CN111523208B - Kalman filtering method for human walking plantar ground reaction force - Google Patents
Kalman filtering method for human walking plantar ground reaction force Download PDFInfo
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Abstract
The invention discloses a Kalman filtering method for human walking plantar ground reaction force, which specifically comprises the following steps: s1: establishing a dynamics control equation according to the stress characteristics of the legs during walking; s2: constructing a ground test reaction force equation according to the dynamics control equation; s3: discretizing the ground test reaction force equation, and establishing a Kalman filtering state updating equation and a measuring updating equation according to the influence of noise; s4: and filtering the test data by using the Kalman filtering state updating equation and the Kalman filtering measurement updating equation to obtain the test data after the filtering treatment. The Kalman filtering method of the invention utilizes the Kalman principle to realize the rapid filtering of the non-fluctuation test ground reaction force, effectively processes the signal to noise ratio of the ground reaction force test signal, lays a foundation for the further processing of the test signal, and can well process the ground reaction force filtering problem obtained by the actual test.
Description
Technical Field
The invention relates to the technical field of civil engineering structure prediction, in particular to a Kalman filtering method for human walking plantar ground reaction force.
Background
With the development of society, architects pursue slim and beautiful appearance of a structure in the process of civil engineering design, and direct structural problems brought by the architect are: the scale of the structural system is continuously increased, the frequency and damping energy consumption capability are continuously reduced, and resonance is easily caused to occur when the frequency is reduced to a certain degree close to the excitation frequency of a person, so that the problem of comfort in using a plurality of structures is caused. To explore the vibration mechanism of a structure under the action of a pedestrian, engineers and researchers need to test the bipedal reaction force of the structure by a person to extract the load excitation characteristics of the structure by the person in a single gait. However, the test instrument is affected by manufacturing errors of the surrounding itself and environments such as surrounding electromagnetism, so that a lot of noise is contained in the measurement model, the noise not only affects the analysis result, but also causes severe distortion of the test signal when serious, and therefore, filtering processing is required before the test signal is applied to engineering calculation. However, since the conventional filtering method is mostly based on vibration signals, it cannot be directly applied to the ground reaction force test signal with significant non-fluctuation.
Disclosure of Invention
The invention aims to: aiming at the problem that the ground reaction force generated by the human sole is a non-fluctuation signal and is difficult to process by the traditional filtering algorithm, the invention provides a Kalman filtering method for the ground reaction force of the human walking sole.
The technical scheme is as follows: in order to achieve the purpose of the invention, the technical scheme adopted by the invention is as follows:
a Kalman filtering method for the reaction force of human walking plantar ground specifically comprises the following steps:
s1: establishing a dynamics control equation according to the stress characteristics of the legs during walking;
s2: constructing a ground test reaction force equation according to the dynamics control equation;
s3: discretizing the ground test reaction force equation, and establishing a Kalman filtering state updating equation and a measuring updating equation according to the influence of noise;
s4: and filtering the test data by using the Kalman filtering state updating equation and the Kalman filtering measurement updating equation to obtain the test data after the filtering treatment.
Further, in the step S1, the dynamics control equation is established as follows:
s1.1: according to the stress characteristics of the legs of the person in the walking process, the synthetic force of the longitudinal, lateral and vertical forces of the sole in space is obtained, and the method specifically comprises the following steps:
wherein: f is the resultant force of the plantar forces in the space longitudinal, lateral and vertical directions, F x For acting force of sole in space longitudinal direction F y For acting force of sole in space side direction, F z The force of the sole in the space is vertical;
s1.2: the included angle between the leg and the gravity direction is obtained by the synthesized force of the sole in the longitudinal direction, the lateral direction and the vertical direction of the space and the force of the sole in the vertical direction of the space, and is specifically as follows:
wherein: theta is the included angle between the leg and the gravity direction, F z The force is the vertical force of the sole in space, and F is the synthesized force of the longitudinal, lateral and vertical forces of the sole in space;
s1.3: according to the included angle between the leg and the gravity direction, the dynamics control equation is established, specifically:
wherein: θ is the angle between the leg and the direction of gravity, t is the time variable, m is the weight of the body, c is the damping, k is the spring rate,for the axial acceleration of the leg->The velocity of the leg, u is the displacement of the leg, g is the gravitational acceleration.
Further, in the step S2, the ground test reaction force equation is constructed as follows:
s2.1: simplifying the dynamics control equation to obtain a ground reaction force relationship, specifically
Wherein: c is the damping, k is the spring rate,the speed of the leg, u is the displacement of the leg, and F is the resultant force of the forces of the sole in the longitudinal, lateral and vertical directions in space;
s2.2: setting a space variable, and converting the ground reaction force relation acquisition formula to obtain the ground test reaction force equation, wherein the ground test reaction force equation is specifically as follows:
Z＝HX
wherein: z is the dimensionless test ground reaction quantity, H is the measurement matrix, and X is the space variable.
