Stairlift-based multi-source signal coupling motion process smoothness measurement method

Abstract

The application discloses a stairlift-based multi-source signal coupling motion process smoothness measurement method, and belongs to the technical field of motion measurement.The method is based on a synchronous acquisition of three-axis acceleration signals and three-axis angular velocity signals of an inertial measurement unit installed on a stairlift pedal, sequentially performs signal preprocessing, period phase locking segmentation, double-channel logarithmic dimensionless first-order derivative smoothness index calculation, Softmax weighted fusion based on a harmonic purity ratio, and cross-period statistical output, and obtains a binary measurement result composed of a coupling smoothness index mean value and a variation coefficient.The application designs a double-channel dual structure to avoid dimension leakage of a single-channel method, improves the robustness in a channel burst interference scene through the harmonic purity ratio and the Softmax weighting, improves the fundamental frequency recognition accuracy through the period length priori, and improves the discrimination ability for different motion quality objects through the binary joint output.

Description

Technical Field

[0001] This invention belongs to the field of motion measurement technology, specifically relating to a method for measuring the smoothness of motion processes based on multi-source signal coupling of staircase machines. Background Technology

[0002] Stair climbers are fitness equipment that simulates climbing stairs and are widely used in physical training, rehabilitation training, and home fitness settings. The smoothness of the stair climber's movement reflects both the operational quality of the machine's mechanical structure under cyclic loads and the user's level of motion control. Therefore, measuring the smoothness of the movement is one of the key technologies for evaluating stair climber products and assessing user movement quality.

[0003] The conventional approach to measuring motion smoothness involves using an inertial measurement unit (IMU) mounted on the object under test to collect acceleration and angular velocity signals. These signals are then analyzed in the time or frequency domain to obtain quantitative indicators reflecting smoothness. Current research on motion smoothness measurement primarily focuses on logarithmic dimensionless indices for acceleration signals. However, applying these techniques to the smoothness measurement of stair machine treads presents several technical challenges. Existing logarithmic dimensionless indices typically apply only to the acceleration channel or only to one of the angular velocity channels. Since stair machine tread motion includes both translational and rotational components, a single-channel index cannot comprehensively reflect the motion quality in both dimensions. Furthermore, a change in smoothness in one dimension may go undetected in the other, leading to a risk of missed detections. Existing multi-channel fusion schemes typically employ fixed weighting coefficients or linear weighting based on signal-to-noise ratio (SNR). Fixed weighting coefficients cannot adapt to dynamic changes in channel quality, while SNR-based weighting requires pre-estimation of the noise floor, which is often difficult to accurately obtain under actual operating conditions. Furthermore, linear weighting is not sensitive enough to changes in channel quality, and the fusion result can still be significantly contaminated when a channel encounters sudden interference. Existing frequency domain analysis methods typically use the frequency of the maximum peak value across the entire frequency band as the signal fundamental frequency. However, under certain operating conditions, the amplitude of the second or higher harmonics in the movement of a stair machine tread may exceed the fundamental frequency amplitude. The full-band maximum peak value strategy easily misidentifies higher harmonics as the fundamental frequency, leading to an overall shift in subsequent harmonic band division and ultimately distorting the obtained harmonic energy index. Existing motion smoothness measurement methods typically output a single scalar value. This single scalar cannot simultaneously reflect both the average smoothness and periodic stability of the measured object, making it difficult to effectively distinguish between objects with similar average smoothness but significant differences in periodic fluctuations.

[0004] To address the aforementioned technical problems, this invention designs a method for measuring the smoothness of multi-source signal coupling motion process based on a stair machine. It employs techniques such as dual-channel dual construction, harmonic purity ratio channel quality measurement, Softmax weighted fusion, and binary joint output to overcome the limitations of existing technologies. Summary of the Invention

[0005] To address the problems existing in the background art, the present invention provides a method for measuring the smoothness of multi-source signal coupling motion process based on a stair machine, comprising the following steps: S1: Synchronously acquire the triaxial acceleration and triaxial angular velocity signals of the stair machine treads, and preprocess the triaxial acceleration and triaxial angular velocity signals respectively to obtain acceleration and angular velocity signals; the preprocessing of the triaxial acceleration signal includes composite amplitude calculation, gravitational acceleration amplitude subtraction and low-pass filtering, and the preprocessing of the triaxial angular velocity signal includes composite amplitude calculation and low-pass filtering; S2: Based on the positive zero-crossing point of the angular velocity signal after detrending by the moving average, the acceleration signal and angular velocity signal are synchronously segmented, and motion cycles with abnormal period lengths are removed to obtain an effective motion cycle sequence; S3: Within each effective motion cycle, calculate the logarithmic dimensionless first derivative smoothness index of the corresponding channel based on the first time derivatives of the acceleration signal and the angular velocity signal, respectively. S4: Within each effective motion cycle, frequency domain analysis is performed on the acceleration signal and angular velocity signal respectively. The prior fundamental frequency is estimated based on the cycle length of the effective motion cycle, and the fundamental frequency of the corresponding channel is identified in the neighborhood of the prior fundamental frequency. Based on the fundamental frequency of the corresponding channel and the proportion of the energy of its first few harmonic bands to the total energy of the corresponding channel's full frequency band, the harmonic purity ratio of the acceleration signal and the harmonic purity ratio of the angular velocity signal are calculated respectively. S5: Based on the harmonic purity ratio of the acceleration signal and the harmonic purity ratio of the angular velocity signal, generate the periodic weighting coefficients of the acceleration channel and the angular velocity channel, and perform weighted fusion of the logarithmic dimensionless first derivative smoothness index of the two channels according to the periodic weighting coefficients to obtain the coupling smoothness index of each effective motion cycle. S6: Statistically analyze the coupling smoothness index of each effective motion cycle in the effective motion cycle sequence to obtain the mean and coefficient of variation or invalid coefficient of variation indicator of the coupling smoothness index. The measurement result consisting of the mean and coefficient of variation or invalid coefficient of variation indicator is used as the measurement result of the smoothness of the motion process of the stair machine tread.

[0006] Further, S1 includes the following steps: S11: The inertial measurement unit is rigidly fixed at the center position below the stair machine tread, so that the direction of one sensitive axis of the inertial measurement unit is consistent with the up and down movement direction of the stair machine tread. S12: The inertial measurement unit synchronously outputs triaxial acceleration signals at a sampling rate of not less than 100Hz. , , and triaxial angular velocity signals , , ,in , , These are the acceleration components along the x, y, and z sensitive axes of the inertial measurement unit, respectively. , , These are the angular velocity components along the three sensitive axes of the inertial measurement unit: x, y, and z. For time; S13: Calculate the acceleration synthesis amplitude deviation signal point by point according to the following formula. Combined amplitude signal with angular velocity : ; ; In the formula, The acceleration synthesis amplitude deviation signal is physically defined as the deviation of the synthesized amplitude of the triaxial acceleration signal relative to the amplitude of gravitational acceleration, and its value can be negative. The amplitude signal is synthesized from the angular velocity. This refers to the local gravitational acceleration. S14: Synthesize the acceleration amplitude deviation signal respectively Combined amplitude signal with angular velocity A zero-phase fourth-order Butterworth low-pass filter is used for filtering to obtain the filtered acceleration signal. and the filtered angular velocity signal .

[0007] Further, S2 includes the following steps: S21: Calculate the angular velocity signal using a preset window length. moving average The detrending signal of the angular velocity signal is obtained by the following formula. : ; In the formula, the preset window length ranges from 10 to 50 sampling points; Angular velocity signal The moving average; The detrended signal is obtained by detrending the angular velocity signal through the moving average; The moments when a negative value changes to a positive value are recorded in chronological order as a positive zero-crossing candidate time sequence. , ,in For the first One positive zero-crossing candidate moment; The sequence number of the candidate time point for the positive zero crossing; This represents the total number of positive zero-crossing candidate moments; S22: For the positive zero-crossing candidate time sequence Perform interval merging: If two adjacent positive zero-crossing candidate times and The interval is less than Then only keep And delete Continue merging the remaining sequences until all adjacent intervals are no less than [a certain value]. The resulting sequence is denoted as the positive zero-crossing time sequence in chronological order. , ,in For the first A positive zero-crossing moment; The sequence number of the positive zero crossing moment; This represents the total number of positive zero-crossing moments; This is the lower limit of the effective period length; S23: The two adjacent positive zero-crossing moments and Limited time interval As the first The nth candidate motion cycle is calculated using the following formula. The length of each candidate motion cycle : ; In the formula, For the first The length of each candidate motion cycle; For the first A positive zero-crossing moment; S24: Set the upper limit of the effective period length Remove Do not fall into Candidate motion cycles, among which This is the upper limit of the effective period length; S25: Renumber the remaining candidate motion cycles after S24 in chronological order as number 1 to number 2. The first effective exercise cycle will be the first Each effective exercise cycle is denoted as From the 1st to the 2nd The effective motion cycles constitute an effective motion cycle sequence, in which: This is the sequence number of the effective exercise cycle. ; The total number of effective motion cycles; For the first The starting moment of an effective exercise cycle; For the first The end time of the first effective motion cycle; after eliminating ineffective cycles, the first... The first effective exercise cycle and the first Discontinuity in time is allowed between effective motion cycles.

[0008] Further, S3 includes the following steps: S31: For each effective motion cycle Calculate the acceleration signal using the following formulas respectively. First time derivative and angular velocity signal First time derivative : ; ; In the formula, Acceleration signal The first time derivative; Angular velocity signal The first time derivative; For acceleration signals The time-first derivative operation; For angular velocity signal The time-first derivative operation; S32: During the effective exercise cycle Inside, calculate separately and The maximum value, as the first Peak acceleration over one effective motion cycle and the Peak angular velocity over one effective motion cycle ,in Acceleration signal The absolute value; Angular velocity signal The absolute value; For the first Peak acceleration for each effective motion cycle; For the first Peak angular velocity of one effective motion cycle; S33: When and At that time, calculate the acceleration signal according to the following formula. In the The square integral of the first-order time derivative over each effective motion cycle and angular velocity signal In the The square integral of the first-order time derivative over each effective motion cycle : ; ; And on and Implement lower limit protection: when season ;when season Then, calculate the acceleration signal using the following formulas respectively. In the Logarithmic dimensionless acceleration index within a valid motion cycle and angular velocity signal In the Logarithmic dimensionless angular acceleration index within a valid motion cycle : ; ; In the formula, Acceleration signal In the The first-order time derivative square integral term over an effective motion cycle; Angular velocity signal In the The first-order time derivative square integral term over an effective motion cycle; Acceleration signal In the Logarithmic dimensionless acceleration index within one effective motion cycle; Angular velocity signal In the Logarithmic dimensionless angular acceleration index within one effective motion cycle; For the first The length of an effective exercise cycle ; The peak acceleration threshold; The peak threshold for angular velocity; This is the lower limit threshold of the squared integral term of the first-order time derivative of the acceleration channel. The default positive number is greater than zero; This is the lower limit threshold of the squared integral term of the first-order time derivative of the angular velocity channel. The default positive number is greater than zero; This refers to logarithmic operations with the natural constant e as the base. For in the interval Up to time Definite integral operations; , They are respectively , The square of; , They are respectively , The square of; S34: When the condition in S33 is met and If it is not true, then the first One valid motion cycle is removed from the valid motion cycle sequence, and the remaining valid motion cycles are renumbered in chronological order.

