In practice,simultaneous impact localization and time history reconstruction can hardly be achieved,due to the illposed and under-determined problems induced by the constrained and harsh measuring conditions.Although ...In practice,simultaneous impact localization and time history reconstruction can hardly be achieved,due to the illposed and under-determined problems induced by the constrained and harsh measuring conditions.Although l_(1) regularization can be used to obtain sparse solutions,it tends to underestimate solution amplitudes as a biased estimator.To address this issue,a novel impact force identification method with l_(p) regularization is proposed in this paper,using the alternating direction method of multipliers(ADMM).By decomposing the complex primal problem into sub-problems solvable in parallel via proximal operators,ADMM can address the challenge effectively.To mitigate the sensitivity to regularization parameters,an adaptive regularization parameter is derived based on the K-sparsity strategy.Then,an ADMM-based sparse regularization method is developed,which is capable of handling l_(p) regularization with arbitrary p values using adaptively-updated parameters.The effectiveness and performance of the proposed method are validated on an aircraft skin-like composite structure.Additionally,an investigation into the optimal p value for achieving high-accuracy solutions via l_(p) regularization is conducted.It turns out that l_(0.6)regularization consistently yields sparser and more accurate solutions for impact force identification compared to the classic l_(1) regularization method.The impact force identification method proposed in this paper can simultaneously reconstruct impact time history with high accuracy and accurately localize the impact using an under-determined sensor configuration.展开更多
Symmetric alternating directionmethod of multipliers(ADMM)is an efficient method for solving a class of separable convex optimization problems.This method updates the Lagrange multiplier twice with appropriate step si...Symmetric alternating directionmethod of multipliers(ADMM)is an efficient method for solving a class of separable convex optimization problems.This method updates the Lagrange multiplier twice with appropriate step sizes at each iteration.However,such step sizes were conservatively shrunk to guarantee the convergence in recent studies.In this paper,we are devoted to seeking larger step sizes whenever possible.The logarithmic-quadratic proximal(LQP)terms are applied to regularize the symmetric ADMM subproblems,allowing the constrained subproblems to then be converted to easier unconstrained ones.Theoretically,we prove the global convergence of such LQP-based symmetric ADMM by specifying a larger step size domain.Moreover,the numerical results on a traffic equilibrium problem are reported to demonstrate the advantage of the method with larger step sizes.展开更多
Linearly constrained separable convex minimization problems have been raised widely in many real-world applications.In this paper,we propose a homotopy-based alternating direction method of multipliers for solving thi...Linearly constrained separable convex minimization problems have been raised widely in many real-world applications.In this paper,we propose a homotopy-based alternating direction method of multipliers for solving this kind of problems.The proposed method owns some advantages of the classical proximal alternating direction method of multipliers and homotopy method.Under some suitable condi-tions,we prove global convergence and the worst-case O(k/1)convergence rate in a nonergodic sense.Preliminary numerical results indicate effectiveness and efficiency of the proposed method compared with some state-of-the-art methods.展开更多
In this paper,we propose a new stopping criterion for Eckstein and Bertsekas’s generalized alternating direction method of multipliers.The stopping criterion is easy to verify,and the computational cost is much less ...In this paper,we propose a new stopping criterion for Eckstein and Bertsekas’s generalized alternating direction method of multipliers.The stopping criterion is easy to verify,and the computational cost is much less than the classical stopping criterion in the highly influential paper by Boyd et al.(Found Trends Mach Learn 3(1):1–122,2011).展开更多
