阅读说明：本技术 联合变分模态分解和排列熵的gnss变形监测去噪方法 (GNSS deformation monitoring denoising method combining variational modal decomposition and permutation entropy ) 是由 汤俊 李垠健 林海飞 董晓燕 于 2021-07-16 设计创作，主要内容包括：本发明公开了联合变分模态分解和排列熵的GNSS变形监测去噪方法,针对模态分解去噪方法中的高频噪声判别问题,首次提出通过计算各模态分量排列熵值的方法判别低频有效分量和高频噪声。此方法可将各分量的时间复杂程度量化,定量的表示各分量的特性,根据其数值大小判别高频噪声,对任意GNSS监测序列均具有自适应性。该方法可以有效的缓解EMD模态混叠、局部信息丢失以及小波去噪受小波基等外部选择影响大、不具有自适应性等问题。通过实测数据实验证明,该方法去噪精度较EMD、小波去噪有明显提高,验证了该方法具备有更好的精度和可靠性。在GNSS导航定位精度提高和空间环境的减灾和防灾能力具有重要的应用价值。(The invention discloses a GNSS deformation monitoring denoising method combining variational modal decomposition and permutation entropy, which firstly proposes a method for judging low-frequency effective components and high-frequency noise by calculating permutation entropy values of modal components aiming at the problem of judging high-frequency noise in the modal decomposition denoising method. The method can quantify the time complexity of each component, quantitatively express the characteristic of each component, judge high-frequency noise according to the numerical value of the characteristic, and has self-adaptability to any GNSS monitoring sequence. The method can effectively relieve the problems of EMD modal aliasing, local information loss, large influence of wavelet basis and other external selections on wavelet denoising, no adaptivity and the like. Proved by an actual measurement data experiment, the denoising precision of the method is obviously improved compared with that of EMD and wavelet denoising, and the method is verified to have better precision and reliability. The method has important application value in GNSS navigation positioning accuracy improvement and disaster reduction and prevention capability in space environment.)

1. The GNSS deformation monitoring denoising method combining variational modal decomposition and permutation entropy is characterized by comprising the following specific steps:

(1) the GNSS monitoring sequence is decomposed into modal components with different frequencies by utilizing a VMD algorithm, a constraint variational model in the VMD algorithm is divided into an equality model and an inequality model, equality constraint means that signals obtained after the IMF components are superposed are still equal to original signals, inequality constraint means that the corresponding estimation bandwidth of each IMF component is minimum, and the specific model is as follows:

in the formula, delta_tIs a dirac function; is the convolution operator; u. of_kFor the K IMF components decomposed by VMD, i.e. { u }_k}＝{u₁,u₂,u₃,…,u_k}；{w_kIs the center frequency of the corresponding IMF component, i.e. { w }_k}＝{w₁,w₂,w₃,…,w_k}；

(2) Constructing an augmented Lagrange function, introducing a penalty factor alpha and a Lagrange multiplier alpha, and converting a constraint variable problem into non-constraint to solve;

(3) the above unconstrained variation problem is solved by using an alternative direction multiplication operator method, and the unconstrained variation problem is alternately updated by a formulaλⁿ⁺¹Iteratively calculating to find Lagrange expression saddle point, and outputting when certain convergence condition is satisfiedK modal components are given, and the formula is as follows:

in the formulaIs the iteration number;is composed ofu (t), λ (t), Fourier transform of X (t);

(4) calculating arrangement entropy value of each modal component decomposed by VMD algorithm, and setting time sequence of each modal component as { u }_t}＝{u₁,u₂,u₃,…,u_nAnd obtaining a corresponding reconstruction matrix through phase space reconstruction as follows:

wherein j is 1,2, … k; t is a time series; m is the embedding dimension; k is the number of the reconstruction components;

(5) dividing the reconstruction components into K reconstruction components in a row vector form, and sorting each reconstruction component in an ascending order according to the size, if the reconstruction components are equal to each other, arranging according to an index value:

U(i)＝{u(i+(j₁-1)t),u(i+(j₂-1)t),…,u(i+(j_m-1)t)}

u(i+(j₁-1)t)≤u(i+(j₂-1)t)≤…≤u(i+(j_m-1)t)

a new set of symbol sequences is obtained:

S(i)＝(j₁,j₂,…j_m)…(i＝1,2,...,k)

(6) in m! Wherein the total number of the mapping relations can be divided into m! Wherein the probability of occurrence of S (i) is p₁,p₂,...,p_jThe sum of the probabilities is constant to 1, so the time series can be: { u_t}＝{u₁,u₂,u₃,...,u_nThe permutation entropy of } is defined as follows:

(7) and (3) carrying out standardization treatment:

wherein ln (m!) is H_pA maximum value;

(8) and screening out the low-frequency signals through the arrangement entropy, setting a threshold value theta to be more consistent within an interval of 0.55-0.6 under the common condition, and regarding modal components with the arrangement entropy higher than theta as high-frequency noise elimination, thereby filtering out the high-frequency signals containing noise in a time sequence, and reserving the low-frequency signal reconstruction to obtain the de-noising data.