[0009] Further, S4 includes the following steps: S41: In each effective exercise cycle Inside, respectively, the acceleration signals and angular velocity signal The acceleration spectrum is obtained by subtracting the mean value of each data segment within the effective motion period from the mean value of its respective period and then performing a discrete Fourier transform. and angular velocity spectrum ,in Acceleration signal In the Discrete Fourier transform results within one effective motion cycle; Angular velocity signal In the Discrete Fourier transform results within one effective motion cycle; For the first Discrete frequency points (Hz); These are the serial numbers of the discrete frequency points. ; For the first Number of sampling points within a valid motion cycle; This is a floor function; S42: According to the following formula, the first The length of a valid exercise cycle Calculate the prior fundamental frequency : ; In the formula, For the first The prior fundamental frequency (Hz) of each effective motion cycle; For the first The length of an effective motion cycle (s); and further in the frequency neighborhood Inside, search separately and The discrete frequency corresponding to the maximum value They were respectively used as acceleration channels in the first... The fundamental frequency within one effective motion cycle and angular velocity channel in the first The fundamental frequency within one effective motion cycle When the frequency neighborhood When there are no discrete frequency points within the range, select respectively with closest discrete frequency point As and ;in for The amplitude; for The amplitude; For the acceleration channel in the first The fundamental frequency within one effective motion cycle; For the angular velocity channel in the first The fundamental frequency within one effective motion cycle; S43: Set harmonic order The acceleration channel and angular velocity channel are calculated according to the following formula in the first... Harmonic band half-width within one effective motion cycle and : ; ; In the formula, For the acceleration channel in the first Harmonic band half-width within one effective motion cycle; For the angular velocity channel in the first Harmonic band half-width within one effective motion cycle; For harmonic order, It is a positive integer between 3 and 10; Depend on and and ,forward The subharmonic bands do not overlap with each other, and the same discrete frequency point is contained by at most a single harmonic band; S44: Calculate the acceleration channel and angular velocity channel respectively according to the following formula in the [missing information]. Within one effective exercise cycle The total energy of the subharmonic band and : ; ; In the formula, For the acceleration channel in the first Within one effective exercise cycle The total energy of the subharmonic band; For the angular velocity channel in the first Within one effective exercise cycle The total energy of the subharmonic band; Harmonic sequence number ; for The power value; for The power value; To From 1 to Summation operation; To meet the conditions each Summation of corresponding terms; To meet the conditions each Summation of corresponding terms; S45: Calculate the acceleration channel and angular velocity channel respectively in the following formulas at the [number]th [year]. Total energy across the entire frequency band within one effective motion cycle and : ; ; In the formula, For the acceleration channel in the first Total energy across the entire frequency band within one effective motion cycle; For the angular velocity channel in the first Total energy across the entire frequency band within one effective motion cycle; To From 1 to Summation operation; S46: When and At that time, calculate the acceleration signal according to the following formula. In the Harmonic purity ratio within each effective motion cycle and angular velocity signal In the Harmonic purity ratio within each effective motion cycle : ; ; when or At that time, the first Each effective motion cycle is removed from the effective motion cycle sequence, and the logarithmic dimensionless accelerometer index corresponding to that effective motion cycle generated by S3 is also deleted simultaneously. And logarithmic dimensionless angular acceleration index The remaining effective motion cycles and their corresponding , Renumbered in chronological order; among which Acceleration signal In the The harmonic purity ratio within each effective motion cycle, with a value range of [value missing]. ; Angular velocity signal In the The harmonic purity ratio within each effective motion cycle, with a value range of [value missing]. ; The total energy threshold across the entire frequency band. It is a preset positive number greater than zero.

[0010] Further, S5 includes the following steps: S51: For each effective motion cycle Introducing a temperature coefficient The acceleration signal is converted into the following formula: In the Harmonic purity ratio within each effective motion cycle and angular velocity signal In the Harmonic purity ratio within each effective motion cycle Transformed into an acceleration channel by the Softmax function at the 1st... Period weighting coefficient within each effective motion cycle and angular velocity channel in the first Period weighting coefficient within each effective motion cycle : ; ; In the formula, For the acceleration channel in the first Period weighting coefficients within each effective motion cycle; For the angular velocity channel in the first Period weighting coefficients within a valid motion cycle, and The sum equals 1; Temperature coefficient; For exponential operations with the natural constant e as the base; S52: Calculate the following formula Coupling smoothness index per effective motion cycle : ; In the formula, For the first The coupling smoothness index for each effective motion cycle; Acceleration signal In the Logarithmic dimensionless acceleration index within one effective motion cycle; Angular velocity signal In the Logarithmic dimensionless angular acceleration index over a valid motion cycle.

[0011] Further, S6 includes the following steps: S61: Determine the total number of valid motion cycles in the valid motion cycle sequence. :when When the value equals 0, an invalid measurement flag is output, and the method execution ends; when... When the value equals 1, execute S62 and mark the coefficient of variation as invalid, then execute S65; when If the value is not less than 2, execute steps S62, S63, S64, and S65 sequentially. S62: Calculate the coupling smoothness index of each motion cycle in the effective motion cycle sequence using the following formula. mean : ; In the formula, The mean of the coupling smoothness index represents the average motion smoothness of the stair machine treads; This represents the total number of valid motion cycles in the valid motion cycle sequence. For the first The coupling smoothness index for each effective motion cycle; To From 1 to Summation operation; S63: Calculate the coupling smoothness index of each motion cycle in the effective motion cycle sequence using the following formula. Standard deviation : ; In the formula, The standard deviation of the coupling smoothness index; S64: When The coefficient of variation of the coupling smoothness index is calculated using the following formula. ;when The coefficient of variation is marked as invalid at this time: ; In the formula, The coefficient of variation of the coupling smoothness index characterizes the periodic stability of the stair machine's tread motion process; for The absolute value; The absolute value threshold of the mean. The default positive number is greater than zero; S65: Based on the mean and coefficient of variation The measurement results output, which may include invalid identifiers for the coefficient of variation, are used as the measurement results for the smoothness of the movement process of the stair machine treads, where the mean value is... The coefficient of variation characterizes the average motion smoothness of the stair machine treads. The invalid identifier of the coefficient of variation characterizes the periodic stability of the stair machine's tread motion process.

[0012] The beneficial effects achieved by this invention are as follows: This invention uses triaxial acceleration and triaxial angular velocity signals acquired by an inertial measurement unit as inputs. It sequentially completes preprocessing, period segmentation, dual-channel dimensionless index calculation, dual-channel harmonic purity ratio calculation, Softmax weighted fusion, and cross-cycle statistical output to obtain a binary measurement result reflecting the smoothness of the stair machine's tread motion. In implementation, a logarithmic dimensionless index is constructed from the two acquired signals in a dual form, allowing for weighted summation of the two indices. The harmonic purity ratio is introduced as a channel quality metric, avoiding the dependence of traditional signal-to-noise ratio on prior noise floor estimation. A temperature-coefficient Softmax function is used to generate periodic weighting coefficients, achieving adaptive suppression of sudden interference channels. The binary output, consisting of the mean and coefficient of variation, considers both average smoothness and periodic stability, as detailed below: In step S3, this invention constructs strictly dual logarithmic dimensionless first-derivative smoothness indices for both the acceleration and angular velocity channels. Both indices are dimensionless and remain unchanged by amplitude scaling and time scale transformations. Mathematically, they are directly weighted and additive. Through weighted fusion in step S5, a coupled smoothness index is obtained that comprehensively reflects the motion quality of the stair machine's treads in both translation and rotation dimensions. The beneficial effect of this dual-channel construction and weighted fusion technique is that any change in motion stability in any dimension can be reflected by the fused coupled smoothness index, avoiding the missed detection problem caused by the lack of dimension in single-channel indices. Experimental results show that the method of this invention can effectively distinguish smooth modes from stable modes in various motion modes, including only acceleration channel turbulence, only angular velocity channel turbulence, and both channels turbulence. In contrast, single-channel methods may miss detections when turbulence occurs in dimensions unrelated to the target channel, demonstrating the comprehensiveness of the dual-channel fusion method in identifying multiple motion modes.

[0013] In step S4, this invention introduces the harmonic purity ratio as a channel quality metric. The harmonic purity ratio is defined as the ratio of the signal energy in the fundamental frequency and its preceding harmonic bands to the total energy across the entire frequency band. In step S5, a temperature-coefficient Softmax function is used to convert the harmonic purity ratio of the two channels into periodic weighting coefficients. The beneficial effect of the harmonic purity ratio technique is that channel quality assessment can be achieved solely based on the frequency domain distribution characteristics of the signal itself, without the need for prior estimation of the noise floor, thus lowering the engineering implementation threshold. The beneficial effect of the temperature-coefficient Softmax weighting technique is that, since the Softmax function responds exponentially to input differences, the introduction of the temperature coefficient further amplifies the response to harmonic purity ratio differences, resulting in a rapid reduction in the weights of channels subjected to sudden interference and a prominence of the weights of undisturbed channels, significantly improving the robustness of the fusion result. Experimental results show that the coupling smoothness index obtained by the method of the present invention hardly deviates from the steady-state value during the interference period, while the fixed equal weight fusion method and the linear weighting method both show obvious index deviations, indicating the advantages of the harmonic purity ratio and Softmax weighted fusion adopted in the present invention in resisting sudden channel interference.

[0014] In step S42, this invention introduces a fundamental frequency identification strategy based on a priori motion period length. The reciprocal of the effective motion period length obtained in step S2 is used as the prior fundamental frequency estimate, and the fundamental frequency is searched within the neighborhood of the prior fundamental frequency. The beneficial effect of this fundamental frequency identification strategy is that it avoids the risk of misidentifying higher harmonics as the fundamental frequency when directly searching for the maximum peak value across the entire frequency band. This ensures that the harmonic bands calculated in subsequent steps S43 to S46 accurately cover the true fundamental frequency and its harmonic positions, guaranteeing the reliability of the obtained harmonic purity ratio index. Experimental results show that the method of this invention can accurately identify the true fundamental frequency, while existing methods using the full-band maximum peak strategy misidentify the second harmonic as the fundamental frequency, demonstrating the robustness of the fundamental frequency identification strategy of this invention in complex signal scenarios.

[0015] In step S6 of this invention, a binary result consisting of the mean and coefficient of variation of the coupled smoothness index is used as the final output. The mean reflects the average motion smoothness of the tested object, and the coefficient of variation reflects the periodic motion stability of the tested object. The beneficial effect of the binary joint output is that, compared with the existing single scalar output, the output form of this invention provides two independent discriminative dimensions: average level and fluctuation stability. This can effectively distinguish tested objects with similar average levels but large fluctuation differences. Experimental results show that the binary joint output of this invention significantly outperforms the single scalar output using only the mean in distinguishing between two types of samples, indicating that the binary output form of this invention has a significant advantage in discriminating between different motion quality groups. Attached Figure Description

[0016] Figure 1 This is a box plot comparing the smoothness index distribution of Example 1, Comparative Example 1, and Comparative Example 2 under four motion modes, where the horizontal axis represents the motion mode and the vertical axis represents the smoothness index value.

