## 2 Materials and Methods
### Spatial Multi-Dimensional Pulse Wave Signal Processing Method
The single-point vibration signal acquired by the former acts as a standard input signal. \(x_{ZM-300}\) is the pulse wave signal collected by ZM-300 and \(x_{i}\) is the pulse wave correspondingly collected by the \(i\)-th sensor in the PAWS sensor array, as shown in Equations (17) and (18). \(A\) and \(A_{i}\) are the amplitude of the waveform, \(\omega\) is the vibration frequency, \(t\) is the time, and \(\varphi\) is the initial phase. The pulse waveform collected by both are almost identical, only differing in amplitude. Figure 5c shows the dynamic pressure waveform collected by the PAWS sensor array. As shown in Figure 5b, the SPVG probe's center is sequentially changed to align at location 1, location 2, and location 3 of PAWS' sensor array. Six consecutive trials were conducted at each test position to verify the test's repeatability, just like the method described above. Setting the pressure and vibration frequency of the SPVG to be the same in each experiment ensures the standard input signal's consistency over multiple experiments. Comparing the algorithm's processing results and the standard input signal will evaluate the algorithm's performance. \[F_{ZM-300}=-F_{PWAS} \tag{16}\]

\[x_{ZM-300}=Asin(\omega*t+\varphi) \tag{17}\]

\[x_{i}=A_{i}sin(\omega*t+\varphi) \tag{18}\]

Figure 5: (**a**) Diagram of SPVG and ZM-300 mutual extrusion; (**b**) diagram of the test area at three different locations on the PAWS sensor array; (**c**) pulse waveform graphs collected by twelve sensors in the PAWS sensor array; (**d**) at location 1, waveforms of the standard input signal and the signal processed by the three algorithms. In Figure 5d, the blue curves are the standard input signals collected by the ZM-300 at position 1, while the rest are the signal curves processed by the three methods. The waveforms processed by the three algorithms have very similar trends to the standard input signal waveforms, and their phases and frequencies are the same. The six replicated experiments' standard deviations were 7.2%, 7.0%, and 8.3% at the three test positions, respectively, indicating good repeatability. As shown in Table 1, the DTW distances between the three algorithms' processing results and the standard input signals are quite different. Both Algorithm I and Algorithm II have large DTW distances, while Algorithm III has the smallest DTW distance. Additionally, the gain of different algorithms varies, as shown in Table 2. The gain of Algorithm III is closest to zero, meaning that Algorithm III has the least energy loss in processing results relative to Algorithms I and II. ## 4 Discussion

This article is intended to provide a novel multi-dimensional composition method based on time series similarity. In order to test the stability and validity of the new algorithm, the methods used by previous workers were summarized in Algorithm I and Algorithm II and analyzed in the same set of collected data [24; 27; 30]. As mentioned above, we describe and evaluate the algorithms' characteristics in two ways: the degree to which the processing result of the algorithm is close to the standard input signal, including DTW distance and gain; and the magnitude of the change in the processing result of the algorithm in different test areas. As shown in column 2 of Table 1, the DTW distances between the processing results of Algorithm I and the standard input signal are all greater than 10. Simultaneously, Algorithm II processes very close to Algorithm I, which also has a DTW distance of more than 10, shown in column 3 of Table 1. In contrast, the processing results of Algorithm III are more similar to the standard input signal, with a DTW distance between them of less than 3.