2. The GNSS deformation monitoring denoising method based on joint variational modal decomposition and permutation entropy as claimed in claim 1, wherein: h in the step (7)_pThe degree of complexity, H, of the signal can be mapped_pThe larger the signal, the more random and complex the signal, and vice versa, the signal is regular and simple.

3. The GNSS deformation monitoring denoising method based on joint variational modal decomposition and permutation entropy as claimed in claim 1, wherein: and (4) setting the threshold theta in the step (8) to be 0.55-0.6.

Technical Field

The invention relates to the technical field of modal decomposition denoising, in particular to a GNSS deformation monitoring denoising method combining variational modal decomposition and permutation entropy.

Background

The GNSS observation has the advantage of acquiring a continuous three-dimensional coordinate observation sequence in real time, and is widely applied to the fields of engineering monitoring, earth deformation, earthquake prediction and the like. However, due to the randomness of the measurement environment and the complexity of the deformation process, the monitored object is often subjected to the composite influence of various complex factors, and non-stationary and high-noise observation data is generated, so that a corresponding error occurs in the GNSS time sequence, and the actual deformation displacement of the monitored object is difficult to accurately obtain. The data containing noise is used for deformation analysis and prediction, so that an ideal effect is difficult to achieve, even an error conclusion is obtained, and early warning cannot be timely carried out when a disaster happens, so that the safety of lives and properties of people is endangered. Therefore, how to effectively reduce the influence of the measurement noise on the GNSS observation data is significant.

At present, many scholars mainly use Kalman filtering, wavelet analysis, Empirical Mode Decomposition (EMD) and other methods to perform denoising processing on GNSS deformation monitoring data. The Kalman filtering can well analyze the monitoring sequence in a time domain range, but cannot express the characteristics of the non-stationary monitoring sequence in a frequency domain range, so that the method has great limitation. The wavelet transformation can simultaneously analyze the frequency domain and the time domain of the GNSS time sequence, has good time-frequency characteristics and multi-resolution analysis characteristics, has good effect on data denoising, but the denoising effect is influenced by decomposition scale, wavelet base selection and the like to a great extent, so that the GNSS time sequence has no self-adaptability, and each decomposed component has no physical significance. The EMD method is suitable for nonlinear and non-stationary signals, can effectively realize the separation of random noise and obtain higher signal-to-noise ratio when applied to GNSS deformation monitoring and denoising, and is widely applied to data denoising in recent years. However, when the EMD is used for transformation, there are problems such as modal aliasing and the like, and frequency components which cannot be explained and have no practical significance may appear. And how to distinguish the effective information from the noise component is difficult to distinguish effectively, which may cause the loss of the effective information.

The existing mode decomposition type denoising method is to regard a GNSS deformation sequence as a continuous one-dimensional signal, and consider that all complex signals are composed of simple and different component signals with non-sinusoidal functions. According to the denoising theory, firstly, a GNSS monitoring sequence is decomposed into modal components (IMF) with different frequencies and a trend term, then high-frequency noise is separated according to a certain method, and low-frequency component reconstruction is reserved to achieve the purpose of denoising. The modal component should satisfy two conditions: firstly, the times of the zero crossing points of the characteristic mode function curve must be the same as or different from the number of maximum and minimum value points by one; and the mean value of the upper envelope line and the lower envelope line formed by the maximum value point and the minimum value point is zero, namely the upper envelope line and the lower envelope line are symmetrical about the x axis. The empirical mode decomposition denoising method mainly comprises the following steps:

(1) setting the GNSS deformation monitoring time sequence as x (t), and finding out all extreme points in the input time sequence;

(2) calculating difference values of the maximum value and the minimum value in the time sequence by a cubic spline method to form an upper envelope m and a lower envelope m_maxAnd m_min；

(3) Calculating the mean value m (t) of the upper envelope and the lower envelope, and obtaining the difference h between the mean value m (t) and the time series_j(t)；

(4) Judging whether h (t) is an inherent mode function component, if h (t) satisfies two requirements, IMF_i(t)＝h_j(t), then subtracting IMF from the original sequence_i(t) obtaining the residual terms and continuing to adopt the method to decompose until the signal is monotonous;

(5) and judging the frequency of each modal component, and carrying out high-pass, low-pass or band-pass filtering to obtain a final denoising result.

