CN116058818A - Ultra-wideband radar heart rate detection method based on multi-sequence WOA-VMD algorithm - Google Patents
Ultra-wideband radar heart rate detection method based on multi-sequence WOA-VMD algorithm Download PDFInfo
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Abstract
The invention belongs to the technical field of ultra wideband radar, and relates to an ultra wideband radar heart rate detection method based on a multi-sequence WOA-VMD algorithm, which is used for acquiring multi-sequence vital sign vectors by utilizing vital sign information carried by reflected echoes of the ultra wideband radar, inhibiting respiratory interference and accurately separating heartbeat signals to obtain heart rate values, and comprises the following steps: the radar transmits pulses in a certain pulse repetition period, and the receiving end samples and records data in a certain time interval; performing clutter suppression, linear trend suppression and signal-to-noise ratio improvement preprocessing on radar echo signals, and calculating a slow time direction data variance to obtain a target position so as to obtain a multi-sequence vital sign vector; and (5) integrating a whale algorithm WOA and a variation modal decomposition algorithm to obtain the heart rate value. The method is mainly applied to occasions for acquiring vital sign information by using ultra-wideband radar.
Description
Technical Field
The invention relates to the technical field of ultra-wideband radar, in particular to an ultra-wideband radar heart rate detection method based on a multi-sequence WOA-VMD algorithm.
Background
Vital signs are commonly used to determine whether current vital activity exists and to understand the physiological state of a living body. Wherein, the heart rate can reflect the current physiological state of human body most directly. With the development of modern technology, heart rate detection methods gradually tend to be diversified. Compared with the traditional contact life detection system, the non-contact detection method does not need a user to connect any sensor, meets the requirements of some special scenes, and is extremely high in comfort. These methods employ Wi-Fi signal, RFID, FMCW radar, ultra wideband radar, doppler radar, and the like. The ultra-wideband radar has the advantages of low power consumption, high resolution, strong anti-interference capability and the like, and can effectively measure vital signs of human bodies. Therefore, the ultra-wideband radar technology has wide application prospect, and the related research results are applied to the fields of ruin rescue, patient medical treatment, safe driving and the like.
Various schemes exist in the prior art to accurately extract the heartbeat signal, for example, the periodicity of harmonic distribution is utilized, so that the accuracy of heart rate detection is improved; the extraction of the heartbeat frequency is realized by combining singular value decomposition with empirical mode decomposition (Empirical mode decomposition, EMD), but EMD has the problem of mode mixing; detecting heartbeat parameters by using clustering empirical mode decomposition improves the performance of EMD, but inevitably leaves residual white noise in the mode; separating the heartbeat signal using a variational modal decomposition (Variational Mode Decomposition, VMD) improves the decomposition efficiency but requires determining the decomposition level based on the target number.
Current vital sign detection algorithms can accurately extract heartbeat signals by spectral analysis of single frame time series, but rely on long-term radar data accumulation. When the sampling frequency is fixed, the longer the participation sequence, the better the spectrum. Therefore, long-term observation data is required for the experiment, and the efficiency of the radar is reduced. Meanwhile, the VMD can effectively overcome modal aliasing, and the frequency domain division capability is better, but the superiority of the VMD depends on the accurate setting of the decomposition layer number K and the penalty value alpha. The alpha value ensures the reconstruction accuracy of the signal, the K value determines the number of modes of decomposition, and the two parameters are often set empirically, thus reducing the adaptability of the VMD.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide an ultra-wideband radar heart rate detection method based on a multi-sequence WOA-VMD algorithm. The method aims at acquiring multi-sequence vital sign vectors by utilizing vital sign information carried by ultra-wideband radar reflected echoes, optimizing parameters by integrating a whale algorithm (Whale Optimization Algorithm, WOA) and a variation modal decomposition algorithm (VMD), restraining respiratory interference and accurately separating heartbeat signals to obtain heart rate values. Therefore, the technical scheme adopted by the invention is that the ultra-wideband radar heart rate detection method based on the multi-sequence WOA-VMD algorithm comprises the following steps:
firstly, a radar transmits pulses in a certain pulse repetition period, a human body target is reflected back to the radar, the round trip time interval reflects distance information, and a receiving end samples and records data in a certain time interval;
secondly, preprocessing such as clutter suppression, linear trend suppression, signal-to-noise ratio improvement and the like is carried out on radar echo signals, an average cancellation method is used for filtering received signals reflected by surrounding stationary targets, background clutter is eliminated, a least square method is used for removing linear trend terms, and a Butterworth band-pass filter is used for filtering out other frequency band signals to keep heartbeat frequency band signals so as to improve the signal-to-noise ratio;
thirdly, calculating the variance of the slow time direction data to obtain a target position, and obtaining a multi-sequence vital sign vector;
and (IV) integrating a whale algorithm WOA and a variation modal decomposition algorithm, constructing an adaptability function by using the energy difference and the sample entropy to obtain a globally optimal parameter combination, and inhibiting respiratory disturbance to obtain a heart rate value.
