CN117556218A - Linear engineering seasonal deformation monitoring method - Google Patents

Abstract

The invention discloses a linear engineering seasonal deformation monitoring method, which comprises the steps of obtaining linear engineering long-time sequence deformation data; acquiring a modal IMF Sm with seasonal components and a seasonal window parameter Tm through the deformation data; performing secondary decomposition on the mode to extract seasonal components with Tm as a period; and judging the seasonal deformation cause of the linear engineering through the correlation analysis of the seasonal components of different periods and the seasonal factors. The seasonal deformation extraction method integrating pole symmetry modal decomposition and seasonal trend decomposition can effectively inhibit the noise part of an original signal, improves the separation precision of seasonal components, and realizes the accurate extraction of the seasonal components of a plurality of periods.

Description

Linear engineering seasonal deformation monitoring method

Technical Field

The invention relates to the technical field of building detection, in particular to a linear engineering seasonal deformation monitoring method.

Background

Seasonal deformation is a key factor affecting the structural strength and stability of linear engineering. The accurate monitoring of seasonal deformation not only can ensure the stability and safety of the structure in different seasons, but also seasonal trend decomposition (STL) is one of the most common methods for realizing the seasonal decomposition of time sequence signals. Based on the local regression (Loess) method, it can decompose the signal into three parts, namely Seasonal (Seasonal), trend (Trend) and Residual (Residual), and optimize the decomposition result through an iterative process. The method is suitable for signals with obvious seasonal variation, has a good smoothing effect, can accurately decompose seasonal and trending components of the signals, and the decomposition scale of the seasonal component can be changed along with the change of the size of a seasonal window. Based on the above advantages, STL has been successfully applied to seasonal analysis of various civil engineering structure deformation monitoring data, but still faces some problems to be solved: (1) Sensitive to parameter selection, the seasonal decomposition effect depends on the setting of the seasonal window size; (2) The prior knowledge is needed, and the size of the seasonal window is needed to be input externally according to a specific application scene; (3) The decomposition result is single, and only a fixed period of seasonal component can be obtained by single decomposition.

The pole symmetry modal decomposition (ESMD) is a new development based on Hilbert-Huang transform, and a signal decomposition method is realized through a set of simple decomposition rules, and the method has certain advantages in processing nonlinear and nonstationary signals without selecting a basis function in advance and can effectively extract seasonal components in the signals. Compared with the STL method, the method has the advantages that the method can decompose the seasonal component energy into corresponding Intrinsic Mode Functions (IMFs) according to the time sequence signal, the seasonal IMF components have no preset function forms and seasonal parameters, the seasonal IMF components are determined by an algorithm in a self-adaptive mode, and the seasonal window size corresponding to the seasonal component can be judged according to the time-frequency information of the seasonal IMF components. In addition, the method can inhibit noise components when decomposing signals, extract local characteristics of the signals in time domain and frequency domain, and detect abnormal values in time sequence signals through IMF modal frequency and amplitude information, so that the method is widely applied to the field of seasonal analysis of the time sequence signals. However, in practical applications, there are problems if this method is used alone for seasonal extraction: first, since the extraction of the modes is based on the characteristics and energy distribution of the signals, it is not guaranteed that each IMF mode has seasonal components; second, since the ESMD method performs signal decomposition based on a simple decomposition rule, there is no explicit constraint to ensure the uniqueness and completeness of the decomposition result, and thus, there may be some aliased or mixed components in a complex signal, resulting in insufficient accuracy in extraction of seasonal components. There is therefore a need for a linear engineering seasonal deformation monitoring method.

Disclosure of Invention

Aiming at the defects of the prior art, the invention aims to provide a linear engineering seasonal deformation monitoring method.

In order to achieve the above purpose, the present invention adopts the following technical scheme:

the invention comprises the following steps:

a, obtaining long-time sequence deformation data of a linear engineering;

b, acquiring modal and seasonal window parameters with seasonal components through the deformation data;

c, carrying out secondary decomposition on the mode, and extracting seasonal components taking the seasonal window parameter as a boundary period;

and D, judging the seasonal deformation cause of the linear engineering through the correlation analysis of the seasonal components of different periods and the seasonal factors.

Further, the method for acquiring the modal and seasonal window parameters with seasonal components in the step B comprises the following steps:

1) Performing interpolation processing on the deformation signal missing value of the deformation data;

2) Decomposing the resampled time sequence deformation signal by utilizing a pole symmetry mode decomposition algorithm to obtain a plurality of IMF modes;

3) Performing spectrum analysis on the plurality of IMF modes obtained by decomposition, screening out IMF modes which show periodic peaks in the spectrum or have frequencies concentrated in a specific frequency range, and judging that the IMF modes have seasonal components;

4) And using the IMF modes with m screened seasonal components for judging the corresponding seasonal window parameters Tm.