The modal decomposition method is suitable for nonlinear and non-stationary signals, is applied to GNSS deformation monitoring denoising, can effectively realize the separation of random noise and obtain higher signal-to-noise ratio, and is widely applied to data denoising in recent years. Such methods currently rely primarily on correlation coefficient methods or normalized modulus running average methods to separate noise, which exhibit different results in the case of different modal decompositions. The correlation coefficient method discriminates the high-frequency noise according to the minimum value appearing for the first time, however, the position where the first minimum value point appears in each modal component has uncertainty, and the high-frequency noise cannot be discriminated accurately. The accumulated mean value of the standardized modulus of each modal component is calculated, and high-frequency noise is distinguished through abrupt change of the accumulated mean value, but the magnitude change of each modal component calculated by the method is large, the abrupt change mode cannot be accurately judged, and the high-frequency noise cannot be accurately determined.

Disclosure of Invention

The invention aims to overcome the technical defects and provide a GNSS deformation monitoring denoising method combining variational modal decomposition and permutation entropy, and aims at solving the problems that the noise discrimination standard is not uniform and high-frequency noise and effective deformation information cannot be accurately distinguished in a modal decomposition type denoising method, so that denoising is not thorough or excessive. The invention quantifies the complexity of each modal component, can quantitatively and accurately judge the high-frequency noise according to the actual situation, and can achieve the purpose of accurate denoising without complex parameter setting.

In order to solve the problems, the technical scheme of the invention is as follows: the GNSS deformation monitoring denoising method combining variational modal decomposition and permutation entropy comprises the following specific steps:

(1) the GNSS monitoring sequence is decomposed into modal components with different frequencies by utilizing a VMD algorithm, a constraint variational model in the VMD algorithm is divided into an equality model and an inequality model, equality constraint means that signals obtained after the IMF components are superposed are still equal to original signals, inequality constraint means that the corresponding estimation bandwidth of each IMF component is minimum, and the specific model is as follows:

in the formula, delta_tIs a dirac function; is the convolution operator; u. of_kFor the K IMF components decomposed by VMD, i.e. { u }_k}＝{u₁,u₂,u₃,…,u_k}；{w_kIs the center frequency of the corresponding IMF component, i.e. { w }_k}＝{w₁,w₂,w₃,…,w_k}；

(2) Constructing an augmented Lagrange function, introducing a penalty factor alpha and a Lagrange multiplier alpha, and converting a constraint variable problem into non-constraint to solve;

(3) the above unconstrained variation problem is solved by using an alternative direction multiplication operator method, and the unconstrained variation problem is alternately updated by a formulaλⁿ⁺¹Iteration is carried out for resolving, Lagrange expression saddle points are searched, K modal components are output when certain convergence conditions are met, and the formula is as follows:

in the formulaIs the iteration number;is composed ofu (t), λ (t), Fourier transform of X (t);

(4) calculating arrangement entropy value of each modal component decomposed by VMD algorithm, and setting time sequence of each modal component as { u }_t}＝{u₁,u₂,u₃,...,u_nAnd obtaining a corresponding reconstruction matrix through phase space reconstruction as follows:

wherein j is 1,2,. k; t is a time series; m is the embedding dimension; k is the number of the reconstruction components;

(5) dividing the reconstruction components into K reconstruction components in a row vector form, and sorting each reconstruction component in an ascending order according to the size, if the reconstruction components are equal to each other, arranging according to an index value:

U(i)＝{u(i+(j₁-1)t),u(i+(j₂-1)t),...,u(i+(j_m-1)t)}

u(i+(j₁-1)t)≤u(i+(j₂-1)t)≤…≤u(i+(j_m-1)t)

a new set of symbol sequences is obtained:

S(i)＝(j₁,j₂,...j_m)…(i＝1,2,...,k)

(6) in m! Wherein the total number of the mapping relations can be divided into m! Wherein the probability of occurrence of S (i) is p₁,p₂,...,p_jThe sum of the probabilities is constant to 1, so the time series can be: { u_t}＝{u₁,u₂,u₃,...,u_nThe permutation entropy of } is defined as follows:

(7) and (3) carrying out standardization treatment:

wherein ln (m!) is H_pA maximum value;

(8) and screening out the low-frequency signals through the arrangement entropy, setting a threshold value theta to be more consistent within an interval of 0.55-0.6 under the common condition, and regarding modal components with the arrangement entropy higher than theta as high-frequency noise elimination, thereby filtering out the high-frequency signals containing noise in a time sequence, and reserving the low-frequency signal reconstruction to obtain the de-noising data.