The ultra-wideband radar heartbeat detection model is constructed as follows:
in a static environment, a person is spaced from an ultra wideband antenna by a distance d 0 X (t) is the chest wall displacement signal caused by respiration and heartbeat; chest motion caused by human respiration and heartbeat is approximately simple harmonic motion, representingThe method comprises the following steps:
x(t)＝A r cos(2πf r t)+A h cos(2πf h t) (1)
wherein: a is that r For respiratory signal amplitude, f r For respiratory signal frequency, A h For the amplitude of the heartbeat signal, f h Is the frequency of the heartbeat signal; the actual distance d (t) between the chest and the radar is:
d(t)＝d 0 +x(t) (2)
propagation time of pulse τ v (t) is:
wherein: c is the propagation speed of electromagnetic wave, τ 0 ＝d 0 And/c is the fixed time delay between the antenna and human body, τ r ＝d r /c，τ h ＝d h And/c is the time delay caused by respiration and heartbeat respectively, the pulse sequence received by the radar is sampled, the respiration and heartbeat frequency is obtained by utilizing a signal processing algorithm, and the channel impulse response h (t, tau) of the ultra-wideband radar is as follows:
wherein: t and tau are respectively slow time and fast time of radar scanning signals, the slow time represents observation time, the fast time represents radar detection distance, and a i δ(τ-τ i (t)) is the response of a stationary object, a v δ(τ-τ v (t)) is the response of the human respiratory heartbeat, let s (τ) be the transmission signal of the ultra wideband radar, then the received signal R (t, τ) is expressed as:
by T s 、δ T Discretizing the signal for slow and fast sampling intervals, respectivelyAnd (3) obtaining:
wherein m=1, 2, …, M; n=1, 2, …, N, the radar return signal model is a discrete matrix R (m, N) with the sign information hidden in this two-dimensional matrix.
Echo selection to obtain multiple sequences of vital sign vectors
UWB life detection can be generally divided into two ranges: there is a range of human targets and a range of unmanned targets, so the main purpose of echo selection is to find the range containing the most obvious human vital sign signals, determine the human target position by analyzing the data variance in the slow time direction, for the n-th column of the echo matrix, the variance σ 2 (n) is defined as:
the variance value in the human body target range is far larger than the result in the non-human body target range, a data basis is provided for human body target positioning, and the human body target P is determined by searching the maximum value point of the variance 0 The distance information is obtained, the vital sign signals are distributed on the adjacent distance gates, the signals are selected on the adjacent distance gates, more vital sign information than single frame signals is obtained, the observation time is shortened, and the distance outside the chest of the human body is set as D th The number P of points occupied by the chest distance of the human body th The calculation is as follows:
the vital sign signal matrix ψ is expressed as:
will target position P of human body 0 And selecting and combining a plurality of sequence signals of adjacent distance gates according to rows to obtain a vital sign signal vector zeta.
