ABIDE: A Novel Scheme for Ultrasonic Echo Estimation by Combining CEEMD-SSWT Method with EM Algorithm

Ultrasonic echo estimation has played an important role in industrial non-destructive testing and analysis. The ability to estimate parameters in the ultrasonic echo model is crucial to ensure the effectiveness of practical ultrasonic testing applications. In this paper, a scheme called ABIDE for identifying both multiple noises in the echo signal and the distribution of the denoised signal is proposed for ultrasonic echo signal parameter estimation. ABIDE integrates complementary ensemble empirical mode decomposition and the synchrosqueezed wavelet transform (CEEMD-SSWT) as well as the expectation maximization (EM) algorithm. The echo signal is split into a series of IMF components and a residual with the help of CEEMD, and then these IMFs are classified into the noise-dominant part and signal-dominant part by analyzing the correlation of each IMF and the echo signal using grey relational analysis. Considering the effect of noise in the signal-dominant part, SSWT is adopted to remove the noise in the signal-dominant part. Lastly, the signal output by the SSWT algorithm is used for reconstructing a denoised signal combined with the residual from CEEMD. Considering the distribution characteristic of the denoised signal, the EM algorithm is used to estimate parameters in the ultrasonic echo model. The relative performance of the proposed scheme was evaluated on synthetic data and real-world data and then compared with the state-of-the-art methods. Simulation results on synthetic data show that ABIDE outperforms the state-of-the-art methods in parameter estimation. Physical results on real-world data show that the proposed scheme has a greater PCC value in estimating echo model parameters. This paper also shows that ABIDE requires less convergence time than competitive methods.