A joint angle prediction method, apparatus, device and medium

Abstract

This invention provides a method, apparatus, device, and medium for predicting joint angles. It relates to the field of electromyography (EMG) data processing technology. The method includes: acquiring surface EMG signals of a target lower limb; introducing an adaptive adjustment coefficient positively correlated with the number of iterations into the original particle swarm optimization (PSO) algorithm to adaptively adjust the update step size of the particle positions representing the parameter combination (K, α), so that the particle search range transitions from global exploration to local development as the iteration progresses, thus obtaining an improved PSO algorithm; optimizing the parameter combination (K, α) of a variational mode decomposition (VMD) algorithm using the improved PSO algorithm to obtain the optimal parameter combination (K, α); decomposing the surface EMG signals of the target lower limb into K intrinsic mode components using the VMD algorithm with the optimal parameter combination (K, α); extracting features from each of the K intrinsic mode components, and obtaining a joint angle prediction result based on the feature extraction results.

Description

Technical Field

[0001] This invention relates to the field of electromyography data processing technology, and in particular to a method, apparatus, device, and medium for predicting joint angles. Background Technology

[0002] The number of patients with lower limb motor dysfunction caused by neurological diseases or trauma continues to rise. Rehabilitation exoskeletons, as an emerging means of motor assistance and rehabilitation, show promising prospects in clinical rehabilitation by providing power support and motion guidance to improve patients' gait. To achieve safer, more comfortable, and more efficient human-machine collaboration, higher demands are placed on the accurate recognition and real-time response of exoskeleton system users' movement intentions. Bioelectrical signals, due to their convenient detection and non-invasive safety, have become a mainstream research subject in the field of human-machine collaboration. Among them, surface electromyography (sEMG) records muscle electrophysiological activity and has a higher signal-to-noise ratio and stability compared to electroencephalography (EEG), and has been widely used in continuous joint motion estimation. sEMG-based continuous motion prediction can significantly improve the efficiency of human-machine collaboration in rehabilitation equipment, and accurate prediction of changes in motion volume is a core prerequisite for achieving compliant control in rehabilitation robots.

[0003] Variational Mode Decomposition (VMD), as a novel adaptive signal processing method, has gradually gained attention in the field of sEMG signal decomposition due to its solid mathematical theoretical foundation and superior noise robustness.

[0004] However, VMD performance is highly dependent on the parameter combination of the decomposition mode number K and the penalty factor α. Traditional setting methods rely on trial and error based on human experience, making it difficult to adapt to the dynamic changes in the time-frequency characteristics of sEMG signals. Particle Swarm Optimization (PSO) is widely used for adaptive optimization of VMD parameters due to its fast convergence speed and fewer parameter settings. However, standard PSO suffers from premature convergence defects, which easily get trapped in local optima, thus limiting the accuracy of VMD parameter optimization and affecting the performance of subsequent motion prediction. Summary of the Invention

[0005] Therefore, it is necessary to provide a joint angle prediction method, device, equipment, and medium to address the aforementioned technical problems, thereby overcoming the deficiencies in the existing technology and achieving better prediction.

[0006] The following technical solution is adopted in this specification: Acquire surface electromyographic signals of the target lower limb; The optimal parameter combination (K, α) of the variational mode decomposition algorithm is obtained by optimizing K, where K is the number of decomposed modes, used to control the number of decomposed modes in the variational mode decomposition algorithm, and α is a penalty factor used to balance the strictness of the bandwidth constraint. The improved particle swarm optimization algorithm introduces negative gradient update and adaptive adjustment coefficients on the basis of the original particle swarm optimization algorithm. The negative gradient update is based on the fitness function gradient of the current particle and the best particle, which enhances the guidance of particles to converge to the individual optimal position and the global optimal position. The adaptive adjustment coefficient is positively correlated with the number of iterations and is used to adaptively adjust the update step size of particles representing the parameter combination (K, α), so that the particle search range transitions from local to global as the iteration process progresses. The variational mode decomposition algorithm with the optimal parameter combination (K, α) decomposes the electromyographic signal of the target lower limb surface into K intrinsic mode components; the K intrinsic mode components, based on the bandwidth constraint determined by α, represent the slow contraction mode of the lower limb muscles to the fast contraction mode of the lower limb muscles in order of increasing center frequency. Feature extraction is performed on each of the K intrinsic mode components, and the joint angle prediction result is obtained based on the feature extraction results.

[0007] Furthermore, the step of optimizing the parameter combination (K, α) of the variational mode decomposition algorithm by improving the particle swarm optimization algorithm to obtain the optimal parameter combination (K, α) specifically includes: Initialize the parameters of the improved particle swarm algorithm, including particle position and particle velocity, where each particle position represents a set of parameter combinations (K, α); Based on the current particle position, the variational mode decomposition algorithm is configured with the corresponding parameter combination (K, α). The variational mode decomposition algorithm based on the configured parameter combination (K, α) is used to perform variational mode decomposition on the electromyographic signal of the target lower limb surface, and the fitness value of the current particle is obtained according to the variational mode decomposition result. in, Represents the fitness function. Indicates signal reconstruction error. Indicates the modality number penalty weight; This represents the result of variational mode decomposition; Indicates the current iteration number; Indicates total electromyographic signal; Indicates the original electromyographic signal; Update the individual historical best position of the particle and the global historical best position of the particle swarm based on the current fitness value: The particle velocity is updated based on the negative gradient direction, and the particle position is adjusted according to the updated particle velocity: in, and Indicates the first The second iteration and the first In the nth iteration The velocity of each particle; , and These represent the first, second, and third learning factors, respectively. , , and These represent the first, second, third, and fourth random search factors, respectively, with a range of... 0,1 ; The negative gradient direction represents the optimal position of an individual particle, driving the particle to move closer to its historical optimal position. It represents the negative gradient direction of the global optimal position of the population, driving particles to move closer to the global optimal position of the population; Indicates the first The optimal fitness value corresponding to the individual historical best position of each particle; Indicates the first The current fitness value of each particle; Indicates the first The individual historical best position of each particle; Indicates the first The current position of each particle; This represents the optimal fitness value in the current particle swarm. This represents the global optimal position in the current particle swarm; Indicates the first In the nth iteration The position of each particle; This represents the adaptive adjustment coefficient. Indicates the maximum number of iterations. Monotonically increases with the number of iterations; Iteratively perform fitness value calculation, optimal position update and particle state update until the preset convergence condition is met, and output the optimal parameter combination (K, α) corresponding to the global optimal particle position.