Further, the formula for acquiring the dimensionless test ground reaction quantity and the measurement matrix is specifically as follows:
wherein: z is the dimensionless test ground reaction quantity, H is a measurement matrix, F is the synthesized force of the longitudinal, lateral and vertical forces of the sole in space, m is the weight of a human body, g is the gravity acceleration, ω is the natural vibration angular frequency of the human leg, and ζ is the natural vibration damping ratio of the human leg.
Further, in the step S3, a state update equation and a measurement update equation of the kalman filter are established, specifically as follows:
s3.1: substituting an acquisition formula of the included angle between the leg and the gravity direction into a dynamics control equation to obtain a space state equation, wherein the space state equation specifically comprises the following steps:
wherein:the speed variable is a speed variable in a space state, A is a state matrix, X is a space variable, and B is a state vector;
s3.2: substituting the identity into the space state equation, and converting the space state equation to obtain a converted space state equation, wherein the method specifically comprises the following steps of:
wherein: x is a space variable, A is a state matrix, B is a state vector, t is a time variable, e is a natural logarithmic base, t 0 Is the initial time;
s3.3: from the t-th space state equation after the transformation i Time integration to t i+1 At the moment, obtain the t i+1 The spatial variable of the moment is specifically:
X i+1 ＝e AΔt X i +(e AΔt -I)A -1 B
wherein: x is X i+1 Is t th i+1 Time space variable, A is state matrix, B is state vector, e is natural logarithmic base, I is identity matrix, X i Is t th i The time space variable, deltat, is the time interval between two continuous time points in discrete state;
s3.4: discretizing the ground test reaction force equation while according to the t < th > i+1 The space variable and noise influence of moment, establish state updating equation and measurement updating equation of said Kalman filtering, specifically:
wherein: x is X i+1 Is t th i+1 Spatial variation of time, Z i+1 Is t th i+1 Measuring ground reaction quantity, C i Is t th i Time of day system matrix, H i+1 Is t th i+1 Time measurement matrix, D i Is t th i System vector of time, v i+1 Is t th i+1 Measurement error noise vector of time, w i Is t th i Systematic error of time of day, X i Is t th i Spatial variation of time of day.
Further, in the step S3.2, the identity in the spatial state equation is substituted, specifically:
wherein: e is a natural logarithmic base, X is a spatial variable, A is a state matrix, t is a temporal variable,is a speed variable in a space state.
Further, the t i System matrix and t-th of time i The system vector obtaining formula at the moment specifically comprises the following steps:
wherein: c (C) i Is t th i Time of day system matrix, D i Is t th i The system vector at the moment, e is a natural logarithmic base number, A is a state matrix, delta t is the time interval between two continuous time points in a discrete state, I is a unit matrix, and B is a state vector.
Further, in the step S4, test data after the filtering process is obtained, specifically as follows:
s4.1: the state updating equation and the measurement updating equation of the Kalman filtering acquire prior estimation errors and prior estimated covariance matrixes according to prior state estimation, and specifically comprise the following steps:
wherein: epsilon i+1|i Is t th i+1 A priori estimation error of time, P i+1|i Is t th i+1 Covariance of a priori estimates of time, X i+1 Is t th i+1 The spatial variation of the moment of time,is t th i+1 Priori state estimation of time epsilon i|i Is t th i A priori estimation error of time C i Is t th i Time of day system matrix, w i Is t th i Systematic error of time, P i|i Is t th i Covariance of a priori estimates of time, Q i Is t th i System noise at time;
s4.2: the state updating equation and the measurement updating equation of the Kalman filtering acquire a posterior estimation error and a covariance matrix of the posterior estimation according to posterior state estimation, and specifically the covariance matrix comprises the following steps:
wherein: epsilon i+1|i+1 Is t th i+1 Time posterior estimation error, P i+1|i+1 T th i+1 Covariance matrix of time posterior estimation, X i+1 Is t th i+1 The spatial variation of the moment of time,is t th i+1 Time posterior state estimation, I is an identity matrix, K i+1 For Kalman gain matrix, H i+1 Is t th i+1 Time measurement matrix epsilon i+1|i Is t th i+1 A priori estimation error of time, v i+1 Is t th i+1 Time measurement error noise vector, P i+1|i Is t th i+1 Covariance of a priori estimates of time of day, R i+1 Is t th i+1 Measuring covariance matrix of noise at moment;
s4.3: the covariance matrix of the posterior estimation is subjected to derivation, and a Kalman gain matrix is obtained according to the covariance matrix of the prior estimation, specifically:
wherein: k (K) i+1 Is a Kalman gain matrix, P i+1|i Is t th i+1 Covariance of a priori estimates of time, H i+1 Is t th i+1 Time measurement matrix, R i+1 Is t th i+1 Measuring covariance matrix of noise at moment;
s4.4: substituting the Kalman gain matrix into the posterior state estimation, and obtaining a filtered signal through the posterior state estimation substituted with the Kalman gain matrix, wherein the method specifically comprises the following steps of:
wherein:is t th i+1 Filtered signals corresponding to time, H i+1 Is t th i+1 Measurement matrix of time of day->Is t th i+1 Estimating a posterior state of the moment;
s4.5: according to the filtered signals, the ground reaction force of the test force in the three directions of the space longitudinal direction, the lateral direction and the vertical direction is obtained, and meanwhile, whether the data time corresponding to the ground reaction force of the test force in the three directions of the space longitudinal direction, the lateral direction and the vertical direction and the total time data of the test data meet the following relation or not is judged, if so, the ground reaction force of the test force in the three directions of the space longitudinal direction, the lateral direction and the vertical direction is the test data after the filtering treatment;
if not, returning to the step S4.1, and acquiring ground reaction forces of the test force corresponding to the next data time after filtering in three directions of space longitudinal direction, lateral direction and vertical direction until the following relation is satisfied;
the relation between the data time corresponding to the ground reaction force after the test force is filtered in the three directions of the longitudinal direction, the lateral direction and the vertical direction and the total time data of the test data is satisfied, specifically:
i＝n-1
wherein: i is the data time corresponding to the ground reaction force of the test force after being filtered in the three directions of the longitudinal direction, the lateral direction and the vertical direction of the space, and n is the total time data of the test data.
