A pathological gait nonlinear compensation analysis method and system based on a duffing oscillator graph convolution network

Abstract

This invention discloses a method and system for nonlinear compensation analysis of pathological gait based on a Duffing oscillator graph convolutional network, belonging to the fields of visual gait analysis, nonlinear dynamics modeling, and intelligent rehabilitation assessment. The method acquires the temporal sequence of the human gait skeleton and constructs a spatiotemporal skeleton graph. It then uses a spatiotemporal graph convolutional network to extract joint node features. The end-time node features are extracted as external driving forces to drive the Duffing oscillators corresponding to each joint. Based on a dynamic model including linear stiffness, nonlinear stiffness, and damping terms, and using semi-implicit Euler integrals to update the oscillator states, the nonlinear responses of each joint are obtained. The response results are then constructed as a global feature modulation field to enhance the original spatiotemporal features, ultimately outputting abnormal muscle categories, lesion combinations, or stability analysis results. This invention can explicitly characterize the nonlinear dynamic features in pathological gait, improving the recognition effect of pathological gait analysis and enhancing the interpretability of the results.

Description

Technical Field

[0001] This invention relates to the fields of visual gait analysis, graph neural networks, nonlinear dynamics modeling and intelligent rehabilitation assessment, and in particular to a method and system for nonlinear compensation analysis of pathological gait based on Duffing oscillator graph convolutional networks. Background Technology

[0002] Compensatory behaviors in pathological gait are often accompanied by significant nonlinear dynamics, especially near key phases such as heel strike, support-turn swing, and sudden instability. These phases exhibit strong trajectory deflection, amplified local oscillations, and complex phenomena such as evolution from stable to periodic, bistable, or even chaotic states. While traditional graph convolutional networks based on skeleton sequences can extract spatiotemporal correlation features, they mostly compress these nonlinear changes into statistical features, making it difficult to clearly characterize the physical evolution mechanism of pathological gait.

[0003] In existing technologies, some deep learning-based gait recognition methods rely on simple convolution stacking or attention reweighting to enhance feature representation. However, these methods lack specialized dynamic modeling for the nonlinear state transitions of gait, making it difficult to explain why certain joints exhibit continuous oscillations, bistable switching, or slowed recovery speeds under pathological conditions. Therefore, a gait analysis method is needed that can directly embed the Duffing nonlinear oscillation mechanism into graph convolutional networks to extract interpretable nonlinear compensation features from skeleton time-series data, thereby improving the ability to recognize and analyze pathological gait. Summary of the Invention

[0004] The purpose of this invention is to provide a nonlinear compensation analysis method for pathological gait based on Duffing oscillator graph convolutional networks, in order to solve the problems of existing methods being unable to explicitly characterize the nonlinear state evolution in pathological gait, insufficient numerical modeling, and limited interpretability.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: First, the temporal sequence of the human gait skeleton is obtained and a spatiotemporal skeleton graph is constructed. Then, a spatiotemporal graph convolutional network is used to extract the spatiotemporal features of the joint nodes. Next, the joint features at the end of the sequence are selected as the external driving force to drive the Duffing oscillator group corresponding to each joint node. Then, the second-order nonlinear oscillation equation containing linear stiffness, nonlinear stiffness, and damping terms is rewritten in the first-order state space, and the position and velocity states of each joint node are updated iteratively using semi-implicit Euler integrals. After that, the position and state responses of each joint are spliced, normalized, and learnedably scaled to form a global feature modulation field, which is used to enhance the original spatiotemporal features. Finally, the pathological gait recognition results are output.

[0006] This invention is achieved through the following technical solution: a nonlinear compensation analysis method for pathological gait based on Duffing oscillator graph convolutional networks, comprising the following steps: Step S1: Obtain the temporal sequence of the human gait skeleton and construct a spatiotemporal skeleton diagram based on the human joint connection relationship; Step S2: Extract the spatiotemporal features of each joint node using a spatiotemporal graph convolutional network; Step S3: Extract the spatiotemporal features of the nodes at the end time as the external driving force, establish the Duffing oscillator model for each joint node and perform numerical integration update to obtain the response result of the Duffing oscillator. In step S3, each joint node i corresponds to a Duffing oscillator, whose dynamics satisfy:

[0007] in, This represents the oscillator state at the joint nodes. The external driving force is formed by the features at the ends of the spatiotemporal graph convolution. The linear stiffness coefficient is... For nonlinear stiffness coefficients, is the damping coefficient.