The WOA-VMD algorithm optimizes two parameters of K and alpha, the specific flow is as follows, ρ is a random value, a| is a coefficient vector, firstly, the WOA algorithm is introduced to initialize the whale group vector position [ K, alpha ], the fitness function is constructed by using the energy difference and the sample entropy, the fitness of each individual is calculated, the optimal whale position is stored, the corresponding iteration formula is selected according to the value of the convergence factor to update the position until the maximum iteration times is reached, the optimal VMD parameter is output, and the fitness function is selected:
according to energy conservation, the energy difference before and after signal decomposition should be 0, and when the energy difference is small and there is no obvious trend of change, the energy difference is considered to be approximately 0, and the energy loss rate F λ The definition is as follows:
wherein: e (E) k For the energy of each modal component, E is the energy of the original signal, in addition, the sample entropy represents the complexity of the non-stationary signal, the smaller the sample entropy is, the more periodic the representative signal is, the sample entropy F is SE Expressed as:
wherein: r is a similarity tolerance threshold, m is the reconstructed phase space dimension, B m (r) is the probability of matching the m points of two sequences at r, using F λ And F SE Constructing a fitness function of the WOA algorithm:
the number of decomposition layers and penalty factors corresponding to the minimum fitness value are the optimal parameters, at the moment, the signals are thoroughly decomposed by the VMD, modal aliasing does not exist, the heartbeat energy ratio is calculated for each modal component IMF of the frequency domain, and a proper IMF is selected for carrying out heartbeat signal reconstruction, so that an accurate heart rate estimated value is obtained.
The invention has the characteristics and beneficial effects that:
the invention provides a new solution to the heart rate detection problem of the ultra-wideband radar. In general, the method is characterized in that: 1. and preprocessing such as clutter suppression, linear trend suppression, signal to noise ratio improvement and the like is carried out on the radar echo signals, and clutter signals are filtered. 2. And obtaining a target position by using the slow time direction data variance, and accurately positioning a human body target to obtain a maximum distance door. 3. And recombining adjacent range gates to obtain multi-sequence vital sign vectors, so that the observation time is shortened, and the radar efficiency is improved. 4. And a whale algorithm and a variation modal decomposition algorithm are fused to decompose the vital sign signals, inhibit respiratory disturbance and accurately reconstruct heartbeat signals.
Description of the drawings:
fig. 1 ultra wideband radar heartbeat detection model.
Figure 2 is a schematic diagram of the echo selection part algorithm.
FIG. 3WOA-VMD algorithm flow chart.
FIG. 4 is a diagram of an experimental scenario employed by the present invention.
Fig. 5 is a reconstructed heartbeat signal and its spectrogram.
FIG. 6 compares heart rate spectra of other detection methods.
Fig. 7 is a graph of average heart rate absolute error versus other detection methods.
Detailed Description
In general, the present invention describes the proposed heart rate detection method in three sections. Firstly, before the echo signal is decomposed, preprocessing such as clutter suppression, linear trend suppression, signal to noise ratio improvement and the like needs to be performed on the echo signal, which has a great influence on the accuracy of vital sign extraction. Secondly, echo selection is carried out to solve the problems of long data monitoring time and reduced radar efficiency, the slow time direction data variance is calculated to obtain the target position, signals are selected and recombined on adjacent range gates, the observation time is shortened, and the radar efficiency is improved. Then, a WOA-VMD algorithm is introduced to obtain a globally optimal parameter combination, and heartbeat signals are accurately separated. Finally, the validity and accuracy of the method are verified through experiments.
The technical scheme adopted by the invention comprises the following specific steps:
the experimental object sits on a chair which is 1m away from the ultra-wideband radar, the chest and the radar are kept at the same horizontal plane, and normal breathing is kept. The radar transmits pulses in a certain pulse repetition period, the radar is reflected back to the human body target, the round trip time interval reflects distance information, and the receiving end samples and records data in a certain time interval.
And secondly, preprocessing such as clutter suppression, linear trend suppression, signal to noise ratio improvement and the like is needed to be carried out on the radar echo signals in order to filter noise and improve the signal to noise ratio. And filtering the received signals reflected by surrounding stationary targets by using an average cancellation method to eliminate background clutter. And removing the linear trend term by using a least square method, and filtering out the signals of other frequency bands by using a Butterworth band-pass filter to reserve the heartbeat frequency band signals so as to improve the signal-to-noise ratio.
Aiming at the problems of long data monitoring time and reduced radar efficiency, calculating the data variance in the slow time direction to obtain a target position, obtaining a multi-sequence vital sign vector, obtaining more vital sign information than a single frame signal, shortening the observation time and improving the radar efficiency.
And fourthly, introducing a WOA-VMD algorithm on the basis of the last step, constructing an adaptability function by utilizing the energy difference and the sample entropy, obtaining a globally optimal parameter combination, inhibiting respiratory disturbance, accurately separating heartbeat signals, and obtaining an accurate heart rate value.
The invention provides a high-efficiency accurate solution to the ultra-wideband radar heart rate detection problem through the steps 3 and 4. Further, the effectiveness of the method was verified through simulation and experimentation.