[0017] Figure 2 This is a comparison chart of the time series of indicators for Example 1, Comparative Examples 3 and 4 under a sudden interference scenario, where (a) is the coupling smoothness index of the three methods. The time series comparison diagram (b) shows the acceleration channel period weighting coefficients for the three methods. Time series comparison chart.

[0018] Figure 3 This is a comparison chart of the discriminative abilities of Example 1 and Comparative Example 6 in distinguishing between two groups of athletic quality groups, where (a) is... (b) is a comparison of the two-dimensional scatter distribution and the discriminant line. It is a comparison of the ROC curves of the two classification features.

[0019] Figure 4This is a comparison chart of the fundamental frequency identification accuracy of Example 1 and Comparative Example 5 under a strong second harmonic signal, where (a) is the simulated signal spectrum and the labeling of the fundamental frequency position identified by the two strategies, and (b) is the final result of the two strategies. Comparison of successive numerical simulation results.

[0020] Figure 5 This is a flowchart of the method for measuring the smoothness of motion process of a stair machine based on multi-source signal coupling according to the present invention. Detailed Implementation

[0021] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. In addition, the forms of the various structures described in the following embodiments are merely illustrative. The present invention is not limited to the structures described in the following embodiments. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] The implementation process of the multi-source signal coupling motion smoothness measurement method based on a stair machine provided by this invention is described in detail below. Before implementing the method of this invention, an inertial measurement unit is first installed on the stair machine treads, and the output terminal of the inertial measurement unit is connected to a data processing unit. The inertial measurement unit integrates a three-axis accelerometer and a three-axis gyroscope, which are used to synchronously acquire the three-axis acceleration signal and the three-axis angular velocity signal of the stair machine treads, respectively. The data processing unit can be one of an embedded microcontroller, a host computer, or a cloud server-based processing platform, and receives the output data of the inertial measurement unit and executes the following steps S1 to S6.

[0023] This invention utilizes the strong periodicity of the reciprocating motion of stair climber treads. It sequentially performs signal preprocessing, periodic phase-locked segmentation, calculation of dual-channel logarithmic dimensionless smoothness index, calculation of dual-channel harmonic purity ratio, Softmax weighted fusion based on the harmonic purity ratio, and cross-cycle statistical output, ultimately obtaining a binary measurement result reflecting the motion quality of the stair climber treads. (Refer to...) Figure 5 Step S1 preprocesses the raw signal output by the inertial measurement unit, specifically divided into four sub-steps: S11, S12, S13, and S14. In S11, the inertial measurement unit is rigidly fixed to the center position below the stair tread. The fixing method can be a reliable rigid connection using mechanical clamping, bolting, or adhesive adhesion, ensuring no relative movement between the inertial measurement unit and the stair tread. After fixing the inertial measurement unit, one of its sensitive axes is aligned with the vertical movement direction of the stair tread. This alignment process aims to concentrate the main motion component of the tread onto this sensitive axis, facilitating the stable extraction of motion-related signal features in subsequent steps.

[0024] In S12, the inertial measurement unit synchronously outputs triaxial acceleration signals at a sampling rate of not less than 100Hz. , , and triaxial angular velocity signals , , ,in , , These are the acceleration components along the x, y, and z sensitive axes of the inertial measurement unit, respectively, with units of m / s². 2 ; , , These are the angular velocity components along the x, y, and z sensitive axes of the inertial measurement unit, respectively, with units of rad / s. The time is measured in seconds. The sampling rate is selected based on the Nyquist sampling theorem. The tread frequency of the stair machine is usually within a few Hz, and the first few harmonics are within tens of Hz. Selecting a sampling rate of 100Hz or higher can ensure frequency band coverage. Preferably, a sampling rate of 200Hz or higher can be used in practice to improve the time domain resolution.

[0025] In S13, the acceleration synthesis amplitude deviation signal is calculated point by point according to the following formula. Combined amplitude signal with angular velocity : ; ; In the formula, The acceleration amplitude deviation signal is synthesized, with units of m / s². 2 Its physical meaning is the deviation of the synthesized amplitude of the triaxial acceleration signal from the amplitude of gravitational acceleration, and the value can be negative; The amplitude signal is synthesized from the angular velocity, and the unit is rad / s; , , They are respectively , , The square of; , , They are respectively , , The square of; This refers to the local gravitational acceleration. This is a square root calculation. The composite amplitude calculation combines the components of the three sensitive axes into a single scalar, making subsequent smoothness measurements independent of the specific installation orientation of the inertial measurement unit. The introduction of the acceleration composite amplitude deviation signal is based on the following considerations: In a stationary state, the composite amplitude of the three-axis acceleration is approximately equal to the gravitational acceleration amplitude; subtracting the gravitational acceleration amplitude allows for the separation of the dynamic acceleration component. When the stair machine's treads move, the composite amplitude may be higher or lower than the gravitational acceleration amplitude, therefore... Negative values ​​are allowed. The simplified processing method is applicable to working conditions where vertical reciprocating motion is dominant and the horizontal acceleration component is small, and the motion of the stair machine's treads conforms to the above-mentioned working condition characteristics.

[0026] In S14, the acceleration synthesis amplitude deviation signal is processed respectively. Combined amplitude signal with the angular velocity A zero-phase fourth-order Butterworth low-pass filter is used for filtering, and the filter cutoff frequency is denoted as . The value ranges from 10Hz to 30Hz, where The cutoff frequency of the low-pass filter is given in Hz. The Butterworth filter has the flattest amplitude-frequency response within its passband and is a classic filter type in digital signal processing. The fourth-order configuration strikes a balance between a steep transition band and filter stability. The zero-phase implementation can be achieved by performing forward filtering followed by reverse filtering on the signal, which eliminates phase delay and avoids phase shift introduced by filtering during subsequent zero-crossing detection. The cutoff frequency... The value is determined by balancing the energy preservation of the first few harmonics and the suppression of high-frequency noise; preferably, the cutoff frequency... This can be taken as a multiple of the upper limit of the fundamental frequency of the stair machine's treads. The two signals obtained after filtering by S14 are the acceleration signals used in subsequent steps. and the angular velocity signal ,in This is the preprocessed acceleration signal, in m / s². 2 The value can be negative; This is the preprocessed angular velocity signal, in rad / s. Generated by S14. and For use by subsequent S2 to S6.

[0027] Step S2 on the acceleration signal and the angular velocity signal Synchronous segmentation is performed to obtain an effective motion cycle sequence. The purpose of step S2 is to utilize the strong periodicity of the stair machine's pedal movement to divide the continuous signal into multiple complete motion cycles, providing a basis for subsequent periodic index calculations. Step S2 specifically includes five sub-steps: S21, S22, S23, S24, and S25.

[0028] In S21, the angular velocity signal is calculated using a preset window length. moving average Then, the detrending signal of the angular velocity signal is obtained by the following formula. : ; In the formula, the preset window length ranges from 10 to 50 sampling points, and the window duration corresponding to different sampling rates is approximately tens to hundreds of milliseconds. The angular velocity signal The moving average, in rad / s; The detrended signal, measured in rad / s, is obtained by detrending the angular velocity signal using a moving average. The moving average is preferably implemented using a symmetrical central window method to avoid introducing additional phase shift. The principle of the detrending process is that the angular velocity signal... The amplitude, calculated from the composite value, is always non-negative and does not exhibit zero-crossing. By subtracting the local moving average, the fluctuation of the angular velocity amplitude relative to its local average can be extracted, yielding a detrended signal that can be either positive or negative. The detrending signal The stair machine treads exhibit good zero-crossing characteristics during periodic reciprocating motion. The moments when a negative value changes to a positive value are recorded in chronological order as a positive zero-crossing candidate time sequence. , ,in For the first There are 10 positive zero-crossing candidate times, in seconds; The sequence number of the candidate time point for the positive zero crossing; This represents the total number of positive zero-crossing candidate moments.

[0029] In S22, the positive zero-crossing candidate time sequence Perform interval merging. Specifically, if two adjacent positive zero-crossing candidate times... and The interval is less than Then only keep And delete Continue merging the remaining sequences until all adjacent intervals are no less than [a certain value]. The resulting sequence is denoted as the positive zero-crossing time sequence in chronological order. , ,in For the first The number of positive zero-crossing moments is measured in seconds (s). The sequence number of the positive zero crossing moment; This represents the total number of positive zero-crossing moments; This is the lower limit of the effective period length, measured in seconds, and ranging from 0.4 seconds to 1 second. The purpose of the interval merging is to eliminate false zero crossings caused by slight signal jitter or local noise, and to avoid incorrectly dividing a real motion cycle into multiple candidate cycles.

[0030] In S23, the two adjacent positive zero-crossing moments are... and Limited time interval As the first The candidate motion cycle is calculated according to the following formula. The length of each candidate motion cycle : ; In the formula, For the first The length of each candidate motion cycle, in seconds; For the first The positive zero-crossing times are given in seconds.

[0031] In S24, an upper limit for the effective period length is set. Remove all Do not fall into Candidate motion cycles, among which The effective cycle length is the upper limit, measured in seconds (s), and ranges from 2s to 4s. The effective cycle length range is set based on the reasonable range of tread frequency under normal operating conditions of the stair machine. A cycle that is too short is usually caused by non-motional vibration, while a cycle that is too long may be caused by data interruption or prolonged stationary pedal movement; neither of these is considered an effective motion cycle to be measured.

[0032] In S25, the remaining candidate motion cycles after being eliminated in S24 are renumbered in chronological order as number 1 to number 2. The first effective exercise cycle will be the first Each effective exercise cycle is denoted as From the first to the second The effective motion cycle sequence consists of 10 effective motion cycles, wherein... This is the sequence number of the effective exercise cycle. ; The total number of effective motion cycles; For the first The starting time of each effective motion cycle, in seconds; For the first The end time of the first effective motion cycle, measured in seconds. It should be noted that after eliminating ineffective cycles in S24, the first... The first effective exercise cycle and the first The effective motion cycles are allowed to be discontinuous in time, using mutually independent... and Using this to indicate the start and end times can avoid symbolic ambiguity when the expression period is discontinuous.

[0033] Step S3: Within each effective motion cycle, calculate the logarithmic dimensionless acceleration index of the acceleration signal using a unified form based on the first-order time derivative and peak square normalization. and the logarithmic dimensionless angular acceleration index of the angular velocity signal The method for constructing the logarithmic dimensionless index originates from the family of dimensionless smoothness measures proposed by Hogan et al. in motion control research. This family of measures normalizes the first or higher-order time derivatives of the motion signal by square integration, and then takes the negative logarithm to obtain a dimensionless value. This method extends the dimensionless smoothness measure to both the acceleration and angular velocity channels, and constructs the two indices using a strictly dual form. Step S3 specifically includes four sub-steps: S31, S32, S33, and S34.