[0008] Step S4: The response results of the Duffing oscillator are spliced ​​into a global feature modulation field, and the original spatiotemporal features are nonlinearly enhanced to obtain the enhanced spatiotemporal features; In step S4, the updated position states of each joint node are concatenated along the joint dimension to obtain the global response vector. Its expression is:

[0009] For the global response direction The quantities are L2 normalized, learnable scaled, and Sigmoid mapped to form a global feature modulation field. This field is then fused with the original spatiotemporal features through element-wise multiplication to obtain a nonlinear enhancement representation that uniformly affects all time frames. The expression is as follows:

[0010] in, For global characteristic modulation field, For learnable scaling parameters, It is the L2 norm. To prevent constants with zero denominators, σ( ) is the Sigmoid activation function, X is the original spatiotemporal feature, X′ is the enhanced spatiotemporal feature, and ⊙ represents element-wise multiplication.

[0011] In step S5, the identification output includes using the phase diagram trajectory of each joint oscillator to perform auxiliary analysis on the stability of pathological gait. The phase diagram trajectory includes stable state, bistable state, periodic state or chaotic state response in the position-velocity plane.

[0012] Step S5: Input the enhanced spatiotemporal features into the classification network and output the abnormal muscle category, lesion area, lesion combination, or stability analysis results corresponding to the pathological gait.

[0013] The second-order dynamics of the Duffing oscillator are rewritten in a first-order state-space form by simultaneously maintaining the position state. With speed state Implement numerical updates:

[0014] in, This represents the oscillator velocity state corresponding to the i-th joint node.

[0015] The numerical updates are performed using a semi-implicit Euler integration method, that is, the velocity state is updated first. Then update the position state using the updated velocity state. To improve the numerical stability of the nonlinear oscillatory iterative process, its update formula is expressed as:

[0016] Where Δt is the integration step size and n is the number of discrete iteration steps; by updating the velocity state first and then the position state, the numerical stability of the nonlinear oscillatory iterative process is improved.

[0017] The analysis system used in the pathological gait nonlinear compensation analysis method based on Duffing oscillator graph convolutional network includes: a data input module, a spatiotemporal feature extraction module, a Duffing dynamics modeling module, a numerical integration module, a feature modulation module, and a recognition output module. The data input module is used to acquire the temporal sequence of the human gait skeleton and preprocess the temporal sequence of the gait skeleton. The preprocessing includes normalizing the skeleton scale based on the relative distance between key human joints to reduce the impact of differences in body proportions of different subjects on subsequent analysis results, and filtering and denoising the skeleton point coordinate data to reduce the impact of sensor acquisition noise on the stability of numerical calculation. After the preprocessing is completed, a spatiotemporal skeleton diagram is constructed based on the human joint connection relationship. The aforementioned spatiotemporal feature extraction module is used to extract the spatiotemporal features of each joint node using a spatiotemporal graph convolutional network; The Duffing dynamics modeling module is used to extract the node features of the high-level spatiotemporal features at the end moment as external driving force, and to establish corresponding Duffing oscillator models for each joint node to describe the nonlinear oscillation behavior and state transition characteristics of joint movement during pathological gait. The numerical integration module is used to iteratively update the state of the oscillator corresponding to each joint node using a semi-implicit Euler integration method, so as to obtain the dynamic response results of each joint node in terms of position and velocity state, thereby improving the stability of the nonlinear oscillation system in numerical calculation process. The feature modulation module is used to construct a global feature modulation field based on the nonlinear response results of each joint node, and to enhance the original spatiotemporal features to highlight abnormal compensation features, stability difference features and key motion pattern features related to pathological gait. The identification output module is used to output abnormal muscle categories, lesion regions, lesion combinations, or stability analysis results based on the enhanced spatiotemporal features, and to provide results support for pathological gait recognition, rehabilitation assessment, and auxiliary diagnosis. The classification head is trained using a pre-labeled pathological gait dataset to establish a mapping relationship between gait features and abnormal muscle categories, lesion regions, and lesion combinations. Compared with existing technologies, the present invention has at least the following beneficial effects: First, it describes the nonlinear state transition process in pathological gait and enhances the ability to express complex compensatory patterns; second, it improves the training stability during deep numerical iteration by using a semi-implicit Euler integral update method that updates velocity first and then position; and third, it enables clinically interpretable analysis by using intermediate results such as phase diagrams, oscillatory responses, and global modulation fields. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the overall process of the method of the present invention; Figure 2 This is a schematic diagram comparing lower limb movement phase diagrams of normal individuals and patients with abnormalities. Detailed Implementation