The invention will be further described in detail with reference to the accompanying drawings and specific examples.
1. Ultra-wideband radar heartbeat detection model construction
As shown in fig. 1, the principle of ultra wideband radar vital sign detection is detection periodicityFigure 1 is an ultra wideband radar sign detection model. In a static environment, a person is spaced from an ultra wideband antenna by a distance d 0 X (t) is the chest wall displacement signal caused by respiration and heartbeat.
Chest motion caused by the respiration and heartbeat of a person is approximately simple harmonic motion, and can be expressed as:
x(t)＝A r cos(2πf r t)+A h cos(2πf h t) (13)
wherein: a is that r For respiratory signal amplitude, f r For respiratory signal frequency, A h For the amplitude of the heartbeat signal, f h Is the heart beat signal frequency. The actual distance d (t) between the chest and the radar is:
d(t)＝d 0 +x(t) (14)
propagation time of pulse τ v (t) is:
wherein: c is the propagation speed of electromagnetic wave, τ 0 ＝d 0 And/c is the fixed time delay between the antenna and human body, τ r ＝d r /c，τ h ＝d h And/c is the time delay caused by respiration and heartbeat, respectively. It can be seen that the respiration and heartbeat frequency can be obtained by sampling the pulse sequence received by the radar and utilizing a proper signal processing algorithm. Pulse echoes of periodic and stationary targets are shown in fig. 1. The slow time reflects the observation time information and the fast time reflects the radar detection distance information. The echo time delay of a stationary target is constant, and the time delay of a periodic target is periodically changed. It is assumed that in the detection scenario, there is only human respiratory motion and heartbeat motion, and that other objects are stationary. The channel impulse response h (t, τ) of the ultra-wideband radar is:
wherein: t and τ are respectivelySlow time and fast time of radar scanning signal, slow time represents observation time, fast time represents radar detection distance, a i δ(τ-τ i (t)) is the response of a stationary object, a v δ(τ-τ v (t)) is the response of the human respiratory heartbeat. Let s (τ) be the transmit signal of the ultra wideband radar, then the receive signal R (t, τ) is denoted as:
by T s 、δ T Discretizing the signal for slow and fast sampling intervals, respectively, to obtain:
wherein m=1, 2, …, M; n=1, 2, …, N, the radar return signal model is a discrete matrix R (m, N) with the sign information hidden in this two-dimensional matrix.
2. Echo selection to obtain multiple sequences of vital sign vectors
UWB vital detection can generally be divided into two ranges, a range with a human target and a range without a human target, so the main purpose of echo selection is to find the range containing the most obvious human vital sign signal. The human target position is determined by analyzing the data variance in the slow time direction. For the n-th column of the echo matrix, the variance σ 2 (n) is defined as:
the variance value in the human body target range is far larger than that in the non-human body target range, and a data basis is provided for human body target positioning. Determination of human target P by finding variance maximum point 0 Distance information is obtained. The vital sign signals are distributed in adjacent distance gates, and more than single frame signals can be obtained by selecting the signals on the adjacent distance gatesAnd vital sign information, and shortens the observation time. Let the distance D outside the chest of human body th The number P of points occupied by the chest distance of the human body th It can be calculated as:
the vital sign signal matrix ψ is expressed as:
will target position P of human body 0 And selecting and combining a plurality of sequence signals of adjacent distance gates according to rows to obtain a vital sign signal vector zeta. Fig. 2 shows a schematic diagram of this part of the algorithm.
3. Heartbeat signal extraction to obtain accurate heart rate
In order to improve the performance of the VMD, the invention provides that a WOA-VMD algorithm optimizes two parameters, namely K and alpha. The specific flow is shown in fig. 3, where ρ is a random value and |a| is a coefficient vector. Firstly, a WOA algorithm is introduced, the whale group vector position [ K, alpha ] is initialized, an fitness function is constructed by utilizing an energy difference and a sample entropy, the fitness of each individual is calculated, the optimal whale position is stored, a corresponding iteration formula is selected according to the value of a convergence factor to update the position until the maximum iteration times are reached, and the optimal VMD parameter is output. The key to this algorithm is the choice of fitness function, which is described below.
