CN112001559A - Deformation monitoring and forecasting method - Google Patents

Deformation monitoring and forecasting method Download PDF

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CN112001559A
CN112001559A CN202010898433.9A CN202010898433A CN112001559A CN 112001559 A CN112001559 A CN 112001559A CN 202010898433 A CN202010898433 A CN 202010898433A CN 112001559 A CN112001559 A CN 112001559A
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deformation
sequence
monitoring
deformation monitoring
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汤俊
李垠健
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East China Jiaotong University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/32—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring the deformation in a solid
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Systems or methods specially adapted for specific business sectors, e.g. utilities or tourism
    • G06Q50/08—Construction

Abstract

The invention discloses a deformation monitoring and forecasting method, which comprises the following steps of S1: acquiring a deformation monitoring sequence; s2: decomposing the deformation monitoring sequence to obtain a plurality of mode function IMF components and residual items; s3: predicting through an ARMA (autoregressive moving average) model based on the plurality of modal function components and the residual items to obtain a deformation prediction value of each modal function component; s4: and determining deformation trend based on the deformation prediction values of the modal function components. According to the method, the deformation monitoring sequence is decomposed to obtain a plurality of mode function IMF components and residual items, the ARMA model is used for respectively carrying out fine prediction, and finally, predicted values obtained through prediction are superposed to obtain the deformation trend of the engineering building, so that the defects of excessive extreme values and unbalanced stability of a single model are effectively overcome.

Description

Deformation monitoring and forecasting method
Technical Field
The invention relates to the technical field of monitoring and forecasting, in particular to a deformation monitoring and forecasting method.
Background
The deformation monitoring is to measure the engineering building by means of special instrument and method to obtain the displacement, settlement, vibration, inclination and other information of the building and to ensure the safety of the engineering building. With the development of civil engineering technology, more and more super projects are produced in recent years, such as super high-rise buildings, high-speed railways, sea-crossing bridges and the like, and the buildings are extremely sensitive to the abnormal deformation of the shape. Because factors such as engineering load, ground surface settlement and the like are difficult to predict in engineering design, the engineering operation period is also influenced by climate, human activities, geological changes and the like, so that the engineering deformation causes serious consequences.
Measuring instruments and technologies are continuously developed, and more data acquisition technologies are applied to the field of deformation monitoring. The Global Navigation Satellite System (GNSS) is another revolution of the measurement technology, and compared with the conventional method, GNSS deformation monitoring has the advantages of high measurement speed, simultaneous acquisition of three-dimensional coordinates, all-weather automatic observation and the like, but the observation accuracy is easily influenced by a field observation environment, an atmosphere, particularly an ionosphere and a troposphere. Radar interferometry (interferometric SAR) is a new remote sensing technology, which utilizes radar to emit microwaves to a monitored area, obtains two or more SAR images of a target area by receiving echoes, performs interference processing and analysis on phase data in the SAR images to obtain deformation information of the earth surface, and has the advantages of high precision, wide coverage and the like. In addition, the technologies of close-range photogrammetry, optical fiber sensors, laser scanning and the like are rapidly developed in the field of deformation monitoring, so that the reliability and the precision of the deformation monitoring are further improved.
Although the traditional ARMA model is widely applied to the field of deformation monitoring and prediction, because monitoring data contains errors, a single model is used for prediction, error factors are also contained, the prediction result can still contain errors even amplified errors according to the error propagation law, the prediction has instability, and the accuracy is seriously influenced.
Disclosure of Invention
To address the above-mentioned problems, the present invention is directed to a deformation monitoring and forecasting method that substantially obviates one or more of the problems due to limitations and disadvantages of the related art.
A method of deformation monitoring and forecasting, comprising:
s1: acquiring a deformation monitoring sequence;
s2: decomposing the deformation monitoring sequence to obtain a plurality of mode function IMF components and residual items;
s3: predicting through an ARMA (autoregressive moving average) model based on the plurality of modal function components and the residual items to obtain a deformation prediction value of each modal function component;
s4: and determining deformation trend based on the deformation prediction values of the modal function components.
Further, the decomposing the deformation monitoring sequence includes:
and decomposing the deformation monitoring sequence by adopting an improved empirical mode decomposition (MEEMD) algorithm or decomposing the deformation monitoring sequence by adopting a self-adaptive complete set empirical mode decomposition (CEEMDAN) algorithm.