[0034] In S31, for each of the effective motion cycles... The acceleration signals are calculated using the following formulas respectively. First time derivative and the angular velocity signal First time derivative : ; ; In the formula, The acceleration signal First-order time derivative, in m / s 3 In physics, jerk is the rate of change of acceleration. The angular velocity signal First-order time derivative, in rad / s 2 In physics, angular acceleration is the acceleration that occurs at an angle. For the acceleration signal The time-first derivative operation; For the angular velocity signal The time-first derivative operation; The time unit is seconds (s). In practice, the first-order time derivative can be approximated using the central difference method or the forward and backward difference method in a discrete numerical manner. The central difference method has better numerical accuracy.

[0035] In S32, during the effective motion cycle Inside, calculate separately and The maximum value, as the first Peak acceleration over one effective motion cycle and the Peak angular velocity over one effective motion cycle ,in The acceleration signal The absolute value; The angular velocity signal The absolute value; For the first Peak acceleration over one effective motion cycle, in m / s² 2 ; For the first The peak angular velocity of each effective motion cycle, in rad / s. This peak value is used for normalization in subsequent calculations of the logarithmic dimensionless index, ensuring that the index remains unchanged under overall scaling transformations of its amplitude.

[0036] In S33, when and At that time, the acceleration signal is calculated according to the following formula. In the The square integral of the first-order time derivative over each effective motion cycle and the angular velocity signal In the The square integral of the first-order time derivative over each effective motion cycle : ; ; In the formula, The acceleration signal In the The first-order time derivative square integral term over a number of effective motion cycles, in units of m. 2 / s 5 ; The angular velocity signal In the The integral of the square of the first-order time derivative over one effective motion cycle, in rad. 2 / s 3 ; In the interval Up to time Definite integral operations; , They are respectively , The square of the integral term. The physical meaning of the integral term is the total energy of the first-order time derivative of the corresponding channel within that period. The smoother the motion, the slower the change in the derivative, and the smaller the value of the corresponding integral term. The definite integral can be calculated using numerical integration methods such as the trapezoidal rule and Simpson's method. Then, for... and Implement lower limit protection: when season ;when season The purpose of the lower limit protection is to prevent the signal from becoming too stable within a certain period, causing the integral term to approach zero, thereby making the input for subsequent logarithmic operations approach zero and the logarithmic value diverge to negative infinity. Then, the acceleration signal is calculated according to the following formula. In the Logarithmic dimensionless acceleration index within a valid motion cycle and the angular velocity signal In the Logarithmic dimensionless angular acceleration index within a valid motion cycle : ; ; In the formula, The acceleration signal In the The logarithmic dimensionless acceleration index within a valid motion cycle is dimensionless. The angular velocity signal In the The logarithmic dimensionless angular acceleration index within a number of effective motion cycles has a dimensionless dimension. For the first The length of an effective motion cycle, measured in seconds (s). ; Peak acceleration threshold, in m / s² 2 The value range is 0.05 m / s 2 up to 0.5m / s 2 ; This is the peak angular velocity threshold, measured in rad / s, with a value ranging from 0.01 rad / s to 0.1 rad / s. This is the lower limit threshold of the squared integral term of the first-order time derivative of the acceleration channel, in meters. 2 / s 5 , is a preset positive number greater than zero; This is the lower limit threshold of the squared integral term of the first-order time derivative of the angular velocity channel, in rad. 2 / s 3 , is a preset positive number greater than zero; This refers to logarithmic operations with the natural constant e as the base. , They are respectively , The square of the threshold. and The value is determined based on the typical magnitude of acceleration and angular velocity of the stair machine under normal operating conditions. Values ​​that are too small typically correspond to stationary treads or abnormal detection conditions, and are therefore not included in the index calculation. The threshold value... and The value of can be determined by the implementer based on the sensor's noise floor level. It only serves to prevent logarithmic divergence and has almost no impact on the index calculation results under normal operating conditions.

[0037] To illustrate the above and For a dimensionless quantity, the following dimensional verification is performed. For example, the numerator term The dimension is s·m 2 / s 5 , equal to m 2 / s 4 denominator The dimension of m 2 / s 4 The ratio of the two is a dimensionless quantity; the natural logarithm operation, when applied to a dimensionless quantity, yields a dimensionless result. Perform similar verification, numerator term The dimension is s·rad 2 / s 3 , equal to rad 2 / s 2 denominator The dimension of rad 2 / s 2 The ratio between the two is also dimensionless. The acceleration channel index and the angular velocity channel index are strictly dual in mathematical form. Both are dimensionless and remain unchanged by amplitude scaling and time scale transformation. They are additivity by direct weighted summation, providing a mathematical basis for cross-channel fusion in S5.

[0038] In S34, when the condition in S33 is... and If it is not true, then the first One valid motion cycle is removed from the valid motion cycle sequence, and the remaining valid motion cycles are renumbered in chronological order. The sequence generated by S33... and For subsequent S5 weighted fusion use.

[0039] Step S4: Within each effective motion cycle, the acceleration signal is processed respectively. and the angular velocity signal Perform a Discrete Fourier Transform. Based on the motion period length obtained in S2, estimate the prior fundamental frequency and identify the fundamental frequency in its neighborhood. Then, calculate the harmonic purity ratio of the acceleration signal and the harmonic purity ratio of the angular velocity signal according to the proportion of the fundamental frequency and the energy of its preceding harmonic bands to the total energy of the entire frequency band. S4 specifically includes six sub-steps: S41, S42, S43, S44, S45, and S46.

[0040] The harmonic purity ratio is introduced based on the following principle: when the stair machine treads perform normal periodic reciprocating motion, the energy of their acceleration and angular velocity signals is concentrated in the fundamental frequency and its preceding harmonics in the frequency domain. If the signal is affected by external interference, such as impacts, sensor drift, or electromagnetic noise, a significant amount of energy will be dispersed into the non-harmonic frequency band. The harmonic purity ratio is defined as the ratio of energy within the harmonic band to the total energy across the entire frequency band. The closer the harmonic purity ratio is to 1, the more concentrated the energy of the corresponding channel signal is in the harmonic band, and the lower the degree of external interference; the closer the harmonic purity ratio is to 0, the more dispersed the energy of the corresponding channel signal is in the non-harmonic frequency band, and the higher the degree of external interference. The design of the harmonic purity ratio as a channel quality metric differs from the traditional signal-to-noise ratio in the following ways: the calculation of the traditional signal-to-noise ratio depends on the prior estimation of the noise floor, which is often difficult to obtain accurately in engineering; the harmonic purity ratio depends only on the frequency domain distribution characteristics of the signal itself, and can be directly calculated by a first discrete Fourier transform, which is simple to implement in engineering and has a lower dependence on prior information.

[0041] In S41, in each of the effective motion cycles Within, respectively, the acceleration signals and the angular velocity signal The acceleration spectrum is obtained by subtracting the mean value of each data segment within the effective motion period from the mean value of its respective period and then performing a discrete Fourier transform. and angular velocity spectrum In the formula The acceleration signal In the Discrete Fourier transform results within one effective motion cycle; The angular velocity signal In the Discrete Fourier transform results within one effective motion cycle; For the first A discrete frequency point, in Hz; These are the serial numbers of the discrete frequency points. ; For the first Number of sampling points within a valid motion cycle; This is a floor function. The subtraction of the mean within the period is used to remove the DC component of the signal, preventing it from forming large peak values ​​in the spectrum and interfering with fundamental frequency identification. The Discrete Fourier Transform can be efficiently calculated using the Fast Fourier Transform algorithm, whose frequency resolution is equal to the ratio of the sampling rate to the number of sampling points. For the ... One effective exercise cycle equals .

[0042] In S42, the following formula is used to determine the order of the first... The length of a valid exercise cycle Calculate the prior fundamental frequency : ; In the formula, For the first The prior fundamental frequency of each effective motion cycle, in Hz; For the first The length of an effective motion cycle, measured in seconds. Furthermore, in the frequency neighborhood... Internal search and The discrete frequency corresponding to the maximum value They were respectively used as acceleration channels in the first... The fundamental frequency within one effective motion cycle and angular velocity channel in the first The fundamental frequency within one effective motion cycle When there are no discrete frequency points within the frequency neighborhood, select frequencies corresponding to the frequency range. closest discrete frequency point As and ,in for The amplitude; for The amplitude; For the acceleration channel in the first The fundamental frequency within one effective motion cycle, in Hz; For the angular velocity channel in the first The fundamental frequency within a valid motion cycle is expressed in Hz. The fundamental frequency identification method utilizes the motion cycle length obtained in step S2. As a priori method, it has the following advantages compared to directly searching for the maximum peak value across the entire frequency band: Under certain operating conditions, the amplitude of the second or higher harmonics of the signal may be greater than the fundamental frequency amplitude. Directly searching for the maximum peak value across the entire frequency band will misjudge the higher harmonics as the fundamental frequency, thereby causing a deviation in the calculation of harmonic band energy. This method limits the search to the neighborhood centered on the prior fundamental frequency, which can avoid the above misjudgment and improve the robustness of fundamental frequency identification.

[0043] In S43, the harmonic order is set. The acceleration channel and angular velocity channel are calculated according to the following formula in the first... Harmonic band half-width within one effective motion cycle and : ; ; In the formula, For the acceleration channel in the first The harmonic band half-width within one effective motion cycle, in Hz; For the angular velocity channel in the first The harmonic band half-width within one effective motion cycle, in Hz; The harmonic order is a positive integer between 3 and 10; preferably, A value of 5 can be chosen. The harmonic order is... The selection criteria are based on a balance between harmonic energy coverage and noise suppression: If the value is too small, the energy contribution at higher harmonics will be missed. If the value is too large, it will introduce more frequency bands far from the fundamental frequency and may include non-harmonic noise. The method for determining the half-width of the harmonic band ensures that adjacent harmonic bands do not overlap. The specific derivation is as follows: For the first... Subharmonic band and the Subharmonic band The center frequencies of the two are spaced apart. The width of a single harmonic band is ;because , Therefore, the center spacing between two adjacent harmonic bands Greater than the harmonic band width Dividing twice by two, that is, there is at least one [value] between adjacent harmonic bands. The intervals between the two do not overlap, and the same discrete frequency point is contained by at most a single harmonic band, thus ensuring that the energy summation of subsequent harmonic bands will not be double-counted.

[0044] In S44, the acceleration channel and angular velocity channel are calculated respectively according to the following formulas in the 1st... Within one effective exercise cycle The total energy of the subharmonic band and : ; ; In the formula, For the acceleration channel in the first Within one effective exercise cycle The total energy of the subharmonic band; For the angular velocity channel in the first Within one effective exercise cycle The total energy of the subharmonic band; Harmonic sequence number ; for The power value; for The power value; To From 1 to Summation operation; To meet the conditions each Summation of corresponding terms; To meet the conditions each The summation operation of the corresponding terms.

[0045] In S45, the acceleration channel and angular velocity channel are calculated respectively according to the following formulas in the 1st... Total energy of the entire frequency band within one effective motion cycle and : ; ; In the formula, For the acceleration channel in the first Total energy across the entire frequency band within one effective motion cycle; For the angular velocity channel in the first Total energy across the entire frequency band within one effective motion cycle; To From 1 to The summation operation is performed. The total energy of the entire frequency band is equal to the sum of the power of the corresponding channel's spectrum at all non-DC discrete frequency points. By Passevar's theorem, the total energy of the entire frequency band is proportional to the energy of the corresponding channel's time-domain signal after removing the DC component.