Further, the method for extracting seasonal components bounded by the seasonal window parameter in step C includes:

a, decomposing the IMFSm with seasonal components by using a seasonal trend decomposition algorithm by taking the corresponding seasonal window parameters as constraint conditions;

b taking a seasonal window Tm as an input, decomposing the seasonal trend to obtain a seasonal component, a trend component and a remainder, and extracting the seasonal component.

Further, the method for decomposing the resampled time sequence deformation signal by utilizing the pole symmetry mode decomposition algorithm comprises the following steps:

(1) find all maximum value points and minimum value points of the original signal Y and record them as E _i (i＝1，2，3，…，n)；

(2) Connecting adjacent poles by using line segments, and sequentially marking midpoints of the line segments as F _i (i＝1，2，3，…，n)；

(3) Supplement left and right boundary midpoint F ₀ ，F _n ；

(4) Constructing p interpolation lines L by using the obtained n+1 midpoints ₁ ，L ₂ ，L ₃ ，…,L _n (P.gtoreq.1), calculating their mean curves L;

L*＝(L1+L2+L3+...+L _P )/p (1)

wherein L is a mean curve, L _p The P interpolation line is the P-th interpolation line, and P is the total number of the interpolation lines;

(5) repeating steps 1 to 4 for Y-L until L +.epsilon.epsilon.is the set tolerance or the number of screenings reaches a preset maximum K, whereupon a first empirical model M is obtained by decomposition ₁ ；

(6) For Y-M ₁ Repeating the steps 1 to 5 to obtain M in turn ₂ ，M ₃ … only a certain number of poles remain until the final margin R;

(7) let the maximum screening times K lie in the integer interval [ K _MIN ,K _MAX ]Performing internal transformation and repeating the steps 1 to 6 to obtain a series of decomposition results, further calculating a variance ratio, and drawing a change chart of the variance ratio along with K;

(8) in the integer interval [ K _MIN ,K _MAX ]The maximum screening times K corresponding to the minimum variance ratio are selected ₀ And then repeating the steps 1 to 6 to obtain a decomposition result n IMF modes and 1 self-adaptive global average line R.

Further, the seasonal trend decomposition comprises an outer loop and a nested inner loop, the seasonal item and the trend item are updated once every iteration of the inner loop, the complete inner loop comprises iterations, and each iteration of the outer loop comprises the inner loop and the calculation of the robustness weight; all robustness weights at the time of the initial outer loop iteration are equal to 1, and then the secondary outer loop is performed.

Further, each iteration of the inner loop includes a season term smoothly updated once, followed by a trend term smoothly updated trend term, assuming for t=1 to N, S _t ^(k) And T _t ^(k) The method comprises the steps of (1) respectively obtaining a seasonal term and a trend term after the kth iteration, and S when the kth iteration is the (1) th iteration _t ^(k+1) And T _t ^(k+1) The calculation method is as follows:

(1) trending: calculation of trending sequence D _t ；

D _t ＝Y _t -T _t ^(k) (2)

Wherein Y is _t Is the original time sequence, T _t ^(k) Is a trend term after the kth iteration;

(2) periodic subsequence smoothing: pair D _t Applying a Loess smoothing, smoothing using a locally weighted regression of parameters λ and d=1, the smoothed values at all time points being calculated, including a value before the first point of the time series and a value after the last point of the time series;

(3) low pass filter application: applying a low-pass filter to the smoothed periodic sub-sequence S _t ^(k) This filter comprises a moving average of length m, a moving average of length 3, and a Loess smoothing using parameters λ and d=1;

(4) removing season: updating seasonal item S _t ^(k+1) ＝S _t ^(k) -(D _t -S _t ^(k) )；

(5) Season term removal calculation: calculating the sequence E of the seasonal items _t ＝Y _t -S _t ^(k+1) ；

(6) Trend smoothing: pair E _t Updating trend term Tt using parameters λ and d=1 using Loess smoothing ^(k+1) ；

(7) Judging whether convergence is carried out: if the convergence is carried out, outputting a result, otherwise, returning to the step 1;

setting the initial value of the trend term to 0, i.e. T, before execution _t ⁽⁰⁾ =0; assume that an initial run of the inner loop has been performed to obtain an estimate: t (T) _t And S is _t Trend terms and season terms, respectively, and then the remaining terms can be obtained:

R _t ＝Y _t -T _t -S _t (3)

wherein R is _t Is the residual component, Y _t Is the original time sequence, T _t Is a trend component, S _t Is a seasonal component;

the outer loop was used to adjust Lu Bangquan weights in the Loess regression of inner loops (2) and (6), set:

δ _t ＝6·median(|R _t |) (4)

wherein delta _t Is the residual R _t 6 times the median of the absolute values;

the robust weights can be expressed as:

wherein t is the data point location; delta _t H is a scaling parameter, and B () is a robustness adjusting function;

further, in the step D, the correlation is analyzed by using a spearman correlation coefficient, and then there are:

wherein N is the time series data length, x (t) is the original observed data, seasonalIMFSm (t) is the seasonal term with Tm as the seasonal period, and t is the time variable;

the value of the spearman correlation coefficient ranges from-1 to 1, where |0.8 to 1.0| represents a very strong correlation; 0.6-0.8| represents strong correlation; 0.4-0.6| represents moderate correlation; 0.2-0.4 represents weak correlation; and 0.0 to 0.2 represents no correlation.

Compared with the prior art, the invention has the beneficial effects that:

1. the invention utilizes the pole symmetry modal decomposition method to obtain the seasonal component IMF and the seasonal window parameter corresponding to the seasonal component IMF in the linear engineering time sequence displacement data, effectively inhibits the noise signal in the original signal, and provides the periodic characteristic and deformation abnormality information of the seasonal component.

2. The invention utilizes the seasonal trend decomposition method to carry out secondary decomposition on the seasonal component IMF obtained by polar symmetry modal decomposition, further separates seasonal and non-seasonal components in the signal, solves the problem of aliasing of the seasonal component and other components, and improves the accuracy of seasonal component extraction.

3. The seasonal deformation extraction method integrating pole symmetry modal decomposition and seasonal trend decomposition can effectively inhibit the noise part of an original signal, improve the separation precision of seasonal components, realize the accurate extraction of a plurality of periodic seasonal components and provide a more accurate and comprehensive data basis for researching the seasonal deformation of linear engineering.

Drawings

FIG. 1 is a flow chart of a method for monitoring seasonal deformation of a linear engineering according to the present invention;

FIG. 2 is a schematic diagram of the decomposition result of the ESMD at point Q2 in this embodiment of a method for monitoring seasonal deformation of linear engineering according to the present invention;

FIG. 3 is a schematic diagram showing the variation of the modal frequency and amplitude of the Q2 point in the method for monitoring seasonal deformation of linear engineering according to the present invention;

fig. 4 is a schematic diagram showing the results of decomposing season terms at Q2 points IMFS1, IMFS2, IMFS3 by STL in the present embodiment of the method for monitoring seasonal deformation of linear engineering according to the present invention.

FIG. 5 is a schematic diagram showing the relationship between the Q2 point SeasonalIMFS3 mode and the temperature change in the present embodiment of a linear engineering seasonal deformation monitoring method according to the present invention;

Detailed Description

The present invention will be described in detail below with reference to the following examples and the accompanying drawings, but it should be understood that the examples and the accompanying drawings are only for illustrative purposes of the present invention and are not to be construed as limiting the scope of the present invention in any way.

As shown in fig. 1, the method comprises the following steps:

(1) IMF (inertial measurement unit) for acquiring seasonal components in displacement data by utilizing pole symmetry modal decomposition method and corresponding seasonal window

The linear engineering is easy to be influenced by seasonal factors such as ambient temperature, precipitation, humidity and the like to generate seasonal deformation due to the structural material characteristics, and how to accurately extract seasonal components in time sequence deformation information is important to research the seasonal deformation of the linear engineering. The pole symmetry modal decomposition and the seasonal trend decomposition are one of the conventional time sequence signal decomposition methods, and the seasonal components in the time sequence signal can be effectively extracted by the two methods. However, both methods have limitations in practical applications, for example, using only pole symmetric modal decomposition methods may result in extracted information that may not contain seasonal components or be mixed with other non-seasonal components, while using seasonal decomposition models alone may require providing priori knowledge of seasonal window parameters and may only decompose out only a single period of seasonal components. Therefore, the linear engineering seasonal deformation extraction method integrating pole symmetry modal decomposition and seasonal trend decomposition is provided, the pole symmetry modal decomposition method is utilized to reduce noise of an original time sequence deformation signal, and an IMF mode with seasonal components and a corresponding seasonal window are primarily screened out based on spectrum analysis, so that accurate data is provided for extracting a plurality of periodic seasonal components by further utilizing the seasonal decomposition method. Taking an original time sequence deformation signal as an example, the pole symmetry mode decomposition part specifically comprises the following steps:

1) Interpolation processing is carried out on the original time sequence deformation signal missing value, and the time sequence deformation is resampled by using a one-dimensional interpolation Akima algorithm so as to realize the same acquisition interval;