The energy difference before and after signal decomposition should be 0 in terms of energy conservation. When the energy difference is small and there is no significant trend of change, the energy difference is considered to be approximately 0. Rate of energy loss F λ The definition is as follows:
wherein: e (E) k The energy of each modal component, E is the original signal energy. In addition, the sample entropy represents the complexity of the non-stationary signalThe smaller the sample entropy, the more periodic the signal. Entropy of sample F SE Expressed as:
wherein: r is a similarity tolerance threshold, m is the reconstructed phase space dimension, B m (r) is the probability that the two sequences m-point match at r. By F λ And F SE Constructing a fitness function of the WOA algorithm:
the number of decomposition layers and penalty factor corresponding to the minimum fitness value are the optimal parameters, at this time, the signal is thoroughly decomposed by the VMD, and no modal aliasing exists. For each modal component IMF of the frequency domain, calculating the heart rate energy ratio, selecting a proper IMF for heart rate signal reconstruction, and further obtaining an accurate heart rate estimated value.
4. Experimental results
The effectiveness of the method is verified through experiments, the experimental scene is shown in fig. 4, and heart rate detection is carried out on 6 volunteers through ultra-wideband radar. The heart beat signal and the frequency spectrum of the primary reconstruction are shown in fig. 5, the vital sign signal is thoroughly decomposed to obtain a purer heart beat signal, and the measured heart rate estimated value is 1.113Hz. Meanwhile, in order to verify the effectiveness of the algorithm of the present invention, the conventional FFT and EEMD algorithms are used to process the same heartbeat frequency band signal as a comparison, and the spectrum of the extracted heartbeat signal is shown in fig. 6. Wherein, the reference value is 1.119Hz, and the heart rate estimated values measured by FFT, EEMD and WOA-VMD algorithms are 1.167Hz, 1.163Hz and 1.113Hz respectively, and the heart rate estimation of the traditional FFT algorithm and EEMD algorithm has larger errors. In addition, the 1.172Hz signal in the figure is the 4 th harmonic of the respiratory signal. It can be seen that the accuracy of the first two algorithms is affected by respiratory harmonics. The WOA-VMD algorithm is spectrum-concentrated and can obtain accurate heart rate estimation value. The algorithm effectively suppresses the influence of respiratory harmonics and spurious frequency components on the heartbeat signal, and can effectively separate the life signal from the spurious. In addition, in order to compare the accuracy of the three algorithms, the average heart rate error ratio of the three algorithms is analyzed, and the average error ratio of the traditional FFT algorithm, EEMD algorithm and WOA-VMD algorithm is 9.36%, 3.70% and 1.58% respectively. Overall, the WOA-VMD algorithm is significantly better than the other two algorithms.
The foregoing is merely illustrative of the present invention, and the present invention is not limited thereto, and any changes or substitutions easily contemplated by those skilled in the art within the scope of the present invention should be included in the scope of the present invention.
Claims (4)
1. The ultra-wideband radar heart rate detection method based on the multi-sequence WOA-VMD algorithm is characterized by comprising the following steps:
firstly, a radar transmits pulses in a certain pulse repetition period, a human body target is reflected back to the radar, the round trip time interval reflects distance information, and a receiving end samples and records data in a certain time interval;
secondly, clutter suppression, linear trend suppression and signal-to-noise ratio improvement preprocessing are carried out on radar echo signals, an average cancellation method is used for filtering received signals reflected by surrounding stationary targets, background clutter is eliminated, a least square method is used for removing linear trend terms, and a Butterworth band-pass filter is used for filtering out other frequency band signals to keep heartbeat frequency band signals so as to improve the signal-to-noise ratio;
thirdly, calculating the variance of the observation time data to obtain a target position, and obtaining a multi-sequence vital sign vector;
and (IV) integrating a whale algorithm WOA and a variation modal decomposition algorithm, constructing an adaptability function by using the energy difference and the sample entropy to obtain a globally optimal parameter combination, and inhibiting respiratory disturbance to obtain a heart rate value.
