Analysis method for constructing gait mechanics network based on multivariate transfer entropy
By constructing a gait biomechanics network and using multivariate transfer entropy analysis of gait signals, the intrinsic relationships between gait signals are revealed, providing a new indicator for assessing gait abnormalities. This solves the problem that traditional gait analysis cannot reveal the relationships between signals and can be applied in clinical practice and exercise optimization.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- UNIV OF ELECTRONICS SCI & TECH OF CHINA
- Filing Date
- 2024-06-03
- Publication Date
- 2026-05-15
AI Technical Summary
Traditional gait analysis mainly focuses on analyzing different dimensions and frequencies of gait signals independently, failing to reveal the intrinsic connections and common mechanisms among gait signals.
An analytical method based on multivariate transfer entropy to construct a gait mechanics network is adopted. The ground reaction force signal is decomposed into high, medium and low frequency components by ensemble empirical mode decomposition (EEMD). The transfer entropy gait mechanics network is constructed using multivariate transfer entropy (MuTE). The transfer entropy is calculated by combining non-uniform embedding (NUM) and entropy estimator, and its significance is tested to analyze the operation law of gait mechanism.
This study reveals the intrinsic connections between gait signals, provides new indicators for assessing gait abnormalities and modularity, offers a reference for clinical assessment of patients' gait abnormalities, and optimizes athletic performance in the fields of sports and engineering.
Smart Images
Figure CN118626788B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of gait mechanics technology, and more specifically, to an analytical method for constructing gait mechanics networks based on multivariate transfer entropy. Background Technology
[0002] Gait is fundamental to daily living activities and maintaining movement. Gait analysis studies the posture and behavioral characteristics of the human body during walking, involving a series of continuous movements of the hip, knee, ankle, and toes, and how these movements propel the body in a specific direction. Traditional gait analysis often focuses on independently analyzing different dimensions and frequencies of gait signals, but these components are actually generated synchronously and cooperate with each other. To reveal the intrinsic connections and collaborative mechanisms among gait signals, an analytical method based on constructing a gait biomechanical network using multivariate transfer entropy is needed to address these issues. Summary of the Invention
[0003] The present invention provides an analysis method for constructing gait mechanics networks based on multivariate transfer entropy, which can overcome some or all of the defects of the prior art.
[0004] The analytical method for constructing gait mechanics networks based on multivariate transfer entropy according to the present invention includes the following steps:
[0005] Step 1: The raw data channel signal of the ground reaction force signal is processed by ensemble empirical mode decomposition (EEMD) to obtain signals of multiple channels. Each signal is decomposed into three frequency bands: high, medium and low.
[0006] Step 2: Construct a transfer entropy gait mechanics network using multivariate transfer entropy MuTE;
[0007] Step 2.1: Establish the past state of the system by non-uniform embedding NUM;
[0008] Step 2.2: Calculate the transit entropy using the entropy estimator;
[0009] Step 2.3: Test the significance of the propagation entropy;
[0010] Step 3: Analyze the operational patterns of individual physiological mechanisms and multiple physiological mechanisms during walking using a gait mechanics network with transfer entropy.
[0011] As a preferred method, the decomposition steps of EEMD are as follows:
[0012] Step 1.1: Set the overall average number of times m: Determine the number of EMD decompositions to be performed;
[0013] Step 1.2: Add standard normally distributed white noise n i(t): Adding white noise with a standard normal distribution to the original signal x(t) generates a new noisy signal;
[0014] Step 1.3: Perform EMD decomposition: For each noisy signal x i (t) is decomposed into EMD to obtain a series of intrinsic mode functions (IMFs);
[0015]
[0016] Where c i,j (t) represents the j-th IMF obtained by adding white noise for the i-th time, r i,j (t) is the residual function, representing the average trend of the signal, and J is the number of IMFs;
[0017] Step 1.4: Repeat steps 1.2 and 1.3 M times, adding white noise signals of different amplitudes each time to obtain the set of IMFs:
[0018] c 1,j (t)c 2,j (t)...c m,j (t), j=1,2,...J (1-2)
[0019] Step 1.5, Calculate the mean: Average the IMF components of the corresponding modes to obtain the final EEMD decomposition result;
[0020]
[0021] Where c j (t) is the j-th IMF of the EEMD decomposition, i = 1, 2, ..., m, j = 1, 2, ..., J;
[0022] In the entire process, the overall average number of times m and the ratio of white noise to signal standard deviation Nstd are two key parameters. The more average the number of times, the more representative the characteristics of the original signal will be by the integrated IMF, and the influence of noise will be reduced, but the computation time will increase. The larger Nstd is, the stronger the noise added with each decomposition.
