A. Limb condition effect analysis(1) Performance comparison among different electrode locations

The average inter-condition and intra-condition classification errors for the three electrode locations were calculated across all subjects and gestures, as shown in Fig. 5. Ten distinct condition-specific classifiers were trained, each using data exclusively from one specific limb condition and then tested on data from all limb conditions. The matrix cells represent the average error for all gestures across subjects, with the vertical and horizontal axes indicating the training and testing conditions, respectively. Intra-condition classification errors, shown on the main diagonal, represent errors within the same limb condition, while off-diagonal elements represent inter-condition errors. The mean intra-condition classification errors along the diagonal for three electrode locations were 9.77%, 10.31%, and 12.26%, respectively. The mean inter-condition errors were 25.42%, 24.51%, and 32.14%, respectively. The performance of wrist sEMG and mid sEMG was similar, and they were both better than elbow sEMG.

Fig. 5

Confusion matrix of classification errors (in %) averaged across all subjects and all classes when single-condition classifiers (LDA) are used. Darker blue boxes imply greater errors. a Wrist sEMG has the best dynamic recognition ability when training in dynamic conditions. b Mid sEMG has the best performance of inter-condition. c Elbow sEMG is the worst in all four training and testing conditions

Figure 6 shows the impact of electrode locations on class-specific outcome. This illustration mirrors the results in Fig. 5, but averages them across limb conditions rather than gestures. Figure 6 shows HO, HP, LG have the lowest accuracy in elbow sEMG while wrist sEMG has the much higher accuracy of HO, HP and LG than the mid of forearm and elbow location. This phenomenon implies that the sEMG signals from wrist location has the best performance of decoding fine movements of fingers. And for mid sEMG, HC, WF and RE have the best performance among the three kinds of sEMG. And it is noteworthy that WE’s error rate is much lower than wrist sEMG and almost the same as the best one-elbow sEMG. This phenomenon tells us that the movement of the wrist will influence the sEMG of the wrist and within a certain range, the farther away from the wrist, the better the signal quality, of which the elbow signal quality is the highest. For reliable sEMG-based equipment design, we can select the gestures suitable for different locations of sEMG signals to do the corresponding decoding work. For example, the wrist sEMG is suitable for fine finger movements, the mid and elbow sEMG is better for wrist movements.

Fig. 6

Confusion matrix of classification error (in %) of gestures averaged across all subjects and all limb conditions. Darker blue boxes imply greater errors. a Wrist. b Mid. c Elbow

To delve deeper into the impact of limb conditions on the discrimination of individual classes, the inter-condition classification matrix presented in Fig. 5, the results have been dissected into class-specific matrices, as depicted in Fig. 7. The gestures that are particularly influenced by limb conditions are evident through darker red-colored elements situated away from the main diagonal. It is displayed that certain conditions worsen the discrimination challenges for these specific classes more than others.

Fig. 7

Confusion matrix of classification errors (in %) averaged across all subjects for each class in three electrode locations: wrist, mid and elbow. Darker red means greater values. a HC. b HO. c WF. d WE. e HP. f LG. g RE

For hand closure (HC), the LDA classifiers trained on static limb conditions performed the worst on all dynamic limb conditions, particularly at the wrist. This indicates that for the hand closure action, sEMG signals at the wrist are significantly affected by dynamic limb conditions, whereas the impact on sEMG signals at the mid forearm and elbow is much smaller. The average recognition error rates for the three areas are 28.38%, 22.36%, and 29.34%, respectively. Additionally, by summing the errors across all testing conditions for each training condition, the best training conditions for the three electrode locations were identified as D/AUDS, D/AAAS, and D/AUDF.

For HO, the wrist sEMG has the best performance with error of 18.89%, while mid sEMG is 24.17%, elbow sEMG is 31.66%. The same as HC, the best training conditions for three electrode locations are S/FU, D/FUDS, D/FUDS.

For WF, the mid sEMG has the best performance with error of 23.69% among these three sEMG electrode locations, while wrist sEMG is 32.35% and elbow sEMG is 30.09%. The best training conditions for three electrode locations are D/AUDS, D/AUDS, D/AUDS.

For WE, the elbow sEMG has the lowest error of 15.15%, the mid sEMG has the error of 16.82% and the wrist sEMG has the highest error of 21.30%. The best training conditions for three electrode locations are D/FUDF, D/FUDF, S/AA.

For HP and LG, the wrist sEMG has the best performance, which indicates that wrist sEMG has the best ability of recognizing the fine hand movements among these three kinds of EMG. The best training conditions for HP in three electrode locations are D/FUDF, D/FUDS, D/FUDF. And the best training conditions for LG in three electrode locations are D/FUDF, D/AAAF, D/AUDS.