2. The ultra-wideband radar heart rate detection method based on the multi-sequence WOA-VMD algorithm as claimed in claim 1, wherein the ultra-wideband radar heart rate detection model in the step (III) is constructed as follows:
in a static environment, a person is spaced from an ultra wideband antenna by a distance d 0 X (t) is the chest wall displacement signal caused by respiration and heartbeat; chest motion caused by the respiration and heartbeat of a person is approximately simple harmonic motion, expressed as:
x(t)＝A r cos(2πf r t)+A h cos(2πf h t) (1)
wherein: a is that r For respiratory signal amplitude, f r For respiratory signal frequency, A h For the amplitude of the heartbeat signal, f h Is the frequency of the heartbeat signal; the actual distance d (t) between the chest and the radar is:
d(t)＝d 0 +x(t) (2)
propagation time of pulse τ v (t) is:
wherein: c is the propagation speed of electromagnetic wave, τ 0 ＝d 0 And/c is the fixed time delay between the antenna and human body, τ r ＝d r /c，τ h ＝d h And/c is the time delay caused by respiration and heartbeat respectively, the pulse sequence received by the radar is sampled, the respiration and heartbeat frequency is obtained by utilizing a signal processing algorithm, and the channel impulse response h (t, tau) of the ultra-wideband radar is as follows:
wherein: t and tau are respectively slow time and fast time of radar scanning signals, the slow time represents observation time, the fast time represents radar detection distance, and a i δ(τ-τ i (t)) is the response of a stationary object, a v δ(τ-τ v (t)) is the response of the human respiratory heartbeat, let s (τ) be the transmission signal of the ultra wideband radar, then the received signal R (t, τ) is expressed as:
by T s 、δ T Discretizing the signal for slow and fast sampling intervals, respectively, to obtain:
wherein m=1, 2, …, M; n=1, 2, …, N, the radar return signal model is a discrete matrix R (m, N) with the sign information hidden in this two-dimensional matrix.
3. Ultra wideband radar heart rate detection method based on the multi-sequence WOA-VMD algorithm as claimed in claim 2, wherein the echoes are selected to obtain a multi-sequence vital sign vector:
UWB life detection falls into two ranges: there is a range of human targets and a range of unmanned targets, so the main purpose of echo selection is to find the range containing the most obvious human vital sign signals, determine the human target position by analyzing the data variance in the slow time direction, for the n-th column of the echo matrix, the variance σ 2 (n) is defined as:
the variance value in the human body target range is far larger than the result in the non-human body target range, a data basis is provided for human body target positioning, and the human body target P is determined by searching the maximum value point of the variance 0 The distance information is obtained, the vital sign signals are distributed on the adjacent distance gates, the signals are selected on the adjacent distance gates, more vital sign information than single frame signals is obtained, the observation time is shortened, and the distance outside the chest of the human body is set as D th The number P of points occupied by the chest distance of the human body th The calculation is as follows:
the vital sign signal matrix ψ is expressed as:
will target position P of human body 0 And selecting and combining a plurality of sequence signals of adjacent distance gates according to rows to obtain a vital sign signal vector zeta.
4. The ultra wideband radar heart rate detection method based on the multi-sequence WOA-VMD algorithm as claimed in claim 1, wherein in the step (four), the WOA-VMD algorithm optimizes two parameters of K and alpha, the specific flow is as follows, rho is a random value, a|is a coefficient vector, firstly, the WOA algorithm is introduced, the whale group vector position [ K, alpha ] is initialized, the fitness function is constructed by using the energy difference and the sample entropy, the fitness of each individual is calculated, the optimal whale position is stored, the corresponding iteration formula is selected according to the value of the convergence factor to update the position until the maximum iteration times is reached, the optimal VMD parameter is output, and the fitness function is selected:
according to energy conservation, the energy difference before and after signal decomposition should be 0, and when the energy difference is small and there is no obvious trend of change, the energy difference is considered to be approximately 0, and the energy loss rate F λ The definition is as follows:
wherein: e (E) k For the energy of each modal component, E is the energy of the original signal, in addition, the sample entropy represents the complexity of the non-stationary signal, the smaller the sample entropy is, the more periodic the representative signal is, the sample entropy F is SE Expressed as:
wherein: r is a similarity tolerance threshold, m is the reconstructed phase space dimension, B m (r) is the probability of matching the m points of two sequences at r, using F λ And F SE Constructing a fitness function of the WOA algorithm:
the number of decomposition layers and penalty factors corresponding to the minimum fitness value are the optimal parameters, at the moment, the signals are thoroughly decomposed by the VMD, modal aliasing does not exist, the heartbeat energy ratio is calculated for each modal component IMF of the frequency domain, and a proper IMF is selected for carrying out heartbeat signal reconstruction, so that an accurate heart rate estimated value is obtained.
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