Further, the decomposing the deformation monitoring sequence by using the improved empirical mode decomposition (MEEMD) algorithm comprises:
two groups of Gaussian white noises with equal absolute values and opposite signs are constructed
Figure 159398DEST_PATH_IMAGE002
Adding the two groups of white noises into the deformation monitoring sequence to obtain two groups of new sequences, namely:
Figure DEST_PATH_IMAGE003
(1)
Figure 642332DEST_PATH_IMAGE004
(2)
to pair
Figure 583743DEST_PATH_IMAGE005
Respectively carrying out Ensemble Empirical Mode Decomposition (EEMD) algorithm decomposition to obtain two groups of intermediate IMF components
Figure 268497DEST_PATH_IMAGE006
Taking the average value to obtain the following formula:
Figure 662569DEST_PATH_IMAGE007
(3)
and then performing Empirical Mode Decomposition (EMD) algorithm decomposition on the obtained product to obtain a final decomposition result:
Figure 214773DEST_PATH_IMAGE008
(4)
in the formula (I), the compound is shown in the specification,
Figure 620478DEST_PATH_IMAGE009
in order to be the final IMF component,
Figure 232725DEST_PATH_IMAGE010
are residual terms.
Still further, the predicting by the ARMA model based on the plurality of modal function components and the residual term to obtain a deformation prediction value of each modal function component includes:
establishing ARMA model forecast and design
Figure 114093DEST_PATH_IMAGE011
For monitoring time series for deformation, for arbitrary
Figure 719256DEST_PATH_IMAGE012
Satisfies the following conditions:
Figure 104101DEST_PATH_IMAGE013
(5)
in the formula, p and q are ARMA model orders,
Figure 152828DEST_PATH_IMAGE014
is the variance
Figure 521493DEST_PATH_IMAGE015
The white gaussian noise of (a) is,
Figure 431811DEST_PATH_IMAGE016
a non-zero parameter to be estimated;
the ARMA model is ordered by adopting an AIC criterion, and the AIC function expression is as follows:
Figure 202321DEST_PATH_IMAGE017
(6)
in the formula (I), the compound is shown in the specification,
Figure 156370DEST_PATH_IMAGE018
for noise term variance estimation, L is the highest order, and N is the number of monitoring data samples; finding out p and q by using an AIC criterion to minimize the AIC, wherein the p and q are the optimal models;
and (3) performing parameter estimation by adopting a least square method, and rewriting the formula (5) into a vector form:
Figure 12331DEST_PATH_IMAGE019
(7)
in the formula (I), the compound is shown in the specification,
Figure 428138DEST_PATH_IMAGE020
representing observation data
Figure 912208DEST_PATH_IMAGE021
Representing the parameter to be estimated
Figure 53471DEST_PATH_IMAGE022
(ii) a Sum the squares of the residuals
Figure 131148DEST_PATH_IMAGE023
Minimum calculation of the parameter to be estimated
Figure 898116DEST_PATH_IMAGE024
The function is:
Figure 377639DEST_PATH_IMAGE025
(8)
and (5) forecasting and reconstructing each IMF component by using the formula (5) to obtain a deformation monitoring prediction value.
Further, the method further includes determining the deformation prediction value by using the root mean square error, as shown in formula (9):
Figure 922759DEST_PATH_IMAGE026
（9）
wherein RMSE is the root mean square error; n is the predicted length;
Figure 753311DEST_PATH_IMAGE027
is an original sequence;
Figure 792812DEST_PATH_IMAGE028
is a predicted sequence.
Further, the method further includes determining the deformation prediction value by using the average absolute error, as shown in equation (10):
Figure 392420DEST_PATH_IMAGE029
（10）
wherein AME is the mean absolute error; n is the predicted length;
Figure 875485DEST_PATH_IMAGE030
is an original sequence;
Figure 193334DEST_PATH_IMAGE031
is a predicted sequence.
Further, the method further includes determining the deformation prediction value by using the average absolute percentage error, as shown in formula (11):
Figure 177471DEST_PATH_IMAGE032
（11）
wherein MAPE is the mean absolute percent error; n is the predicted length;
Figure 756220DEST_PATH_IMAGE033
is an original sequence;
Figure 800399DEST_PATH_IMAGE034
is a predicted sequence.