2) Decomposing the resampled time sequence deformation signal by utilizing a pole symmetry mode decomposition algorithm, wherein the decomposition steps are as follows:

(1) find all extreme points (maximum and minimum points) of the original signal Y and record them as E _i (i＝1，2，3，…，n)；

(2) Connecting adjacent poles by using line segments, and sequentially marking midpoints of the line segments as F _i (i＝1，2，3，…，n)；

(3) Supplement left and right boundary midpoint F ₀ ，F _n ；

(4) Constructing p interpolation lines L by using the obtained n+1 midpoints ₁ ，L ₂ ，L ₃ ，…,L _n (P.gtoreq.1), calculating their mean curves L;

L*＝(L1+L2+L3+...+L _P )/p (1)

wherein L is a mean curve, L _p The P interpolation line is the P-th interpolation line, and P is the total number of the interpolation lines;

(5) repeating steps 1 to 4 for Y-L until |L|++ε (ε is a set tolerance) or the number of screening has reachedThe preset maximum value K is decomposed to obtain a first empirical mode M ₁ ；

(6) For Y-M ₁ Repeating the steps 1 to 5 to obtain M in turn ₂ ，M ₃ … only a certain number of poles remain until the final margin R;

(7) let the maximum screening times K lie in the integer interval [ K _MIN ,K _MAX ]Performing internal transformation and repeating the steps 1 to 6 to obtain a series of decomposition results, further calculating a variance ratio, and drawing a change chart of the variance ratio along with K;

(8) in the integer interval [ K _MIN ,K _MAX ]The maximum screening times K corresponding to the minimum variance ratio are selected ₀ And then repeating the steps 1 to 6 to obtain a decomposition result n IMF modes and 1 self-adaptive global average line R.

3) The n IMF modes obtained by the decomposition are respectively named as IMF1, IMF2, IMF3, … and IMFn, each IMF is subjected to spectrum analysis to check whether a spectrum peak obvious in a specific season or period exists, and if a certain IMF shows a periodic peak in the spectrum or the frequency is concentrated in a specific frequency range, the IMF can be considered to have seasonal components;

4) Based on the observation result of the frequency spectrum characteristics, m IMF modes with seasonal components are screened out, and are renamed as IMFS1, IMFS2, IMFS3, … and IMFSm (m is more than or equal to 0 and less than or equal to n), and the corresponding seasonal window parameters Tm are judged according to the periodic characteristics of the seasonal fluctuation of the frequency spectrum curve of the seasonal component IMFSm mode.

(2) Decomposing the IMF mode with seasonal components by using seasonal trend decomposition method, and extracting seasonal components with different periods

The linear engineering time sequence deformation signals are decomposed through the pole symmetry modal decomposition algorithm, so that seasonal components in the signals can be effectively extracted, noise signals are restrained, and meanwhile, information such as periodic characteristics, deformation abnormality and the like of the seasonal components can be provided through frequency spectrum information. However, in practice it is found that not all IMF modal components in the pole symmetric modal decomposition result have seasonal components, and some IMF components may contain different components, such as trend, seasonal and other oscillation components. Although screening IMF components with seasonal components using spectral analysis can largely reject interference from non-seasonal signals, there still exist some aliased or mixed components in the seasonal component IMF modality, resulting in insufficient accuracy in the extraction of the seasonal components. Therefore, the algorithm fusion idea is introduced, the IMF mode with seasonal components is secondarily decomposed by utilizing the seasonal trend decomposition method based on the pole symmetry mode decomposition result, so that the seasonal components of various periods are obtained, and the accuracy of seasonal component extraction is improved. The seasonal component modes IMFS1, IMFS2, IMFS3, …, IMFSm (m is more than or equal to 0 and less than or equal to n) and the corresponding seasonal window parameters Tm are treated and screened by using a pole symmetry mode decomposition method, and the specific contents of the seasonal trend decomposition part are as follows:

1) The IMFSm having seasonal components is decomposed by using a seasonal trend decomposition algorithm, wherein the decomposition is performed by requiring external input of corresponding seasonal window parameters as constraint conditions. The core idea of the seasonal trend decomposition algorithm is to decompose the time series into three parts, each part having a different time scale and law of variation, so as to better analyze and predict the behavior of the time series. Time series data, trend term, seasonal and residual terms are respectively Y _t ，T _t ，S _t ，R _t The expression, therefore, is:

Y _t ＝T _t +S _t +R _t (2)

wherein R is _t Is the residual component, Y _t Is the original time sequence, T _t Is a trend component, S _t Is a seasonal component;

for a given time sequence signal, the main steps of data decomposition by using the seasonal trend decomposition method are as follows:

seasonal trend decomposition involves two cyclical processes: an inner loop is nested in the outer loop. The season term and trend term are updated once for each iteration of the inner loop, and the complete inner loop includes the iterations. Each iteration of the outer loop comprises the calculation of the inner loop and the robustness weight; these weights will be used in the next inner loopReducing the impact of transient, outlier points on trend and seasonal terms. All robustness weights at the time of the initial outer loop iteration are equal to 1, and then the secondary outer loop is performed. Assuming that each period or cycle in the seasonal term contains n number of observations _(p) For example, if the time series is one cycle per year for month, then n _(p) =12. So is called n _(p) Is a periodic sub-sequence, where n _(p) Determined by the seasonal window Tm.

The internal circulation part is as follows:

each iteration of the inner loop includes a smooth update of the seasonal term followed by a smooth update of the trend term. Assume that for time t=1 to N, S _t ^(k) And T _t ^(k) The method comprises the steps of (1) respectively obtaining a seasonal term and a trend term after the kth iteration, and S when the kth iteration is the (1) th iteration _t ^(k+1) And T _t ^(k+1) The calculation method is as follows:

(1) trending: calculation of trending sequence D _t ；

D _t ＝Y _t -T _t ^(k) (3)

Wherein Y is _t Is the original time sequence, T _t ^(k) Is a trend term after the kth iteration;

(2) periodic subsequence smoothing: pair D _t Applying a Loess smoothing, smoothing using a locally weighted regression of parameters λ and d=1, the smoothed values at all time points being calculated, including a value before the first point of the time series and a value after the last point of the time series;

(3) low pass filter application: applying a low-pass filter to the smoothed periodic sub-sequence S _t ^(k) This filter comprises a moving average of length m, a moving average of length 3, and a Loess smoothing using parameters λ and d=1;

(4) removing season: updating seasonal item S _t ^(k+1) ＝S _t ^(k) -(D _t -S _t ^(k) )；

(5) Season term removal calculation: calculating the sequence E of the seasonal items _t ＝Y _t -S _t ^(k+1) ；

(6) Trend smoothing: pair E _t Using Loess smoothing, trend term T is updated using parameters λ and d=1 _t ^(k+1) ；

(7) Judging whether convergence is carried out: if the convergence is carried out, outputting a result, otherwise, returning to the step 1;

setting the initial value of the trend term to 0, i.e. T, before execution _t ⁽⁰⁾ =0; assume that an initial run of the inner loop has been performed to obtain an estimate: t (T) _t And S is _t Trend terms and season terms, respectively, and then the remaining terms can be obtained:

R _t ＝Y _t -T _t -S _t (4)

wherein R is _t Is the residual component, Y _t Is the original time sequence, T _t Is a trend component, S _t Is a seasonal component;

the outer loop was used to adjust Lu Bangquan weights in the Loess regression of inner loops (2) and (6), set:

δ _t ＝6·median(|R _t |) (5)

wherein delta _t Is the residual R _t 6 times the median of the absolute values;

the robust weights can be expressed as:

wherein t is the data point location; delta _t H is a scaling parameter, and B () is a robustness adjusting function;

2) Taking one IMFSm with seasonal components as an example, based on the seasonal window Tm as an input, the seasonal components, trending components, and remainder obtained by the decomposition of the seasonal trend are respectively noted as SeasonalIMFSm, trendIMFSm, residualIMFSm, wherein:

IMFSm＝(SeasonalIMFSm)+(TrendIMFSm)+(ResidualIMFSm)(7)

wherein IMFSm is IMFSm, seasonalIMFSm having a seasonal component as a seasonal component, trendIMFSm is a trending component, and residual IMFSm is a residual component;

(3) Judging seasonal deformation cause of linear engineering based on correlation analysis of seasonal components of different periods and seasonal factors

And (3) carrying out correlation analysis on a seasonal component SeasenalIMFSm which is extracted by utilizing a method of integrating pole symmetry modal decomposition and seasonal trend decomposition and takes Tm as a period and seasonal factors such as ambient temperature, precipitation, humidity and the like, so as to judge seasonal deformation causes of the linear engineering. Wherein, the correlation is analyzed by adopting a Szelman correlation coefficient.

