阅读说明：本技术 不同趋势下Logistic映射序列的非线性趋势项消除方法 (Nonlinear trend item elimination method of Logistic mapping sequence under different trends ) 是由 李鑫钊 于 2020-12-25 设计创作，主要内容包括：本发明公开了不同趋势下Logistic映射序列的非线性趋势项消除方法,包括步骤：步骤S1：采用数据集构造Logistic映射序列,基于Logistic映射序列构造混沌系统Logistic映射序列；步骤S2：将混沌系统Logistic映射序列与不同趋势叠加,得到不同趋势下的Logistic映射序列z,z＝z-s+z-t,z-s是平稳项,z-t是趋势项,步骤S3：采用构造的不同趋势下的Logistic映射序列消除原始信号中的非线性趋势项,得到信号的平稳部分。本发明计算简单、快速,是基于正则化原理的去趋势化方法,确定平滑先验法的正则化参数；根据趋势项的截止频率与特征值参数之间的一对一的数值关系,获得与频率分量对应的趋势项。(The invention discloses a method for eliminating nonlinear trend items of Logistic mapping sequences under different trends, which comprises the following steps: step S1: constructing a Logistic mapping sequence by adopting a data set, and constructing the Logistic mapping sequence of the chaotic system based on the Logistic mapping sequence; step S2: superposing the Logistic mapping sequence of the chaotic system with different trends to obtain the Logistic mapping sequence z under the different trends, wherein z is z s +z t ，z s Is a stationary term, z t Is a trend item, step S3: and eliminating a nonlinear trend item in the original signal by adopting the constructed Logistic mapping sequences under different trends to obtain a stationary part of the signal. The method is simple and quick in calculation, is a regularization removing method based on the regularization principle, and determines the regularization parameters of the smooth prior method; and obtaining the trend item corresponding to the frequency component according to the one-to-one numerical relationship between the cut-off frequency of the trend item and the characteristic value parameter.)

1. A method for eliminating nonlinear trend items of Logistic mapping sequences under different trends is characterized by comprising the following steps:

step S1: constructing a Logistic mapping sequence by adopting a data set, and constructing the Logistic mapping sequence of the chaotic system based on the Logistic mapping sequence;

step S2: superposing the Logistic mapping sequence of the chaotic system with different trends to obtain the Logistic mapping sequence z under the different trends, wherein z is z_s+z_t，z_sIs a stationary term, z_tIs a trend term, z_tH theta + v, where H epsilon R^N×M，R^N×MRepresenting an observation matrix, N being the data length, theta ∈ R^MRepresents a regression parameter, vRepresenting observation errors, wherein R is a column vector, and M is the number of regression parameters;

step S3: eliminating a nonlinear trend item in an original signal by adopting constructed Logistic mapping sequences under different trends to obtain a stable part of the signal, which specifically comprises the following steps:

estimating a regression parameter theta;

where λ is the regularization parameter, D_dFor discretizing a d-order differential operator matrix, a Logistic mapping sequence z under the trend comprises N data points and is represented by a column vector R, wherein R is ═ R₁,R₂,…R_N]^T∈R^NThe first order trend for R is:

R₁＝[R₂-R₁,…,R_N-R_N-1]^T

the second order trend for R is:

R₂＝[R₃-R₂-(R₂-R₁),R₄-R₃-(R₃-R₂),…,R_N-R_N-1-(R_N-1-R_N-2)]^T

d for D-order differentiation of R_dExpressed as:

D_dis 2, D₂∈R^(N-2)×NRepresents a second order difference matrix, expressed as:

the stationary part of the original signal after eliminating the trend term is expressed as:

wherein I is an identity matrix.

2. The method for eliminating nonlinear trend term of Logistic mapping sequence under different trends according to claim 1, wherein the step S1 comprises:

constructing a Logistic mapping sequence by adopting a data set: y (i +1) ═ F [ y (i) ] ═ r × y (i) x [1-y (i +1) ], in which a state variable y (i) e (0,1), r denotes a nonlinear parameter, and i denotes the number of iterations of the entire system;

setting an initial value y1 to be 0.65, setting the value interval of the nonlinear parameter r to be (3.57,4.0), and setting the incremental step length of r to be 0.005 to obtain a Logistic mapping sequence y of the chaotic system, wherein { y (i):1 is not less than i and not more than N }.