针对工业机械设备实时监测中不可控因素导致的振动信号数据缺失问题,提出一种基于自适应二次临近项交替方向乘子算法(adaptive quadratic proximity-alternating direction method of multipliers, AQ-ADMM)的压缩感知缺失信号重构方法...针对工业机械设备实时监测中不可控因素导致的振动信号数据缺失问题,提出一种基于自适应二次临近项交替方向乘子算法(adaptive quadratic proximity-alternating direction method of multipliers, AQ-ADMM)的压缩感知缺失信号重构方法。AQ-ADMM算法在经典交替方向乘子算法算法迭代过程中添加二次临近项,且能够自适应选取惩罚参数。首先在数据中心建立信号参考数据库用于构造初始字典,然后将K-奇异值分解(K-singular value decomposition, K-SVD)字典学习算法和AQ-ADMM算法结合重构缺失信号。对仿真信号和两种真实轴承信号数据集添加高斯白噪声后作为样本,试验结果表明当信号压缩率在50%~70%时,所提方法性能指标明显优于其它传统方法,在重构信号的同时实现了对含缺失数据机械振动信号的快速精确修复。展开更多
In this paper,we design an efficient,multi-stage image segmentation framework that incorporates a weighted difference of anisotropic and isotropic total variation(AITV).The segmentation framework generally consists of...In this paper,we design an efficient,multi-stage image segmentation framework that incorporates a weighted difference of anisotropic and isotropic total variation(AITV).The segmentation framework generally consists of two stages:smoothing and thresholding,thus referred to as smoothing-and-thresholding(SaT).In the first stage,a smoothed image is obtained by an AITV-regularized Mumford-Shah(MS)model,which can be solved efficiently by the alternating direction method of multipliers(ADMMs)with a closed-form solution of a proximal operator of the l_(1)-αl_(2) regularizer.The convergence of the ADMM algorithm is analyzed.In the second stage,we threshold the smoothed image by K-means clustering to obtain the final segmentation result.Numerical experiments demonstrate that the proposed segmentation framework is versatile for both grayscale and color images,effcient in producing high-quality segmentation results within a few seconds,and robust to input images that are corrupted with noise,blur,or both.We compare the AITV method with its original convex TV and nonconvex TVP(O<p<1)counterparts,showcasing the qualitative and quantitative advantages of our proposed method.展开更多
稀疏约束下的合成孔径雷达(SyntheticApertureRadar,SAR)成像技术,通过对稀疏先验建模的稀疏特征进行增强,能有效获取目标特显点的有用信息,但无法对目标的结构特征进行恢复,且对不可避免的非系统误差十分敏感。为此,提出一种依靠交替...稀疏约束下的合成孔径雷达(SyntheticApertureRadar,SAR)成像技术,通过对稀疏先验建模的稀疏特征进行增强,能有效获取目标特显点的有用信息,但无法对目标的结构特征进行恢复,且对不可避免的非系统误差十分敏感。为此,提出一种依靠交替方向多乘子法(Alternating Direction Method of Multipliers,ADMM)面向结构特征增强的稀疏恢复高分辨SAR成像(Structure-feature Enhancement-ADMM,SE-ADMM)算法。该算法引入全变分(Total Variation,TV)正则项建模结构特征,起到增强结构的作用;引入ℓ1范数建模稀疏特征,起到压制噪声作用;引入最小熵范数建模聚焦特征,以保证算法对非系统乘性误差的不敏感性。在ADMM多特征优化框架下,利用“局部-全局”的运算机制,首先分别进行三个特征的邻近算子推导,以获得对应特征解析解,再进行目标全局优化保证特征解之间的协调平衡,以实现目标的多特征增强。另外,ADMM多特征优化框架下变量分裂和多正则项的引入,保证了算法的效率和稳健性。实验部分先后选取SAR仿真数据与实测数据来验证算法的有效性,通过相变热力图定量分析所提算法的恢复性能,进而验证了所提SE-ADMM算法的稳健性与优越性。展开更多
提出面向合成孔径雷达(Synthetic Aperture Radar,SAR)回波数据的复杂结构特征增强算法(Complex Structure Feature Enhancement Algorithm,CEA),面向SAR成像目标的复杂结构特征,算法利用高阶方向全变分(High-order Total Direction Var...提出面向合成孔径雷达(Synthetic Aperture Radar,SAR)回波数据的复杂结构特征增强算法(Complex Structure Feature Enhancement Algorithm,CEA),面向SAR成像目标的复杂结构特征,算法利用高阶方向全变分(High-order Total Direction Variation,HOTDV)正则算子表示,面向SAR成像目标的稀疏特征,算法用ℓ_(1)正则算子表示。算法利用交替方向多乘子法(Alternating Direction Method of Multipliers,ADMM)建立多正则约束优化框架,设计复杂结构分裂变量和稀疏分裂变量,并求出分裂变量解析更新解以实现SAR成像目标的复杂结构特征与稀疏特征的增强。多正则约束优化框架中的对偶分解保证多特征多任务处理能力,增广拉格朗日项的使用则保证了算法的收敛性和稳健性。最后,设计了仿真和实测SAR数据特征增强实验以验证算法的有效性,对比多种传统结构特征增强算法以验证所提复杂结构特征增强算法的优越性。展开更多
针对传统稀疏特征增强的方式仅能完成对目标场景中特显点的增强,对复杂的目标结构特征无能为力的问题,考虑目标细节特征的复杂性,提出方向性结构全变分(directional total structure variation, DTSV)正则子进行结构先验表征,实现对成...针对传统稀疏特征增强的方式仅能完成对目标场景中特显点的增强,对复杂的目标结构特征无能为力的问题,考虑目标细节特征的复杂性,提出方向性结构全变分(directional total structure variation, DTSV)正则子进行结构先验表征,实现对成像目标复杂结构特征任意梯度变化的拟合,进而实现对结构特征的高精度正则优化处理。首先,在交替方向多乘子方法(alternating direction method of multipliers, ADMM)的协同优化框架下实现DTSV正则优化求解(DTSV-ADMM),利用该框架提供的对偶上升思想可有效提升迭代优化算法的收敛性能。其次,基于ADMM框架提供的多变量"分解-调和"机理,通过建立分裂变量组可以实现多个正则项的协同优化增强。然后,进一步引入?;范数对成像目标稀疏特征进行表征,并在协同优化框架下实现对方向性结构特征和稀疏特征的稳健计算,有效减小多特征优化存在的"误差传播"问题。最后,通过近端算子对特征进行解析计算,获得对应特征的闭合解析解,进一步提升算法运算稳健性和计算效率。实验证明了所提算法相比传统方法的优越性。展开更多