The Spearman correlation coefficient (Spearman' S rank correlation coefficient) is a non-parametric statistic for measuring the correlation between two variables, and it measures the degree of correlation between the levels of the two variables, and if the Spearman correlation coefficient is S (k), there are:

wherein N is the data length, x (t) is the original observed data, seasonalIMFSm (t) is the seasonal term with Tm as the seasonal period, and t is the time variable;

the value of the spearman correlation coefficient ranges from-1 to 1, where |0.8 to 1.0| represents a very strong correlation; 0.6-0.8| represents strong correlation; 0.4-0.6| represents moderate correlation; 0.2-0.4 represents weak correlation; and 0.0 to 0.2 represents no correlation. By calculating the spearman correlation coefficients of different periodic components SeasonalIMFSm and factors such as ambient temperature, precipitation, humidity and the like, not only the cause category of the linear engineering seasonal deformation can be determined, but also the contribution of different seasonal factors to the time sequence seasonal change can be further quantitatively analyzed.

In the case, seasonal component extraction research is carried out on a north-line expressway located in an airport, the time sequence deformation result of a point Q1 at the position is used as an original signal, and an IMF (inertial measurement unit) of the seasonal component in displacement data and a seasonal window corresponding to the IMF are obtained by using an ESMD (extreme symmetric mode decomposition) method. Since the deformation result obtained by MT-InSAR is limited by the image obtaining time, the result is not equal time interval data. When the ESMD algorithm is used for decomposing time series data, interpolation processing is needed for the time series data missing value to obtain a better decomposition effect. Therefore, the present case resamples the time series displacement using a one-dimensional interpolation Akima algorithm to achieve a 12 day acquisition interval. Based on the time sequence deformation result after interpolation, the time sequence deformation result is decomposed by using an ESMD algorithm, the decomposition result is shown in figure 2, and the Q1 point ESMD decomposition result can be known, wherein the time sequence deformation result is adaptively decomposed into 6 modes (IMFs) and an adaptive global average line R. From spectral analysis, IMFs1, 2 and 3 have significant seasonal wave characteristics, so it can be considered that the above three IMFs have seasonal components and are renamed IMFs1, IMFs2 and IMFs3. As can be found from the three periodic component IMF curve fluctuation periods, IMFs1 and the periodic fluctuation of the deformation data are the most similar, and the periodic fluctuation with an average period of about 360 days corresponds to the periodic fluctuation, i.e. the seasonal window t1=360; IMFS2 corresponds to seasonal fluctuations of about 400 days in time period, i.e. a seasonal window t2=400; IMFS3 corresponds to seasonal fluctuations with an average period of about 120 days, i.e. a seasonal window t3=120. In addition to the above three high frequency IMF curves, other IMF curves do not fluctuate significantly periodically.

As shown in fig. 3, the ESMD signal decomposition algorithm can determine the time and frequency band at which deformation anomalies occur by decomposing the time series data into a plurality of eigenmode functions (IMFs), in addition to determining whether the time series signal has seasonal fluctuations. By analyzing the modal frequency and modal amplitude time-varying map of each IMF, it can be determined whether or not there is an anomaly in the signal. As is clear from the following figures, the deformation anomaly values of the characteristic points mainly occur in 6 to 9 months and 12 to 3 months each year, and particularly, the deformation anomalies of 7 months and 12 months are very obvious.

The ESMD decomposes the linear engineering time sequence deformation signal, so that not only can seasonal components in the signal be effectively extracted and noise signals be restrained, but also information such as periodic characteristics, deformation abnormality and the like of the seasonal components can be provided through frequency spectrum information. However, in practice it has been found that IMF modalities with seasonal components in ESMD decomposition results may contain different components, such as trend, seasonal and other oscillating components. Therefore, in this case, the seasonal component is extracted not only in a plurality of cycles but also with improved accuracy by secondarily decomposing the IMF mode having the seasonal component by the seasonal trend decomposition method (STL).

As shown in fig. 4, the seasonal term results obtained by decomposing the seasonal components IMFS1, IMFS2, and IMFS3 of the feature point Q1 through STL are shown, and as can be seen from fig. 4, the STL algorithm decomposes the seasonal term curves obtained by decomposing the three seasonal modes of the Q1 point according to the set seasonal window T to exhibit different periodic variation rules. The curves of IMFS1 and IMFS2 show seasonal variation with a period of about 1 year, and IMFS3 shows seasonal variation with a period of about 3 months, so that the STL algorithm is utilized to decompose the modes of the seasonal components decomposed by the ESMD algorithm, and different periodic seasonal components can be obtained.