[0008] Furthermore, the step of extracting features from the K intrinsic mode components and obtaining joint angle prediction results based on the feature extraction results specifically includes: Time-domain features, frequency-domain features, and nonlinear features are extracted from K intrinsic mode components respectively to obtain a multi-domain feature sequence; Principal component analysis is used to reduce the dimensionality of multi-domain feature sequences to obtain dimensionality-reduced feature sequences. The dimensionality-reduced feature sequence is input into the pre-trained Informer model, which outputs the joint angle prediction results.

[0009] Furthermore, the Informer model includes an encoder and a decoder. The encoder includes at least one ProbSparse self-attention mechanism module and at least one self-attention distillation module. The decoder includes a multi-head probabilistic sparse self-attention module, an encoder-decoder cross-attention module, and a fully connected layer. The process of inputting the dimensionality-reduced feature sequence into a pre-trained Informer model and outputting joint angle prediction results specifically includes: The dimensionality-reduced feature sequence is input into the encoder. The encoder extracts the long-range temporal dependency between the multi-scale features of the electromyography signal and the dynamic changes of joint angle through the ProbSparse self-attention mechanism module. The output of the ProbSparse self-attention mechanism module is hierarchically compressed by the self-attention distillation module to output high-dimensional semantic code. The high-dimensional semantic code and the preset starting label sequence are input into the decoder. The decoder models the internal temporal logic of the joint angle prediction sequence through a multi-head probabilistic sparse self-attention module. The encoder-decoder cross-attention module simultaneously receives the output of the multi-head probabilistic sparse self-attention module and the high-dimensional semantic code output of the encoder, and dynamically focuses on the features in the high-dimensional semantic code that are most relevant to the muscle activation state at the current prediction time. The output of the encoder-decoder cross-attention module is mapped to a continuous joint angle prediction sequence through a fully connected layer.

[0010] Furthermore, the extraction of time-domain features, frequency-domain features, and nonlinear features from the K intrinsic mode components specifically includes: Temporal features are extracted from K intrinsic mode components, and the temporal features include mean absolute value, root mean square value and number of zero crossings; Frequency domain features are extracted from K intrinsic mode components, and the frequency domain features include the median frequency and the average power frequency. Nonlinear features are extracted from K intrinsic mode components, and the nonlinear features include fuzzy entropy.

[0011] Furthermore, the step of performing dimensionality reduction processing on the multi-domain feature sequence using principal component analysis to obtain a dimensionality-reduced feature sequence includes: The multi-domain feature sequences are subjected to mean-variance standardization to obtain a standardized matrix; Calculate the sample covariance matrix of the standardized matrix, and perform eigenvalue decomposition on the sample covariance matrix to obtain eigenvalues ​​and corresponding eigenvectors; Calculate the contribution rate and cumulative contribution rate of each principal component based on the eigenvalues; Based on a preset cumulative contribution rate threshold, the top N principal components are selected, and the multi-domain feature sequence is projected onto the subspace formed by the top N principal components to obtain the dimensionality-reduced feature sequence.

[0012] This specification provides a joint angle prediction device based on surface electromyography signals, comprising: The data acquisition module is used to acquire electromyographic signals from the surface of the target lower limb. The parameter optimization module is used to optimize the parameter combination (K, α) of the variational mode decomposition algorithm to obtain the optimal parameter combination (K, α). K is the number of decomposed modes, used to control the number of decomposed modes in the variational mode decomposition algorithm, and α is a penalty factor used to balance the strictness of the bandwidth constraint. The improved particle swarm optimization algorithm introduces negative gradient update and adaptive adjustment coefficients on the basis of the original particle swarm optimization algorithm. The negative gradient update is based on the fitness function gradient of the current particle and the best particle, which enhances the guidance of particles to converge to the individual optimal position and the global optimal position. The adaptive adjustment coefficient is positively correlated with the number of iterations and is used to adaptively adjust the update step size of particles representing the parameter combination (K, α), so that the particle search range transitions from local to global as the iteration process progresses. The signal decomposition module is used to decompose the electromyographic signal of the target lower limb surface into K intrinsic mode components by configuring the variational mode decomposition algorithm with the optimal parameter combination (K, α); the K intrinsic mode components are based on the bandwidth constraint determined by α, and represent the slow contraction mode of the lower limb muscles to the fast contraction mode of the lower limb muscles in order of increasing center frequency. The angle prediction module is used to extract features from K intrinsic mode components and obtain joint angle prediction results based on the feature extraction results.

[0013] This specification provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described joint angle prediction method.

[0014] This specification provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the above-described joint angle prediction method.

[0015] The above-mentioned technical solutions adopted in this specification can achieve the following beneficial effects: This invention reconstructs the search dynamics of the particle swarm optimization algorithm by deeply integrating negative gradient guidance and adaptive adjustment coefficients. The negative gradient guidance term elevates parameter optimization from random walks to gradient-driven directional navigation. Particles update along the optimal direction based on the gradient of the fitness function relative to their current position with respect to the individual and global optima. Each search step revolves around the gradient information of the optimal solution, avoiding the blind oscillations caused by the reliance on velocity inertia in the original particle swarm optimization algorithm, and significantly improving the accuracy and efficiency of approximating the optimal parameter combination (K, α). The adaptive adjustment coefficients, which smoothly transition from local to global as the iteration progresses, initially use a compact search radius to finely mine the current gradient-directed region, fully exploring the potential of local extrema. In the later stages, the search step size is actively expanded, giving particles the kinetic energy to break through the current gradient trap. This effectively breaks the inherent constraint of negative gradients easily getting trapped in local optima and avoids premature convergence problems. The combination of these two approaches maintains both the high convergence efficiency and directional accuracy brought by gradient guidance throughout the iteration process, while also gaining continuous global exploration capabilities through adaptive range adjustment. This allows the optimal parameter combination (K, α) obtained through optimization to accurately adapt to the non-stationary characteristics and multi-scale features of electromyographic signals. K can cover the complete motor unit recruitment pattern from low-frequency slow contraction to high-frequency fast contraction, while α accurately balances the bandwidth constraints of each modal component. Finally, the K intrinsic modal components obtained through VMD decomposition achieve the physical interpretability separation of muscle contraction patterns in the frequency domain, laying a feature foundation for high-precision and robust joint angle prediction. Attached Figure Description

