基于非负Tucker 3分解的稀疏分量分析在故障信号提取中的应用

Sparse component analysis based on nonnegative Tucker 3 decomposition for fault signal extraction

针对初始故障信号不稀疏难于判断的问题,在非负Tucker 3分解(NTD)的基础上,提出了一种基于NTD的稀疏分量分析(SCA)处理二次特征信号的方法.同时,为了克服NTD算法收敛慢、易陷入过拟合等局限性,对分解因子增加了非负约束,并提出了对分解因子一次更新的算法.对比传统的最小交替二乘法,该更新算法能一次性地计算所有分解因子,避免了计算大规模的Jacobian矩阵,从而较大地提高了算法的效率.实验结果表明:NTD和SCA相结合的方法(SCA_NTD)只需迭代约150步可达到收敛,而且在频谱稀疏性处理方面优于NTF等传统的方法;在分解相同维数张量的条件下,SCA_NTD的最高精度达到了97.16%.因此,SCA_NTD不仅能够改善信号特征的稀疏性,而且对提高算法的收敛速度和精度也具有重要的意义.

Aiming at the problem of non-sparseness of original diagnosis signal and being difficult to distinguish,a method of sparse component analysis（SCA） based on nonnegative Tucker 3 decomposition（NTD） is proposed to process the quadratic feature of faults for improving the sparseness.Meanw hile,a new updating algorithm w ith nonnegative constraints is put forw ard to overcome the limitation of slow convergence and data overfitting in NTD.Compared w ith the conventional alternative least squares（ALS）,the updating algorithm can simultaneously compute all the factors in one time that avoids calculating the large-scale Jacobian matrix and therefore improves the efficiency.The experimental results show that the method of combining NTD and SCA（SCA_NTD） only needs 150 steps to achieve convergence w hich is superior to other typical methods like NTF,etc;SCA_NTD also gets the highest accuracy of 97.16% under the same dimension of a tensor.Therefore,SCA_NTD not only improves the sparseness but also is significant to improve the convergence and efficiency.