Further, the prior state estimation and the posterior state estimation are specifically:
wherein:is t th i+1 A priori state estimation of time of day,/->Is t th i+1 Time posterior state estimation, C i Is t th i System matrix of time of day->Is t th i A priori state estimation of time, D i Is t th i Time of day system vector, K i+1 As a Kalman gain matrix, Z i+1 Is t th i+1 Non-dimensionality test ground reaction quantity at moment, H i+1 Is t th i+1 A measurement matrix of time of day.
Further, the ground reaction force after the test force is filtered in three directions of space longitudinal direction, lateral direction and vertical direction is specifically:
wherein:is t th i+1 Moment-of-time test force ground reaction force after spatial longitudinal filtering, +.>Is t th i+1 Moment-of-time test force ground reaction force after spatial lateral filtering, +.>Is t th i+1 The moment test force is ground reaction force after spatial vertical filtering, m is weight of a person, g is gravitational acceleration, and +.>Is t th i+1 The projection ratio of the combined force of the filtering forces in the three directions of the spatial longitudinal direction, the lateral direction and the vertical direction of the test force at the moment in the spatial longitudinal direction is +.>Is t th i+1 The projection ratio of the combined force of the filtering forces in the longitudinal, lateral and vertical directions of the space and the lateral direction of the space of the test force at the moment is +.>Is t th i+1 The projection ratio of the synthesized force of the filtering force in the three directions of the longitudinal direction, the lateral direction and the vertical direction of the space,is t th i+1 And filtering the signal corresponding to the moment.
The beneficial effects are that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:
the Kalman filtering method of the invention utilizes the Kalman principle to realize the rapid filtering of the non-fluctuation test ground reaction force, effectively processes the signal to noise ratio of the ground reaction force test signal, lays a foundation for the further processing of the test signal, and can well process the ground reaction force filtering problem obtained by the actual test.
Drawings
FIG. 1 is a schematic flow chart of the Kalman filtering method of the present invention;
FIG. 2 is a simplified model schematic of the dynamics of the present inventors' legs;
FIG. 3 is a graph showing the filtering effect of the present invention under different noise conditions;
FIG. 4 is a graph of filtered error versus different noise conditions of the present invention;
fig. 5 is a comparison of the filtered results of the actual measured signal results of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Wherein the described embodiments are some, but not all embodiments of the invention. Thus, the following detailed description of the embodiments of the invention, as presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention.
Example 1
Referring to fig. 1, the present embodiment provides a kalman filtering method for the reaction force of human walking plantar surface, which specifically includes the following steps:
step S1: referring to fig. 2, which is a simplified model schematic of the dynamics of a human leg, the letters in the figure are defined as: m is the weight of the human body,the axial acceleration of the leg, theta is the included angle between the leg and the gravity direction, g is the gravity acceleration, k is the spring rate, u is the displacement of the leg, c is the damping,>for leg speed, F z For the vertical acting force of the sole in space, F y For acting force of sole in space side direction, F x The force of the sole in the space longitudinal direction is F, and the combined force of the sole in the space longitudinal direction, the lateral direction and the vertical direction is F. In this embodiment, the formulas for calculating the spring rate k and the damping c are specifically:
wherein: k is spring stiffness, c is damping, m is human body weight, ω is human leg natural vibration angular frequency, and ζ is human leg natural vibration damping ratio.
According to fig. 2, the stress characteristics of the legs of a person during walking can be obtained, so as to establish a dynamics control equation, which is specifically as follows:
step S1.1: according to the stress characteristics of the leg during walking of figure 2, the force F of the sole in the longitudinal space can be obtained by direct test of a force measuring table x Force F exerted by sole in lateral space y And the acting force F of the sole in the space vertical direction z The synthetic force of the plantar force in the space longitudinal direction, the lateral direction and the vertical direction can be obtained according to the three, and the synthetic force is specifically:
wherein: f is the resultant force of the plantar forces in the space longitudinal, lateral and vertical directions, F x For acting force of sole in space longitudinal direction F y For acting force of sole in space side direction, F z Is the vertical acting force of the sole in space.
