*2.1. Overview of the Procedure for Signal Similarity Measure*

As shown in Figure 1, the proposed method and performance test constituted the processing flow for the similarity measurement of one-dimensional time-series signals. The method in the left part of Figure 1 contained dimensionality reduction of the original sequence through feature extraction based on the SDAE network and distance measurement for the extracted feature sequences of equal length through the improved DTW algorithm. The silhouette coefficients and one nearest neighbor (1-NN) classifier in the right part of Figure 1 were used to evaluate the performances of feature extraction and distance measure, respectively.

**Figure 1.** Similarity measurement and evaluation process.

For the general time series involving the similarity measure, the need for dataset partitioning and the purpose of each divided dataset are shown in Figure 2, which primarily included two parts, namely, the unsupervised learning through the SDAE network and the supervised learning through the 1-NN classifier. Since the cost of collecting and processing the distributed high-dimensional vibration responses is often expensive or even prohibitive, two datasets with data labels (CinCECGTorso and SemgHandMovementCh2 [38]) were selected from the UCR time series archives to help explain the implementation process. The two selected datasets have moderate sample sizes and relatively long sequence lengths, ensuring the operation feasibility of dimensionality reduction based on the SDAE network under acceptable computing overhead. Moreover, both the selected datasets and the vibration of interest face some negatives in common, such as redundant information and outliers, which should be overcome when measuring the similarity of sequences, although their appearance and type are varied. The default training set and test set ratio of each dataset in UCR databases are different. For each of the selected raw datasets used for the subsequent research, we first merged the training and test sets, then shuffled the samples, and finally set a uniform split ratio to form datasets A and B. Table 1 shows the final processing results, in which the ratio of datasets A to B was three. Note that other

partitioning ratios were also acceptable as long as the dataset to be partitioned had a sufficient sample size to ensure corresponding algorithm training. The Python packages Tensorflow and Keras, as well as their libraries [39], were utilized to establish the SDAE network and calculate different distance metrics, in which the operation of the 1-NN classifier that can choose different distance measurement methods referred to in the work by Regan [40].

**Figure 2.** Functions of the dataset used for similarity measurement during implementation.

**Table 1.** Experimental datasets for validation method.