基金Supported by National Natural Science Foundation of China (Grant Nos.52305127,52075414)China Postdoctoral Science Foundation (Grant No.2021M702595)。
文摘In practice,simultaneous impact localization and time history reconstruction can hardly be achieved,due to the illposed and under-determined problems induced by the constrained and harsh measuring conditions.Although l_(1) regularization can be used to obtain sparse solutions,it tends to underestimate solution amplitudes as a biased estimator.To address this issue,a novel impact force identification method with l_(p) regularization is proposed in this paper,using the alternating direction method of multipliers(ADMM).By decomposing the complex primal problem into sub-problems solvable in parallel via proximal operators,ADMM can address the challenge effectively.To mitigate the sensitivity to regularization parameters,an adaptive regularization parameter is derived based on the K-sparsity strategy.Then,an ADMM-based sparse regularization method is developed,which is capable of handling l_(p) regularization with arbitrary p values using adaptively-updated parameters.The effectiveness and performance of the proposed method are validated on an aircraft skin-like composite structure.Additionally,an investigation into the optimal p value for achieving high-accuracy solutions via l_(p) regularization is conducted.It turns out that l_(0.6)regularization consistently yields sparser and more accurate solutions for impact force identification compared to the classic l_(1) regularization method.The impact force identification method proposed in this paper can simultaneously reconstruct impact time history with high accuracy and accurately localize the impact using an under-determined sensor configuration.
基金This research was supported by National Natural Science Foundation of China Grant 11771078Natural Science Foundation of Jiangsu Province Grant BK20181258+1 种基金Project of 333 of Jiangsu Province Grant BRA2018351Postgraduate Research&Practice Innovation Program of Jiangsu Province Grant KYCX18_0200.
文摘Symmetric alternating directionmethod of multipliers(ADMM)is an efficient method for solving a class of separable convex optimization problems.This method updates the Lagrange multiplier twice with appropriate step sizes at each iteration.However,such step sizes were conservatively shrunk to guarantee the convergence in recent studies.In this paper,we are devoted to seeking larger step sizes whenever possible.The logarithmic-quadratic proximal(LQP)terms are applied to regularize the symmetric ADMM subproblems,allowing the constrained subproblems to then be converted to easier unconstrained ones.Theoretically,we prove the global convergence of such LQP-based symmetric ADMM by specifying a larger step size domain.Moreover,the numerical results on a traffic equilibrium problem are reported to demonstrate the advantage of the method with larger step sizes.
基金the National Natural Science Foundation of China(Nos.11571074 and 61672005)the Natural Science Foundation of Fujian Province(No.2015J01010).
文摘Linearly constrained separable convex minimization problems have been raised widely in many real-world applications.In this paper,we propose a homotopy-based alternating direction method of multipliers for solving this kind of problems.The proposed method owns some advantages of the classical proximal alternating direction method of multipliers and homotopy method.Under some suitable condi-tions,we prove global convergence and the worst-case O(k/1)convergence rate in a nonergodic sense.Preliminary numerical results indicate effectiveness and efficiency of the proposed method compared with some state-of-the-art methods.
文摘In this paper,we propose a new stopping criterion for Eckstein and Bertsekas’s generalized alternating direction method of multipliers.The stopping criterion is easy to verify,and the computational cost is much less than the classical stopping criterion in the highly influential paper by Boyd et al.(Found Trends Mach Learn 3(1):1–122,2011).