[0016] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments of this application and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0017] Figure 1 This is a schematic diagram of joint angle prediction provided in this specification; Figure 2 This is a schematic diagram of an experimental data collection process provided in this manual; Figure 3 This manual provides a schematic diagram of sEMG acquisition under different motion modes. Figure 4 This is a schematic diagram showing a comparison of sEMG time domain before and after filtering, as provided in this specification. Figure 5 A schematic diagram of the convergence curves of NGSPSO and standard PSO provided for this specification; Figure 6 This document provides a schematic diagram of the NGSPSO algorithm for optimizing VMD parameters. Figure 7 This is a schematic diagram of the principal component contribution rate of PCA provided in this specification; Figure 8 This is a schematic diagram of an Informer model structure provided in this specification; Figure 9 This is a schematic diagram of a VMD decomposition waveform provided in this specification; Figure 10 The following diagrams illustrate joint angle prediction provided in this specification: (a) is a diagram of hip joint angle prediction for walking on flat ground; (b) is a diagram of knee joint angle prediction for walking on flat ground; (c) is a diagram of hip joint angle prediction for climbing stairs; and (d) is a diagram of knee joint angle prediction for climbing stairs. Figure 11 The following diagrams illustrate a method for predicting joint angles provided in this specification: (a) is a diagram of the hip joint angle when walking on flat ground; (b) is a diagram of the knee joint angle when walking on flat ground; (c) is a diagram of the hip joint angle when climbing stairs; and (d) is a diagram of the knee joint angle when climbing stairs. Figure 12 This is a schematic diagram of a joint angle prediction device provided in this specification. Figure 13 This is a schematic diagram of a computer device provided for this specification. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this specification clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments in this specification without creative effort are within the scope of protection of this application.

[0019] The technical solution provided by this invention can be applied to motion intention recognition scenarios based on sEMG. sEMG feature extraction is a key prerequisite for realizing motion intention recognition and joint angle prediction. Researchers have used Discrete Wavelet Transform (DWT) to extract electromyographic time-frequency features, combined with an artificial neural network classifier, achieving an accuracy of 98.5% in action classification. However, traditional time-domain and frequency-domain methods are difficult to adapt to the time-varying characteristics of signals, and time-frequency analysis methods suffer from modal aliasing and weak adaptive decomposition capabilities. Against this backdrop, Variational Mode Decomposition (VMD) methods have gradually attracted attention. Traditional VMD parameter settings rely on empirical trial and error, making it difficult to adapt to sudden changes in sEMG time-frequency characteristics. Wu Tian et al. proposed an improved Sparrow Algorithm (ISSA) to optimize VMD, improving the sEMG noise reduction signal-to-noise ratio by 15.2%. Li Xiao et al. proposed a CEEMD-VMD-SIST hybrid architecture that significantly suppressed frequency aliasing effects; however, its Sparrow Algorithm is prone to getting trapped in local optima, and the computational complexity of CEEMD-VMD limits its application in real-time exoskeleton control. Particle Swarm Optimization (PSO) is widely used for VMD parameter tuning due to its fast convergence speed and few parameters, but standard PSO also suffers from premature convergence. Directly using the multimodal components after VMD decomposition as input features leads to the curse of dimensionality. Principal Component Analysis (PCA) extracts principal directions through orthogonal transformations, providing an effective path for high-dimensional feature compression. Li et al. verified that PCA can compress the dimensionality of lower limb sEMG features by 80% while retaining 90% of the original variance, but they did not thoroughly verify its cross-gait generalization ability.

[0020] Establishing a precise predictive relationship between multi-dimensional sEMG features and continuous joint angles is crucial for achieving high-precision lower limb motion estimation. Early studies relied heavily on linear models with limited accuracy. With the development of deep learning technology, Convolutional Neural Networks (CNNs) and Long Short-Term Memory Networks (LSTMs) have been successfully applied to continuous joint angle estimation. Tang et al. proposed a CNN-LSTM network based on an attention mechanism, using 10-channel sEMG to predict knee angles in three gait states, achieving better accuracy than traditional models. Liu used a backpropagation neural network (BPNN) to fuse sEMG and kinematic data, achieving an average RMSE of 3.9°. However, LSTM models suffer from information decay when processing long-sequence data, making it difficult to effectively extract key sEMG information. The Transformer architecture, due to its self-attention mechanism's advantages in long-range dependency modeling, has been introduced into lower limb motion estimation tasks. Zeng et al. proposed a Transformer-based prediction model that reduced the RMSE to 3.094°. However, the standard Transformer struggles to handle extremely long sequences due to its computational complexity and memory consumption. In contrast, the Informer model, as an efficient variant of the Transformer, can more effectively capture temporal dependencies and key features in data when processing sequences. Wan et al. verified the effectiveness of fusing gait features with the Informer model in continuous joint angle prediction, but their method focuses on external information fusion rather than addressing the core challenge of non-stationarity within sEMG. Lu et al. applied the Informer model to sEMG, achieving interval prediction of elbow joint forces. However, their wavelet transform approach has limitations in adaptive signal decomposition, and relying solely on mean and variance features cannot fully represent all information related to complex motion.

