## 3 Results
### Comparison of EONND with Popular Detectors  
EONND is an energy-operator-based method, and, as a reference, the traditional TKEO method and a variant version, MTEO, are used for comparison [34,36]. Other detectors used for comparison were the Envelope method, the Pelt method, the Biosppy method [59], the Silva method [60], and the traditional amplitude-based method. Among them, Pelt detector and Silva detector were excluded first for their poor performance on the test data. The TKEO and MTEO use a double-threshold detector after full-wave rectification; for details of the detector parameters, refer to [34,36]. The Envelope method first requires noise reduction of the signal through a fourth-order 100 Hz high-pass Butterworth filter followed by a constant detrending, then the signal is conditioned by the TKEO, and finally the envelope of the signal is obtained by second-order Butterworth filter with zero lag to complete the complex signal pre-processing [56]. Based on the above reduction of signal noise, Biosppy also needs to perform a two-step operation of full-wave rectification and sliding average. The amplitude-based method is based on noise reduction by a fourth-order 100 Hz high-pass Butterworth filter and detrending, followed by a sliding average to smooth the signal and the square of the filtered sample points as signal features, and, finally, a double-threshold detector for classification. For convenience, the above detectors are named abs_TKEO, abs_MTEO, Biosppy, ENV, and AMP, respectively. In addition, all algorithms require threshold parameters. For the experimental data in this paper, the method of automatic threshold update based on SNR [32,61] was not very effective, so before proposing an effective mutual mapping relationship between the threshold and signal features, this paper determined the threshold by the traversal method. Figures 8 and 9 show the schematic diagrams of the detection results of the six detectors for the simulated and real EMG signals, respectively. As shown in Figures 8 and 9, each detector had different requirements for signal pre-processing, resulting in significant changes in signal features, with Biosppy being the closest to the raw EMG signal. Although EONND was still the best performing detector, the statistical metric, F1 score, only achieved 77.46%, but with 98.75% Precision. The reason for this phenomenon is analyzed in detail in the Discussion section. Figure 8: Schematic diagram of the detection results of the six detectors on the simulated EMG signal. (**a**) The raw data with labels. (**b–g**) Detection results of the six detectors. The green vertical lines and red vertical lines represent the onset points and offset points detected by the detectors, respectively. “abs\({}_{,}\)” stands for full-wave rectification. Figure 9: Schematic of the detection results of the detectors on the real EMG signal. **(a)** The raw data with labels. (**b–g**) Detection results of the six detectors. Table 2 gives the comparison results of the accuracy of all detectors. For onset points, the \"energy\"-based methods did not change significantly as the SNR decreased and were relatively stable, with EONND being obviously more accurate. The bias of Biosppy gradually increased, and the performance of the ENV method was very extreme; when the SNR was high (SNR > 12 dB), the accuracy of ENV was substantially better than the other methods, but after the SNR fell below 10 dB, almost no accurate change points were detected. In terms of offset points, the performance of ENV showed a similar trend to that of onset detection; Biosppy had a good detection accuracy for signals with SNR > 5 dB, but as the SNR continued to decrease, the performance of Biosppy also decreased significantly. EONND maintained a low detection bias, and, as the SNR decreased, the detection accuracy of EONND for offset points only showed a small increase in bias. For the detection of real EMG signals, EONND had the smallest detection bias, indicating the highest accuracy.