3. The method for eliminating nonlinear trend term of Logistic mapping sequences under different trends according to claim 2, wherein in the step S2:

superposing the Logistic mapping sequence of the chaotic system with a linear trend to obtain the Logistic mapping sequence under the linear trend: y (i +1) ═ F [ y (i) ] + u (i), wherein the linear trend u (i) ═ a1 × i, a1 is the slope of the linear trend;

superposing the Logistic mapping sequence of the chaotic system with a periodic trend to obtain the Logistic mapping sequence under the periodic trend: y (i +1) ═ F [ y (i)]+ w (i), wherein the periodic trend w (i) is a_s·sin(2π·i/T)，A_sIs amplitude, T is period;

superposing the Logistic mapping sequence of the chaotic system with a power law trend to obtain the Logistic mapping sequence under the power law trend: y (i +1) ═ F [ y (i)]+ v (i), wherein v (i) is a_p*i*j，A_pPower law strength, j is a power law index;

u (i), w (i), v (i) correspond to a trend term in the Logistic mapping sequence under a linear trend, a trend term in the Logistic mapping sequence under a periodic trend, and a trend term in the Logistic mapping sequence under a power law trend, respectively.

Technical Field

The invention relates to the technical field of electrocardiosignal processing, in particular to a method for eliminating a nonlinear trend term of a Logistic mapping sequence under different trends.

Background

Aiming at the research of the complex dynamics characteristic of the chaotic system of the human heart, a plurality of scholars at home and abroad gradually draw close to a nonlinear method from an initial linear method, and research finds that nonlinear indexes can more accurately reflect the intrinsic physiological characteristics of the heart system. However, in the process of extracting signals in these researches, trend components with different degrees are often mixed in the signals, and under the strong interference of the different trend components, the nonlinear indexes are often very sensitive, and the obtained results are not stable, so that the influence of the trends and baseline shift on the electrocardiosignals must be eliminated.

Disclosure of Invention

The invention aims to provide a method for eliminating nonlinear trend items of Logistic mapping sequences under different trends, which is used for solving the problems that trend components of different programs are mixed in the signal extraction process in the prior art, and the obtained nonlinear index result is unstable.

The invention solves the problems through the following technical scheme:

a method for eliminating nonlinear trend items of Logistic mapping sequences under different trends comprises the following steps:

step S1: constructing a Logistic mapping sequence by adopting a data set, and constructing the Logistic mapping sequence of the chaotic system based on the Logistic mapping sequence;

step S2: superposing the Logistic mapping sequence of the chaotic system with different trends to obtain the Logistic mapping sequence z under the different trends, wherein z is z_s+z_t，z_sIs a stationary term, z_tIs a trend term, z_tH theta + v, where H epsilon R^N×MRepresents the observation matrix and the observation matrix of the observation matrix,_Nfor data length, θ ∈ R^MRepresenting regression parameters, v representing observation error, R being the column vector,_Mthe number of regression parameters;

step S3: eliminating a nonlinear trend item in an original signal by adopting constructed Logistic mapping sequences under different trends to obtain a stable part of the signal, which specifically comprises the following steps:

estimating a regression parameter theta;

where λ is the regularization parameter, D_dFor discretizing a d-order differential operator matrix, a Logistic mapping sequence z under the trend comprises N data points and is represented by a column vector R, wherein R is ═ R₁,R₂,…R_N]^T∈R^NThe first order trend for R is:

R₁＝[R₂-R₁,…,R_N-R_N-1]^T

the second order trend for R is:

R₂＝[R₃-R₂-(R₂-R₁),R₄-R₃-(R₃-R₂),…,R_N-R_N-1-(R_N-1-R_N-2)]^T

d for D-order differentiation of R_dExpressed as:

D_dis 2, D₂∈R^(N-2)^×NRepresents a second order difference matrix, expressed as:

the stationary part of the original signal after eliminating the trend term is expressed as:

wherein I is an identity matrix.

The step S1 includes:

constructing a Logistic mapping sequence by adopting a data set: y (i +1) ═ F [ y (i) ] ═ r × y (i) x [1-y (i +1) ], in which a state variable y (i) e (0,1), r denotes a nonlinear parameter, and i denotes the number of iterations of the entire system;

setting an initial value y1 to be 0.65, setting the value interval of the nonlinear parameter r to be (3.57,4.0), and setting the incremental step length of r to be 0.005 to obtain a Logistic mapping sequence y of the chaotic system, wherein { y (i):1 is not less than i and not more than N }.