[0021] In summary, this invention proposes a joint angle prediction method based on multi-channel sEMG, aiming to improve prediction accuracy. Specifically, sEMG and corresponding joint angle data are first collected, and then the VMD method is used to decompose the sEMG. The number of IMF components and the penalty factor in VMD are optimized using negative gradient and adaptive particle swarm optimization (NGSPSO). Subsequently, multi-domain features are extracted from each IMF, and PCA is used to reduce the dimensionality of the features. Finally, the Informer joint angle prediction model is introduced. The effectiveness of this method is verified experimentally, and the results show that it has higher accuracy than traditional methods.

[0022] The following is combined with Figures 1-11 The joint angle prediction method of the present invention is described.

[0023] Figure 1 This is one of the flowcharts illustrating the joint angle prediction method provided by the present invention, such as... Figure 1As shown, the method includes the following: S1. Acquire electromyographic signals on the surface of the target lower limb.

[0024] S2. Optimize the parameter combination (K, α) of the variational mode decomposition algorithm to obtain the optimal parameter combination (K, α), where K is the number of decomposed modes, used to control the number of decomposed modes in the variational mode decomposition algorithm, and α is a penalty factor used to balance the strictness of the bandwidth constraint. The improved particle swarm optimization algorithm introduces negative gradient updates and adaptive adjustment coefficients based on the original particle swarm optimization algorithm. The negative gradient update is based on the fitness function gradient of the current particle and the optimal particle, enhancing the guidance of particles towards their individual optimal position and the global optimal position. The adaptive adjustment coefficient is positively correlated with the number of iterations and is used to adaptively adjust the update step size of the particles representing the parameter combination (K, α), so that the particle search range transitions from local to global as the iteration progresses.

[0025] S3. The electromyographic signal on the surface of the target lower limb is decomposed into K intrinsic mode components by a variational mode decomposition algorithm with the optimal parameter combination (K, α). The K intrinsic mode components are based on the bandwidth constraint determined by α, and represent the slow contraction mode of the lower limb muscles to the fast contraction mode of the lower limb muscles in order of increasing center frequency.

[0026] S4. Extract features from each of the K intrinsic mode components and obtain the joint angle prediction results based on the feature extraction results.

[0027] Based on the above Figure 1 In the illustrated embodiment, for example, in S1 above, sEMG acquisition is a key prerequisite for achieving precise exoskeleton control. Lower limb movement patterns are driven by the coordinated action of specific muscle groups. Based on the main active muscles in the lower limbs during walking and climbing stairs, six muscles were selected: rectus femoris, biceps femoris, vastus lateralis, tibialis anterior, gastrocnemius lateralis, and soleus. The experimental data acquisition process is as follows: Figure 2 As shown, sEMG data was acquired using the RS-EMG8 biosignal acquisition system at a sampling frequency of 1000Hz. Joint angle data were acquired using the WT901BC-TTL posture angle sensor, which was attached to the corresponding position of the subject's lower limb at a sampling frequency of 200Hz.

[0028] Before the experiment, the subjects' skin was cleaned to prevent sweat and oil from affecting electrode adhesion and signal quality; the electrode array was oriented in the same direction as muscle activity to maintain stable and clear signals. A total of 10 healthy subjects participated in this study, including 9 healthy individuals and 1 individual with mild motor impairment. Subject information is shown in Table 1. All subjects were able to perform the flat walking and stair climbing exercises normally.

[0029] Table 1 Physical characteristics of the subjects In the flat-ground walking exercise experiment, subjects performed cyclical alternations of walking at a constant pace; in the stair-climbing exercise experiment, each subject completed one step up a stair as a data set; each data collection session lasted at least 30 seconds, and subjects rested for 5 minutes after every 3 data sets to ensure the accuracy of the motion data. Taking subject 3 as an example, the initial state and signal acquisition for the two movement modes were as follows: Figure 3 As shown.

[0030] Furthermore, for the acquired raw sEMG, a fourth-order Butterworth bandpass filter (20-450Hz) and a 50Hz notch filter were used to remove noise and power frequency interference; taking the rectus femoris muscle under flat ground walking as an example, the following results were obtained: Figure 3 The image shows the time-domain plots of the electromyography (EMG) signals before and after filtering. (From...) Figure 4 It can be seen that high-frequency noise and power frequency interference in the filtered signal are effectively suppressed, the overall waveform is smoother, and the signal quality is significantly improved, providing a reliable data foundation for subsequent signal feature extraction.

[0031] Based on the above Figure 1 The illustrated embodiment, for example, in S2 above, VMD is an adaptive signal processing method based on constrained variational optimization, which obtains subsequences at different frequency scales through mode decomposition. VMD decomposes the original electromyography signal into a series of modal components, with the goal of minimizing the sum of the estimated bandwidths of each modality. It may include the following steps:

[0032] S2.1, Original Signal It can be directly defined as: ; in, Let represent the k-th modal component, and K represent the number of decomposed modes. The decomposition process solves a variational problem under constraints, with the objective function being:

[0033] ; In the formula: These are the sets of decomposed subsequences and center frequencies, respectively. represents the time derivative, and * represents convolution.

[0034] S2.2, NGSPSO optimizes VMD parameters.

[0035] When VMD is used to decompose sEMG, the number of preset IMF components K and penalty factors α has a significant impact on decomposition performance. Standard PSO is prone to getting trapped in local optima when optimizing VMD parameters. This invention uses NGSPSO to achieve adaptive selection of VMD parameters. The improved particle velocity update and position formulas are as follows:

[0036] ; ; In the formula: This represents the difference between the current optimal fitness value and the current fitness value of the i-th particle. Taking the negative of both values ​​reflects the particle's search direction. This represents the difference between the optimal fitness value of the population and the fitness of the current particle. and Indicates the first The second iteration and the first In the nth iteration The velocity of each particle; It is the historical best position of particle i. It is the globally optimal position; , and These represent the first, second, and third learning factors, respectively; a = 0.01, b = 1, c = 0.002; This represents the adaptive adjustment coefficient; , , and These represent the first, second, third, and fourth random search factors, respectively, with a range of 0. <R<1。

[0037] Adaptive adjustment coefficient Based on the definition of the arctangent function, the expression is: ; In the formula: This represents the current iteration number. To find the maximum number of iterations, when its derivative... , As the iteration process monotonically increases, when , At this stage, the algorithm focuses on global exploration; As the number of nodes increases, the algorithm shifts to a locally refined search, thereby achieving an adaptive balance in the search strategy. When NGSPSO searches for the optimal solution, the chosen fitness function is achieved by constructing an optimization objective function that balances the accuracy of fused signal reconstruction with modal sparsity, as shown in the following formula:

[0038] ; ; In the formula: where, Represents the fitness function. Indicates signal reconstruction error. Indicates the modality number penalty weight; This represents the result of variational mode decomposition; Indicates the current iteration number; Indicates total electromyographic signal; This represents the original electromyographic signal.