Step S1.2: the synthesized force F of the sole in the space longitudinal, lateral and vertical directions obtained by the step S1.1 is combined with the force F of the sole in the space vertical direction z The included angle between the leg and the gravity direction can be obtained, specifically:
wherein: theta is the included angle between the leg and the gravity direction, F z The force is the vertical force of the sole in space, and F is the combined force of the longitudinal, lateral and vertical forces of the sole in space.
Step S1.3: according to the included angle theta between the leg and the gravity direction obtained in the step S1.2, a dynamic control equation can be established, specifically:
wherein: θ is the angle between the leg and the direction of gravity, t is the time variable, m is the weight of the body, c is the damping, k is the spring rate,for the axial acceleration of the leg->The velocity of the leg, u is the displacement of the leg, g is the gravitational acceleration.
Step S2: according to the dynamics control equation, a ground test reaction force equation is constructed, and the method specifically comprises the following steps:
step S2.1: reference is made to the dynamics control equation in step S1.3, where t is a time variable, so that omission can be made in the following equations. The dynamics control equation in the step S1.3 is simplified to obtain the ground reaction force relation, in particular
Wherein: c is the damping, k is the spring rate,the velocity of the leg, u is the displacement of the leg, and F is the resultant of the forces of the sole in space, longitudinal, lateral and vertical.
Step S2.2: setting a space variable X, and converting a ground reaction force relation acquisition formula to obtain a ground test reaction force equation, wherein the ground test reaction force equation specifically comprises the following components:
Z＝HX
wherein: z is the dimensionless test ground reaction quantity, H is the measurement matrix, and X is the space variable.
In this embodiment, the formula for obtaining the space variable X, the dimensionless test ground reaction Z, and the measurement matrix H is specifically:
wherein: x is a space variable, Z is a dimensionless test ground reaction quantity, H is a measurement matrix,the speed of the leg is u is the displacement of the leg, F is the resultant force of the forces of the sole in the space longitudinal, lateral and vertical directions, m is the weight of the human body, g is the gravitational acceleration, ω is the natural vibration angular frequency of the human leg, and ζ is the natural vibration damping ratio of the human leg.
Step S3: discretizing the ground test reaction force equation in the step S2.2, and establishing a Kalman filtering state updating equation and a measurement updating equation according to noise influence, wherein the state updating equation and the measurement updating equation are specifically as follows:
step S3.1: substituting an acquisition formula of the included angle theta between the leg and the gravity direction in the step S1.2 into a dynamics control equation in the step S1.3 to acquire a space state equation, wherein the space state equation is specifically:
wherein:is in a space stateThe lower speed variable, A is the state matrix, X is the space variable, and B is the state vector.
Specifically, the state matrix a and the state vector B are specifically:
wherein: a is a state matrix, B is a state vector, k is a spring rate, m is a human body weight, c is damping, F z The force is the vertical force of the sole in space, and F is the combined force of the longitudinal, lateral and vertical forces of the sole in space.
Step S3.2: substituting the identity into the space state equation in the step S3.1, and converting the space state equation to obtain a converted space state equation, wherein the method specifically comprises the following steps of:
wherein: x is a space variable, A is a state matrix, B is a state vector, t is a time variable, e is a natural logarithmic base, t 0 Is the initial time.
Specifically, the identities substituted into the spatial state equation are:
wherein: e is a natural logarithmic base, X is a spatial variable, A is a state matrix, t is a temporal variable,is a speed variable in a space state.
Step S3.3: from the t-th space state equation after conversion i Time integration to t i+1 After the moment, processing to obtain the t i+1 The spatial variable of the moment is specifically:
X i+1 ＝e AΔt X i +(e AΔt -I)A -1 B
wherein: x is X i+1 Is t th i+1 Time space variable, A is state matrix, B is state vector, e is natural logarithmic base, I is identity matrix, X i Is t th i The time of day spatial variable, Δt, is the time interval between two consecutive time points in a discrete state.
Step S3.4: discretizing the ground test reaction force equation in the step S2.2 and simultaneously according to the t-th step in the step S3.3 i+1 Space variable X of time i+1 And noise influence, establish Kalman filtering state updating equation and measurement updating equation, specifically:
wherein: x is X i+1 Is t th i+1 Spatial variation of time, Z i+1 Is t th i+1 Measuring ground reaction quantity, C i Is t th i Time of day system matrix, H i+1 Is t th i+1 Time measurement matrix, D i Is t th i System vector of time, v i+1 Is t th i+1 Measurement error noise vector of time, w i Is t th i Systematic error of time of day, X i Is t th i Spatial variation of time of day.
Specifically, the first equation in the above equation is a state update equation of the kalman filter, and the second equation in the above equation is a measurement update equation of the kalman filter.
In the present embodiment, the t i Time of day system matrix C i And t i Time of day system vector D i The acquisition formula of (1) is specifically:
wherein: c (C) i Is t th i Time of day system matrix, D i Is t th i The system vector at the moment, e is a natural logarithmic base number, A is a state matrix, delta t is the time interval between two continuous time points in a discrete state, I is a unit matrix, and B is a state vector.
