2.1 Acquisition and feature extraction of sEMG

sEMG signal is the bioelectric change phenomenon that occurs when the human muscle activity is excited and the muscle tissue is stimulated to contract [26]. In this work, the EMG signals were recorded using a multi-channel EMG acquisition system (model ELONXI EMG 100-Ch-Y-RA, Hangzhou JiaoPu Technology Co., Ltd., Hangzhou, China). The raw EMG signal of the muscle collected by the EMG acquisition instrument is a weak electrical signal with an amplitude range of 0.1–5 mV. The muscle activation of 0–1 was obtained after removing power frequency interference, filtering, normalization, and other operations. The processing flow of muscle sEMG signals is shown in Fig. 2.

Figure 2 Flow chart of muscle sEMG signal processing.

The raw sEMG signals are subjected to a standardized preprocessing protocol to mitigate contamination from noise and artifacts. Initial processing involves the elimination of power-line interference (PLI), a 50 Hz phenomenon arising from electromagnetic coupling with electrical infrastructure. This is achieved by applying adaptive notch filters with harmonic suppression capabilities, effectively attenuating fundamental frequency components and their integer multiples. Subsequent spectral refinement employs a fourth-order Butterworth band-pass filter (20–500 Hz cutoff frequencies) to isolate the physiologically relevant myoelectric spectrum. This frequency window optimally captures motor unit action potential trains while rejecting extraneous low-frequency baseline drift (<20 Hz) and high-frequency instrumentation noise (>500 Hz). Signal normalization is performed using the min-max scaling technique.

Feature extraction is a crucial step in fully using sEMG signals for human lower limb movement intention recognition. This study extracted six features, including one frequency domain feature and five time domain features, from the collected sEMG signals.

(1) Power spectral ratio (PSR) as a frequency domain feature for gait phase-specific muscle contraction quantification, which is defined as the logarithmic energy proportion between specific neuromuscular frequency bands, provides biomechanical insights into gait-dependent muscle recruitment strategies. This metric is mathematically expressed as:$PSR=10{\log }_{10}\left(\frac{{\displaystyle {\int }_{f_L}^{f_H}P(f)df}}{{\displaystyle {\int }_{f_{base}}^{f_{cutoff}}P(f)df}}\right)$(1)where P(f) denotes the power spectral density (PSD) estimated via Welch's method (512-point Hamming window, 50% overlap), f_H−f_L represents the characteristic contraction band (typically 30–150 Hz), and f_base − f_cutoff ​spans the full sEMG bandwidth (20–500 Hz).

(2) Mean absolute value (MAV)‌. Quantifies the average intensity of an sEMG signal segment:$MAV=\frac{1}{n}{\displaystyle \sum _{i=1}^{n}x(i)}$(2)

(3) Zero crossing rate (ZCR)‌. Characterizes the frequency of amplitude polarity changes in sEMG signals:$ZCR={\displaystyle \sum _{i=1}^{n-1}\mathrm{sgn}[-x(i)\times x(i+1)]}$(3)$\mathrm{sgn}(x)=\{\begin{array}{c}0x\ge 0\\ 1else\end{array}$(4)

(4) Standard deviation. Measures the dispersion of sEMG intensity around the mean value:$ST=\sqrt{\frac{{\displaystyle \sum _{i=1}^n{(x(i)-MVA)}^2}}{n-1}}$(5)

(5) Root mean square (RMS). Represents the signal's average power, reflecting sustained muscle contraction:$RMS=\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^n{x}^2(i)}}$(6)

(6) Slope sign change (SSC). Counts the alternations in sEMG signal slope polarity:$\begin{array}{l}SSC={\displaystyle \sum _{i=2}^{n-1}\mathrm{sgn}[x^2(i)\times x(i+1)\times x(i-1)]}\\ \mathrm{sgn}=\{\begin{array}{l}0x\ge Threshold\hfill \\ 1else\hfill \end{array}\end{array}$(7)