[0039] To evaluate the performance of the NGSPSO algorithm in VMD parameter optimization, this invention compares it with the standard PSO algorithm under the same fitness function. The convergence performance comparison results are as follows: Figure 5 As shown, from Figure 5 As can be seen, the NGSPSO algorithm exhibits a faster convergence speed in the early stages of iteration and achieves a better fitness value, indicating that it achieves a better balance between global search and local optimization. Therefore, the flowchart of the NGSPSO algorithm for optimizing VMD parameters is as follows: Figure 6 As shown, when the maximum number of iterations (100) is reached, the optimal parameter K=5 is output. To further quantify the optimization effect of NGSPSO on VMD parameters, the number of IMF components and the penalty factor values ​​corresponding to different lower limb muscle sEMGs after NGSPSO optimization are shown in Table 2.

[0040] Table 2 Optimal VMD parameters for each muscle As shown in Table 2, after global optimization by NGSPSO, the sEMG signals of different muscles can be most effectively separated into modes strongly associated with lower limb joint movement when decomposed into 5 IMF components, laying a solid foundation for subsequent accurate feature extraction and high-precision joint angle prediction.

[0041] Based on the above Figure 1 In the illustrated embodiment, for example, in S4 above, in order to fully express the changing trend of electromyographic signals and their relationship with joint movement, time-domain, frequency-domain, and nonlinear features are extracted from each modal data as inputs to the prediction model.

[0042] S4.1 Time-domain characteristics include mean absolute value, root mean square value, and number of zero crossings.

[0043] S4.1.1 The mean absolute value (MAV) can intuitively reflect the average intensity of the electromyographic signal amplitude, while the root mean square value (RMS) can display the effective value of the electromyographic signal. The calculation formula is as follows: ; In the formula: For a single IMF component, the time interval is [0,T].

[0044] S4.1.2. The number of zero-crossing points represents the fluctuation of electromyographic signals over time. The calculation formula is as follows: ; In the formula: sgn(⋅) is the sign function. .

[0045] S4.2. Frequency domain characteristics include median frequency and average power frequency. The median frequency (mf) and average power frequency (mpf) represent the median frequency and the average power frequency distribution of the electromyographic signal, respectively. The calculation formulas are as follows:

[0046] ; ; In the formula: For the Nyquist frequency, Let be the power spectral density function of the electromyographic signal. This is an integral cumulative function.

[0047] S4.3. To quantify the complexity and irregularity of electromyographic signals, fuzzy entropy is introduced as a nonlinear dynamic feature. A vector sequence is constructed for each individual IMF component. The formula for calculating fuzzy entropy is: ; In the formula: m is the segment length, and r is the tolerance. This represents the average similarity between m-dimensional vectors. This represents the average similarity between m+1 dimensional vectors.

[0048] Using the above feature extraction method, the six features are arranged sequentially to construct a 6-dimensional feature vector for each IMF. Finally, the six channels are concatenated to obtain the global feature vector as follows: ; .

[0049] S4.4 Principal Component Analysis (PCA) Dimensionality Reduction.

[0050] To reduce redundant information in the features, improve the accuracy of joint angle estimation, and maintain the computational efficiency of the model, the PCA method is applied to the global feature vector after feature extraction. First, the 180-dimensional feature vector is standardized column-wise to obtain the standardized matrix. Calculate the sample covariance matrix:

[0051] ; Then solve for the eigenvalues ​​and eigenvectors of the covariance matrix. Arrange the eigenvalues ​​in descending order. Calculate the contribution rate. and cumulative contribution rate The formula is as follows:

[0052] ; To retain most of the information while minimizing the input dimensionality, such as Figure 7 As shown, the cumulative contribution rate of the first four principal components has reached 90%. The first four feature sequences are selected to replace the original variables as the input of the Informer model, and the dimensionality-reduced feature input is shown in Equation (17): ; In the formula: The dimensionality reduction feature is for time step t.

[0053] Based on the above Figure 1 The illustrated embodiment, for example, shows that in S4 above, the Transformer model suffers from quadratic time complexity and high memory consumption. Therefore, this invention employs the Informer model, which probabilistically simplifies the original self-attention mechanism of the Transformer, reduces computational complexity, and effectively improves accuracy. The structure of the Informer model is as follows: Figure 8 As shown.

[0054] Compared to traditional self-attention mechanisms, the ProbSparse self-attention mechanism sparsifies the query vector in the traditional mechanism and generates a new sparse query, thereby reducing computational complexity. The formula for the sparse self-attention mechanism is as follows: ; In the formula: A is the attention mechanism; Q, K, and V are matrices formed by linear transformations; T is the matrix transpose; softmax is the activation function; and d is the input dimension of the variable. This is the sparsed matrix.

[0055] The encoder consists of multiple ProbSparse self-attention mechanisms and distillation mechanisms, designed to process input from time-series data and capture long-term dependencies within the data. The feature sequence, after PCA dimensionality reduction, is added to a sinusoidal positional code and used as input to the encoder, processed by a multi-head ProbSparse self-attention module. The output is then processed through residual connections and layer normalization (LayerNorm) to obtain intermediate features. To progressively compress the sequence length, a distillation module is introduced after each layer.