T th i Systematic error w of time of day i And t i+1 Time measurement error noise vector v i+1 The method specifically comprises the following steps:
wherein: v i+1 Is t th i+1 Measurement error noise vector of time, w i Is t th i Systematic error of time, Q i Is t th i System noise at time, R i+1 Is t th i+1 And measuring a covariance matrix of noise at the moment, wherein N is normal distribution.
Step S4: the state update equation and the measurement update equation of the Kalman filtering in the step S3.4 carry out filtering processing on the test data to obtain the test data after the filtering processing, and the specific steps are as follows:
step S4.1: the state updating equation and the measurement updating equation of the Kalman filtering acquire prior estimation errors and prior estimated covariance matrixes according to prior state estimation, and specifically comprise the following steps:
wherein: epsilon i+1|i Is t th i+1 A priori estimation error of time, P i+1|i Is t th i+1 Covariance of a priori estimates of time, X i+1 Is t th i+1 The spatial variation of the moment of time,is t th i+1 Priori state estimation of time epsilon i|i Is t th i A priori estimation error of time C i Is t th i Time of day system matrix, w i Is t th i Systematic error of time, P i|i Is t th i Covariance of a priori estimates of time, Q i Is t th i System noise at time.
In this embodiment, the prior state estimation is specifically:
wherein:is t th i+1 A priori state estimation of time, C i Is t th i System matrix of time of day->Is t th i A priori state estimation of time, D i Is t th i System vector of time of day.
Step S4.2: the Kalman filtering state updating equation and the measurement updating equation acquire a posterior estimation error and a posterior estimated covariance matrix according to posterior state estimation, and specifically comprise the following steps:
wherein: epsilon i+1|i+1 Is t th i+1 Time posterior estimation error, P i+1|i+1 T th i+1 Covariance matrix of time posterior estimation, X i+1 Is t th i+1 The spatial variation of the moment of time,is t th i+1 Time posterior state estimation, I is an identity matrix, K i+1 For Kalman gain matrix, H i+1 Is t th i+1 Time measurement matrix epsilon i+1|i Is t th i+1 A priori estimation error of time, v i+1 Is t th i+1 Time measurement error noise vector, P i+1|i Is t th i+1 Covariance of a priori estimates of time of day, R i+1 Is t th i+1 The covariance matrix of the noise is measured at the moment.
In this embodiment, the posterior state estimation is specifically:
wherein:is t th i+1 A priori state estimation of time of day,/->Is t th i+1 Time posterior state estimation, K i+1 As a Kalman gain matrix, Z i+1 Is t th i+1 Non-dimensionality test ground reaction quantity at moment, H i+1 Is t th i+1 A measurement matrix of time of day.
Step S4.3: and deriving the covariance matrix of the posterior estimation to obtain the following formula, wherein the formula is as follows:
wherein: p (P) i+1|i+1 T th i+1 Covariance matrix of time posterior estimation, K i+1 For Kalman gain matrix, H i+1 Is t th i+1 Time measurement matrix, P i+1|i Is t th i+1 Covariance of a priori estimates of time of day, R i+1 Is t th i+1 The covariance matrix of the noise is measured at the moment.
T in step S4.1 i+1 Covariance P of a priori estimates of time instants i+1|i Substituting the obtained Kalman gain matrix into the above formula to obtain the Kalman gain matrix, wherein the Kalman gain matrix specifically comprises:
wherein: k (K) i+1 Is a Kalman gain matrix, P i+1|i Is t th i+1 Covariance of a priori estimates of time, H i+1 Is t th i+1 Time measurement matrix, R i+1 Is t th i+1 The covariance matrix of the noise is measured at the moment.
Step S4.4: the Kalman gain matrix K in the above method i+1 Substituting the filtered signal into the posterior state estimation in the step S4.2, and meanwhile obtaining the filtered signal through substituting the posterior state estimation after the Kalman gain matrix, wherein the method specifically comprises the following steps:
wherein:is t th i+1 Filtered signals corresponding to time, H i+1 Is t th i+1 Measurement matrix of time of day->Is t th i+1 And (5) posterior state estimation of time.
Step S4.5: according to the filtered signals, the ground reaction force of the test force after being filtered in three directions of space longitudinal direction, lateral direction and vertical direction is obtained, and the ground reaction force is specifically:
wherein:is t th i+1 Moment-of-time test force ground reaction force after spatial longitudinal filtering, +.>Is t th i+1 Moment-of-time test force ground reaction force after spatial lateral filtering, +.>Is t th i+1 The moment test force is ground reaction force after spatial vertical filtering, m is weight of a person, g is gravitational acceleration, and +.>Is t th i+1 The projection ratio of the combined force of the filtering forces in the three directions of the spatial longitudinal direction, the lateral direction and the vertical direction of the test force at the moment in the spatial longitudinal direction is +.>Is t th i+1 The projection ratio of the combined force of the filtering forces in the longitudinal, lateral and vertical directions of the space and the lateral direction of the space of the test force at the moment is +.>Is t th i+1 The projection ratio of the combined force of the filtering forces in the longitudinal direction, the lateral direction and the vertical direction of the space of the test force at the moment in the vertical direction of the space is +.>Is t th i+1 And filtering the signal corresponding to the moment.
