Recovering the low-rank structure of data matrix from sparse errors arises in the principal component pursuit （PCP）. This paper exploits the higher-order generalization of matrix recovery, named higher-order princip...Recovering the low-rank structure of data matrix from sparse errors arises in the principal component pursuit （PCP）. This paper exploits the higher-order generalization of matrix recovery, named higher-order principal component pursuit （HOPCP）, since it is critical in multi-way data analysis. Unlike the convexification （nuclear norm） for matrix rank function, the tensorial nuclear norm is stil an open problem. While existing preliminary works on the tensor completion field provide a viable way to indicate the low complexity estimate of tensor, therefore, the paper focuses on the low multi-linear rank tensor and adopt its convex relaxation to formulate the convex optimization model of HOPCP. The paper further propose two algorithms for HOPCP based on alternative minimization scheme： the augmented Lagrangian alternating direction method （ALADM） and its truncated higher-order singular value decomposition （ALADM-THOSVD） version. The former can obtain a high accuracy solution while the latter is more efficient to handle the computationally intractable problems. Experimental results on both synthetic data and real magnetic resonance imaging data show the applicability of our algorithms in high-dimensional tensor data processing.展开更多
行星齿轮箱广泛应用于低速重载的大型机电设备中,其故障检测尤为重要。当前行星齿轮箱的故障检测主要依靠振动信号分析,然而低转速工况导致的冲击微弱以及故障冲击难以分离等问题,使得行星齿轮箱故障冲击难以发掘。针对上述瓶颈,提出一...行星齿轮箱广泛应用于低速重载的大型机电设备中,其故障检测尤为重要。当前行星齿轮箱的故障检测主要依靠振动信号分析,然而低转速工况导致的冲击微弱以及故障冲击难以分离等问题,使得行星齿轮箱故障冲击难以发掘。针对上述瓶颈,提出一种基于编码器信号的低转速行星齿轮箱故障诊断方法。该方法首先通过内置编码器获取故障信息,避免了冗长的振动传递路径带来的不利影响。在此基础上,建立稀疏低秩分解模型,引入快速主成分追踪算法(fast principal component pursuit,FPCP)进行求解,实现低转速下行星齿轮箱故障冲击的提取。行星齿轮箱故障实验结果表明,该方法不仅能获取输入轴转速为30r/min下的故障信息,而且有效地实现故障冲击的分离。研究工作可为低转速旋转机械的故障诊断提供有效的工具。展开更多
基金supported by the National Natural Science Foundationof China(51275348)
文摘Recovering the low-rank structure of data matrix from sparse errors arises in the principal component pursuit （PCP）. This paper exploits the higher-order generalization of matrix recovery, named higher-order principal component pursuit （HOPCP）, since it is critical in multi-way data analysis. Unlike the convexification （nuclear norm） for matrix rank function, the tensorial nuclear norm is stil an open problem. While existing preliminary works on the tensor completion field provide a viable way to indicate the low complexity estimate of tensor, therefore, the paper focuses on the low multi-linear rank tensor and adopt its convex relaxation to formulate the convex optimization model of HOPCP. The paper further propose two algorithms for HOPCP based on alternative minimization scheme： the augmented Lagrangian alternating direction method （ALADM） and its truncated higher-order singular value decomposition （ALADM-THOSVD） version. The former can obtain a high accuracy solution while the latter is more efficient to handle the computationally intractable problems. Experimental results on both synthetic data and real magnetic resonance imaging data show the applicability of our algorithms in high-dimensional tensor data processing.
文摘行星齿轮箱广泛应用于低速重载的大型机电设备中,其故障检测尤为重要。当前行星齿轮箱的故障检测主要依靠振动信号分析,然而低转速工况导致的冲击微弱以及故障冲击难以分离等问题,使得行星齿轮箱故障冲击难以发掘。针对上述瓶颈,提出一种基于编码器信号的低转速行星齿轮箱故障诊断方法。该方法首先通过内置编码器获取故障信息,避免了冗长的振动传递路径带来的不利影响。在此基础上,建立稀疏低秩分解模型,引入快速主成分追踪算法(fast principal component pursuit,FPCP)进行求解,实现低转速下行星齿轮箱故障冲击的提取。行星齿轮箱故障实验结果表明,该方法不仅能获取输入轴转速为30r/min下的故障信息,而且有效地实现故障冲击的分离。研究工作可为低转速旋转机械的故障诊断提供有效的工具。