2.2 Acquisition and feature extraction of angular signals

This study used the BWT901CL attitude sensor to obtain the ankle angle signal. The sensor cooperated with the dynamic Kalman filter algorithm, and the measurement accuracy reached 0.05° in the dynamic environment, and the ankle angle and angular velocity signals could be output simultaneously. In the feature extraction process, the angle change rate reflects the speed and acceleration of ankle movement, which is one of the important indicators used to judge the movement intention. The angle range, on the other hand, reflects the ankle's range of motion in different actions and helps distinguish different motion modes. On the other hand, the average angle provides information about the stable state of the ankle joint maintained over a period, which is important for understanding the continuous movement intention. This study used advanced signal processing techniques to extract these features more accurately. Firstly, the dynamic Kalman filtering algorithm was used to filter the original angle signal, eliminating noise and interference and improving the signal-to-noise ratio. Secondly, by calculating the first and second derivatives of the angle, the angle change rate and acceleration information are obtained, which further enriches the feature set. Therefore, the signal amplitude domain (SMA) is proposed to represent the intensity of body movement per unit time, which is expressed as follows:$\begin{array}{c}SMA=\frac{1}{T}({\displaystyle {\int }_0^T\left|x_1(t)\right|dt}+{\displaystyle {\int }_0^T\left|{\dot{x}}_1(t)\right|dt}+\\ {\displaystyle {\int }_0^T\left|x_2(t)\right|dt}+{\displaystyle {\int }_0^T\left|{\dot{x}}_2(t)\right|dt})\end{array}$(8)where, T is the time width of the moving window, and T=0.2 s is chosen in this paper.

2.3 Gait recognition based on MPSO-SVM algorithm

Support vector machine is a highly efficient supervised learning algorithm primarily used for classification tasks [27, 28]. Its core principle involves finding an optimal hyperplane that separates samples of different classes while maximizing the minimum margin between the two classes to enhance the model's generalization capability. The hyperplane is determined by the closest sample points (termed support vectors), which act as critical anchors for the classification boundary. Mathematically, solving for the optimal hyperplane can be formulated as a convex quadratic optimization problem:$\{\begin{array}{l}\underset{w,b}{\min }\frac{1}{2}{\Vert w^T\Vert }^2\hfill \\ s.t.y_i\left(w^T{x}_i+b\right)⩾1,i=1,2,\cdots ,m\hfill \end{array}$(9)where, w is the hyperplane normal vector, b denotes the bias term, x_i represents the input sample data, and y corresponds to the gait pattern.

Human lower limb motion patterns constitute a linearly non-separable problem, necessitating the introduction of kernel functions and soft margins. The kernel function maps the sample data from the original space to a high-dimensional feature space so that the sample data is linearly separable in the high-dimensional feature space. However, the role of the soft margin is to allow the partition of the hyperplane to be wrong on some samples by introducing penalty factors and slack variables. In this case, the updated objective function and constraints for solving the generalized optimal classification hyperplane are:$\{\begin{array}{l}\underset{\omega ,b}{\min }\frac{1}{2}\Vert w^T\Vert +C{\displaystyle \sum }_{i=1}^n{\xi }_i\hfill \\ \begin{array}{l}s.t.y_i\left(w^T\varphi \left(x_i\right)+b\right)\ge 1-{\xi }_i\\ {\xi }_i\ge 0,\forall i\end{array}\hfill \end{array}$(10)where, C is the penalty factor, ξ_i denotes the slack variable, and ϕ(x_i) the feature vector of the reduced x_i mapping to the high-dimensional feature space.

Using the Lagrange multiplier method and the duality principle, the dual problem of Eq. (2) is obtained as follows:$\{\begin{array}{l}\underset{a}{\max }\sum _m^{i=1}{a}_i-\frac{1}{2}\sum _{i=1}^m\sum _{j=1}^m{a}_i{a}_j{y}_i{y}_{j}K\left(x,x_i\right)\hfill \\ s.t.\sum _{i=1}^m{a}_i{y}_i=0,0⩽a_i⩽C,i=1,2,\cdots ,m\hfill \end{array}$(11)where, a is the Lagrange multiplier vector, a_i is the Lagrange multiplier, and K(x, x_i). is the kernel function.

