CN114010167A - Pulse wave fitting method based on Weibull function - Google Patents
Pulse wave fitting method based on Weibull function Download PDFInfo
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Abstract
The invention discloses a pulse wave fitting method based on a Weibull function, which comprises the following steps: cutting off data, wherein the collected human radial artery pulse wave data is cut and divided by taking a pulse cycle as a unit to obtain a data set of single-cycle pulse waves; and fitting the pulse wave data by using a two-parameter or three-parameter Weibull function mode. The method has the beneficial effect that a fitting function, namely a Weibull function, suitable for each wavelet of the pulse wave is selected according to the shape of the pulse wave. The method can obviously improve the goodness of fit, obviously reduce the number of data which cannot be fitted and has universality.
Description
Technical Field
The invention belongs to the field of computational mathematics, and particularly relates to a pulse wave fitting method based on a Weibull function.
Background
The measurement of the pulse wave is an important method in Chinese and western medicine, is an empirical summary of long-term medical practice, and is widely applied in the medical field and the family market. Certain characteristics of the pulse wave signal can be used as important indicators of certain diseases. Currently, clinical workers mainly rely on the pulse wave of the radial artery to judge the health state of the cardiovascular system.
The pulse wave analysis method is developed along with the development of mathematics, biomechanics and engineering, and the fitting mode of the pulse wave signal is a key item in the research field.
In the prior art, a mathematical model synthesized by a plurality of gaussian functions (bell waves) is generally adopted to fit pulse wave data. The pulse wave waveform obtained by non-invasive measurement mainly comprises a main peak wave, a counterpulsation wave and a counterpulsation front wave. The dicrotic wave may be considered in the form of a reflection of the main peak wave, and each wave is therefore approximated by a gaussian function bell. The analysis method can make the characteristics of the pulse wave become clear, and the change of the pulse wave waveform is completely composed of the changes of nine parameters of the three Gaussian functions. However, the method does not consider possible asymmetry of the main peak wave, and the main peak wave is fitted by adopting a symmetric Gaussian function, so that the existing asymmetry phenomenon is difficult to capture. This is a problem with most current pulse wave fitting methods.
Some researches adopt a lognormal function to fit the pulse wave, the lognormal function is an asymmetric function and is matched with the asymmetry of the pulse wave, so that the fitting goodness is remarkably improved compared with a mode of simply adopting a Gaussian function to fit, but simultaneously, the function has the problem of fitting the pulse wave waveform that the wave crest of the constructed lognormal curve has a strong leftward-inclining characteristic in most ranges covered by parameters, and the inclination of the physiological main peak wave of the pulse wave is not obvious, so that the fitting effect of the method is poor.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a pulse wave fitting method based on a Weibull function, wherein the Weibull function which has asymmetry and is distributed similar to pulse wave wavelets is used as each sub-equation of a fitting equation, so that the goodness of fit of pulse wave data can be well improved.
In order to achieve the purpose, the invention adopts the following technical scheme:
a pulse wave fitting method based on a weibull function, the method comprising the steps of:
s1, cutting the data, wherein, cutting and dividing the collected human body radial artery pulse wave data by taking the pulse period as a unit to obtain a data set of single period pulse waves;
s2 fits the pulse wave data using a two-or three-parameter weibull function.
It should be noted that each term in the equation is set as a two-parameter or three-parameter weibull function, and the equation is curve-fitted to the obtained pulse wave data.
It should be noted that the formula of the two-parameter weibull function is:
the Weibull function pulse wave fitting equation is shown as the following formula:
wherein the first term, the second term and the third term of the equation are all two-parameter Weibull functions. The index of the parameter is n, which indicates that the item in which the parameter belongs to the nth item of the equation.
It should be noted that the formula of the three-parameter weibull function is:
the Weibull function pulse wave fitting equation is shown as the following formula:
wherein the first term, the second term and the third term of the equation are all three-parameter Weibull functions. The index of the parameter is n, which indicates that the item in which the parameter belongs to the nth item of the equation.
The method has the beneficial effect that a fitting function, namely a Weibull function, suitable for each wavelet of the pulse wave is selected according to the shape of the pulse wave. The method can obviously improve the goodness of fit, obviously reduce the number of data which cannot be fitted and has universality.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a schematic diagram of a fitting in an embodiment of the present invention.
Detailed Description
The present invention will be further described with reference to the accompanying drawings, and it should be noted that the following examples are provided to illustrate the detailed embodiments and specific operations based on the technical solutions of the present invention, but the scope of the present invention is not limited to the examples.
As shown in fig. 1, the present invention is a pulse wave fitting method based on weibull function, the method includes the following steps:
s1, cutting the data, wherein, cutting and dividing the collected human body radial artery pulse wave data by taking the pulse period as a unit to obtain a data set of single period pulse waves;
s2 fits the pulse wave data using a two-or three-parameter weibull function.
It should be noted that each equation is set as a two-parameter or three-parameter weibull function, and the equation is curve-fitted to the obtained pulse wave data.
It should be noted that the formula of the two-parameter weibull function is:
the Weibull function pulse wave fitting equation is shown as the following formula:
wherein the first term, the second term and the third term of the equation are all two-parameter Weibull functions. The index of the parameter is n, which indicates that the item in which the parameter belongs to the nth item of the equation.
It should be noted that the formula of the three-parameter weibull function is:
the Weibull function pulse wave fitting equation is shown as the following formula:
wherein the first term, the second term and the third term of the equation are all three-parameter Weibull functions. The index of the parameter is n, which indicates that the item in which the parameter belongs to the nth item of the equation.
Examples
Taking fig. 1 as an example, the pulse wave data is segmented into a group of monocycle pulse wave data sets by taking the heartbeat cycle as a unit, and the data sets are fitted by using a fitting equation composed of three two-parameter weibull functions or three-parameter weibull functions, so as to obtain values of six or nine parameters of the weibull functions.
As shown in fig. 2, the solid line is a fitted curve, the large circle points are raw data, and the small circle points, the positive sign, and the asterisk are waveforms representing three subfunctions of the first term weibull function, the second term weibull function, and the third term weibull function, respectively. The goodness of fit of this fitted curve is 0.9944.
Various corresponding changes and modifications can be made by those skilled in the art based on the above technical solutions and concepts, and all such changes and modifications should be included in the protection scope of the present invention.
Claims (4)
1. A pulse wave fitting method based on a weibull function, the method comprising the steps of:
s1, cutting the data, wherein, cutting and dividing the collected human body radial artery pulse wave data by taking the pulse period as a unit to obtain a data set of single period pulse waves;
s2 fits the pulse wave data using a two-or three-parameter weibull function.
2. The weibull function-based pulse wave fitting method according to claim 1, wherein each term in the equation is set as a two-parameter or three-parameter weibull function, and the equation is curve-fitted to the obtained pulse wave data.
3. The weibull function-based pulse wave fitting method according to claim 1, wherein the formula of the two-parameter weibull function is:
the Weibull function pulse wave fitting equation is shown as the following formula:
wherein the first term, the second term and the third term of the equation are all two-parameter Weibull functions. The index of the parameter is n, which indicates that the item in which the parameter belongs to the nth item of the equation.
4. The weibull function-based pulse wave fitting method according to claim 1, wherein the formula of the three-parameter weibull function is:
the Weibull function pulse wave fitting equation is shown as the following formula:
wherein the first term, the second term and the third term of the equation are all three-parameter Weibull functions. The index of the parameter is n, which indicates that the item in which the parameter belongs to the nth item of the equation.
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Application publication date: 20220208 |