Specifically, for each moment, in order to enable the test force to accurately obtain the filtering force in three directions of the space longitudinal direction, the lateral direction and the vertical direction after the synthesis filtering, projection calculation of the synthesis force F in the three directions of the space longitudinal direction, the lateral direction and the vertical direction is needed, specifically:
wherein:is t th i+1 The projection ratio of the combined force of the filtering forces in the three directions of the spatial longitudinal direction, the lateral direction and the vertical direction of the test force at the moment in the spatial longitudinal direction is +.>Is t th i+1 The projection ratio of the combined force of the filtering forces in the longitudinal, lateral and vertical directions of the space and the lateral direction of the space of the test force at the moment is +.>Is t th i+1 The projection ratio of the combined force of the filtering forces in the longitudinal direction, the lateral direction and the vertical direction of the space of the test force at the moment in the vertical direction of the space is +.>Is t th i+1 Moment-of-time test force ground reaction force in the longitudinal direction of the space,/->Is t th i+1 Ground reaction force of test force at moment in space side,/->Is t th i+1 Moment test force is in space vertical ground reaction force, F i+1 Is t th i+1 The test force at the moment filters the resultant force of the forces in three directions, namely the longitudinal, lateral and vertical directions in space.
After the ground reaction force of the test force filtered in the three directions of the space longitudinal direction, the lateral direction and the vertical direction is obtained, judging whether the data time corresponding to the ground reaction force of the test force filtered in the three directions of the space longitudinal direction, the lateral direction and the vertical direction and the total time data of the test data meet the following relation, and if so, the ground reaction force of the test force filtered in the three directions of the space longitudinal direction, the lateral direction and the vertical direction is the test data after the filtering treatment.
Otherwise, if not, returning to the step S4.1, and acquiring the ground reaction force of the test force corresponding to the next data time after filtering in the three directions of the space longitudinal direction, the lateral direction and the vertical direction until the following relation is satisfied. In this embodiment, the relational expression that the data time corresponding to the ground reaction force after the test force is filtered in the three directions of the longitudinal direction, the lateral direction and the vertical direction and the total time data of the test data satisfy is specifically:
i＝n-1
wherein: i is the data time corresponding to the ground reaction force of the test force after being filtered in the three directions of the longitudinal direction, the lateral direction and the vertical direction of the space, and n is the total time data of the test data.
In order to test the effectiveness of the kalman filtering method in this embodiment, the ideal ground reaction force signal and the field test signal under different noise are respectively subjected to filtering processing.
Wherein the time interval between two consecutive time points in the discrete state is set to:
Δt＝0.001s
the human leg self-vibration damping ratio is set as follows:
ξ＝15％
the spring rate is set to:
k＝650N/m
the system noise is set as:
the covariance matrix of the measurement noise is set as:
R＝0.36
the initial value covariance is set as:
P 0/0 ＝0
the initial state estimation is set as:
the human leg self-oscillation angular frequency ω is set as:
referring to fig. 3, a graph of the filtering results under three different noise levels, 5%, 10% and 20% for a human body mass m=80 kg, is shown. As can be seen from the figure, the kalman filtering method in the present embodiment can obtain a better filtering result.
Referring to fig. 4, the filtering errors at the three different noise levels are shown, and in the middle main stage, the errors between the results and the accurate values are within 10% after filtering, so that the signal-to-noise ratio of the ground reaction force is greatly improved.
Referring to fig. 5, the figure shows 17 sets of single-step data obtained by walking on the force measuring plate by a man with a body mass of m=69 kg, and the filtering result of the kalman filtering method in this embodiment is shown that the filtering method can better remove noise and obtain a correct and smoother shape of the ground reaction force, and if not satisfied, the filtering method can be further applied to the filtered data for multiple times, so that a better satisfied result can be obtained.
The invention and its embodiments have been described above by way of illustration and not limitation, and the actual construction and method of construction illustrated in the accompanying drawings is not limited to this. Therefore, if one of ordinary skill in the art is informed by this disclosure, a structural manner and an embodiment similar to the technical scheme are not creatively designed without departing from the gist of the present invention, and all the structural manners and the embodiments belong to the protection scope of the present invention.