Different kernel functions can lead to different classification results, and the choice of kernel function is crucial for solving specific problems. Commonly used kernel functions include linear kernel, polynomial kernel, radial basis function (RBF) kernel, and sigmoid kernel. In the context of gait recognition, the RBF kernel is often selected due to its strong ability to handle nonlinear relationships and its good performance in practical applications. By adjusting the parameters of the RBF kernel, the complexity of the decision boundary can be controlled, thereby achieving better classification effects. The expression of the RBF kernel function is:$K(x_i,x_j)=\exp (-\gamma {\Vert x_i-x_j\Vert }^2)$(12)where, γ is the kernel parameter. The final classification decision function is:$f(x)={\displaystyle \sum _{i=1}^m{a}_j{y}_{i}K(x,x_i)+b}$(13)

In conclusion, the classification performance of SVM is closely related to the settings of the penalty factor C and the kernel function parameter γ. Therefore, this paper employs the particle swarm optimization (PSO) algorithm to optimize the parameters of SVM, thereby enhancing its classification accuracy and robustness.

2.4 Modified particle swarm optimization

The PSO algorithm is inspired by the foraging behavior of birds [29, 30]. It treats the position of individual birds or food sources as potential solutions to optimization problems. Through information exchange between individuals and the optimal solution within the group, the algorithm guides each particle to converge toward the current best solution while retaining its own historical information. By iteratively updating positions, the swarm ultimately reaches the optimal solution [31]. Due to its advantages, such as ‌fast convergence rate‌ and ‌simple yet efficient workflow‌, PSO has been widely applied in multi-objective parameter optimization. The core of PSO lies in the ‌velocity and position updates‌ of particles, which can be expressed as:$\{\begin{array}{l}{p}_{i,k+1}=p_{i,k}+v_{i,k+1}\hfill \\ \begin{array}{l}{v}_{i,k+1}=\omega v_{i,k}+c_1\cdot ran{d}_1(p{b}_k-p_{i,k})\\ +c_2\cdot ran{d}_2(g{b}_k-p_{i,k})\end{array}\hfill \end{array}$(14)where, p_i,k and v_i,k represent the position and velocity of the i-th individual in the population during the k-th iteration, respectively, pb_k denotes the particle best solution in the k-th iteration, gb_k is the historical global best solution, rand₁ and rand₂ are random numbers uniformly distributed in the range [0, 1], c₁ and c₂ are the individual learning factor and global learning factor, typically valued between 0 and 2, ω_k is the inertia factor that balances the trade-off between local exploration and global exploitation. Prior research demonstrates that implementing a concave function-based decreasing strategy for inertia weight adjustment not only prevents premature convergence but also enhances convergence rates during later optimization stages. Therefore, the inertia factor is adjusted using a concave function, expressed as:${\omega }_k={\omega }_{max}-\left({\omega }_{max}-{\omega }_{min}\right)\cdot {\left(\frac{k}{k_{max}}\right)}^{\delta }(\delta >1)$(15)where, ω_max and ω _min are the upper and lower bounds of the inertia weight, k_max is the ‌total number of iterations‌, δ controls the concavity of the adjustment curve.

The individual learning factor c₁ and the global learning factor c₂ influence the particle's optimization search capability by biasing the particle's new positions. A higher c₁ provides new positions in distant regions of the search space, enhancing global exploration, and a lower c₂ refines local search capabilities by focusing on nearby areas [32, 33]. In the initial stage and the later stage of optimization, the requirements of global search and local search ability of the algorithm are different. This paper adopts an adaptive learning factor, so that c₁ gradually decreases with iteration, and c₂ gradually increases with iteration, which is expressed as:$\{\begin{array}{c}{c}_1{}_{,k}=c_{1,max}-(c_{1,max}-c_{1,min})\sin (\frac{\pi }{2}\cdot \frac{k}{k_{max}})\\ c_2{}_{,k}=c_{2,min}+(c_{2,max}-c_{2,min})\sin (\frac{\pi }{2}\cdot \frac{k}{k_{max}})\end{array}$(16)where, c_1,max and c_1,min are the upper and lower limits of the individual learning factor, c_2,max and c_2,min are the upper and lower limits of the global learning factor, respectively. This work applies the particle swarm optimization algorithm to the SVM to optimize the input weights and bias values. In this paper, the PSO algorithm is used to optimize the penalty factor C and the kernel function parameter γ in SVM, and the schematic diagram of the algorithm is shown in Fig. 3. The main steps of the MPSO-SVM algorithm are as follows:

Figure 3 Flow chart of MPSO-SVM algorithm.