[0046] In S46, when and At that time, the acceleration signal is calculated according to the following formula. In the Harmonic purity ratio within each effective motion cycle and the angular velocity signal In the Harmonic purity ratio within each effective motion cycle : ; ; when or At that time, the first Each effective motion cycle is removed from the effective motion cycle sequence, and the logarithmic dimensionless accelerometer index corresponding to that effective motion cycle generated by S3 is simultaneously deleted. And logarithmic dimensionless angular acceleration index The remaining effective motion cycles and their corresponding , Renumber in chronological order. In the formula... The acceleration signal In the The harmonic purity ratio within each effective motion cycle, dimensionless, and ranging from [value missing]. ; The angular velocity signal In the The harmonic purity ratio within each effective motion cycle, dimensionless, and ranging from [value missing]. ; This is the total energy threshold for the entire frequency band, a preset positive number greater than zero. Combined with the analysis of harmonic band non-overlapping in S43, the harmonic band energy... Not greater than the total energy of the entire frequency band The harmonic purity ratio The value of does indeed fall within Within the interval, for This is also true. The process of synchronously deleting the LDJ indicator ensures that the subsequent S5 uses... , and , The numbers correspond one-to-one to avoid index misalignment.

[0047] Step S5, based on the harmonic purity ratio obtained in S46, generates periodic weighting coefficients for the acceleration channel and the angular velocity channel using a Softmax function with a temperature coefficient, and then applies the periodic weighting coefficients to the corresponding... and A weighted summation is performed to obtain the coupling smoothness index of the effective motion cycle. Step S5 specifically includes two sub-steps, S51 and S52.

[0048] In S51, for each of the effective motion cycles... Introducing a temperature coefficient The harmonic purity ratio is calculated using the following formula. and Transformed into an acceleration channel by the Softmax function at the 1st... Period weighting coefficient within each effective motion cycle and angular velocity channel in the first Period weighting coefficient within each effective motion cycle : ; ; In the formula, For the acceleration channel in the first The period weighting coefficient within each effective motion cycle is dimensionless. For the angular velocity channel in the first The period-weighted coefficients within each effective motion cycle are dimensionless. and The sum equals 1; This is a temperature coefficient, dimensionless, with a value ranging from 3 to 30; preferably, 10 is acceptable; This refers to exponential operations with the natural constant e as the base. The Softmax function is a commonly used probability normalization transformation in machine learning, also known as the normalized exponential function, which transforms a set of real numbers into a probability vector where each component is positive and the sum is 1. (Temperature coefficient) Used to adjust the sensitivity of the weights to differences in harmonic purity ratios: The smaller the value, the more the weights of the two channels tend to be weighted average; The larger the value, the more the two-channel weights tend towards a winner-takes-all pattern. The Softmax function with a temperature coefficient, compared to the linear weighting method, offers smoother differential responses, better tolerance for estimation errors in harmonic purity ratios, and the weights always fall within a certain range. Within the open interval, there will be no extreme situation where a single channel is completely suppressed. When a channel is subjected to sudden interference within a certain effective motion cycle, the harmonic purity ratio of the corresponding channel decreases, and the cycle weighting coefficient will decrease accordingly. This makes the final fusion result more dependent on the indicators of the higher quality channel, which helps to improve the robustness of the measurement.

[0049] In S52, the first is calculated according to the following formula. Coupling smoothness index per effective motion cycle : ; In the formula, For the first The coupling smoothness index of an effective motion cycle, dimensionless; The acceleration signal In the The logarithmic dimensionless acceleration index within each effective motion cycle is generated by S3; The angular velocity signal In the The logarithmic dimensionless angular acceleration index for each effective motion cycle is generated by S3. Based on the dimensionless verification in S33, and Both are dimensionless quantities and strictly dual in form; their weighted sum has a clear physical meaning in mathematics. The coupling smoothness index... Comprehensively reflects the first Within a valid motion cycle, the smoothness of the stair machine treads' motion in both translational and rotational dimensions: When the stair machine treads move smoothly in both dimensions, the LDJ indexes of both channels take larger values. Also take the larger value; when there is a ripple in any dimension, the corresponding channel's LDJ index decreases. The corresponding decrease is also observed. The aforementioned index, which comprehensively reflects both translation and rotation dimensions, contains more comprehensive motion quality information compared to a single-channel smoothness measurement.

[0050] Step S6: The coupling smoothness index of each motion cycle in the effective motion cycle sequence. The mean and coefficient of variation are calculated, and the measurement result consisting of the mean and the coefficient of variation, or the invalid identifier of the coefficient of variation, is used as the measurement result of the smoothness of the movement process of the stair machine tread. S6 specifically includes five sub-steps: S61, S62, S63, S64, and S65.

[0051] In S61, the total number of valid motion cycles in the valid motion cycle sequence is determined. .when When the value equals 0, an invalid measurement flag is output, and the execution of the method ends. A value of 0 may be caused by the following reasons: the acquired signal segment is too short, causing all candidate period lengths to fall outside the valid range; or the stair machine treads remain stationary for an extended period within the acquired signal segment, causing all periods to be discarded by S34 and S46. When the value equals 1, execute step S62 and mark the coefficient of variation as invalid, then execute step S65. A value of 1 means there is only one valid motion cycle. In statistics, the sample standard deviation cannot be defined, and the corresponding coefficient of variation is naturally meaningless. When... If the value is not less than 2, then S62, S63, S64 and S65 are executed sequentially.

[0052] In S62, the coupling smoothness index of each motion cycle in the effective motion cycle sequence is calculated using the following formula. mean : ; In the formula, The mean of the coupling smoothness index is dimensionless and represents the average motion smoothness of the stair machine treads. The total number of valid motion cycles in the valid motion cycle sequence; For the first The coupling smoothness index for each effective motion cycle is generated by S5; To From 1 to The summation operation. The closer the value is to 0, the smoother the average movement of the stair machine's treads; The larger the absolute value, the less smooth the average movement of the stair machine treads.

[0053] In S63, the coupling smoothness index of each motion cycle in the effective motion cycle sequence is calculated using the following formula. Standard deviation : ; In the formula, is the standard deviation of the coupling smoothness index, which is dimensionless; for The square of; This is for the square root calculation. The standard deviation is in the sample standard deviation form, with the denominator being... Instead This is a common practice in statistics for unbiased estimation.

[0054] In S64, when The coefficient of variation of the coupling smoothness index is calculated using the following formula. ;when The coefficient of variation is then marked as invalid: ; In the formula, The coefficient of variation of the coupling smoothness index is dimensionless and characterizes the periodic stability of the stair machine's tread motion process. for The absolute value; The absolute value threshold is a preset positive number greater than zero. The coefficient of variation, which is the ratio of the standard deviation to the absolute value of the mean, is a commonly used dimensionless indicator in statistics to measure the relative dispersion of data. The smaller the value, the closer the motion quality between each cycle, and the better the motion stability of the stair machine treads; The larger the value, the greater the difference in motion quality between different cycles, and the worse the motion stability of the stair machine treads. The threshold value for the absolute value of the mean. The introduction of this is to prevent the mean from being... When it approaches zero, the coefficient of variation as a denominator causes divergence. The specific value is determined by the implementer based on the actual working conditions. The typical magnitude is determined, and it only plays a protective role in extreme cases.

[0055] In S65, the mean is used to calculate the mean. and the coefficient of variation Alternatively, the measurement result output consisting of invalid identifiers for the coefficient of variation may be used as the measurement result for the smoothness of the movement process of the stair machine treads. The mean value in the measurement result... The coefficient of variation characterizes the average smoothness of motion of the stair machine treads. Or its invalid identifier characterizes the periodic stability of the stair machine's tread movement. The binary output format contains richer information dimensions compared to traditional single-scalar smoothness indices: for the user of the stair machine, its overall motion smoothness may reach a satisfactory level, but its periodic stability is poor, indicating insufficient motion control capability; for the stair machine itself, the binary output can separately reflect the overall vibration level and fluctuation stability of the mechanical system, facilitating equipment quality assessment and fault diagnosis.

[0056] Example 1: In this example, an inertial measurement unit (IMU) integrating a 3-axis accelerometer and a 3-axis gyroscope is rigidly fixed to the center position below the stair treads. The z-axis of the IMU is aligned with the vertical movement direction of the stair treads, corresponding to step S11. The IMU synchronously outputs a three-axis acceleration signal at a sampling rate of 200Hz. , , and triaxial angular velocity signals , , This corresponds to step S12. In step S13, the result is calculated by subtracting the magnitude of gravitational acceleration from the magnitude of the composite magnitude. Calculated by composite amplitude method In step S14, a zero-phase fourth-order Butterworth low-pass filter with a cutoff frequency of 20Hz is used to filter the filter. and Filtering yields the acceleration signal. and angular velocity signal .

[0057] The specific steps of S2 in Example 1 are as follows: In step S21, the calculation is performed with a window length of 30 sampling points. moving average Obtain detrending signal ; Set in step S22 The interval for merging is 0.6s; calculations are performed in step S23. ; Set in step S24 Abnormal cycles are removed in 3 seconds; in step S25, the remaining valid cycles are renumbered. .

[0058] Step S3 of Example 1 is specifically as follows: Step S31 calculates using the central difference method. and Step S32 is used to obtain and ; Set in step S33 0.1 m / s 2 , The peak threshold was set to 0.05 rad / s. It is 0.001m 2 / s 5 , 0.001 rad 2 / s 3 As the lower limit threshold of the integration term, it is calculated according to the LDJ formula described in this invention. and Step S34 removes cycles that do not meet the peak threshold.

[0059] Step S4 of Example 1 specifically involves: Step S41 using Fast Fourier Transform to calculate the spectrum; Step S42 based on... After calculating the prior fundamental frequency, the fundamental frequency is identified within the neighborhood; step S43 sets the harmonic order. The value is 5, calculated according to the harmonic band half-width formula described in this invention. and Steps S44 and S45 calculate the harmonic band energy and the total energy across the entire frequency band, respectively; step S46 sets... Using 0.001 as the full-band energy threshold, calculate... and .

[0060] Step S5 of Example 1 is specifically as follows: Step S51: Set the temperature coefficient. The value is 10, calculated according to the Softmax function described in this invention. and Step S52 calculates the weighted summation using a dual-channel method. The specific steps of S6 in Example 1 are as follows: Step S61: Determine... The calculation is performed according to the following cases: steps S62 to S64. , , and set If the value is 0.1, step S65 outputs a binary result.

[0061] Example 2 is the same as Example 1 in the overall process from S1 to S6, except that the parameter values ​​are set near the lower limit of the parameter value range described in this invention. Specifically, the sampling rate is set to 100Hz and the cutoff frequency is set to 10Hz. Take 0.4s, Take 2s, harmonic number Take 3, temperature coefficient Take 3.