In the step S2:

superposing the Logistic mapping sequence of the chaotic system with a linear trend to obtain the Logistic mapping sequence under the linear trend: y (i +1) ═ F [ y (i) ] + u (i), wherein the linear trend u (i) ═ a1 × i, a1 is the slope of the linear trend;

superposing the Logistic mapping sequence of the chaotic system with a periodic trend to obtain the Logistic mapping sequence under the periodic trend: y (i +1) ═ F [ y (i)]+ w (i), wherein the periodic trend w (i) is a_s·sin(2π·i/T)， A_sIs amplitude, T is period;

superposing the Logistic mapping sequence of the chaotic system with a power law trend to obtain the Logistic mapping sequence under the power law trend: y (i +1) ═ F [ y (i)]+ v (i), wherein v (i) is a_p*i*j，A_pPower law strength, j is a power law index;

u (i), w (i), v (i) correspond to a trend term in the Logistic mapping sequence under a linear trend, a trend term in the Logistic mapping sequence under a periodic trend, and a trend term in the Logistic mapping sequence under a power law trend, respectively.

Compared with the prior art, the invention has the following advantages and beneficial effects:

the method is simple and quick in calculation, is a regularization removing method based on the regularization principle, and determines the regularization parameters of the smooth prior method; and obtaining the trend item corresponding to the frequency component according to the one-to-one numerical relationship between the cut-off frequency of the trend item and the characteristic value parameter.

Drawings

FIG. 1 is a flow chart of the present invention;

fig. 2 is a frequency response diagram of L in the embodiment of the present invention.

Detailed Description

The present invention will be described in further detail with reference to examples, but the embodiments of the present invention are not limited thereto.

Example (b):

referring to fig. 1, a method for eliminating a nonlinear trend term of Logistic mapping sequences under different trends includes:

1. selecting data in Physioet as a research data set, wherein the Physioet is a large and continuously expanded data document set which is shared by biomedical research institutions and records complex physiological signals and related data;

2. constructing a Logistic mapping sequence by using the selected data set:

y(i+1)＝F[y(i)]＝r×y(i)×[1-y(i+1)] (1)

the state variable y (i) epsilon (0,1), r represents a nonlinear parameter, and i represents the iteration number of the whole system;

3. because the randomness of the non-stationary random signal is large and almost has no trend, a Logistic mapping sequence of the chaotic system needs to be constructed, and in the formula (1), when r belongs to (3.4,3.57), the system presents a period-doubling sequence; when r belongs to (3.57,4, 0), the system is a chaotic system, the generated Logistic sequence y: { y (i):1 ≦ i ≦ N }, the initial value y1 ≦ 0.65, the value interval of r is (3.57,4.0), and the incremental step size of r is 0.005.

4. The Logistic sequence generated in 3 was superimposed with linear, periodic and power law trends. Selecting linear trend parameter (the slope A1 of the linear trend is 0.001) and periodic trend parameter (amplitude A)_s0.2, period T50), power law trend parameter (power law intensity a)_p0.1 and the power law index j is 0.35), and at this time, the Logistic mapping sequence under different trends is successfully constructed;

the Logistic mapping sequence expression under the linear trend is as follows:

y(i+1)＝F[y(i)]+u(i) (2)

u (i) ═ a1 × i, a1 is the slope of the linear trend;

the Logistic mapping sequence expression under the periodic trend is as follows:

y(i+1)＝F[y(i)]+w(i) (3)

wherein the trend is as follows: w (i) ═ a_sSin (2 π i/T), wherein A_sIs amplitude, T is period;

the Logistic mapping sequence expression under the power law trend is as follows:

y(i+1)＝F[y(i)]+v(i) (4)

wherein v (i) ═ a_pI j, wherein A_pPower-law strength, j is the power-law index. In formulae (2) to (4), F [ y (i)]Represents a stationary term, u (i), w (i), v (i) represent a trend term;

5. the following algorithm is used for trend term elimination,

assuming that the Logistic mapping sequence is z, and z consists of two parts, the stationary term z_sAnd a trend term z_t，

z＝z_s+z_t (5)

Wherein z is_sIs F [ y (i)]，z_tU (i) or w (i) or v (i), can also be represented by the following formula:

z_t＝Hθ+v (6)