文摘针对工业机械设备实时监测中不可控因素导致的振动信号数据缺失问题,提出一种基于自适应二次临近项交替方向乘子算法(adaptive quadratic proximity-alternating direction method of multipliers, AQ-ADMM)的压缩感知缺失信号重构方法。AQ-ADMM算法在经典交替方向乘子算法算法迭代过程中添加二次临近项,且能够自适应选取惩罚参数。首先在数据中心建立信号参考数据库用于构造初始字典,然后将K-奇异值分解(K-singular value decomposition, K-SVD)字典学习算法和AQ-ADMM算法结合重构缺失信号。对仿真信号和两种真实轴承信号数据集添加高斯白噪声后作为样本,试验结果表明当信号压缩率在50%~70%时,所提方法性能指标明显优于其它传统方法,在重构信号的同时实现了对含缺失数据机械振动信号的快速精确修复。
基金partially supported by the NSF grants DMS-1854434,DMS-1952644,DMS-2151235,DMS-2219904,and CAREER 1846690。
文摘In this paper,we design an efficient,multi-stage image segmentation framework that incorporates a weighted difference of anisotropic and isotropic total variation(AITV).The segmentation framework generally consists of two stages:smoothing and thresholding,thus referred to as smoothing-and-thresholding(SaT).In the first stage,a smoothed image is obtained by an AITV-regularized Mumford-Shah(MS)model,which can be solved efficiently by the alternating direction method of multipliers(ADMMs)with a closed-form solution of a proximal operator of the l_(1)-αl_(2) regularizer.The convergence of the ADMM algorithm is analyzed.In the second stage,we threshold the smoothed image by K-means clustering to obtain the final segmentation result.Numerical experiments demonstrate that the proposed segmentation framework is versatile for both grayscale and color images,effcient in producing high-quality segmentation results within a few seconds,and robust to input images that are corrupted with noise,blur,or both.We compare the AITV method with its original convex TV and nonconvex TVP(O<p<1)counterparts,showcasing the qualitative and quantitative advantages of our proposed method.
文摘稀疏约束下的合成孔径雷达(SyntheticApertureRadar,SAR)成像技术,通过对稀疏先验建模的稀疏特征进行增强,能有效获取目标特显点的有用信息,但无法对目标的结构特征进行恢复,且对不可避免的非系统误差十分敏感。为此,提出一种依靠交替方向多乘子法(Alternating Direction Method of Multipliers,ADMM)面向结构特征增强的稀疏恢复高分辨SAR成像(Structure-feature Enhancement-ADMM,SE-ADMM)算法。该算法引入全变分(Total Variation,TV)正则项建模结构特征,起到增强结构的作用;引入ℓ1范数建模稀疏特征,起到压制噪声作用;引入最小熵范数建模聚焦特征,以保证算法对非系统乘性误差的不敏感性。在ADMM多特征优化框架下,利用“局部-全局”的运算机制,首先分别进行三个特征的邻近算子推导,以获得对应特征解析解,再进行目标全局优化保证特征解之间的协调平衡,以实现目标的多特征增强。另外,ADMM多特征优化框架下变量分裂和多正则项的引入,保证了算法的效率和稳健性。实验部分先后选取SAR仿真数据与实测数据来验证算法的有效性,通过相变热力图定量分析所提算法的恢复性能,进而验证了所提SE-ADMM算法的稳健性与优越性。
文摘提出面向合成孔径雷达(Synthetic Aperture Radar,SAR)回波数据的复杂结构特征增强算法(Complex Structure Feature Enhancement Algorithm,CEA),面向SAR成像目标的复杂结构特征,算法利用高阶方向全变分(High-order Total Direction Variation,HOTDV)正则算子表示,面向SAR成像目标的稀疏特征,算法用ℓ_(1)正则算子表示。算法利用交替方向多乘子法(Alternating Direction Method of Multipliers,ADMM)建立多正则约束优化框架,设计复杂结构分裂变量和稀疏分裂变量,并求出分裂变量解析更新解以实现SAR成像目标的复杂结构特征与稀疏特征的增强。多正则约束优化框架中的对偶分解保证多特征多任务处理能力,增广拉格朗日项的使用则保证了算法的收敛性和稳健性。最后,设计了仿真和实测SAR数据特征增强实验以验证算法的有效性,对比多种传统结构特征增强算法以验证所提复杂结构特征增强算法的优越性。
文摘针对传统稀疏特征增强的方式仅能完成对目标场景中特显点的增强,对复杂的目标结构特征无能为力的问题,考虑目标细节特征的复杂性,提出方向性结构全变分(directional total structure variation, DTSV)正则子进行结构先验表征,实现对成像目标复杂结构特征任意梯度变化的拟合,进而实现对结构特征的高精度正则优化处理。首先,在交替方向多乘子方法(alternating direction method of multipliers, ADMM)的协同优化框架下实现DTSV正则优化求解(DTSV-ADMM),利用该框架提供的对偶上升思想可有效提升迭代优化算法的收敛性能。其次,基于ADMM框架提供的多变量"分解-调和"机理,通过建立分裂变量组可以实现多个正则项的协同优化增强。然后,进一步引入?;范数对成像目标稀疏特征进行表征,并在协同优化框架下实现对方向性结构特征和稀疏特征的稳健计算,有效减小多特征优化存在的"误差传播"问题。最后,通过近端算子对特征进行解析计算,获得对应特征的闭合解析解,进一步提升算法运算稳健性和计算效率。实验证明了所提算法相比传统方法的优越性。
