## 4 Preprocessing of the Measured Data
### EMD Analysis of the Measured Signals  
Empirical mode decomposition (EMD) provides time-frequency analysis by decomposing signals into component modes. Its adaptive and empirical nature also enables  
Figure 5: STFT images of the measured signal for 20 s: (**a**) when the debris is empty. A subject is inside the debris with orientation of: (**b**) \(\phi=0^{\circ}\). (**c**) \(\phi=45^{\circ}\). (**d**) \(\phi=90^{\circ}\). (**e**) \(\phi=180^{\circ}\). (**f**) \(\phi=270^{\circ}\).  
Figure 6: CWT images of the measured signal for 20 s : (**a**) when the debris is empty. A subject is inside the debris with orientation of: (**b**) \(\phi=0^{\circ}\). (**c**) \(\phi=45^{\circ}\). (**d**) \(\phi=90^{\circ}\). (**e**) \(\phi=180^{\circ}\). (**f**) \(\phi=270^{\circ}\).  
nonstationary and nonlinear processes to be dealt with. EMD highlights the instantaneous frequencies that express the frequency characteristics of each mode over time. This provides a detailed analysis of the frequency distribution of the signal. It decomposes a signal into a finite set of functions with different frequency components. In other words, the EMD method is based on the principle that any real-valued input signal consists of the sum of simple sub-signals that oscillate differently. Each of these sub-signals is called an intrinsic mode function (IMF), and each of these intrinsic modes represents a simple oscillation with the same number of extrema and zero-crossings [71; 72].  
In EMD analysis, a signal can be decomposed into many IMFs. IMFs with higher frequency and/or lower energy generally represent noise and unwanted signals [73]. Therefore, a high-frequency band component is obtained (IMF1) and subtracted from the signal. This process is repeated for other IMFs that have lower frequency band detection until the residual signal is lower than a threshold value. Therefore, as the IMF order (number) increases, the frequency content of the signal components decreases. In this study, the signal is first decomposed into eight IMFs. The FT of each IMF is calculated and represented by IMF\({}_{k}(f)\). Then, the energy density between the frequency ranges of 0 and 1.3 Hz for the \(k^{\text{th}}\) IMF is calculated by Equation (3):  
\[E_{k}=\frac{\sum_{f=0}^{1.3}|\text{IMF}_{k}(f)|^{2}}{\sum_{f=0}^{5}|\text{IMF }_{k}(f)|^{2}}, \tag{3}\]  
where \(f\) denotes the frequency index, and the \(\mathbf{E}=[E_{1},E_{2},\dots,E_{k}]\) vector is obtained. Finally, four IMF indices, the \(E_{k}\) of which is greater than 0.07, are selected. If there are fewer than four IMF indices that satisfy this condition, the other IMFs are assumed to be zero vectors. The limits of summation in Equation (3) are determined considering the fact that the frequency components of the respiratory data are in the range of 0.1-0.5 Hz. Thus, we selected the four IMFs with the highest energy density between the 0 and 1.3 Hz frequency interval. According to Equation (3) and this IMF selection rule, IMFs 3, 4, 5, and 6 are selected. These IMFs construct a matrix with a size of \(L\times 4\), where \(L\) represents the signal length of the IMFs.  
The IMFs obtained for the signal of a moving subject with an orientation angle of \(\phi=0^{\circ}\) inside the debris are shown in Figure 7. It can be seen that the first two IMFs (IMF 3 and IMF 4) contain higher frequency components compared to IMF 5 and IMF 6.