For RE, the wrist sEMG has the similar good performance as the mid sEMG, and are much better than elbow EMG. The best training conditions for three electrode locations are D/AAAF, D/AAAS, D/FUDS.

(2) Comparison between dynamic and static limb conditions

Further, the matrix in Fig. 5 was divided in four blocks, which included different training and testing combinations. Among them, black parts mean training in static limb conditions and testing in static limb conditions, red parts mean training in static limb conditions and testing in dynamic limb conditions, green parts mean training in dynamic limb conditions and testing in static limb conditions, and purple parts mean training in dynamic limb conditions and testing in dynamic limb conditions. The averages of these four blocks in three electrode locations were 19.09%, 33.12%, 25.76%, 18.52% vs 17.48%, 30.39%, 23.02%, 20.77% vs 23.28%, 38.74%, 29.52%, 27.90%.

By observing the limb conditions carefully, some similarity between different conditions can be found. The dynamic conditions can be seen as some combinations of different static conditions. For example, dynamic condition D/FUD can be seen as the combination of static conditions S/AD and S/FU. D/AUD can be seen as the combination of S/AD and S/AU. D/AAA can be seen as the combination of S/AD and S/AA. The hypothesis is that the similarity of the condition can lead to the similarity of performance. In fact, for wrist sEMG, the recognition accuracy of each dynamic condition has the relationship with the related static conditions. The numbers in the small yellow boxes represent the classification results of the classifiers trained for the limb condition represented by this column. These classifiers perform best among the static or dynamic classifiers to which this column belongs when classifying the limb conditions represented by this row. This fact indicates that limb conditions with certain similarity in form play a role in enhancing the robustness of sEMG pattern recognition. In other words, sEMG signals corresponding to the same gestures of these limb conditions exhibit a higher correlation than signals from other limb conditions. It is noteworthy that the classifier trained in the fast limb conditions does not exhibit the same distinct advantage over the relative static limb conditions as the classifier trained in the slow dynamic limb conditions. A similar phenomenon can be observed in the middle forearm and the elbow, except for one test in the elbow which is not as expected (the corresponding area is marked in a small red box in Fig. 5), but it is very close to the best. This phenomenon indicts that dynamic limb conditions’ sEMG can include the information of related static limb conditions’ sEMG. And vice versa, static limb conditions also can include the information of the related transient conditions of dynamic conditions. This phenomenon also inspires us to design some complex dynamic limb conditions to cover more usual and normal static limb conditions we usually show in daily life to include more diverse sEMG information. This operation can improve the robustness of recognition models.

From Fig. 8, wrist sEMG has the best performance in dynamic training and dynamic testing. This is very suitable for the wearable equipment’s design. Because the application scenarios of the wearable equipment are almost dynamic. This phenomenon demonstrates the feasibility of wrist sEMG in complicated real world. And by observing the other three groups, the gap between the wrist sEMG and mid sEMG is not large while much better than elbow sEMG.

Fig. 8

The error rate of different training and testing conditions,’S’ represents static limb conditions, ‘D’ represents dynamic limb conditions. The character before dash means training limb condition, the character after dash means testing condition

(3) Effect of moving speed in dynamic limb conditions

To analyze the influence of different speeds in dynamic limb conditions, Fig. 9 presents the recognition error rates for various dynamic limb conditions at different speeds. Fast and slow conditions of the same type are positioned adjacently. For sEMG at all three locations, ANOVA results indicate no significant difference between fast and slow dynamic conditions in terms of the robustness of a model trained under these conditions and tested across all limb conditions (including static conditions).

Fig. 9

The comparison of the influence of different speeds for different dynamic limb conditions on gesture recognition. Every result is achieved by one LDA model which is trained in the represented dynamic limb condition and tested in all ten limb conditions. a Wrist. b Mid. c Elbow

In real applications of limb-based sEMG wearables, dynamic conditions are usual. By observing the two kinds of dynamic testing groups, the phenomenon which is that wrist sEMG has the lowest average error of six dynamic condition training models illustrates that wrist sEMG is very suitable for the real applications of human–machine interface.

(4) Feature space analysis

As shown in Fig. 10, wrist sEMG demonstrates the best separation of seven different gestures across 10 limb conditions compared to the other two locations. Figure 11 illustrates the average SI within-class and between-class across 14 subjects, indicating that wrist sEMG offers the best overall performance in the recognition task. ANOVA results reveal a significant difference (p = 0.026) in within-class SI among the wrist, mid, and elbow locations, with wrist and mid sEMG showing similar values, both lower than the elbow. For between-class SI, wrist sEMG has the highest value, indicating the best discrimination of different gestures at this location.