[0062] Example 3 is the same as Example 1 in the overall process from S1 to S6, except that the parameter values ​​are set near the upper limit of the parameter value range described in this invention. Specifically, the sampling rate is set to 500Hz and the cutoff frequency is set to 30Hz. Take 1 second, Take 4s, harmonic number Take 8, temperature coefficient Take 20.

[0063] Comparative Example 1 uses only a single-channel acceleration method. Steps S1 to S4 are the same as in Example 1, but the Softmax weighted fusion in step S5 is omitted, and the acceleration channel index is used directly. As a smoothness index for each period, step S6 uses... The mean and coefficient of variation are used as the final output.

[0064] Comparative Example 2 uses only a single channel of angular velocity. Steps S1 to S4 are the same as in Example 1, but the Softmax weighted fusion in step S5 is omitted, and the angular velocity channel index is used directly. As a smoothness index for each period, step S6 uses... The mean and coefficient of variation are used as the final output.

[0065] Comparative Example 3 uses a dual-channel fusion scheme with fixed equal weights. Steps S1 to S4 are the same as in Example 1. In step S5, the HPR-based Softmax weighting is removed, and fixed weighting is used instead. 0.5 and The value is 0.5, and the remaining steps are the same as in Example 1.

[0066] Comparative Example 4 is a dual-channel scheme using linear HPR weighting. Steps S1 to S4 are the same as in Example 1, except that step S5 uses linear normalized weighting. equal Divide by and The weights are calculated by summing the weights, and the remaining steps are the same as in Example 1.

[0067] Comparative Example 5 is a scheme using a traditional baseband identification strategy, where step S42 is directly performed in... and The discrete frequency corresponding to the maximum peak value is searched across the entire frequency band and used as the fundamental frequency, without introducing a priori fundamental frequency. The process involves neighborhood search, and the remaining steps are the same as in Example 1.

[0068] Comparative Example 6 is a single scalar output scheme. Its steps S1 to S5 are the same as those in Example 1, except that only the mean is output in step S6. The coefficient of variation is not calculated or output. .

[0069] Experiment 1, to verify the sensitivity results of Example 1, Comparative Examples 1 and 2 in recognizing multiple motion patterns, simulated the generation of 4 sets of IMU signals, each set corresponding to one motion pattern, and each set containing 100 effective motion cycles. The 4 motion patterns are: Mode 1 is a smooth mode, with both the acceleration and angular velocity channels exhibiting smooth periodic motion; Mode 2 is a mode with periodic jitter only in the acceleration channel; Mode 3 is a mode with periodic jitter only in the angular velocity channel; and Mode 4 is a mode with periodic jitter in both the acceleration and angular velocity channels. For each effective motion cycle, its smoothness index was calculated using the methods of Example 1, Comparative Example 1, and Comparative Example 2, respectively.

[0070] The indicators for Experiment Example 1 are the exponential distribution, mean, and standard deviation of each method under four models. The indicator data are summarized below, compared with those of Comparative Example 1. The mean and standard deviation of the index under the four models were approximately 10.5±0.8, 5.5±1.0, 10.3±0.8, and 5.5±1.0, respectively; Comparative Example 2... The mean and standard deviation of the index under the four models were approximately 10.5±0.8, 10.3±0.8, 5.5±1.0, and 5.5±1.0, respectively; Example 1 The mean and standard deviation of the index in the four modes are approximately 10.5±0.7, 8.7±0.9, 8.7±0.9, and 5.5±0.9, respectively. The closer the index value is to 0, the less smooth the motion; the larger the value, the smoother the motion.

[0071] The results of Experiment Example 1 are as follows Figure 1 As shown. Figure 1 This is a box plot with four motion modes on the horizontal axis and a smoothness index on the vertical axis. Different colors and legends are used to distinguish Example 1. Comparative Example 1 And Comparative Example 2 There are a total of 3 sets of data, and the box plots of the 3 sets of methods are displayed side by side for each motion mode.

[0072] Depend on Figure 1 It can be seen that, in comparative example 1 The box positions of the index in Modes 1 and 3 almost overlap, with the median line around 10.5 and the box span relatively small. In Modes 2 and 4, the median line drops significantly to around 5.5, and the box span increases to around 1.0. This box distribution indicates that the method in Comparative Example 1 cannot distinguish between Modes 1 and 3, nor between Modes 2 and 4. Comparative Example 2... The box positions of the index almost overlap in Modes 1 and 2, with the median of the box around 10.5; in Modes 3 and 4, the median of the box drops to around 5.5. This box distribution demonstrates that the method in Comparative Example 2 cannot distinguish between Modes 1 and 2, nor between Modes 3 and 4. Example 1 The index's median is at 10.5 in Pattern 1, at 8.7 in Patterns 2 and 3, and at 5.5 in Pattern 4, showing clear positional differences among the four patterns.

[0073] Single-channel indices only reflect motion information in the corresponding physical quantity dimension; bumps or smoothness in a single dimension cannot be perceived by dimensions other than that indice. Step S3 of this invention constructs strictly dual logarithmic dimensionless indices for both the acceleration and angular velocity channels, mathematically ensuring that both indices are dimensionless and invariant to amplitude scaling and time scale transformations, thus enabling direct weighted summation of the two indices. Step S5 of this invention organically combines the information from the two channels through Softmax weighted fusion to obtain a coupling smoothness index that comprehensively reflects both translational and rotational dimensions of motion. This avoids the missed detection problem caused by the lack of dimensions in the single-channel method. Specifically, in mode 2, the acceleration channel is bumpy but the angular velocity channel is stable, while in mode 3 the opposite is true. Single-channel indicators will be indistinguishable from stable modes in either of these two scenarios; and The logarithmic dimensionless indices of the two channels are fused using the Softmax weighting method in step S51. The fused value decreases to approximately 8.7 in both single-channel turbulence modes, which is significantly different from the 10.5 in the stable mode. Therefore, in Example 1... The fact that the dual-channel fusion method of Example 1 can be distinguished in all four modes indicates that it has an advantage over the single-channel method used in Comparative Examples 1 and 2 in distinguishing multiple motion modes.

[0074] Experimental Example 2, to verify the robustness of Example 1 compared to Comparative Examples 3 and 4 under sudden channel interference scenarios, was conducted. Specifically, a synthetic IMU signal of 100 consecutive effective motion cycles was generated. The first 30 cycles were normal steady-state signals. Sudden interference, consisting of high-frequency pulses superimposed with broadband white noise, was injected into the acceleration channel from the 31st to the 50th cycles. From the 51st to the 100th cycles, the normal steady-state signal was restored. For each effective motion cycle, the coupling smoothness index was calculated using the methods of Example 1, Comparative Example 3, and Comparative Example 4, respectively. and acceleration channel period weighting coefficient .

[0075] The indicators in Experiment Example 2 were obtained using various methods within the interference segment. Deviation relative to steady-state value and The response characteristics are summarized below. Comparative example 3 uses an equal-weighted fusion strategy, with the acceleration channel period weighting coefficient... It remains constant at 0.5 over 100 periods. The steady-state value is approximately 10.5, the disturbance value is approximately 6.75, and the maximum deviation is approximately 3.8. Comparative Example 4 uses a linear HPR weighting strategy, within the disturbance range... It dropped to approximately 0.246. In the interference segment, the maximum deviation is approximately 1.9, with a value of approximately 8.66. Example 1 employs a Softmax weighting strategy within the interference segment. It quickly dropped to near 0.002. In the interference segment, the value is approximately 10.49, and the maximum deviation is only about 0.06.

[0076] The results of Experiment Example 2 are as follows Figure 2 As shown, Figure 2 In the middle (a), the coupling smoothness index of the three methods is shown. Timing comparison chart, Figure 2 (b) shows the acceleration channel period weighting coefficients for the three methods. The time series comparison chart shows that the horizontal axis of both parts represents the effective motion cycle number. The interference segments from the 31st to the 50th cycle are marked with shaded areas and explained in the legend. The curves corresponding to the three methods are distinguished by different colors in the figure: Comparative Example 3 uses a blue solid line, Comparative Example 4 uses an orange solid line, and Example 1 uses a green solid line.

[0077] Depend on Figure 2 It can be seen that, Figure 2As shown in (a) In terms of timing, compared to Example 3 The curve drops significantly during the interference segment from the 31st to the 50th cycle, forming a distinct dip with an amplitude of approximately 3.8; Comparative Example 4 The curve exhibits a small dip within the interference segment, with a dip amplitude of approximately 1.9; Example 1 The curve almost coincides with the steady-state curve within the disturbance segment, with a dip amplitude of only about 0.06. Figure 2 As shown in (b) In terms of timing, compared to Example 3 The curve remained at a constant value of 0.5, compared to Example 4. The curve drops to approximately 0.246 within the interference segment, as in Example 1. The curve drops rapidly to near 0 within the interference segment. The Softmax weighted fusion strategy used in Example 1 has a significant advantage in resisting sudden channel interference compared to the fixed equal-weight fusion in Comparative Example 3 and the linear HPR weighting in Comparative Example 4.

[0078] In principle, when a channel is subjected to sudden interference within a certain effective motion cycle, the signal energy of the corresponding channel disperses from the harmonic band to the non-harmonic frequency band, resulting in a decrease in the harmonic purity of the channel compared to... It drops rapidly. The Softmax function responds exponentially to input differences, with a temperature coefficient... The introduction of [something] further amplified The response to the difference. Specifically, when the acceleration channel... When it decreases from 0.92 to 0.30, and The difference is 0.62, multiplied by the temperature coefficient. After setting it to 10, the natural exponent operation amplifies the difference to approximately 493 times exp(6.2), leading to an increase in the weight of the acceleration channel. It rapidly drops to near zero. The weights of the linear HPR-weighted system decrease by only a fraction of the time. The linear change of the ratio, for The response to differences is not sensitive enough. Equal-weighted fusion, on the other hand, is completely unable to respond to changes in channel quality; therefore, Figure 2 Example 1 in (a) During the disturbance segment, it hardly deviates from the steady-state value. Figure 2 Example 1 in (b) A sharp drop occurred in the interference segment.

[0079] Experiment 3 was used to verify the difference in discriminative ability between Example 1 and Comparative Example 6 in distinguishing groups with different motor skill levels. The implementation method of Experiment 3 is as follows: Synthetic IMU signals of 60 subjects were generated. These 60 subjects were divided into two categories of 30 each. Category 1 corresponded to a group with good motor control ability, with similar smoothness indices for each effective movement cycle. Category 2 corresponded to a group with weaker motor control ability, with larger differences in smoothness indices for each effective movement cycle, but the average value was close to that of Category 1. IMU signals were collected for 60 seconds for each subject, and their values ​​were calculated according to the method in Example 1. and The binary output, following the method of Comparative Example 6, only takes... As a single scalar output.

[0080] The indicators in Experiment Example 3 used two types of samples. The distribution of dimensions, in The distribution of two-dimensional planes, and the use of single... and binary The area under the receiver operation feature curve as a classification feature The indicator data is summarized below, for Category 1. The mean is approximately 9.5 and the standard deviation is approximately 0.5. The mean is approximately 0.05, and the standard deviation is approximately 0.02; Category 2 The mean is approximately 9.0, and the standard deviation is approximately 0.7. The mean is approximately 0.15, and the standard deviation is approximately 0.04; Comparative Example 6 only uses... As a classification feature Approximately 0.74; Example 1 with Joint features Approximately 0.95. The aforementioned... The calculation is based on the standard binary classification performance measurement method in statistics. The closer the value is to 1, the better the classification performance.