[0019] This invention provides a nonlinear compensation analysis method for pathological gait based on Duffing oscillator graph convolutional network, which is used to model and analyze the temporal sequence of human gait skeleton and output abnormal muscle categories, lesion areas, lesion combinations or stability analysis results.

[0020] like Figure 1As shown, the method of the present invention includes the following steps: obtaining the temporal sequence of the human gait skeleton and constructing a spatiotemporal skeleton graph based on the connection relationship of human joints; extracting the spatiotemporal features of each joint node using a spatiotemporal graph convolutional network; extracting the node features of the spatiotemporal features at the end time as an external driving force, establishing a Duffing oscillator model for each joint node and performing numerical integration updates; splicing the oscillator response results of each joint node to form a global feature modulation field and enhancing the original spatiotemporal features; inputting the enhanced features into a classification network to obtain pathological gait analysis results.

[0021] In this embodiment, gait data from normal subjects and patients with abnormalities are selected as input samples. First, the temporal sequence of skeletal points during the continuous walking process of the subjects is collected, and a spatiotemporal skeleton map is constructed according to the natural connection relationship of human joints. Subsequently, the spatiotemporal skeleton map is input into a spatiotemporal graph convolutional network to extract high-level spatiotemporal features that can characterize joint motion relationships and gait temporal changes.

[0022] After obtaining the spatiotemporal features, the features of each joint node at the final moment are extracted as external driving forces, and corresponding Duffing oscillator models are established. Numerical integration is used to update the oscillator state to obtain the dynamic response trajectory of each joint node in the position-velocity plane. Furthermore, the oscillator response results of each joint node are concatenated to form a global feature modulation field, which is then used to enhance the original spatiotemporal features. After the enhanced features are input into the classification network, the network can output abnormal muscle categories, lesion regions, lesion combinations, or stability analysis results.

[0023] like Figure 2 As shown in the figure, the lower limb motion phase diagrams of normal subjects and abnormal patients are compared. The top row shows the phase diagrams of normal subjects, and the bottom row shows the phase diagrams of abnormal patients; solid lines represent the trajectory of the left leg, and dashed lines represent the trajectory of the right leg; the horizontal axis represents relative displacement, and the vertical axis represents relative velocity; from left to right, they represent stable phase diagrams, bistable phase diagrams, chaotic phase diagrams, and periodic phase diagrams. Figure 2 As shown, there are differences in the trajectory distribution in the position-velocity plane between normal subjects and abnormal patients. By comparing the range, symmetry, and convergence characteristics of the phase diagram trajectory, the degree of gait impairment and compensatory characteristics can be determined.

Claims

1. A pathological gait nonlinear compensation analysis method based on a Duffing oscillator graph convolution network, characterized by, Includes the following steps: Step S1: Obtain the temporal sequence of the human gait skeleton and construct a spatiotemporal skeleton diagram based on the human joint connection relationship; Step S2: Extract the spatiotemporal features of each joint node using a spatiotemporal graph convolutional network; Step S3: Extract the spatiotemporal features of the nodes at the final time step as the external driving force, establish a Duffing oscillator model for each joint node, and perform numerical integration update to obtain the response results of the Duffing oscillator. Step S4: The response results of the Duffing oscillator are spliced ​​into a global feature modulation field, and the original spatiotemporal features are nonlinearly enhanced to obtain the enhanced spatiotemporal features; Step S5: Input the enhanced spatiotemporal features into the classification network and output the abnormal muscle category, lesion area, lesion combination, or stability analysis results corresponding to the pathological gait.

2. The method for pathological gait nonlinear compensation analysis based on Duffing oscillator graph convolutional network according to claim 1, characterized in that, In step S3, each joint node i corresponds to a Duffing oscillator, whose dynamics satisfy: wherein, is the oscillator state of the joint node, is an external driving force formed by spatio-temporal graph convolution end features, is a linear stiffness coefficient, is a nonlinear stiffness coefficient, is a damping coefficient.