Step 1: Divide all sample data into two parts, training data and test data.

Step 2: Initialize the particle swarm, including PSO parameters ω, c₁ , c₂, and k_max, and set the parameter range of the SVM classifier. That is, the range of penalty factor C, the range of kernel function parameter γ. In this work, the algorithm parameters are configured as follows: an inertia weight ω=0.8, cognitive and social acceleration coefficients c₁=1.6, c₂ =1.8, a maximum iteration count k_max=100, and a population size of 30. The search ranges for both the penalty factor C and kernel parameter γ are defined within the interval [10^–6 10⁶].

Step 3: Calculate the new fitness value of each particle, select the appropriate inertia factor according to Eq. (8), and complete the update of particle position and velocity.

Step 4: The fitness values of the particles are sorted, and the optimal position of the current particle swarm and the historical individual optimal position are calculated.

Step 5: Determine whether the number of evolutions is less than or equal to the maximum number of evolutions. If it is less than or equal to, return to Step 3; otherwise, end the evolution process.

Step 6: Output the optimal solution (C,γ) and create an SVM classifier for model training and classification prediction.

3.1 Information acquisition

A series of experiments were conducted to evaluate the effectiveness of the proposed PSO-SVM for human lower extremity motion intention detection. The study involved four healthy adult participants (2 males, two females; age: 24.5 years ± 2.3 years; height: 170.2 cm ± 5.6 cm; weight: 65.8 kg ± 7.1 kg) with no history of neuromuscular disorders or lower-limb injuries. Participants were instructed to avoid strenuous exercise 24 hours before the experiment to minimize the effects of muscle fatigue. During the experiment, the participants performed four gait phases (CP, CD, PP, SW) on a motorized treadmill (Woodway, USA) at a controlled speed of 1.25 m·s^–1. Each trial lasted 15 min, with 5-min rest intervals to prevent fatigue. A total of 3800 valid gait cycles were recorded.

The EMG signal of the soleus (SOL) during walking is shown in Fig. 4. The raw signals were high-pass filtered (4th-order Butterworth) and normalized to maximum voluntary contraction. As shown in Fig. 5, the ankle angle information was captured using the BWT901CL attitude sensor attached to the shank segment of the participants' legs. The sensor provided real-time data on ankle dorsiflexion and plantarflexion angles, which is crucial for identifying different gait phases. The collected data were synchronized with the sEMG signals to ensure accurate analysis. It can be seen from the figure that the EMG signal and ankle angle information have periodic changes during human walking, and the sEMG has noticeable changes at different moments of the gait cycle.

Figure 4 sEMG of SOL during human walking: (a) raw EMG signal, (b) EMG signal after high-pass filtering, and (c) EMG signal after normalization.

Figure 5 Ankle angle information during human walking.