[0081] The results of Experiment Example 3 are as follows Figure 3 As shown, Figure 3 (a) is A comparison chart of two-dimensional scatter point distribution and discriminant line, with the horizontal axis representing... The vertical axis is The image uses different shapes and colors to distinguish between Category 1 and Category 2 samples, and overlays them to display the contrast. Example 6 only uses... The vertical discriminant line corresponding to the discrimination, and the discriminant line with a positive slope corresponding to the discrimination using binary joint features in Example 1; Figure 3 (b) is a comparison chart of ROC curves, with the horizontal axis representing the false positive rate and the vertical axis representing the true positive rate. The chart uses different colors to plot the ROC curves for the two classification features of Comparative Example 6 and Example 1, and labels them accordingly. Numerical value.

[0082] Depend on Figure 3 It can be seen that, Figure 3 In the two-dimensional scatter plot shown in (a), the samples of category 1 are concentrated in... higher and The lower right area mainly falls Approximately 9 to 10 The range is approximately 0.02 to 0.08; Category 2 samples are concentrated in... Close but The significantly higher upper right area mainly falls on Approximately 7.5 to 10 The range is approximately 0.08 to 0.22. In Comparative Example 6, the vertical discriminant line divides the plane into two discriminant regions, with some category 1 samples and some category 2 samples still distributed on the same side of the vertical discriminant line, falling into the misclassification region of Comparative Example 6; the oblique discriminant line in Example 1 comprehensively utilizes... and Two dimensions of information can separate two types of samples with high accuracy. Figure 3 As shown in (b), the ROC curve of Comparative Example 6 is significantly lower than that of Example 1. Approximately 0.74, of Example 1 The value is approximately 0.95, and the difference between the two is approximately 0.21, indicating that the binary system used in Example 1... The output format is different from the single output format of Comparative Example 6. Scalar output has a clear advantage in distinguishing different groups of athletic quality.

[0083] Reflects the average smoothness of motion of the measured object. These reflect the relative dispersion of the subject's exercise quality during the week, corresponding to the two independent dimensions of level and fluctuation in exercise quality assessment. When the average levels of two subjects are similar but their fluctuations differ significantly, a single... Unable to distinguish between the two, single The corresponding discrimination line can only exist as a vertical line on a two-dimensional plane, and this vertical line cannot be utilized. Differences in dimensions; and It can effectively distinguish fluctuation differences. The binary joint discriminant line in Example 1 utilizes information from two dimensions simultaneously in the form of a diagonal line, thereby enabling better separation of the two types of samples.

[0084] Experiment 4, designed to verify the accuracy of fundamental frequency identification in a scenario containing a strong second harmonic signal compared to Comparative Example 5, is as follows: A synthetic IMU signal within one effective motion cycle is generated. This signal exhibits clear periodicity in the frequency domain, with its fundamental frequency amplitude being less than the second harmonic amplitude. Specifically, the fundamental frequency of the signal is 1.0 Hz with an amplitude of 1.0, the second harmonic frequency is 2.0 Hz with an amplitude of 1.5, and the amplitudes of the third to fifth harmonics decrease sequentially. The length of the motion cycle is... It is 1.0s, corresponding to the prior fundamental frequency. The fundamental frequency of this period is 1.0 Hz, and the neighborhood is 0.8 Hz to 1.2 Hz. The methods of Example 1 and Comparative Example 5 are used to identify the fundamental frequency of this period, and the harmonic purity ratio is calculated according to steps S43 to S46. To obtain Numerical stability assessment involved superimposing small-amplitude noise onto the simulated signal and repeating the simulation 50 times, yielding two methods. The sample distribution.

[0085] The indicators for Experiment Example 4 are the fundamental frequency value identified by each method, the actual harmonic situation of the harmonic band coverage, and the final... Numerical values. The index data is summarized below. Comparative Example 5 uses a full-band maximum peak strategy to misidentify the second harmonic at 2.0Hz as the fundamental frequency. This is demonstrated in 50 repeated simulations. The mean is approximately 0.55 and the standard deviation is approximately 0.03. In Example 1, a priori neighborhood search strategy was used to correctly identify the true fundamental frequency at 1.0 Hz. This was demonstrated in 50 repeated simulations. The mean is approximately 0.88 and the standard deviation is approximately 0.02.

[0086] The results of Experiment Example 4 are as follows Figure 4 As shown, Figure 4 (a) shows the spectrum of the simulated signal and the labeling of the fundamental frequency position identified by the two strategies. The horizontal axis is the frequency (Hz) and the vertical axis is the spectral amplitude. The spectral amplitude curve of the simulated signal is drawn with a solid blue line. The search neighborhood of Example 1 (0.8Hz to 1.2Hz) is marked with a green shading. The fundamental frequency position identified by Comparative Example 5 is marked with a red triangle and the fundamental frequency position identified by Example 1 is marked with a green square. Figure 4 (b) represents the final outcome of the two strategies. A comparison chart of successive numerical simulation results, with the horizontal axis representing the number of simulation iterations from 1 to 50, and the vertical axis representing... The numerical values ​​are shown in the graph with red dots and broken lines, representing Comparative Example 5 in 50 repeated simulations. The results are shown in green squares and broken lines, representing Example 1 in 50 repeated simulations. The results are presented sequentially, with horizontal dashed lines of corresponding colors used to distinguish between the two methods. Mean position.

[0087] Depend on Figure 4 It can be seen that, Figure 4 In the spectrum diagram shown in (a), the amplitude curve of the simulated signal exhibits a fundamental frequency peak at 1.0 Hz and a second harmonic peak at 2.0 Hz. The amplitude of the second harmonic peak is approximately 1.5 times that of the fundamental frequency peak, significantly higher than the fundamental frequency peak. The search neighborhood of Example 1, indicated by the green shading, from 0.8 Hz to 1.2 Hz, only covers the frequency band near the fundamental frequency peak. The fundamental frequency identified in Example 1 is accurately located at 1.0 Hz. Comparative Example 5, without limiting the search range, incorrectly identifies the fundamental frequency at 2.0 Hz, i.e., the second harmonic. Figure 4 In the comparison chart of successive simulation results shown in Figure (b), there are 50 simulation results from Comparative Example 5. The data points remained around 0.55, with a value range of approximately 0.49 to 0.62 and a standard deviation of approximately 0.03. The red line shows slight fluctuations within this range; 50 data points from Example 1. The data points remained around 0.88, with a value range of approximately 0.84 to 0.92 and a standard deviation of approximately 0.02. The green line also showed slight fluctuations within this range. There was no overlap between the point groups of the successive simulation results from the two methods. The difference in their means was approximately 0.33, and the vertical interval was approximately 0.22. This indicates that the fundamental frequency identification strategy based on the prior of the motion period length used in Example 1 has a significant advantage in identification accuracy compared to the full-band maximum peak strategy in Comparative Example 5, especially in scenarios containing strong second harmonic signals.

[0088] For periodic motion, the frequency resolution of the Fast Fourier Transform (FFT) Approximately equal to the fundamental frequency, the motion period length The reciprocal of the fundamental frequency can be used as a reliable prior fundamental frequency estimate. Step S42 of this invention avoids the risk of misidentifying higher harmonics as the fundamental frequency by limiting the fundamental frequency search range to a neighborhood centered on the prior fundamental frequency. After misidentifying the fundamental frequency, the harmonic band positions calculated in step S43 are all shifted to incorrect positions, and some true harmonic energy is excluded from the harmonic band, resulting in an incorrect total harmonic band energy. Decline, eventually The value decreased, therefore Figure 4 (b) Comparison of Example 5 The overall results of successive simulations are significantly lower than those of Example 1, and there is no overlap between the two.

[0089] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for measuring the smoothness of motion process of a staircase machine based on multi-source signal coupling, characterized in that, Includes the following steps: S1: Synchronously acquire the triaxial acceleration and triaxial angular velocity signals of the stair machine treads, and preprocess the triaxial acceleration and triaxial angular velocity signals respectively to obtain acceleration and angular velocity signals; the preprocessing of the triaxial acceleration signal includes composite amplitude calculation, gravitational acceleration amplitude subtraction and low-pass filtering, and the preprocessing of the triaxial angular velocity signal includes composite amplitude calculation and low-pass filtering; S2: Based on the positive zero-crossing point of the angular velocity signal after detrending by the moving average, the acceleration signal and angular velocity signal are synchronously segmented, and motion cycles with abnormal period lengths are removed to obtain an effective motion cycle sequence; S3: Within each effective motion cycle, calculate the logarithmic dimensionless first derivative smoothness index of the corresponding channel based on the first time derivatives of the acceleration signal and the angular velocity signal, respectively. S4: Within each effective motion cycle, frequency domain analysis is performed on the acceleration signal and angular velocity signal respectively. The prior fundamental frequency is estimated based on the cycle length of the effective motion cycle, and the fundamental frequency of the corresponding channel is identified in the neighborhood of the prior fundamental frequency. Based on the fundamental frequency of the corresponding channel and the proportion of the energy of its first few harmonic bands to the total energy of the corresponding channel's full frequency band, the harmonic purity ratio of the acceleration signal and the harmonic purity ratio of the angular velocity signal are calculated respectively. S5: Based on the harmonic purity ratio of the acceleration signal and the harmonic purity ratio of the angular velocity signal, generate the periodic weighting coefficients of the acceleration channel and the angular velocity channel, and perform weighted fusion of the logarithmic dimensionless first derivative smoothness index of the two channels according to the periodic weighting coefficients to obtain the coupling smoothness index of each effective motion cycle. S6: Statistically analyze the coupling smoothness index of each effective motion cycle in the effective motion cycle sequence to obtain the mean and coefficient of variation or invalid coefficient of variation indicator of the coupling smoothness index, and use the measurement result composed of the mean and coefficient of variation or invalid coefficient of variation indicator as the measurement result of the smoothness of the motion process of the stair machine tread. S3 includes the following steps: S31: For each effective motion cycle Calculate the acceleration signal using the following formulas respectively. First time derivative and angular velocity signal First time derivative : ； ； In the formula, Acceleration signal The first time derivative; Angular velocity signal The first time derivative; For acceleration signals The time-first derivative operation; For angular velocity signal The time-first derivative operation; S32: During the effective exercise cycle Inside, calculate separately and The maximum value, as the first Peak acceleration over one effective motion cycle and the Peak angular velocity over one effective motion cycle ,in Acceleration signal The absolute value; Angular velocity signal The absolute value; For the first Peak acceleration for each effective motion cycle; For the first Peak angular velocity of one effective motion cycle; S33: When and At that time, calculate the acceleration signal according to the following formula. In the The square integral of the first-order time derivative over each effective motion cycle and angular velocity signal In the The square integral of the first-order time derivative over each effective motion cycle : ； ； And on and Implement lower limit protection: when season ;when season Then, calculate the acceleration signal using the following formulas respectively. In the Logarithmic dimensionless acceleration index within a valid motion cycle and angular velocity signal In the Logarithmic dimensionless angular acceleration index within a valid motion cycle : ； ； In the formula, Acceleration signal In the The first-order time derivative square integral term over an effective motion cycle; Angular velocity signal In the The first-order time derivative square integral term over an effective motion cycle; Acceleration signal In the Logarithmic dimensionless acceleration index within one effective motion cycle; Angular velocity signal In the Logarithmic dimensionless angular acceleration index within one effective motion cycle; For the first The length of an effective exercise cycle ; The peak acceleration threshold; The peak threshold for angular velocity; This is the lower limit threshold of the squared integral term of the first-order time derivative of the acceleration channel. The default positive number is greater than zero; This is the lower limit threshold of the squared integral term of the first-order time derivative of the angular velocity channel. The default positive number is greater than zero; This refers to logarithmic operations with the natural constant e as the base. In the interval Up to time Definite integral operations; , They are respectively , The square of; , They are respectively , The square of; S34: When the condition in S33 is met and If it is not true, then the first One valid motion cycle is removed from the valid motion cycle sequence, and the remaining valid motion cycles are renumbered in chronological order.