[0056] ; ; ; ; In the formula: P is the sine position code, These are placeholders for the target sequence. Conv1d represents one-dimensional convolution, ELU is the activation function, and MaxPool is max pooling. Finally, after two distillation layers, the encoder output is:

[0057] .

[0058] The decoder employs a generative prediction framework, incorporating multi-head mask sparse self-attention and cross-attention mechanisms to achieve single-step prediction of joint angle sequences. The decoder input consists of a start marker and a target placeholder concatenated, as shown in the following formula:

[0059] ; In the formula: As the starting marker, Placeholders for the target sequence.

[0060] To fuse the global feature information extracted by the encoder, the decoder employs an encoder-decoder cross-attention mechanism, as shown in the following formula: ; In the formula: Generated from the intermediate state of the decoder. From encoder final output .

[0061] Finally, a fully connected layer maps the decoder output to joint angle predictions, as shown in the following formula: ; In the formula: This is the weight matrix. The bias term has an output dimension of 2, corresponding to the predicted angles of the hip and knee joints, respectively.

[0062] To verify the effectiveness of the proposed method, this invention constructs a complete verification framework based on a standard experimental environment. The hardware platform is an NVIDIA RTX 4050 GPU, and the software environment integrates PyTorch, MATLAB 2023a, and TensorBoard to build a collaborative computing architecture. When applying the Informer model to the joint angle estimation task, hyperparameter configuration has a crucial impact on model performance. To fully explore the model's potential and ensure its superior performance in practical applications, this invention adopts a grid search strategy. Grid search systematically traverses the possible combinations of each hyperparameter, and combined with quantitative evaluation of joint angle estimation and comparative analysis of experimental results, ensures the optimal selection of hyperparameters. The final determined basic hyperparameter configuration is shown in Table 3.

[0063] Table 3 Basic hyperparameters of the Informer model Furthermore, the present invention also provides experimental results and analysis, including: sEMG feature extraction results based on NGSPSO-VMD.

[0064] To avoid introducing future data into model training, this invention divides the dataset into training and testing sets. Based on the training set data, NGSPSO is used to optimize the VMD parameters and perform signal decomposition. Taking the electromyographic signal on the surface of the biceps femoris muscle as an example, the waveform obtained after VMD decomposition is as follows: Figure 9 As shown, the NGSPSO-VMD method achieves adaptive decomposition of the modal function, solving problems such as over-decomposition and under-decomposition. This result verifies the feasibility of NGSPSO in optimizing VMD parameters. When evaluating model performance, the difference between predicted and actual joint angles is usually quantified. However, the accuracy of the model cannot be accurately assessed solely based on the goodness of fit between the predicted and actual curves. Therefore, this invention uses root mean square error (RMSE) and mean absolute error (MAE) as standardized evaluation metrics, calculated as follows:

[0065] ; ; In the formula: This is the actual value of the joint angle. is the estimated value of the joint angle, and N is the number of samples.

[0066] This invention proposes a joint angle estimation model combining VMD and Informer models. The decomposition properties of VMD enable the regression model to effectively learn the intrinsic relationship between input and output. To verify the performance of the proposed model, experiments were conducted in two typical motion scenarios: walking on flat ground and climbing stairs. The model's predictions were compared and analyzed with actual angle measurements. Figure 10 As shown in the figure. The prediction experiment results show that the hip and knee joint angle curves predicted by the VMD-Informer model are highly consistent with the original angle curves in terms of the changing trend in the time series dimension, showing good fitting consistency, which proves the high accuracy and reliability of the model. The experiment confirms that after adding the nonlinear feature of fuzzy entropy, the feature set is more complete, which ultimately improves the prediction accuracy.

[0067] To verify the effectiveness of the VMD-Informer model, this invention compares its joint angle prediction performance with that of VMD-LSTM, VMD-Transformer, and VMD-ELMAN models. Figure 11As shown, the VMD-Informer model significantly outperforms the comparison models. In knee joint prediction, its estimation results are closer to the true values, and it exhibits less fluctuation and stronger stability at the inflection point of motion. In hip joint prediction, VMD-Informer demonstrates a clear advantage, with smaller prediction errors and less fluctuation caused by noise interference, indicating stronger resistance to noise interference and more reliable and stable prediction results.

[0068] To verify the generalization performance of the VMD-Informer model, this invention compared and analyzed the prediction RMSE of three models—VMD-ELMAN, VMD-LSTM, VMD-Transformer, and VMD-Informer—for hip and knee joint angles in two typical gait scenarios: walking on flat ground and climbing stairs, based on experimental data from multiple subjects. The results are shown in Table 4. The results indicate that in both walking on flat ground and climbing stairs tasks, the VMD-Informer model significantly outperforms the other comparative models in predicting hip and knee joint angles.

[0069] Table 4. RMSE of the joint angle prediction model under different time states Furthermore, this invention utilizes MAE to quantitatively analyze the performance of different models in joint angle prediction, as shown in Table 5. The results show that the VMD-Informer model performs best in hip and knee joint prediction. Its prediction error is significantly lower than that of the VMD-LSTM and VMD-ELMAN models. Especially in the scenario of climbing stairs, the VMD-Informer's advantage in cross-subject prediction error is more pronounced, further validating the significant advantages of combining multi-scale VMD decomposition with the Informer architecture.

[0070] Table 5 MAE of the joint angle prediction model under different time states To verify the model's cross-individual generalization ability, this invention employs leave-one-out cross-validation, using a dataset containing 10 subjects. To fully reflect the model's adaptability to diverse physiological characteristics, four representative subjects with significant body size differences were selected for analysis. The results are shown in Table 6. Experimental results show that VMD-Informer performs best in cross-individual prediction, reducing errors by 8.4% compared to VMD-Transformer. In the representative individual test, the model maintains optimal performance across subjects with different body sizes, indicating that VMD-Informer possesses good cross-individual generalization ability.