Seasonal components of different periods may be related to air temperature, precipitation, and groundwater changes for different infrastructure goals. In order to quantitatively evaluate the mutual connection between the components, the seasonal components SeasonalIMFSm extracted by using ESMD and STL methods and taking Tm as a period are subjected to correlation analysis with seasonal factors such as ambient temperature, precipitation, groundwater and the like, so as to judge the seasonal deformation cause of the linear engineering. The correlation coefficient adopts a spearman correlation coefficient, and table 1 below shows the statistical result of spearman coefficients between the modal seasonal term components of three seasonal components at the point Q1 and the air temperature, precipitation and groundwater:

TABLE 1 correlation coefficient of Q1 Point SeasonalIMFS1/2/3 with air temperature, precipitation and groundwater

The result shows that the seasonal component SeasonalIMFS3 at the Q1 point is inversely related to the temperature and precipitation, and the spearman correlation coefficient is-0.62 and-0.60; the seasonal component of IMFS2 mode, seasonalamfs 2, is strongly correlated with groundwater changes, with a correlation coefficient of-0.64 at the highest. The influence of air temperature and precipitation is mainly reflected in the time sequence displacement data IMFS3 mode, the seasonal amplitude variation range is about 1mm, the influence of underground water on the displacement of traffic facilities is mainly reflected in the IMFS2 mode, the negative correlation is obvious, and the seasonal amplitude variation range is about 2mm.

Highway bridges are important transportation hubs, however, thermal expansion caused by the influence of air temperature can cause structural deformation and thus cause serious safety problems. In order to study the influence law of air temperature on deformation of the viaduct, the influence law of thermal expansion effect can be more intuitively observed by utilizing the IMFS3 modal seasonal component result SeasonalIMFS3 of the characteristic point Q1 on the viaduct and the air temperature for joint analysis.

As shown in fig. 5, the influence of the air temperature on the deformation of the overpass has a delay effect, and furthermore, the material of the overpass thermally expands or contracts when the temperature changes. In 1-6 months each year, the PS point deformation increment on the viaduct rises along with the rise of temperature, so that the expansion of the structure caused by the rise of air temperature of the viaduct can be deduced, and the deformation or damage of the infrastructure is caused; and the deformation increment of the PS point is reduced along with the temperature reduction in 7-9 months each year, so that the overpass can be deduced, and the overpass is influenced by the temperature reduction in cold winter to cause the structure to shrink. However, the deformation increment of the PS point on the overpass between 6 and 7 months and between 9 and 12 months is in negative correlation with the temperature change, and the thermal expansion effect is not obvious, so that the deformation of the overpass in the two time periods can be judged to be influenced by other factors besides the temperature.

The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art, who is within the scope of the present invention, should make equivalent substitutions or modifications according to the technical scheme of the present invention and the inventive concept thereof, and should be covered by the scope of the present invention.

Claims (7)

1. A method for monitoring seasonal deformation of a linear engineering, comprising the steps of:

a, obtaining long-time sequence deformation data of a linear engineering;

b, acquiring modal and seasonal window parameters with seasonal components through the deformation data;

c, carrying out secondary decomposition on the mode, and extracting seasonal components taking the seasonal window parameter as a boundary period;

and D, judging the seasonal deformation cause of the linear engineering through the correlation analysis of the seasonal components of different periods and the seasonal factors.

2. The method for monitoring seasonal deformation of linear engineering according to claim 1, wherein the method for acquiring the modal and seasonal window parameter having the seasonal component in step B comprises:

1) Performing interpolation processing on the deformation signal missing value of the deformation data;

2) Decomposing the resampled time sequence deformation signal by utilizing a pole symmetry mode decomposition algorithm to obtain a plurality of IMF modes;

3) Performing spectrum analysis on the plurality of IMF modes obtained by decomposition, screening out IMF modes which show periodic peaks in the spectrum or have frequencies concentrated in a specific frequency range, and judging that the IMF modes have seasonal components;

4) And using the IMF modes with m screened seasonal components for judging the corresponding seasonal window parameters Tm.

3. The method for monitoring seasonal deformation of linear engineering according to claim 2, wherein the method for decomposing the resampled time-series deformation signal by using the pole symmetry mode decomposition algorithm comprises the following steps:

(1) find all extreme points of the original signal Y and record them as E in turn _i (i＝1，2，3，…，n)；

(2) Connecting adjacent poles by using line segments, and sequentially marking midpoints of the line segments as F _i (i＝1，2，3，…，n)；

(3) Supplement left and right boundary midpoint F ₀ ，F _n ；

(4) Constructing p interpolation lines L by using the obtained n+1 midpoints ₁ ，L ₂ ，L ₃ ，…,L _p (P.gtoreq.1), calculating their mean curves L;

L*＝(L1+L2+L3+...+L _P )/p (1)

wherein L is a mean curve, L _p The P interpolation line is the P-th interpolation line, and P is the total number of the interpolation lines;

(5) repeating steps (1) to (4) for Y-L until L is less than or equal to epsilon, wherein epsilon is a set tolerance or the screening number reaches a preset maximum K, and decomposing to obtain a first empirical mode M ₁ ；

(6) For Y-M ₁ Repeating the steps (1) to (5) to obtain M in turn ₂ ，M ₃ … only a certain number of poles remain until the final margin R;

(7) let the maximum screening times K lie in the integer interval [ K _MIN ,K _MAX ]Performing internal transformation and repeating the steps 1 to 6 to obtain a series of decomposition results, further calculating a variance ratio, and drawing a change chart of the variance ratio along with K;

(8) in the integer interval [ K _MIN ,K _MAX ]The maximum screening times K corresponding to the minimum variance ratio are selected ₀ And then repeating the steps 1 to 6 to obtain a decomposition result n IMF modes and 1 self-adaptive global average line R.