Further, decomposing the deformation monitoring sequence by using an adaptive complete set empirical mode decomposition (CEEMDAN) algorithm comprises:
1) in the original signal
Figure 605544DEST_PATH_IMAGE035
Adding self-adaptive white noise with average value of 0
Figure 507553DEST_PATH_IMAGE036
Of 1 at
Figure 81754DEST_PATH_IMAGE037
The secondary signal can be expressed as:
Figure 296834DEST_PATH_IMAGE038
(12)
wherein i is the number of experiments; using EMD algorithm pair
Figure 182751DEST_PATH_IMAGE039
Decomposing to obtain a first IMF, and then performing summation average calculation on the first IMF to obtain:
Figure 774269DEST_PATH_IMAGE040
(13)
mixing the original signal with
Figure 202976DEST_PATH_IMAGE041
The subtraction yields the residual component:
Figure 198745DEST_PATH_IMAGE042
(14)
2) obtaining the 2 nd order modal component IMF2, and obtaining the residual component
Figure 978483DEST_PATH_IMAGE043
Continuously adding white noise
Figure 108113DEST_PATH_IMAGE044
Forming a new signal to be decomposed:
Figure 250381DEST_PATH_IMAGE045
(15)
Figure 72843DEST_PATH_IMAGE046
a second IMF was obtained:
Figure 808718DEST_PATH_IMAGE047
(16)
original signal and
Figure 850361DEST_PATH_IMAGE048
the subtraction yields the residual component:
Figure 253661DEST_PATH_IMAGE049
(17)
3) repeating the steps 1) and 2) until the signal can not be decomposed any more, thus obtaining
Figure 981445DEST_PATH_IMAGE050
An IMF, primary signal
Figure 329250DEST_PATH_IMAGE051
Can be expressed as:
Figure 800683DEST_PATH_IMAGE052
(18)。
the invention has the beneficial effects that:
according to the deformation monitoring method provided by the embodiment of the application, the deformation monitoring sequence is decomposed to obtain a plurality of mode function IMF components and residual items, the ARMA model is used for respectively carrying out fine prediction, and finally, predicted values obtained through prediction are superposed to obtain the deformation trend of the engineering building, so that the defects of excessive extreme values and unbalanced stability of a single model are effectively overcome.
In addition to the objects, features and advantages described above, other objects, features and advantages of the present invention are also provided. The present invention will be described in further detail below.
Description of the drawings:
fig. 1 is a schematic view of displacement change of monitoring points of a deformation monitoring and forecasting method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of ZQS90-01 monitor point deformation sequence IMF according to an embodiment of the invention;
FIG. 3 is a graphical illustration of a comparison of MEEMD-ARMA and ARMA predictions for an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
A method of deformation monitoring and forecasting, comprising:
s1: acquiring a deformation monitoring sequence;
s2: decomposing the deformation monitoring sequence to obtain a plurality of mode function IMF components and residual items;
s3: predicting through an ARMA (autoregressive moving average) model based on the plurality of modal function components and the residual items to obtain a deformation prediction value of each modal function component;
s4: and determining deformation trend based on the deformation prediction values of the modal function components.
In the embodiment of the application, the ARMA model predicts future observation data according to past observation data and establishes a mathematical model to express the dynamic characteristics of a certain phenomenon. The method mainly aims at solving the problem that although a single variable forming a sequence of certain time variables depending on time has uncertainty, the change of the whole sequence has a certain rule, and optimal prediction is achieved under the condition of minimum variance by establishing a mathematical model for analysis and research.
Time sequence with stable and normal distribution and zero mean value for characteristics
Figure 58489DEST_PATH_IMAGE053
If, if
Figure 832541DEST_PATH_IMAGE054
Is equal to each value of the previous n steps
Figure DEST_PATH_IMAGE055
Related to the interference value of the previous m steps
Figure 277429DEST_PATH_IMAGE056
To a
Figure 677186DEST_PATH_IMAGE058
The ARMA (n, m) model can be constructed according to the idea of multiple linear regression:
Figure DEST_PATH_IMAGE059
(19)
in the formula (I), the compound is shown in the specification,
Figure 258340DEST_PATH_IMAGE060
is an autoregressive parameter;
Figure DEST_PATH_IMAGE061
is a moving average parameter;
Figure 436249DEST_PATH_IMAGE062
is a white noise sequence. When in use
Figure DEST_PATH_IMAGE063
Then, the model (19) can be an n-th order autoregressive model ar (n):
Figure 493067DEST_PATH_IMAGE064
(20)
when in use
Figure DEST_PATH_IMAGE065
The model (19) can be an m-order moving average model ma (m):
Figure 40723DEST_PATH_IMAGE066
(21)
the ARMA model in the embodiment of the application comprises the following specific steps:
1) monitoring data preprocessing, which mainly comprises gross error elimination and data supplementation, wherein the preprocessed data can truly and accurately reflect the behavior state of a time sequence;
2) the model is ordered, the order p and the moving average order q of the autoregressive part of the model are determined, and the initial judgment can be carried out by adopting the truncation or tailing condition of a sample Autocorrelation Coefficient (ACF) and a sample Partial Autocorrelation Coefficient (PACF). The more precise fixed-order criteria include an Akaike Information Criterion (AIC), a Bayesian Information Criterion (BIC), a Final Prediction Error Criterion (FPE), etc.;
3) parameter estimation, namely estimating unknown parameters in the model according to a certain principle, wherein the main methods comprise a moment estimation method, a maximum likelihood estimation method, a least square method and the like;
4) and data forecasting, namely substituting the historical data into the time sequence model to forecast future values.