As a refinement, H in the step (7)_pThe degree of complexity, H, of the signal can be mapped_pThe larger the signal, the more random and complex the signal, and vice versa, the signal is regular and simple.

As an improvement, the threshold value theta in the step (8) is set to be in the range of 0.55-0.6.

Compared with the prior art, the invention has the advantages that: according to the invention, a GNSS signal sequence is decomposed by using variational modal decomposition, the permutation entropy is introduced to determine the boundary value of high-frequency noise and low-frequency effective information, the high-frequency noise is eliminated, and a novel VMD-PE denoising method is constructed. The method can effectively relieve the problems of EMD modal aliasing, local information loss, large influence of wavelet basis and other external selections on wavelet denoising, no adaptivity and the like. Proved by an actual measurement data experiment, the denoising precision of the method is obviously improved compared with that of EMD and wavelet denoising, and the method is verified to have better precision and reliability. The method has important application value in GNSS navigation positioning accuracy improvement and disaster reduction and prevention capability in space environment.

Drawings

FIG. 1 is a flow chart of a VMD-PE method denoising process.

Fig. 2 is a schematic diagram of the variation modal decomposition of modal components.

FIG. 3 is a graph comparing the VMD-PE denoising method and the traditional denoising method.

Detailed Description

The present invention is further described below by way of specific examples, but the present invention is not limited to only the following examples. Variations, combinations, or substitutions of the invention, which are within the scope of the invention or the spirit, scope of the invention, will be apparent to those of skill in the art and are within the scope of the invention.

Example one

In the experiment, GNSS deformation monitoring data of a certain highway slope is selected, GNSS monitoring data in 10.1-10.25 days are obtained through the experiment, and the total time is 600 epochs with 1 hour as a sampling interval. The specific denoising process is shown in fig. 1.

Fig. 2 shows that the GNSS monitoring time sequence is decomposed sequentially from high frequency to low frequency by VMD to obtain 5 IMF components, and it is obvious that each IMF component sequence has different characteristics, and as the number of decomposition layers increases, the signal sequences from IMF1 to IMF5 gradually tend to be smooth and stable. The noise component shows obvious random characteristics, and the low-frequency effective information is smooth and stable. Therefore, signals with different frequencies can be effectively separated and extracted through VMD modal decomposition, a stable and smooth signal is finally obtained, and a good effect is achieved on extraction and elimination of high-frequency noise.

FIG. 3 shows the denoising results of 3 methods of VMD-PE, EMD and wavelet denoising respectively, and an effect diagram of N, E, U directions after denoising is obtained. The method can be seen that the periodic variation of the information sequence after VMD-PE denoising is closer to the original sequence in the local and overall trend and trend, the periodic amplitude is relatively consistent with the original sequence, more local characteristics of deformation data are reserved compared with other two methods, the denoising precision and reliability are improved, and the problems of incomplete wavelet denoising and EMD denoising effects, effective information sequence loss and the like are solved in all directions of the information sequence.

Table 1 shows the evaluation indexes of the denoising effect of different methods, and the signal-to-noise ratio of VMD-PE in N, E, U direction is respectively improved by 2.33%, 2.42%, 22.14% compared with wavelet denoising, and improved by 2.48%, 2.40%, 23.45% compared with EMD. The correlation coefficient is improved by 15.43 percent, 13.89 percent and 30.87 percent relative to wavelet de-noising, and is improved by 15.87 percent, 13.76 percent and 30.21 percent compared with EMD. The noise mixed in the signal is less, the signal is cleaner, and the denoising precision is higher. The RMSE is reduced by 23.53%, 29.17% and 43.59% relative to wavelet de-noising, and is reduced by 23.53%, 29.17% and 45% compared with EMD. The VMD-PE has relatively less error and high reliability. In conclusion, the VMD-PE is superior to other two methods in each evaluation index, and particularly has obvious improvement in the U direction.

TABLE 1 comparison of denoising effects in N, E, U directions based on different denoising methods

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the present invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention should be included in the scope of the present invention.