[0023] As a preferred embodiment, in the multivariate transfer entropy MuTE, considering the influence of system Y, the transfer entropy from source system X to target system Z is defined as follows:
[0024]
[0025] vector Let Z, X, and Y represent the past states, respectively, where parameters l, τ, and δ represent the time delays of Z, X, and Y. It is the conditional probability of Z in the current state, given the past states of Z and Y.
[0026] The sum of probabilities includes all phase space points constituting the trajectory of the synthetic system; the conditional probability used in the formula is interpreted as the transition probability, quantifying the degree to which the past states of the source system X are influenced when the target system Z transitions to its current state; this conditional transfer entropy formula excludes the information shared between X and Z, which is mediated by their joint interaction with Y; under this definition, TE is considered as the difference between two conditional entropies H:
[0027]
[0028] As a preferred option, use embedded vectors To include as many significant and effective past variables as possible to explain the current state of the target system, non-uniform embedding (NUM) involves stepwise selection among available variables. The selected variables must be able to describe the maximum lag under past conditions of the observation processes X and Z, and the target variable Z is identified. t The most significant variable is Z; therefore, this method applies the criteria of maximum relevance and minimum redundancy to the selection of available variables, and the resulting embedding vector V includes only the vectors that are most significant for Z. t Describe the component that contributes the most; first, establish a matrix of optional variables:
[0029]
[0030] Among them, l max This represents the maximum time delay of the optional variables during the observation process;
[0031] Then, the optional variables are optimized through multiple iterations. For the k-th iteration, let the i-th term in M be denoted as . and Let:
[0032]
[0033] Where V' t Given the iterated embedding vector, V' is calculated using an entropy estimator. t and target state Z t Mutual information, in all Choose the one that maximizes mutual information as At this point, a significance test is performed. If the significance test is passed, then:
[0034]
[0035] Then remove it from M and proceed to the next iteration.
[0036] As a preferred option, the entropy estimator is Binning, which performs uniform quantization on the time series and then uses the access frequency of the quantized state to approximate the probability distribution to calculate the entropy.
[0037] First, the target process Z is normalized to have zero mean and standard deviation, and then its dynamics are divided into ξ quantization levels of amplitude r.
[0038] r=(z max -z min ) / ξ
[0039] Among them, z max and z min ξ and ξ represent the maximum and minimum values of Z after normalization, respectively; quantization assigns each sample a level number corresponding to its coarse-grained partition, from 0 to ξ-1; uniform quantization of the d-dimensional embedding vector transforms this unified d-dimensional space into ξ. d There are three disjoint hypercubes of size r; all vectors falling within the same hypercube are quantized by the same vector V. ξ Related; therefore, the entropy estimate of this hypercube is:
[0040]
[0041] Among them, S d Representing the total space, for each hypercube p(V) ξ The proportion of available vectors falling into the hypercube is denoted as ; to calculate the transfer entropy, equation (2-2) needs to be rewritten as:
[0042]
[0043] This transforms the two conditional entropies into four Shannon entropies, which are then used to calculate the final transit entropy using the four corresponding embedding vectors.
[0044] The beneficial effects of this invention are as follows:
[0045] This invention innovatively treats gait mechanics signals as a whole, uncovering features in gait that are difficult to detect—features not addressed in traditional gait mechanics analysis. Furthermore, the nodes, edges, and global parameters of this invention can be considered as new indicators to assess gait anomalies or the degree of gait modularity, providing a reference for gait evaluation. Attached Figure Description
[0046] Figure 1 This is a flowchart of an analysis method for constructing a gait mechanics network based on multivariate transfer entropy, as described in this embodiment. Detailed Implementation
[0047] To further understand the content of this invention, a detailed description of the invention will be provided in conjunction with the accompanying drawings and embodiments. It should be understood that the embodiments are merely illustrative and not limiting of the invention.
[0048] Example
[0049] like Figure 1 As shown, this embodiment provides an analysis method for constructing gait dynamics networks based on multivariate transfer entropy, which includes the following steps:
[0050] Step 1: The raw ground reaction force signal data (6 channels) is processed by ensemble empirical mode decomposition (EEMD) to obtain multiple (18) channels of signal. Each signal is decomposed into high, medium and low frequency band components.