H∈R^N×Mrepresents the observation matrix and the observation matrix of the observation matrix,_Nfor data length, θ ∈ R^MRepresenting regression parameters, v representing observation errors, the experimental objective is transformed into a use optimization method for estimating the parameter θ, such that z is_tThe trend term in the original signal is estimated H θ + v. The common method for estimating the parameter θ is the least square method, and the smooth prior method is to add a differential term | | D in the optimization process_d(H θ) | |, bringing it to the lowest to ensure that H θ can eliminate the trend term part of the signal:

in the formula: λ is a regularization parameter, D_dIs a discretized d order differential operator matrix. D_dThe solving method is as follows:

let z contain N local extreme points, using the column vector R ═ R₁,R₂,…R_N]^T∈R^NThe first order trend for R is shown as: r₁＝[R₂-R₁,…,R_N-R_N-1]^TThe second order trend for R is:

R₂＝[R₃-R₂-(R₂-R₁),R₄-R₃-(R₃-R₂),…,R_N-R_N-1-(R_N-1-R_N-2)]^T

with this recursion, a discrete form of any order trend of R can be obtained, i.e., the D-order differential of R can be used as D_dExpressed as:

thus D_dIs 2, D₂∈R^(N-2)×NCan be expressed as:

the stationary part of the original signal after eliminating the trend term is thus expressed as:

in the above formula, orderThen there is z_sLz. In the formula, L is equivalent to a high-pass filter, and the frequency response at each discrete time point can be obtained by performing fourier transform on all row vectors of L, as shown in fig. 2, the x axis represents normalized frequency f, the z axis represents amplitude, and due to the principle of symmetry, N in the y axis only selects data between 1 and 25. It can be seen from the figure that the filtering effect of L is mostly smooth, and the filtering effect is not ideal only in the initial and final stages of the signal. Let the regularization parameter λ take different values and perform fourier transform on the N/2 th line of L to obtain frequency responses corresponding to different λ values, the results are shown in table 1 below.

Regularization parameter λ	1	2	5	10	20	100
							Relative cut-off frequency	0.3542	0.2292	0.1458	0.1042	0.0833	0.0417

TABLE 1 regularization parameter vs. relative cut-off frequency

The frequency of the non-linear non-stationary random signal trend term is generally centered in the low frequency range, so in the pre-processing, the sampling frequency of the random signal is reduced to 4 Hz. The corresponding cut-off frequency is 0.0417 × 4 ═ 0.1668Hz, which substantially ensures the elimination of low frequency trend terms in the original data, while preserving the effective signal contribution.

Compared with the prior art, the wavelet transform and EEMD in the prior art are largely taken from experience when determining the decomposition layer number of the signal, and have subjectivity. The algorithm provided by the patent is simple and rapid in calculation method, and is a trend removing method based on the regularization principle, and regularization parameters of a smooth prior method are determined; meanwhile, the method can obtain the trend item corresponding to the frequency component according to the one-to-one numerical relation between the cut-off frequency of the trend item and the characteristic value parameter.

Moreover, although wavelet decomposition and EEMD have certain effect of removing the drift of the low frequency band of the Logistic sequence, the wavelet analysis removes effective components with the frequency less than 100Hz, which brings the loss of a section of effective components of HRV signals and causes great error to experimental results, because the wavelet transformation method is very subjective because the selection of the basic wavelet and the determination of the layer number of the wavelet decomposition are from theoretical screening to a great extent. EEMD has certain effect on eliminating the baseline drift part, however, when the frequency is less than 4Hz, the elimination is not obvious, but the smoothing prior method (SPA algorithm) provided by the patent obviously eliminates the trend item, and the algorithm provided by the patent eliminates the elimination of the trend item with the cutoff frequency of below 0.1668Hz according to the frequency response, so that the advantages of the algorithm provided by the patent can be embodied, the cutoff frequency of the trend item is calculated according to the regularization parameter, and the algorithm has objectivity, and in conclusion, the trend removing processing capability of the algorithm provided by the patent is obviously superior to that of wavelet analysis and empirical mode decomposition.

Although the present invention has been described herein with reference to the illustrated embodiments thereof, which are intended to be preferred embodiments of the present invention, it is to be understood that the invention is not limited thereto, and that numerous other modifications and embodiments can be devised by those skilled in the art that will fall within the spirit and scope of the principles of this disclosure.