## 1 Introduction
In the screening process, the appropriate envelope interpolation algorithm could be automatically selected from multiple envelope interpolation algorithms by utilizing bandwidth criteria. Compared with the traditional method, the obtained decomposition results could effectively avoid the problem of curve distortion and the endpoint effect. This makes up for the lack of present ITD research and will reference subsequent related research. The proposed method in this paper differs from the literature [22] in its iterative approach in the decomposition process in that the literature [22] excludes irrelevant mode components by correlation coefficients of the mode components with the original signal, while the proposed method in this paper only targets the calculation of the bandwidth of the mode components themselves to determine whether they are irrelevant or not. The correlation coefficient is susceptible to interference under strong background noise compared to the bandwidth, so the bandwidth parameter used in the proposed method is more appropriate than the correlation coefficient. We named it 'improved complete ensemble intrinsic time-scale with adaptive noise' (ICEITDAN). ICEITDAN could be regarded as a new denoising method in this program. It can eliminate the frequency component independent of the fault and highlight the frequency of the fault. In addition, we also need a method to demodulate and analyze the reconstructed signal to reduce the effect of residual noise on fault frequency extraction. In recent years, a number of scholars have introduced mathematical morphology from the field of image processing to the analysis of mechanical vibration signals, providing a new way to process nonlinear and unstable signals [23; 24; 25]. In mathematical morphological calculation, the selection of parameters and types of structural elements is important. If the optimal size parameters of the structural unit cannot be obtained while only employing empirical parameters, the performance of the algorithm will be greatly reduced. To solve the problem of adaptive control with uncertain structure size, inspired by Reference [26] we proposed a demodulation method named composite quantum morphology analysis (CQMA). The signal is demodulated to extract the fault frequency. According to Reference [26], quantum signal processing frameworks could exploit the principles of quantum mechanics, various axioms, and constraints to develop new or modify established signal processing algorithms. Therefore, quantum entanglement theory could optimize the size of structural elements adaptively in morphological analysis. In the case of multiple signals, the local feature conversion of structural element size could be realized. In addition,quantum signal processing theory could improve the calculation efficiency of the adaptive structural unit size. The CQMA proposed in this paper includes two steps: Firstly, the amplitude and frequency modulation components of the reconstructed signal are analyzed by the demodulation method. Secondly, the fault characteristic frequency is obtained by envelope spectrum transformation. Compared with the traditional demodulation wavelet transform [27] and Teager-Kaiser energy operator [28], the proposed method achieves a higher demodulation performance. The results show that the reconstructed signal obtained by CQMA demodulation with the ICEITDAN method has strong practicability. The remainder of this article is organized as follows: The second part introduces the method that is proposed in this article and the original method. The third part evaluates the performance of the ICEITDAN and CQMA (ICEITDAN-CQMA) methods through numerical simulation and experimental signals. Finally, the conclusions of this study are presented in the fourth part.