4. The method for monitoring seasonal deformation of a linear engineering according to claim 1, wherein the method for extracting the seasonal component bounded by the seasonal window parameter in step C comprises:

a, decomposing the IMFSm with seasonal components by using a seasonal trend decomposition algorithm by taking the corresponding seasonal window parameters as constraint conditions;

b taking a seasonal window Tm as an input, decomposing the seasonal trend to obtain a seasonal component, a trend component and a remainder, and extracting the seasonal component.

5. The method for monitoring seasonal deformation of linear engineering according to claim 4, wherein the seasonal trend decomposition comprises an outer loop and a nested inner loop, the inner loop is updated once each iteration, the seasonal term and trend term are updated once each iteration, the complete inner loop comprises a plurality of iterations, and each iteration of the outer loop comprises calculation of an inner loop and a robustness weight; all robustness weights at the time of the initial outer loop iteration are equal to 1, and then the secondary outer loop is performed.

6. The method of claim 5, wherein each iteration of the inner loop includes a smooth update of the seasonal term followed by a smooth update of the trend term, assuming S for time t = 1-N _t ^(k) And T _t ^(k) The method comprises the steps of (1) respectively obtaining a seasonal term and a trend term after the kth iteration, and S when the kth iteration is the (1) th iteration _t ^(k+1) And T _t ^(k+1) The calculation method is as follows:

(1) trending: calculation of trending sequence D _t ；

D _t ＝Y _t -T _t ^(k) (2)

Wherein Y is _t Is the original time sequence, T _t ^(k) Is a trend term after the kth iteration;

(2) periodic subsequence smoothing: pair D _t Applying a Loess smoothing, smoothing using a locally weighted regression of parameters λ and d=1, the smoothed values at all time points being calculated, including a value before the first point of the time series and a value after the last point of the time series;

(3) low pass filter application: applying a low-pass filter to the smoothed periodic sub-sequence S _t ^(k) This filter comprises a moving average of length m, a moving average of length 3, and a Loess smoothing using parameters λ and d=1;

(4) removing season: updating seasonal item S _t ^(k+1) ＝S _t ^(k) -(D _t -S _t ^(k) )；

(5) Season term removal calculation: meter with a meter bodyCalculating seasonal term sequence E _t ＝Y _t -S _t ^(k+1) ；

(6) Trend smoothing: pair E _t Using Loess smoothing, trend term T is updated using parameters λ and d=1 _t ^(k+1) ；

(7) Judging whether convergence is carried out: if the convergence is carried out, outputting a result, otherwise, returning to the step 1;

setting the initial value of the trend term to 0, i.e. T, before execution _t ⁽⁰⁾ =0; assume that an initial run of the inner loop has been performed to obtain an estimate: t (T) _t And S is _t Trend terms and season terms, respectively, and then the remaining terms can be obtained:

R _t ＝Y _t -T _t -S _t (3)

wherein R is _t Is the residual component, Y _t Is the original time sequence, T _t Is a trend component, S _t Is a seasonal component;

the outer loop was used to adjust the Lu Bangquan weights in the inner loops (2) and (6) Loess regression, set:

δ _t ＝6·median(|R _t |) (4)

wherein delta _t Is the residual R _t 6 times the median of the absolute values;

the robust weights can be expressed as:

wherein t is the data point location; delta _t For the robustness weight, h is the scaling parameter and B () is the robustness adjustment function.

7. The method for monitoring seasonal deformation of linear engineering according to claim 1, wherein in the step D, the correlation is analyzed by using a spearman correlation coefficient, and the method comprises the following steps:

wherein N is the data length, x (t) is the original observed data, seasonalIMFSm (t) is the seasonal term with Tm as the seasonal period, and t is the time variable;

the value of the spearman correlation coefficient ranges from-1 to 1, where |0.8 to 1.0| represents a very strong correlation; 0.6-0.8| represents strong correlation; 0.4-0.6| represents moderate correlation; 0.2-0.4 represents weak correlation; and 0.0 to 0.2 represents no correlation.