[0051] Step 2: Construct an 18*18 transfer entropy gait mechanics network using multivariate transfer entropy MuTE;
[0052] Step 2.1: Establish the past state of the system by non-uniform embedding NUM;
[0053] Step 2.2: Calculate the transit entropy using the entropy estimator;
[0054] Step 2.3: Test the significance of the propagation entropy;
[0055] Step 3: Analyze the operational patterns of individual physiological mechanisms and multiple physiological mechanisms during walking using a gait mechanics network with transfer entropy.
[0056] EEMD is an analysis method for processing nonlinear and non-stationary signals. Its basic principle is to add a series of different white noises to the original signal, and then perform multiple EMD (Empirical Mode Decomposition) operations on these noisy signals. In this way, EEMD can reduce mode aliasing problems and improve the accuracy and stability of the decomposition results. The decomposition steps of EEMD are as follows:
[0057] Step 1.1: Set the overall average number of times m: Determine the number of EMD decompositions to be performed;
[0058] Step 1.2: Add standard normally distributed white noise n i (t): Adding white noise with a standard normal distribution to the original signal x(t) generates a new noisy signal;
[0059] Step 1.3: Perform EMD decomposition: For each noisy signal x i (t) is decomposed into EMD to obtain a series of intrinsic mode functions (IMFs);
[0060]
[0061] Where ci,j (t) represents the j-th IMF obtained by adding white noise for the i-th time, r i,j (t) is the residual function, representing the average trend of the signal, and J is the number of IMFs;
[0062] Step 1.4: Repeat steps 1.2 and 1.3 M times, adding white noise signals of different amplitudes each time to obtain the set of IMFs:
[0063] c 1,j (t)c 2,j (t)...c m,j (t), j=1,2,...J (1-2)
[0064] Step 1.5, Calculate the mean: Average the IMF components of the corresponding modes to obtain the final EEMD decomposition result;
[0065]
[0066] Where c j (t) is the j-th IMF of the EEMD decomposition, i = 1, 2, ..., m, j = 1, 2, ..., J;
[0067] In the entire process, the overall average number of iterations (m) and the ratio of white noise to the signal standard deviation (Nstd) are two key parameters. A higher average number of iterations results in a more representative IMF (Integrated Multivariate Array) that accurately reflects the characteristics of the original signal, while also reducing the impact of noise, but increasing computation time. A larger Nstd introduces stronger noise with each decomposition, which helps to better separate different scale features in the signal, but may also introduce more noise. Based on the data characteristics and application requirements, the final parameter settings are m = 100 and Nstd = 0.2.
[0068] Multivariate transfer entropy (MuTE) is a powerful tool for detecting information transfer. Its basic principle is based on the assumption that within a complex system with m interacting dynamic subsystems, the goal is to calculate the transfer entropy from the source system X to the target system Z, with the remaining systems represented by a vector Y. Then, the vector... Let Z, X, and Y represent the past states, respectively, where parameters l, τ, and δ represent the time delays of Z, X, and Y. Therefore, considering the influence of system Y, the transfer entropy from source system X to target system Z is defined as follows:
[0069]
[0070] vector Let Z, X, and Y represent the past states, respectively, where parameters l, τ, and δ represent the time delays of Z, X, and Y.
[0071] The sum of probabilities includes all phase space points constituting the trajectory of the synthetic system; the conditional probability used in the formula is interpreted as the transition probability, quantifying the degree to which the past states of the source system X are influenced when the target system Z transitions to its current state; this conditional transfer entropy formula excludes the information shared between X and Z, which is mediated by their joint interaction with Y; under this definition, TE is considered as the difference between two conditional entropies H:
[0072]
[0073] Two methods for determining the number of past variables are uniform embedding (UM) and non-uniform embedding (NUM). Uniform embedding involves appropriately selecting the component lengths in the embedding vector a priori for each time series. Therefore, using a constrained embedding vector... To estimate the second conditional entropy This can lead to problems such as overfitting or incorrect effects on detection, due to the arbitrariness and potential redundancy of the estimation.