Claims (9)
1. The Kalman filtering method for the reactivity of the human body walking plantar ground is characterized by comprising the following steps of:
s1: establishing a dynamics control equation according to the stress characteristics of the legs during walking;
s2: constructing a ground test reaction force equation according to the dynamics control equation;
s3: discretizing the ground test reaction force equation, and establishing a Kalman filtering state updating equation and a measuring updating equation according to the influence of noise;
s4: filtering the test data according to the Kalman filtering state updating equation and the Kalman filtering measurement updating equation to obtain the test data after the filtering treatment;
in the step S1, the dynamics control equation is established, specifically as follows:
s1.1: according to the stress characteristics of the legs of the person in the walking process, the synthetic force of the longitudinal, lateral and vertical forces of the sole in space is obtained, and the method specifically comprises the following steps:
wherein: f is the resultant force of the plantar forces in the space longitudinal, lateral and vertical directions, F x For acting force of sole in space longitudinal direction F y For acting force of sole in space side direction, F z The force of the sole in the space is vertical;
s1.2: the included angle between the leg and the gravity direction is obtained by the synthesized force of the sole in the longitudinal direction, the lateral direction and the vertical direction of the space and the force of the sole in the vertical direction of the space, and is specifically as follows:
wherein: theta is the included angle between the leg and the gravity direction, F z The force is the vertical force of the sole in space, and F is the synthesized force of the longitudinal, lateral and vertical forces of the sole in space;
s1.3: according to the included angle between the leg and the gravity direction, the dynamics control equation is established, specifically:
wherein: θ is the angle between the leg and the direction of gravity, t is the time variable, m is the weight of the body, c is the damping, k is the spring rate,for the axial acceleration of the leg->The velocity of the leg, u is the displacement of the leg, g is the gravitational acceleration.
2. The kalman filtering method of human walking plantar ground reaction force according to claim 1, wherein in the step S2, the ground test reaction force equation is constructed, specifically as follows:
s2.1: simplifying the dynamics control equation to obtain a ground reaction force relationship, specifically
Wherein: c is the damping, k is the spring rate,the speed of the leg, u is the displacement of the leg, and F is the resultant force of the forces of the sole in the longitudinal, lateral and vertical directions in space;
s2.2: setting a space variable, and converting the ground reaction force relation acquisition formula to obtain the ground test reaction force equation, wherein the ground test reaction force equation is specifically as follows:
Z＝HX
wherein: z is the dimensionless test ground reaction quantity, H is the measurement matrix, and X is the space variable.
3. The kalman filtering method for human walking plantar ground reaction force according to claim 2, wherein the acquiring formula of the dimensionless test ground reaction quantity and the measuring matrix is specifically as follows:
wherein: z is the dimensionless test ground reaction quantity, H is a measurement matrix, F is the synthesized force of the longitudinal, lateral and vertical forces of the sole in space, m is the weight of a human body, g is the gravity acceleration, ω is the natural vibration angular frequency of the human leg, and ζ is the natural vibration damping ratio of the human leg.
4. The kalman filtering method for the reaction force of the human walking plantar surface according to claim 2, wherein in the step S3, a state update equation and a measurement update equation of the kalman filtering are established, specifically as follows:
s3.1: substituting an acquisition formula of the included angle between the leg and the gravity direction into a dynamics control equation to obtain a space state equation, wherein the space state equation specifically comprises the following steps:
wherein:the speed variable is a speed variable in a space state, A is a state matrix, X is a space variable, and B is a state vector;
s3.2: substituting the identity into the space state equation, and converting the space state equation to obtain a converted space state equation, wherein the method specifically comprises the following steps of:
wherein: x is a space variable, A is a state matrix, B is a state vector, t is a time variable, e is a natural logarithmic base, t 0 Is the initial time;
s3.3: from the t-th space state equation after the transformation i Time integration to t i+1 At the moment, obtain the t i+1 The spatial variable of the moment is specifically:
X i+1 ＝e AΔt X i +(e AΔt -I)A -1 B
wherein: x is X i+1 Is t th i+1 Time space variable, A is state matrix, B is state vector, e is natural logarithmic base, I is identity matrix, X i Is t th i The time space variable, deltat, is the time interval between two continuous time points in discrete state;
s3.4: discretizing the ground test reaction force equation while according to the t < th > i+1 The space variable and noise influence of moment, establish state updating equation and measurement updating equation of said Kalman filtering, specifically:
wherein: x is X i+1 Is t th i+1 Spatial variation of time, Z i+1 Is t th i+1 Measuring ground reaction quantity, C i Is t th i Time of day system matrix, H i+1 Is t th i+1 Time measurement matrix, D i Is t th i System vector of time, v i+1 Is t th i+1 Measurement error noise vector of time, w i Is t th i Systematic error of time of day, X i Is t th i Spatial variation of time of day.
5. The kalman filtering method of human walking plantar surface reaction force according to claim 4, wherein in said step S3.2, the identity in said space state equation is substituted, specifically:
wherein: e is a natural logarithmic base, X is a spatial variable, A is a state matrix, t is a temporal variable,is a speed variable in a space state.
6. The kalman filtering method for human walking plantar surface reaction force according to claim 4, wherein the t-th i System matrix and t-th of time i The system vector obtaining formula at the moment specifically comprises the following steps:
wherein: c (C) i Is t th i Time of day system matrix, D i Is t th i The system vector at the moment, e is a natural logarithmic base number, A is a state matrix, delta t is the time interval between two continuous time points in a discrete state, I is a unit matrix, and B is a state vector.