3.2 Experimental result

The respective eigenvalues are extracted using the obtained ankle angle signal and muscle electromyography information to form the feature matrix. To verify the influence of training set size on the recognition performance of the proposed improved MPSO-SVM recognition method, the collected original data sets are randomly divided into training and test sets in the ratios of 0.8:0.2, 0.6:0.4, and 0.4:0.6 in this work. Different gait types are recognized using the MPSO-SVM recognition algorithm proposed in this paper. The recognition results of the MPSO-SVM for human valking gait phases recognition are described in Fig. 6. And, (a) The ratio of training and test sets is 0.8:0.2; (b) The ratio of training and test sets is 0.4:0.6; (c) The ratio of training and test sets is 0.6:0.4. The diagonal black box stands for the correctly identify sample number, the white box indicates the incorrectly identify sample number, the last row in the gray box represents the recognition precision rate, The last column in the gray box represents the recall rate, the final gray box is the average recognition precision rate. From the experimental results, it can be clearly seen that the average recognition precision rate is the highest, reaching 93.81%, when the training set and the test set are randomly allocated at the ratio of 0.8:0.2. In this case, the precision rate is more than 92% against the four gait phases, for the CP gait phase, the MPSO-SVM algorithm achieved a high recognition accuracy of 93.13%, with only a small number of misclassified samples. Similarly, the recognition accuracies for the CD, PP, and SW gait phases were 92.75%, 95.25%, and 94.13%, respectively. The recall ratio has the same result. In particular, the recall ratio is more than 92% against the four PD gait phases, which are 93.36%, 92.40%, 93.73%, and 95.80% for CP, CD, PP, and SW, respectively. These results demonstrate that the MPSO-SVM algorithm has excellent performance in recognizing different gait phases. When the training set and test set are randomly assigned in the ratio of 0.6 to 0.4, the average recognition accuracy of the recognition method is 90.84%. When the ratio is 0.4:0.6, the average recognition accuracy of the recognition method is 88.53%. This indicates that as the training data ratio decreases, the MPSO-SVM algorithm's recognition performance declines. However, even when the training-to-test data ratio is as low as 0.4:0.6, the MPSO-SVM algorithm still maintains a relatively high recognition accuracy level, suggesting its robustness and adaptability.

Figure 6 The recognition performance for three different recognition methods, the ratio of training and test sets is (a) 0.8:0.2, (b) 0.4:0.6, and (c) 0.6:0.4.

In addition, to further verify the MPSO-SVM algorithm's performance, we compared it with several common classification algorithms, including the traditional K-nearest neighbor (KNN), decision tree (DT), and random forest (RF).

To further evaluate the performance of the proposed MPSO-SVM algorithm, we compared it with other commonly used gait phase recognition algorithms, such as KNN, DT, and RF. The comparison results are shown in Fig. 7. (a) the KNN recognition performance; (b) the DT recognition performance; and (c) the RF recognition performance. The KNN average recognition accuracy is 88.77%, and the recognition precision rate is 88.06%, 88.71%, 88.58%, and 89.71% for CP, CD, PP, and SW, respectively. And for the DT, the average recognition accuracy is 88.07%, and the recognition precision rate is 87.17%, 88.14%, 87.42%, and 89.58% for CP, CD, PP, and SW, respectively. And for the RF, the average recognition accuracy is 89.02%, and the recognition precision rate is 88.29%, 88.68%, 89.26%, and 89.89% for CP, CD, PP, and SW, respectively. It can be seen from the figure that the proposed MPSO-SVM algorithm has the highest average recognition accuracy among all algorithms, reaching 93.81%. And the recall ratio shows the same result. Specifically, the average recall ratio of MPSO-SVM is about 5.1% higher than KNN, 5.8% higher than decision tree, and 4.8% higher than RF. This demonstrates the superiority of the MPSO-SVM algorithm in gait phase recognition tasks. In addition, we also analyzed the computational efficiency of the proposed MPSO-SVM algorithm. The experimental results show that the MPSO-SVM algorithm has a relatively short recognition time, which meets the real-time requirements of gait phase recognition systems. In summary, the experimental results demonstrate that the proposed MPSO-SVM algorithm has excellent performance in recognizing different gait phases, with high accuracy, strong robustness, and efficient computation. This lays a solid foundation for applying gait phase recognition technology in rehabilitation training, exoskeleton control, and other fields. Within all the phases of human normal walking gait, the probability of the adjacent phases being confusedly classified is the highest. This phenomenon primarily stems from the temporal misalignment inherent in multimodal biosignal acquisition during phase transition. Specifically, surface sEMG signals precede actual movements by approximately 50 ms, while joint angle sensors exhibit 10–30 ms response latency. Such temporal discrepancies induce phase ambiguity regions in feature fusion matrices, thereby compromising classification reliability. In order to deal with this challenge, an attention mechanism can be added to the MPSO-SVM framework in later research. This architecture strategically amplifies the influence of historical data information on gait pattern classification, effectively mitigating temporal bias artifacts through weighted temporal context integration.

Figure 7 The recognition performance for three different recognition methods: (a) KNN recognition performance, (b) DT recognition performance, and (c) RF recog­nition performance.