3. The pathological gait nonlinear compensation analysis method based on Duffing oscillator graph convolution network according to claim 2, characterized in that, Rewriting the second order dynamics of the Duffing oscillator into a first order state space form by simultaneously maintaining the position state and the velocity state Implement numerical update: wherein, is the i-th joint node corresponding to the vibrator velocity state.

4. The pathological gait nonlinear compensation analysis method based on Duffing oscillator graph convolution network according to claim 3, characterized in that, The numerical updating is performed in a semi-implicit Euler integration manner, i.e. first updating the velocity state and then updating the position state by using the updated velocity state to improve the numerical stability of the nonlinear oscillation iteration process, and the updating formula is represented as: Where Δt is the integration step size and n is the number of discrete iteration steps; by updating the velocity state first and then the position state, the numerical stability of the nonlinear oscillatory iterative process is improved.

5. The pathological gait nonlinear compensation analysis method based on Duffing oscillator graph convolution network according to claim 1, characterized in that, The step S4 is to splice the updated position state of each joint node along the joint dimension to obtain a global response vector The expression is: 。 6. The pathological gait nonlinear compensation analysis method based on Duffing oscillator graph convolution network according to claim 5, characterized in that, For the global response direction The quantity is L2 normalized, learnable scaled, and Sigmoid mapped to form a global feature modulation field. This field is then fused with the original spatiotemporal features through element-wise multiplication to obtain a nonlinear enhancement representation that uniformly affects all time frames. The expression is: in, For global characteristic modulation field, For learnable scaling parameters, It is the L2 norm. To prevent constants with zero denominators, σ( ) is the Sigmoid activation function, X is the original spatiotemporal feature, X′ is the enhanced spatiotemporal feature, and ⊙ represents element-wise multiplication.

7. The pathological gait nonlinear compensation analysis method based on Duffing oscillator graph convolution network according to claim 1, characterized in that, In step S5, the identification output includes using the phase diagram trajectory of each joint oscillator to perform auxiliary analysis on the stability of pathological gait. The phase diagram trajectory includes stable state, bistable state, periodic state or chaotic state response in the position-velocity plane.

8. An analysis system for use in the pathological gait nonlinear compensation analysis method based on the Duffing oscillator graph convolution network according to any one of claims 1-7, characterized in that, include: The system includes a data input module, a spatiotemporal feature extraction module, a Duffing dynamics modeling module, a numerical integration module, a feature modulation module, and a recognition output module. The data input module is used to acquire the time sequence of human gait skeleton and preprocess the time sequence of gait skeleton. The preprocessing includes normalizing the skeleton scale based on the relative distance between key joints of the human body to reduce the impact of differences in body proportions of different subjects on the subsequent analysis results, and filtering and denoising the skeleton point coordinate data to reduce the impact of sensor acquisition noise on the stability of numerical calculation. After preprocessing, a spatiotemporal skeleton diagram is constructed based on the connection relationships of human joints; The aforementioned spatiotemporal feature extraction module is used to extract the spatiotemporal features of each joint node using a spatiotemporal graph convolutional network; The Duffing dynamics modeling module is used to extract the node features of the high-level spatiotemporal features at the end moment as external driving force, and to establish corresponding Duffing oscillator models for each joint node to describe the nonlinear oscillation behavior and state transition characteristics of joint movement during pathological gait. The numerical integration module is used to iteratively update the state of the oscillator corresponding to each joint node using a semi-implicit Euler integration method, so as to obtain the dynamic response results of each joint node in terms of position and velocity state, thereby improving the stability of the nonlinear oscillation system in numerical calculation process. The feature modulation module is used to construct a global feature modulation field based on the nonlinear response results of each joint node, and to enhance the original spatiotemporal features to highlight abnormal compensation features, stability difference features and key motion pattern features related to pathological gait. The identification output module is used to output abnormal muscle categories, lesion areas, lesion combinations, or stability analysis results based on the enhanced spatiotemporal features, and to provide results support for pathological gait recognition, rehabilitation assessment, and auxiliary diagnosis; the classification head is trained through a pre-labeled pathological gait dataset to establish a mapping relationship between gait features and abnormal muscle categories, lesion areas, and lesion combinations.

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