2. The method for measuring the smoothness of motion process based on multi-source signal coupling of a stair machine according to claim 1, characterized in that, S1 includes the following steps: S11: The inertial measurement unit is rigidly fixed at the center position below the stair machine tread, so that the direction of one sensitive axis of the inertial measurement unit is consistent with the up and down movement direction of the stair machine tread. S12: The inertial measurement unit synchronously outputs triaxial acceleration signals at a sampling rate of not less than 100Hz. , , and triaxial angular velocity signals , , ,in , , These are the acceleration components along the x, y, and z sensitive axes of the inertial measurement unit, respectively. , , These are the angular velocity components along the three sensitive axes of the inertial measurement unit: x, y, and z. For time; S13: Calculate the acceleration synthesis amplitude deviation signal point by point according to the following formula. Combined amplitude signal with angular velocity : ； ； In the formula, The acceleration synthesis amplitude deviation signal is physically defined as the deviation of the synthesized amplitude of the triaxial acceleration signal relative to the amplitude of gravitational acceleration, and its value can be negative. The amplitude signal is synthesized from the angular velocity. This refers to the local gravitational acceleration. S14: Synthesize the acceleration amplitude deviation signal respectively Combined amplitude signal with angular velocity A zero-phase fourth-order Butterworth low-pass filter is used for filtering to obtain the filtered acceleration signal. and the filtered angular velocity signal .

3. The method for measuring the smoothness of motion process based on multi-source signal coupling of a stair machine according to claim 2, characterized in that, S2 includes the following steps: S21: Calculate the angular velocity signal using a preset window length. moving average The detrending signal of the angular velocity signal is obtained by the following formula. : ； In the formula, the preset window length ranges from 10 to 50 sampling points; Angular velocity signal The moving average; The detrended signal is obtained by detrending the angular velocity signal through the moving average; The moments when a negative value changes to a positive value are recorded in chronological order as a positive zero-crossing candidate time sequence. , ,in For the first One positive zero-crossing candidate moment; The sequence number of the candidate time point for the positive zero crossing; This represents the total number of positive zero-crossing candidate moments; S22: For the positive zero-crossing candidate time sequence Perform interval merging: If two adjacent positive zero-crossing candidate times and The interval is less than Then only keep And delete Continue merging the remaining sequences until all adjacent intervals are no less than [a certain value]. The resulting sequence is denoted as the positive zero-crossing time sequence in chronological order. , ,in For the first A positive zero-crossing moment; The sequence number of the positive zero crossing moment; This represents the total number of positive zero-crossing moments; This is the lower limit of the effective period length; S23: The two adjacent positive zero-crossing moments and Limited time interval As the first The nth candidate motion cycle is calculated using the following formula. The length of each candidate motion cycle : ； In the formula, For the first The length of each candidate motion cycle; For the first A positive zero-crossing moment; S24: Set the upper limit of the effective period length Remove Do not fall into Candidate motion cycles, among which This is the upper limit of the effective period length; S25: Renumber the remaining candidate motion cycles after S24 in chronological order as number 1 to number 2. The first effective exercise cycle will be the first Each effective exercise cycle is denoted as From the 1st to the 2nd The effective motion cycles constitute an effective motion cycle sequence, in which This is the sequence number of the effective exercise cycle. ; The total number of effective motion cycles; For the first The starting point of an effective exercise cycle; For the first The end time of the first effective motion cycle; after eliminating ineffective cycles, the first... The first effective exercise cycle and the first Discontinuity in time is allowed between effective motion cycles.

4. The method for measuring the smoothness of motion process of a staircase machine based on multi-source signal coupling according to claim 3, characterized in that, S4 includes the following steps: S41: In each effective exercise cycle Inside, respectively, the acceleration signals and angular velocity signal The acceleration spectrum is obtained by subtracting the mean value of each data segment within the effective motion period from the mean value of its respective period and then performing a discrete Fourier transform. and angular velocity spectrum ,in Acceleration signal In the Discrete Fourier transform results within one effective motion cycle; Angular velocity signal In the Discrete Fourier transform results within one effective motion cycle; For the first A discrete frequency point; These are the serial numbers of the discrete frequency points. ; For the first Number of sampling points within a valid motion cycle; This is a floor function; S42: According to the following formula, the first The length of a valid exercise cycle Calculate the prior fundamental frequency : ； In the formula, For the first The prior fundamental frequency of a valid motion cycle; For the first The length of an effective motion cycle; and thus in the frequency neighborhood Inside, search separately and The discrete frequency corresponding to the maximum value They were respectively used as acceleration channels in the first... The fundamental frequency within one effective motion cycle and angular velocity channel in the first The fundamental frequency within one effective motion cycle When the frequency neighborhood When there are no discrete frequency points within the range, select respectively with closest discrete frequency point As and ;in for The amplitude; for The amplitude; For the acceleration channel in the first The fundamental frequency within one effective motion cycle; For the angular velocity channel in the first The fundamental frequency within one effective motion cycle; S43: Set harmonic order The acceleration channel and angular velocity channel are calculated according to the following formula in the first... Harmonic band half-width within one effective motion cycle and : ； ； In the formula, For the acceleration channel in the first Harmonic band half-width within one effective motion cycle; For the angular velocity channel in the first Harmonic band half-width within one effective motion cycle; For harmonic order, It is a positive integer between 3 and 10; Depend on and and ,forward The subharmonic bands do not overlap with each other, and the same discrete frequency point is contained by at most a single harmonic band; S44: Calculate the acceleration channel and angular velocity channel respectively according to the following formula in the [missing information]. Within one effective exercise cycle The total energy of the subharmonic band and : ； ； In the formula, For the acceleration channel in the first Within one effective exercise cycle The total energy of the subharmonic band; For the angular velocity channel in the first Within one effective exercise cycle The total energy of the subharmonic band; Harmonic sequence number ; for The power value; for The power value; To From 1 to Summation operation; To meet the conditions each Summation of corresponding terms; To meet the conditions each Summation of corresponding terms; S45: Calculate the acceleration channel and angular velocity channel respectively in the following formulas at the [number]th [year]. Total energy across the entire frequency band within one effective motion cycle and : ； ； In the formula, For the acceleration channel in the first Total energy across the entire frequency band within one effective motion cycle; For the angular velocity channel in the first Total energy across the entire frequency band within one effective motion cycle; To From 1 to Summation operation; S46: When and At that time, calculate the acceleration signal according to the following formula. In the Harmonic purity ratio within each effective motion cycle and angular velocity signal In the Harmonic purity ratio within each effective motion cycle : ； ； when or At that time, the first Each effective motion cycle is removed from the effective motion cycle sequence, and the logarithmic dimensionless accelerometer index corresponding to that effective motion cycle generated by S3 is also deleted simultaneously. And logarithmic dimensionless angular acceleration index The remaining effective motion cycles and their corresponding , Renumbered in chronological order; among which Acceleration signal In the The harmonic purity ratio within each effective motion cycle, with a value range of [value missing]. ; Angular velocity signal In the The harmonic purity ratio within each effective motion cycle, with a value range of [value missing]. ; The total energy threshold across the entire frequency band. It is a preset positive number greater than zero.

5. The method for measuring the smoothness of motion process of a staircase machine based on multi-source signal coupling according to claim 4, characterized in that, S5 includes the following steps: S51: For each effective motion cycle Introducing a temperature coefficient The acceleration signal is converted into the following formula: In the Harmonic purity ratio within each effective motion cycle and angular velocity signal In the Harmonic purity ratio within each effective motion cycle Transformed into an acceleration channel by the Softmax function at the 1st... Period weighting coefficient within each effective motion cycle and angular velocity channel in the first Period weighting coefficient within each effective motion cycle : ； ； In the formula, For the acceleration channel in the first Period weighting coefficient within each effective motion cycle; For the angular velocity channel in the first Period weighting coefficients within a valid motion cycle, and The sum equals 1; Temperature coefficient; For exponential operations with the natural constant e as the base; S52: Calculate the following formula Coupling smoothness index per effective motion cycle : ； In the formula, For the first The coupling smoothness index for each effective motion cycle; Acceleration signal In the Logarithmic dimensionless acceleration index within one effective motion cycle; Angular velocity signal In the Logarithmic dimensionless angular acceleration index over a valid motion cycle.

6. The method for measuring the smoothness of motion process of a staircase machine based on multi-source signal coupling according to claim 5, characterized in that, S6 includes the following steps: S61: Determine the total number of valid motion cycles in the valid motion cycle sequence. :when When the value equals 0, an invalid measurement flag is output, and the method execution ends; when... When the value equals 1, execute S62 and mark the coefficient of variation as invalid, then execute S65; when If the value is not less than 2, execute steps S62, S63, S64, and S65 sequentially. S62: Calculate the coupling smoothness index of each motion cycle in the effective motion cycle sequence using the following formula. mean : ； In the formula, The mean of the coupling smoothness index represents the average motion smoothness of the stair machine treads; This represents the total number of valid motion cycles in the valid motion cycle sequence. For the first The coupling smoothness index for each effective motion cycle; To From 1 to Summation operation; S63: Calculate the coupling smoothness index of each motion cycle in the effective motion cycle sequence using the following formula. Standard deviation : ； In the formula, The standard deviation of the coupling smoothness index; S64: When The coefficient of variation of the coupling smoothness index is calculated using the following formula. ;when The coefficient of variation is then marked as invalid: ； In the formula, The coefficient of variation of the coupling smoothness index characterizes the periodic stability of the stair machine's tread motion process; for The absolute value; The absolute value threshold of the mean. The default positive number is greater than zero; S65: Based on the mean and coefficient of variation The measurement results output, which may include invalid identifiers for the coefficient of variation, are used as the measurement results for the smoothness of the movement process of the stair machine treads, where the mean value is... The coefficient of variation characterizes the average motion smoothness of the stair machine treads. The invalid identifier of the coefficient of variation characterizes the periodic stability of the stair machine's tread motion process.

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