7. The kalman filtering method for human walking plantar surface reaction force according to claim 4, wherein in the step S4, the test data after the filtering process is obtained, specifically as follows:
s4.1: the state updating equation and the measurement updating equation of the Kalman filtering acquire prior estimation errors and prior estimated covariance matrixes according to prior state estimation, and specifically comprise the following steps:
wherein: epsilon i+1|i Is t th i+1 A priori estimation error of time, P i+1|i Is t th i+1 Priori estimation of time of dayCovariance of meter, X i+1 Is t th i+1 The spatial variation of the moment of time,is t th i+1 Priori state estimation of time epsilon i|i Is t th i A priori estimation error of time C i Is t th i Time of day system matrix, w i Is t th i Systematic error of time, P i|i Is t th i Covariance of a priori estimates of time, Q i Is t th i System noise at time;
s4.2: the state updating equation and the measurement updating equation of the Kalman filtering acquire a posterior estimation error and a covariance matrix of the posterior estimation according to posterior state estimation, and specifically the covariance matrix comprises the following steps:
wherein: epsilon i+1|i+1 Is t th i+1 Time posterior estimation error, P i+1|i+1 T th i+1 Covariance matrix of time posterior estimation, X i+1 Is t th i+1 The spatial variation of the moment of time,is t th i+1 Time posterior state estimation, I is an identity matrix, K i+1 For Kalman gain matrix, H i+1 Is t th i+1 Time measurement matrix epsilon i+1|i Is t th i+1 A priori estimation error of time, v i+1 Is t th i+1 Time measurement error noise vector, P i+1|i Is t th i+1 Covariance of a priori estimates of time of day, R i+1 Is t th i+1 Measuring covariance matrix of noise at moment;
s4.3: the covariance matrix of the posterior estimation is subjected to derivation, and a Kalman gain matrix is obtained according to the covariance matrix of the prior estimation, specifically:
wherein: k (K) i+1 Is a Kalman gain matrix, P i+1|i Is t th i+1 Covariance of a priori estimates of time, H i+1 Is t th i+1 Time measurement matrix, R i+1 Is t th i+1 Measuring covariance matrix of noise at moment;
s4.4: substituting the Kalman gain matrix into the posterior state estimation, and obtaining a filtered signal through the posterior state estimation substituted with the Kalman gain matrix, wherein the method specifically comprises the following steps of:
wherein:is t th i+1 Filtered signals corresponding to time, H i+1 Is t th i+1 Measurement matrix of time of day->Is t th i+1 Estimating a posterior state of the moment;
s4.5: according to the filtered signals, the ground reaction force of the test force in the three directions of the space longitudinal direction, the lateral direction and the vertical direction is obtained, and meanwhile, whether the data time corresponding to the ground reaction force of the test force in the three directions of the space longitudinal direction, the lateral direction and the vertical direction and the total time data of the test data meet the following relation or not is judged, if so, the ground reaction force of the test force in the three directions of the space longitudinal direction, the lateral direction and the vertical direction is the test data after the filtering treatment;
if not, returning to the step S4.1, and acquiring ground reaction forces of the test force corresponding to the next data time after filtering in three directions of space longitudinal direction, lateral direction and vertical direction until the following relation is satisfied;
the relation between the data time corresponding to the ground reaction force after the test force is filtered in the three directions of the longitudinal direction, the lateral direction and the vertical direction and the total time data of the test data is satisfied, specifically:
i＝n-1
wherein: i is the data time corresponding to the ground reaction force of the test force after being filtered in the three directions of the longitudinal direction, the lateral direction and the vertical direction of the space, and n is the total time data of the test data.
8. The kalman filtering method of human walking plantar ground reaction force according to claim 7, wherein the prior state estimation and the posterior state estimation are specifically:
wherein:is t th i+1 A priori state estimation of time of day,/->Is t th i+1 Time posterior state estimation, C i Is t th i System matrix of time of day->Is t th i A priori state estimation of time, D i Is t th i Time of day system vector, K i+1 As a Kalman gain matrix, Z i+1 Is t th i+1 Non-dimensionality test ground reaction quantity at moment, H i+1 Is t th i+1 A measurement matrix of time of day.
9. The kalman filtering method for the ground reaction force of the foot sole of the walking of the human body according to claim 7, wherein the ground reaction force after the test force is filtered in three directions of the space longitudinal direction, the lateral direction and the vertical direction is specifically:
wherein:is t th i+1 Moment-of-time test force ground reaction force after spatial longitudinal filtering, +.>Is t th i+1 Moment-of-time test force ground reaction force after spatial lateral filtering, +.>Is t th i+1 The moment test force is ground reaction force after spatial vertical filtering, m is weight of a person, g is gravitational acceleration, and +.>Is t th i+1 The projection ratio of the combined force of the filtering forces in the three directions of the spatial longitudinal direction, the lateral direction and the vertical direction of the test force at the moment in the spatial longitudinal direction is +.>Is t th i+1 The projection ratio of the combined force of the filtering forces in the longitudinal, lateral and vertical directions of the space and the lateral direction of the space of the test force at the moment is +.>Is t th i+1 The projection ratio of the combined force of the filtering forces in the longitudinal direction, the lateral direction and the vertical direction of the space of the test force at the moment in the vertical direction of the space is +.>Is t th i+1 And filtering the signal corresponding to the moment.
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