[0071] Table 6. Validation results of cross-individual generalization ability This invention proposes a joint angle prediction method based on VMD-Informer and surface electromyography (sEMG) signals. It utilizes the NGSPSO algorithm to adaptively adjust VMD parameters, perform PCA feature dimensionality reduction, and collaboratively optimize long-sequence modeling using the Informer model, effectively improving the accuracy of lower limb joint angle prediction using sEMG. To verify the method's performance in real-world scenarios, system tests were conducted on three subjects with significant differences in body size in two typical gait scenarios: walking on flat ground and climbing stairs. Experimental results show that the proposed method significantly outperforms traditional VMD-LSTM and VMD-ELMAN methods in both RMSE and MAE for hip and knee joint angle prediction, while also exhibiting good cross-individual generalization ability and real-time response performance.

[0072] Currently, the experimental tasks only target two common gait scenarios: walking on flat ground and climbing stairs. Future research will further expand the patient sample size and adopt a grouped controlled experimental design to systematically evaluate the applicability and generalization performance of the model in more complex gait scenarios such as going uphill and downhill. At the same time, it will explore the fusion methods of multimodal data such as sEMG, IMU, and plantar force signals, thereby further expanding its application scenarios and practicality in rehabilitation exoskeletons, sports science, and human-computer interaction.

[0073] The joint angle prediction device provided by the present invention is described below. The joint angle prediction device described below and the joint angle prediction method described above can be referred to in correspondence.

[0074] Figure 12 Here is a schematic diagram of the structure of a joint angle prediction device provided by the present invention. For example, please refer to [link to schematic diagram]. Figure 12 As shown, the joint angle prediction device may include: The data acquisition module is used to acquire electromyographic signals on the surface of the target lower limb.

[0075] The parameter optimization module is used to optimize the parameter combination (K, α) of the variational mode decomposition algorithm to obtain the optimal parameter combination (K, α). K is the number of decomposed modes, used to control the number of decomposed modes in the variational mode decomposition algorithm, and α is a penalty factor used to balance the strictness of the bandwidth constraint. The improved particle swarm optimization algorithm introduces negative gradient update and adaptive adjustment coefficients on the basis of the original particle swarm optimization algorithm. The negative gradient update is based on the fitness function gradient of the current particle and the best particle, which enhances the guidance of particles to converge to the individual optimal position and the global optimal position. The adaptive adjustment coefficient is positively correlated with the number of iterations and is used to adaptively adjust the update step size of particles representing the parameter combination (K, α), so that the particle search range transitions from local to global as the iteration process progresses.

[0076] The signal decomposition module is used to decompose the electromyographic signal of the target lower limb surface into K intrinsic mode components by configuring the variational mode decomposition algorithm with the optimal parameter combination (K, α). The K intrinsic mode components represent the slow contraction mode of the lower limb muscles to the fast contraction mode of the lower limb muscles in order of increasing center frequency based on the bandwidth constraint determined by α.

[0077] The angle prediction module is used to extract features from K intrinsic mode components and obtain joint angle prediction results based on the feature extraction results.

[0078] Specific limitations regarding the joint angle prediction device can be found in the limitations on joint angle prediction described above, and will not be repeated here. Each module in the aforementioned joint angle prediction device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in hardware or independently of the processor in a computer device, or stored in software in the memory of a computer device, so that the processor can call and execute the corresponding operations of each module.

[0079] This specification also provides a computer-readable storage medium storing a computer program that can be used to execute the above-described... Figure 1 The provided method for predicting joint angles.

[0080] This instruction manual also provides Figure 13 The schematic diagram of the computer device shown is as follows: Figure 13 At the hardware level, the computer device includes a processor, internal bus, network interface, memory, and non-volatile memory, and may also include other hardware required for business operations. The processor reads the corresponding computer program from the non-volatile memory into memory and then runs it to achieve the above-mentioned functions. Figure 1 The provided method for predicting joint angles.

[0081] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the methods described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0082] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

Claims

1. A method for predicting joint angles, characterized in that, include: Acquire surface electromyographic signals of the target lower limb; The optimal parameter combination (K, α) of the variational mode decomposition algorithm is obtained by optimizing K, where K is the number of decomposed modes, used to control the number of decomposed modes in the variational mode decomposition algorithm, and α is a penalty factor used to balance the strictness of the bandwidth constraint. The improved particle swarm optimization algorithm introduces negative gradient update and adaptive adjustment coefficients on the basis of the original particle swarm optimization algorithm. The negative gradient update is based on the fitness function gradient of the current particle and the best particle, which enhances the guidance of particles to converge to the individual optimal position and the global optimal position. The adaptive adjustment coefficient is positively correlated with the number of iterations and is used to adaptively adjust the update step size of particles representing the parameter combination (K, α), so that the particle search range transitions from local to global as the iteration process progresses. The variational mode decomposition algorithm with the optimal parameter combination (K, α) decomposes the electromyographic signal of the target lower limb surface into K intrinsic mode components; the K intrinsic mode components, based on the bandwidth constraint determined by α, represent the slow contraction mode of the lower limb muscles to the fast contraction mode of the lower limb muscles in order of increasing center frequency. Feature extraction is performed on each of the K intrinsic mode components, and the joint angle prediction result is obtained based on the feature extraction results.