Fig. 10

Visualization of different class of different limb conditions. A very obvious phenomenon can be found in three subfigures which is the wrist EMG has the best separability of seven gestures while the elbow EMG is the worst. a Wrist. b Mid. c Elbow

Fig. 11

Feature Space Analysis: SI – within class distance for same gesture vs. Interclass distance among different gestures. Bars represent value calculated by formula (1)-(4), and standard deviation is computed over the values

B. Strategies comparison for mitigating the limb condition effect(1) Multiple-condition training

The average classification errors of using data from single and multiple (2–5) conditions in the training dataset and all ten conditions in the test dataset were calculated and are presented in Fig. 12. First, we can find that the recognition errors decreased with the number of training conditions increasing. This phenomenon is common in three sEMG electrode locations. And the best combinations for each group are showed in the table below each figure. We can find D/AAAF is the best training condition for single-condition training. It implies the fast swinging around the shoulder joint between S/AD and S/AA has the most information diversity than other 9 limb conditions. But with the computation continues, the best feature sequences for three electrode locations begin to be different. By careful observation, the inner law of the choice of the added feature is clear. It is that cover as more important limb conditions as possible. Through ANOVA method, we can find that each group is significantly different with adjacent groups of three sEMG electrode locations by the p-values less than 0.05. And we can find that each group’s best performance and its combination in Table 3.

Fig. 12

Classification errors when training in each combination of limb condition subsets and testing in all ten limb conditions. The reduction speed of classification errors is much slower after four limb conditions. Wrist sEMG and mid sEMG are much better than elbow sEMG

Table 3 The best effect of combination of different training limb conditions(2) Feature optimization

To develop a more efficient and convenient method for training a robust and accurate pattern recognition system, we employed the sequential forward feature selection (SFFS) method to create a higher-quality feature set for gesture recognition. Within the feature space, we selected three types of signal features: time domain features, frequency domain features, and autoregressive coefficients. These features encompass nearly all key elements used in reliable sEMG-based recognition systems.

For achieving the best feature set for three different sEMG electrode locations, we apply SFFS method on them. Firstly, we run the codes on wrist sEMG and after 16 iterations, we get the best feature sequence for wrist sEMG. The numerical sequence is [4, 2, 15, 3, 8, 6, 7, 10, 0, 23, 22, 19, 21, 18, 20, 16], which can be translated to [DASDV, RMS, SM3, WL, SSC, MPR, WAMP, MDF, MAV, AR6, AR5, AR2, AR4, AR1, AR3, PSR]. Then we run the similar codes on middle location and elbow location to get their best feature sets. They are [3, 0, 14, 4, 8, 6, 7, 10, 9, 5, 1, 17, 18, 19, 23, 22, 21] and [3, 0, 14, 6, 4, 8, 7, 13, 2, 11], respectively after 17 and 10 circles, which can be translated to [WL, MAV, SM2, DASDV, SSC, MPR, WAMP, MDF, MNF, ZC, VAR, VCF, AR1, AR2, AR6, AR5, AR4] and [WL, MAV, SM2, MPR, DASDV, SSC, WAMP, SM1, RMS, PKF].And the best accuracy of wrist, middle and elbow are 81.02%, 80.35% and 72.86%. And every iteration’s accuracy of three sEMG are showed in Fig. 13. For more details, we get the related confusion matrix of ten different limb conditions of wrist, middle and elbow, showed in Fig. 14. By checking the three matrices, we can find that although SFFS algorithm can find a better feature set to improve the accuracy of three sEMG locations’ pattern recognition performance, it still cannot solve some limb conditions’ low robustness like S/FU, D/FUDS, D/AUDF.

Fig. 13

The iteration procedure of classification accuracy in three sEMG electrode locations. Each data point is equivalent to averaging all test results from 14 subjects (the model obtained after each person is trained on one limb condition data needs to be averaged across all 10 limb conditions, for a total of 100 possible choices). a Wrist. b Mid. c Elbow

Fig. 14

The confusion matrix of classification errors of the best feature set on three sEMG electrode locations. For wrist, it is the result of the 16th iteration. For mid, it is the result of the 17th iteration. For elbow, it is the result of 10th iteration. a Wrist. b Mid. c Elbow

As the number of features increases, the improvement in accuracy becomes progressively smaller. Using the t-test, we calculated the significance of accuracy differences across various feature sets. For wrist sEMG, the accuracy in the fifth cycle (78.85%) shows a significant improvement over the fourth feature set, with a p-value of 0.035. For mid sEMG, the fourth feature set (76.15%) significantly improves accuracy compared to the third, with a p-value of 0.014. For elbow sEMG, the third feature set’s accuracy (69.95%) shows a significant improvement over the second, with a p-value of less than 0.001.