[0074] Using embedded vectors To include as many significant and effective past variables as possible to explain the current state of the target system, non-uniform embedding involves a stepwise selection among available variables. The selected variables need to describe the maximum lag of X and Z under past conditions during the observation process and serve as the target variable Z for identification. t The most significant variable is selected from all available variables; therefore, this method applies the criteria of maximum relevance and minimum redundancy to the selection of available variables, and the resulting embedding vector V includes only those vectors that are most significant for Z. t The component that contributes the most to the description. Specifically, first, construct a matrix of optional variables:
[0075]
[0076] Among them, l max This represents the maximum time delay of the optional variables during the observation process; if instantaneous effects are considered, X also needs to be added to M. t Y t .
[0077] Then, the optional variables are optimized through multiple iterations. For the k-th iteration, let the i-th term in M be denoted as . and Let:
[0078]
[0079] Where V' t Given the iterated embedding vector, V' is calculated using an entropy estimator. t and target state Zt Mutual information, in all Choose the one that maximizes mutual information as At this point, a significance test is performed. If the significance test is passed, then:
[0080]
[0081] It is then removed from M, and the process proceeds to the next iteration. The rest is the same as uniform embedding. This method does not require prior selection of the embedding size. Unlike the classic uniform embedding method, non-uniform embedding optimizes for each candidate variable, maximizing the mutual information between the target variable and candidate variables. Furthermore, non-uniform embedding can reduce the dimensionality of the phase space to avoid the curse of dimensionality. The final result of the transfer entropy calculation depends not only on the embedding method but also on the specific entropy estimator.
[0082] Entropy estimators are divided into linear and nonlinear estimators. Linear estimators assume that all processes follow a Gaussian distribution, while nonlinear estimators do not require this assumption and have broader adaptability. Binning, as a nonlinear estimator, has been shown to have the best performance in computing interactions between physiological systems.
[0083] Specifically, the entropy estimator BIN performs uniform quantization on the time series and then uses the access frequency of the quantized state to approximate the probability distribution to calculate the entropy.
[0084] First, the target process Z is normalized to have zero mean and standard deviation, and then its dynamics are divided into ξ quantization levels of amplitude r.
[0085] r=(z max -z min ) / ξ
[0086] Among them, z max and z min ξ and ξ represent the maximum and minimum values of Z after normalization, respectively; quantization assigns each sample a level number corresponding to its coarse-grained partition, from 0 to ξ-1; uniform quantization of the d-dimensional embedding vector transforms this unified d-dimensional space into ξ. d There are three disjoint hypercubes of size r; all vectors falling within the same hypercube are quantized by the same vector V. ξ Related; therefore, the entropy estimate of this hypercube is:
[0087]
[0088] Among them, S d Representing the total space, for each hypercube p(V) ξThe proportion of available vectors falling into the hypercube is denoted as ; to calculate the transfer entropy, equation (2-2) needs to be rewritten as:
[0089]
[0090] This transforms the two conditional entropies into four Shannon entropies, which are then used to calculate the final transit entropy using the four corresponding embedding vectors.
[0091] This embodiment innovatively treats gait biomechanics signals as a whole, uncovering features in gait that are difficult to detect—features not addressed in traditional gait biomechanics analysis. Furthermore, the nodes, edges, and global context of this embodiment can be considered novel indicators for assessing gait abnormalities or the degree of gait modularity, providing a reference for gait evaluation. This embodiment employs complex network theory to study the interactions between different mechanisms of gait biomechanics signals from a global perspective, revealing the correlations and influences of these mechanisms at the network level. In the clinical field, it provides a reference for doctors to assess whether patients have abnormal gait or the nature and extent of gait abnormalities. It can also help athletes optimize and improve athletic performance in the sports and engineering fields, and contribute to the production of sports and rehabilitation aids.
[0092] The present invention and its embodiments have been described above illustratively. This description is not restrictive, and the figures shown are only one embodiment of the present invention; the actual structure is not limited thereto. Therefore, if those skilled in the art are inspired by this description and design similar structures and embodiments without departing from the spirit of the present invention, such designs should fall within the protection scope of the present invention.
