## 3 Test Results and Analysis
### Stress Wave Propagation Characteristics of Bolt Tension Process  
#### 3.2.1 Stress Wave Signal Filtering Based on CEEMD Modal Decomposition Method  
Noise appears in the data recorded from stress wave detection in the test process, so data filtering is needed to process the recorded signal. Commonly used filtering methods are digital filters, wavelet transforms, and modal decomposition methods. After determining the signal bandwidth, digital filters are mainly filtered by setting high pass, low pass, band pass, band reject, etc. Although the design is simple, it does not work well for nonlinear non-smooth signals, and the bandwidth cannot be determined for unknown signals. The wavelet transform method was first proposed to deal with nonlinear non-stationary signals, which has a solid theoretical foundation and can set soft and hard threshold noise elimination. However, detection signals acquired in engineering applications are highly variable, and the choice of soft and hard thresholds for wavelet noise cancellation can have a huge impact on the signal cancellation capability. The modal decomposition method is adaptive and can separate noise and useful signals according to different frequencies by the signal's own characteristics. This signal-processing method does not require manual involvement and also avoids the generation of errors. Complementary ensemble empirical mode decomposition is the commonly used modal decomposition method [28; 29; 30]. The first proposed method is empirical mode decomposition, which decomposes the complex signal into multiple smooth intrinsic mode components Intrinsic Mode Function and a residual term by frequency, and the Intrinsic Mode Functions of different frequencies can reflect the intrinsic characteristics of the original signal to a certain extent. However, the empirical mode decomposition algorithm has limitations and is prone to problems such as the modal confusion phenomenon and endpoint effects. After scholars' continuous research and improvement, the complementary ensemble empirical mode decomposition method is proposed, which uses the addition of opposite white noise to the original signal for auxiliary decomposition, solving the problems of the empirical mode decomposition method, which is more effective for the processing of nonlinear non-smooth signals and widely used. Figure 7 is the flowchart of CEEMD decomposition. Figure 6: Diameter variation curve of bolt necking part. Where \(cj(t)\) denotes the \(j\)-th IMF component finally obtained by CEEMD processing, \(c_{ni}\) denotes the \(j\)-th IMF component in group \(n\) obtained by EMD processing of the signal, \(R_{n}(t)\) denotes the residual term finally obtained by CEEMD processing, and \(r_{i}\) denotes the \(i\)-th residual term in group \(n\) obtained by EMD processing of the signal. Based on complementary ensemble empirical mode decomposition, the process of filtering the original signal is described using the original data when the displacement of mg1 is zero as an example. After exporting the data acquired by the bolt nondestructive tester, the original data were decomposed modally using complementary ensemble empirical mode decomposition programmed by numerical calculation software. Complementary ensemble empirical mode decomposition requires setting parameters such as the proportion of added noise and the number of summed averages. When the total averaging number is fixed, the error increases with the increase of the ratio of added noise; when the ratio of added noise is fixed, the more the total averaging number is and the closer the final result is to the real signal. According to the experimental debugging results, it is finally determined that the ratio of added noise and the number of summed averages are set to 0.01 and 10, respectively, and the decomposition effect is very good at this time.