Constraint Linear Model for Period Estimation and Sparse Feature Extraction Based on Iterative Likelihood Ratio Test

This study proposes a constraint linear model (CLM) to represent periodic signals. Different from the conventional linear model, linear constraints are added to the proposed model to fulfill the continuity constraints of signals. To estimate the period of the signals, a hypothesis testing based on the generalized likelihood ratio is proposed to statistically compare misleading peaks exhibited in the likelihood function of CLM. The misleading peaks usually arise because the likelihood function has a similar value in the true period and its multiples, and this misleading effect obstructs the effectiveness of the conventional maximum likelihood estimation method. An iterative likelihood ratio test (ILRT) is proposed, in which hypothesis testing is iteratively conducted to test the significance of an identified period until no candidate period with significant evidence is found. After the period is estimated by ILRT, an L1 penalty is added to CLM to construct a sparse representation of the signals, and an augmented Lagrangian shrinkage algorithm is applied to extract sparse features from the signals. The effectiveness of the proposed method is verified through a simulation study on synthetic signals and a case study on real vibration signals.