基于变分贝叶斯平行因子分解的缺失信号的恢复

现有的工程信号处理方法都是基于完整的数据采集，并没有考虑缺失信号的处理。而在工程实际中，由于人为因素和自然界不可抗拒的因素，有时会造成传感器失效，从而造成信号采集的缺失。为了消除信号缺失对工程信号处理的消极影响，提出了一种基于变分贝叶斯平行因子分解的信号恢复方法。首先利用平行因子分析理论将采集的振动信号构造成三维张量，同时结合贝叶斯方法，引入潜在变量和超参数，建立贝叶斯平行因子概率图模型；其次采用变分贝叶斯算法推导出因子矩阵和超参数的后验分布，从而进一步推断出缺失元素的分布预测；最后通过分析该模型的下界，初始化参数的选择，使该算法更好的解决信号缺失问题。利用均方根误差和相对平方根误差对该算法的性能进行评估，仿真和实验结果表明，随着缺失比例的增大，变分贝叶斯平行因子分解算法相较于传统的低秩张量补全算法，误差更小，能够更加有效的恢复缺失的信号，有效地解决了工程信号处理中因传感器失效而引起的信号缺失的问题。

Restoration of missing signals based on the variational Bayesian parallel factorization

The existing engineering signal processing methods are based on complete data acquisition, which do not consider the missing signal processing. However, in engineering practice, due to human factors and natural irresistible factors, the sensor may fail and result the lack of signal acquisition. To eliminate the negative influence of signal loss on engineering signal processing, a signal recovery method based on the variational Bayesian parallel factorization is proposed. Firstly, the collected vibration signal is constructed into a three-dimensional tensor by the parallel factor analysis theory. Meanwhile, combined with the Bayesian method, potential variables and super parameters are introduced to formulate Bayesian parallel factor probability graph model. Then, the posterior distribution of the factor matrix and the super parameters are derived by the variational Bayes algorithm. Therefore, the distribution prediction of the missing element can be further deduced. Finally, the proposed algorithm can better solve the problem of signal loss by analyzing the lower bound of the model and the selection of initialization parameters. Two evaluation indexes ( i. e. root mean square error and root relative squared error) are used to evaluate the performance of the algorithm. The simulation and experiment results show that with the increase of missing ratio, the variational Bayesian parallel factorization algorithm has smaller error than the traditional low rank tensor completion algorithm, which can more effectively restore the missing signal. The proposed method provides an effective way to solve the problem of signal missing caused by sensor failure in engineering signal processing.