Claims
1. An analytical method for constructing gait dynamics networks based on multivariate transfer entropy, characterized by: Includes the following steps: Step 1: The raw data channel signal of the ground reaction force signal is processed by ensemble empirical mode decomposition (EEMD) to obtain signals of multiple channels. Each signal is decomposed into three frequency bands: high, medium and low. Step 2: Construct a transfer entropy gait mechanics network using multivariate transfer entropy MuTE; In multivariate transfer entropy MuTE, when considering the system Under the influence of the source system To the target system The transitive entropy (TE) is defined as follows: (2-1)； vector , , They represent , and Past states, where parameters , , express , and The delay; It is known and Under the premise of past state The conditional probability in the current state; The sum of probabilities includes all phase space points that constitute the trajectory of the synthetic system; the conditional probability used in the formula is interpreted as the transition probability, quantifying the target system. The source system considered during the transition to its current state The extent to which the past state has an influence; This conditional transfer entropy formula excludes... and Information shared between them, information provided by them and The interaction between the two conditions mediates the process; under this definition, TE can be considered as the difference between two conditional entropies H: （2-2）； Step 2.1: Establish the past state of the system by non-uniform embedding NUM; Step 2.2: Calculate the transit entropy using the entropy estimator; Step 2.3: Test the significance of the propagation entropy; The entropy estimator is Binning, which performs uniform quantization on the time series and then uses the access frequency of the quantized state to approximate the probability distribution to calculate the entropy. First, the target process Normalize it to have zero mean and standard deviation, then divide its dynamics into amplitudes. of At each quantitative level; ； in, and They represent the normalized values respectively. The maximum and minimum values; quantization assigns each sample a level number to which it belongs in the coarse-grained division, from 0 to... Uniform quantization The dimensional embedding vector makes this unified 3D space transformation The size is Disjoint hypercubes; all vectors falling within the same hypercube are quantized by the same vector. Related; therefore, the entropy estimate of this hypercube is: ； in, Representing the total space, for each hypercube This represents the proportion of available vectors falling into the hypercube; to calculate the transfer entropy, equation (2-2) needs to be rewritten as: ； This transforms the two conditional entropies into four Shannon entropies, and then the final transit entropy is calculated using the four corresponding embedding vectors. Step 3: Analyze the operational patterns of individual physiological mechanisms and multiple physiological mechanisms during walking using a gait mechanics network with transfer entropy.
2. The analysis method for constructing gait dynamics networks based on multivariate transfer entropy according to claim 1, characterized in that: The decomposition steps of EEMD are as follows: Step 1.1: Set the overall average frequency Determine the number of EMD decompositions to be performed; Step 1.2: Add standard normally distributed white noise In the original signal Adding white noise with a standard normal distribution to the signal generates a new noisy signal; Step 1.3: Perform EMD decomposition: For each noisy signal... EMD decomposition is performed to obtain a series of intrinsic mode functions (IMFs). （1-1）； in For the first The first time white noise was added to the decomposition, the result was the first One IMF, It is the residual function, representing the average trend of the signal. It refers to the number of IMFs; Step 1.4: Repeat steps 1.2 and 1.
3. Each time, white noise signals of different amplitudes are added during the decomposition to obtain a set of IMFs: （1-2）； Step 1.5, Calculate the mean: Average the IMF components of the corresponding modes to obtain the final EEMD decomposition result; （1-3）； in It is the first EEMD decomposition One IMF, ; ; Overall average number of times throughout the process The ratio of white noise to the signal standard deviation These are two key parameters; the more times the average is performed, the more representative the IMF obtained through integration will be of the original signal characteristics, and the influence of noise will also be reduced, but the computation time will increase. The larger the value, the stronger the noise added with each decomposition.
3. The analysis method for constructing gait dynamics networks based on multivariate transfer entropy according to claim 2, characterized in that: Using embedded vectors To explain the current state of the target system, non-uniform embedding in NUM involves stepwise selection among available variables, and the selected variables need to be able to describe the observation process. and The maximum lag under past conditions, and the identification of the target variable. The most significant variable; applying the criteria of maximum correlation and minimum redundancy to the selection of available variables, and obtaining the embedding vector Only include pairs of all vectors The component that contributes the most is described; specifically, a matrix of optional variables is first constructed: ； in, This represents the maximum time delay of the optional variables during the observation process; Then, the optional variables are optimized through multiple iterations, for the ... In the next iteration, let's record... The Middle Item for ,and Let the result of the previous iteration be: ； in The embedded vector after iteration is calculated using an entropy estimator. and target state Mutual information, in all Choose the one that maximizes mutual information as At this point, a significance test is performed. If the significance test is passed, then: ； and from Delete it, and then proceed to the next iteration.