalty, which is the difference of the

ℓ 1

and

ℓ 2

norms, as a regularizer, is proposed in this paper. The principle of alternating direction method of multipliers (ADMM) is introduced to tackle the non-convex model by facilitating the decomposition of the complex original problem into easily solvable subproblems. The proposed method named

ℓ 1 − 2 -ADMM

is applied to solve the impact force identification problem with unknown force locations, which can realize simultaneous impact localization and time history reconstruction with an under-determined, sparse sensor configuration. Simulations and experiments are performed on a composite plate to verify the identification accuracy and robustness with respect to the noise of the

ℓ 1 − 2 -ADMM

method. Results indicate that compared with other existing regularization methods, the

ℓ 1 − 2 -ADMM

method can simultaneously reconstruct and localize impact forces more accurately, facilitating sparser solutions, and yielding more accurate results.

关键词： impact force identification inverse problem sparse regularization under-determined condition alternating direction method of multipliers

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应用神经网络进行短期负荷预测

罗枚

《中国工程科学》 2007年第9卷第5期页码 77-80

摘要：

以某地区购网有功功率的负荷数据为背景，建立了３个BP神经网络负荷预测模型———SDBP，LMBP 及BRBP模型进行短期负荷预测工作，并对其结果进行比较。针对传统的BP算法具有训练速度慢，易陷入局部最小点的缺点，采用具有较快收敛速度及稳定性的L-M（Levenberg-Marquardt）优化算法进行预测，使平均相对误差有了很大改善，而采用贝叶斯正则化算法可以解决网络过度拟合，提高网络的推广能力。

关键词：短期负荷预测人工神经网络 L唱M算法贝叶斯正则化算法优化算法

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结构化稀疏学习综述 Review

Lin-bo QIAO, Bo-feng ZHANG, Jin-shu SU, Xi-cheng LU

《信息与电子工程前沿（英文）》 2017年第18卷第4期页码 445-463 doi: 10.1631/FITEE.1601489

摘要：稀疏学习由于其简约特性和计算优势而获得了越来越多的关注，在具有稀疏性的条件下，许多计算问题可以在实践中得到有效的处理。而结构化稀疏学习则进一步将结构信息进行编码，在多个研究领域取得成功。随着各类型结构的发现，人们相继提出了各种结构化正则函数。这些正则函数通过利用特定的结构信息极大提高了稀疏学习算法的性能。在本文中，我们从想法、形式化、算法和应用等方面系统的回顾了结构化稀疏学习。我们将这些算法置于最小化损失函数和惩罚函数的统一框架中，总结了算法的开源软件实现，并比较了典型优化算法解决结构化稀疏学习问题时的计算复杂度。在实验中，我们给出了无监督学习在结构化信号恢复和层次化图像重建中的应用，以及具有图结构引导的逻辑回归的在监督学习中的应用。

关键词：结构化稀疏学习；算法；应用

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标题作者时间类型操作

Adaptive simulation of wave propagation problems including dislocation sources and random media

Hassan YOUSEFI, Jamshid FARJOODI, Iradj MAHMOUDZADEH KANI

期刊论文

A regularization scheme for explicit level-set XFEM topology optimization

Markus J. GEISS, Jorge L. BARRERA, Narasimha BODDETI, Kurt MAUTE

期刊论文

Non-convex sparse optimization-based impact force identification with limited vibration measurements

期刊论文

应用神经网络进行短期负荷预测