2. The joint angle prediction method according to claim 1, characterized in that, The process of optimizing the parameter combination (K, α) of the variational mode decomposition algorithm by improving the particle swarm optimization algorithm to obtain the optimal parameter combination (K, α) specifically includes: Initialize the parameters of the improved particle swarm algorithm, including particle position and particle velocity, where each particle position represents a set of parameter combinations (K, α); Based on the current particle position, the variational mode decomposition algorithm is configured with the corresponding parameter combination (K, α). The variational mode decomposition algorithm based on the configured parameter combination (K, α) is used to perform variational mode decomposition on the electromyographic signal of the target lower limb surface, and the fitness value of the current particle is obtained according to the variational mode decomposition result. in, Represents the fitness function. Indicates signal reconstruction error. Indicates the modality number penalty weight; This represents the result of variational mode decomposition; Indicates the current iteration number; Indicates the total number of iterations; Indicates the original electromyographic signal; Update the individual historical best position of the particle and the global historical best position of the particle swarm based on the current fitness value: The particle velocity is updated based on the negative gradient direction, and the particle position is adjusted according to the updated particle velocity: in, and Indicates the first The second iteration and the first In the nth iteration The velocity of each particle; , and These represent the first, second, and third learning factors, respectively. , , and These represent the first, second, third, and fourth random search factors, respectively, with a range of... 0,1 ; The negative gradient direction represents the optimal position of an individual particle, driving the particle to move closer to its historical optimal position. It represents the negative gradient direction of the global optimal position of the population, driving particles to move closer to the global optimal position of the population; Indicates the first The optimal fitness value corresponding to the individual historical best position of each particle; Indicates the first The current fitness value of each particle; Indicates the first The individual historical best position of each particle; Indicates the first The current position of each particle; This represents the optimal fitness value in the current particle swarm. This represents the global optimal position in the current particle swarm; Indicates the first In the nth iteration The position of each particle; This represents the adaptive adjustment coefficient. Indicates the maximum number of iterations. Monotonically increases with the number of iterations; Iteratively perform fitness value calculation, optimal position update and particle state update until the preset convergence condition is met, and output the optimal parameter combination (K, α) corresponding to the global optimal particle position.

3. The joint angle prediction method according to claim 1, characterized in that, The step of extracting features from K intrinsic mode components and obtaining joint angle prediction results based on the feature extraction results specifically includes: Time-domain features, frequency-domain features, and nonlinear features are extracted from K intrinsic mode components respectively to obtain a multi-domain feature sequence; Principal component analysis is used to reduce the dimensionality of multi-domain feature sequences to obtain dimensionality-reduced feature sequences. The dimensionality-reduced feature sequence is input into the pre-trained Informer model, which outputs the joint angle prediction results.

4. The joint angle prediction method according to claim 3, characterized in that, The Informer model includes an encoder and a decoder. The encoder includes at least one ProbSparse self-attention mechanism module and at least one self-attention distillation module. The decoder includes a multi-head probabilistic sparse self-attention module, an encoder-decoder cross-attention module, and a fully connected layer. The process of inputting the dimensionality-reduced feature sequence into a pre-trained Informer model and outputting joint angle prediction results specifically includes: The dimensionality-reduced feature sequence is input into the encoder. The encoder extracts the long-range temporal dependency between the multi-scale features of the electromyography signal and the dynamic changes of joint angle through the ProbSparse self-attention mechanism module. The output of the ProbSparse self-attention mechanism module is hierarchically compressed by the self-attention distillation module to output high-dimensional semantic code. The high-dimensional semantic code and the preset starting label sequence are input into the decoder. The decoder models the internal temporal logic of the joint angle prediction sequence through a multi-head probabilistic sparse self-attention module. The encoder-decoder cross-attention module simultaneously receives the output of the multi-head probabilistic sparse self-attention module and the high-dimensional semantic code output of the encoder, and dynamically focuses on the features in the high-dimensional semantic code that are most relevant to the muscle activation state at the current prediction time. The output of the encoder-decoder cross-attention module is mapped to a continuous joint angle prediction sequence through a fully connected layer.

5. The joint angle prediction method according to claim 3, characterized in that, The extraction of time-domain features, frequency-domain features, and nonlinear features from the K intrinsic mode components specifically includes: Temporal features are extracted from K intrinsic mode components, and the temporal features include mean absolute value, root mean square value and number of zero crossings; Frequency domain features are extracted from K intrinsic mode components, and the frequency domain features include the median frequency and the average power frequency. Nonlinear features are extracted from K intrinsic mode components, and the nonlinear features include fuzzy entropy.

6. The joint angle prediction method according to claim 3, characterized in that, The step of performing dimensionality reduction processing on multi-domain feature sequences using principal component analysis to obtain dimensionality-reduced feature sequences includes: The multi-domain feature sequences are subjected to mean-variance standardization to obtain a standardized matrix; Calculate the sample covariance matrix of the standardized matrix, and perform eigenvalue decomposition on the sample covariance matrix to obtain eigenvalues ​​and corresponding eigenvectors; Calculate the contribution rate and cumulative contribution rate of each principal component based on the eigenvalues; Based on a preset cumulative contribution rate threshold, the top N principal components are selected, and the multi-domain feature sequence is projected onto the subspace formed by the top N principal components to obtain the dimensionality-reduced feature sequence.

7. A joint angle prediction device based on surface electromyography signals, characterized in that, include: The data acquisition module is used to acquire electromyographic signals from the surface of the target lower limb. The parameter optimization module is used to optimize the parameter combination (K, α) of the variational mode decomposition algorithm to obtain the optimal parameter combination (K, α). K is the number of decomposed modes, used to control the number of decomposed modes in the variational mode decomposition algorithm, and α is a penalty factor used to balance the strictness of the bandwidth constraint. The improved particle swarm optimization algorithm introduces negative gradient update and adaptive adjustment coefficients on the basis of the original particle swarm optimization algorithm. The negative gradient update is based on the fitness function gradient of the current particle and the best particle, which enhances the guidance of particles to converge to the individual optimal position and the global optimal position. The adaptive adjustment coefficient is positively correlated with the number of iterations and is used to adaptively adjust the update step size of particles representing the parameter combination (K, α), so that the particle search range transitions from local to global as the iteration process progresses. The signal decomposition module is used to decompose the electromyographic signal of the target lower limb surface into K intrinsic mode components by configuring the variational mode decomposition algorithm with the optimal parameter combination (K, α); the K intrinsic mode components are based on the bandwidth constraint determined by α, and represent the slow contraction mode of the lower limb muscles to the fast contraction mode of the lower limb muscles in order of increasing center frequency. The angle prediction module is used to extract features from K intrinsic mode components and obtain joint angle prediction results based on the feature extraction results.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the joint angle prediction method as described in any one of claims 1 to 6.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the joint angle prediction method as described in any one of claims 1 to 6.

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