According to the deformation monitoring method provided by the embodiment of the application, the deformation monitoring sequence is decomposed to obtain a plurality of mode function IMF components and residual items, the ARMA model is used for respectively carrying out fine prediction, and finally, predicted values obtained through prediction are superposed to obtain the deformation trend of the engineering building, so that the defects of excessive extreme values and unbalanced stability of a single model are effectively overcome.
Further, the decomposing the deformation monitoring sequence includes:
and decomposing the deformation monitoring sequence by adopting an improved empirical mode decomposition (MEEMD) algorithm or decomposing the deformation monitoring sequence by adopting a self-adaptive complete set empirical mode decomposition (CEEMDAN) algorithm.
According to the deformation monitoring method provided by the embodiment of the application, deformation monitoring data are decomposed by using a MEEMD algorithm or a CEEMDAN algorithm, the algorithm has good adaptability to a non-stable fluctuation sequence, the deformation monitoring sequence is decomposed into a plurality of characteristic Mode functions (IMF), then IMF components and residual items obtained by decomposition are subjected to refined prediction by using an ARMA model, and finally, predicted values obtained by prediction are superposed to obtain the deformation trend of an engineering building, so that the defects of excessive extreme values and unbalanced stability of a single model are effectively avoided.
Further, the decomposing the deformation monitoring sequence by using the improved empirical mode decomposition (MEEMD) algorithm comprises:
two groups of Gaussian white noises with equal absolute values and opposite signs are constructed
Figure DEST_PATH_IMAGE067
Adding the two groups of white noises into the deformation monitoring sequence to obtain two groups of new sequences, namely:
Figure 617329DEST_PATH_IMAGE003
(1)
Figure 857818DEST_PATH_IMAGE004
(2)
to pair
Figure 933090DEST_PATH_IMAGE005
Respectively carrying out Ensemble Empirical Mode Decomposition (EEMD) algorithm decomposition to obtain two groups of intermediate IMF components
Figure 284437DEST_PATH_IMAGE006
Taking the average value to obtain the following formula:
Figure 371341DEST_PATH_IMAGE007
(3)
and then performing Empirical Mode Decomposition (EMD) algorithm decomposition on the obtained product to obtain a final decomposition result:
Figure 891053DEST_PATH_IMAGE008
(4)
in the formula (I), the compound is shown in the specification,
Figure 63409DEST_PATH_IMAGE009
in order to be the final IMF component,
Figure 484026DEST_PATH_IMAGE010
are residual terms.
According to the deformation monitoring method provided by the embodiment of the application, the MEEMD algorithm is adopted to decompose the deformation monitoring sequence, the MEEMD is developed on the basis of the EEMD, the pollution of white noise to an original signal is greatly inhibited while the advantages of the EEMD are kept, and the completeness of decomposition is guaranteed. The basic idea is to add two groups of Gaussian white noises with opposite signs into a sequence to be decomposed and then perform EMD decomposition, so that the problem of mode aliasing in the EMD decomposition process can be effectively solved.
Still further, the predicting by the ARMA model based on the plurality of modal function components and the residual term to obtain a deformation prediction value of each modal function component includes:
establishing ARMA model forecast and design
Figure 284491DEST_PATH_IMAGE011
For monitoring time series for deformation, for arbitrary
Figure 132362DEST_PATH_IMAGE012
Satisfies the following conditions:
Figure 792013DEST_PATH_IMAGE013
(5)
in the formula, p and q are ARMA model orders,
Figure 360529DEST_PATH_IMAGE014
is the variance
Figure 422026DEST_PATH_IMAGE015
The white gaussian noise of (a) is,
Figure 299852DEST_PATH_IMAGE016
a non-zero parameter to be estimated;
the ARMA model is ordered by adopting an AIC criterion, and the AIC function expression is as follows:
Figure 181220DEST_PATH_IMAGE017
(6)
in the formula (I), the compound is shown in the specification,
Figure 943640DEST_PATH_IMAGE018
for noise term variance estimation, L is the highest order, and N is the number of monitoring data samples; finding out p and q by using an AIC criterion to minimize the AIC, wherein the p and q are the optimal models;
and (3) performing parameter estimation by adopting a least square method, and rewriting the formula (5) into a vector form:
Figure 985544DEST_PATH_IMAGE019
(7)
in the formula (I), the compound is shown in the specification,
Figure 175217DEST_PATH_IMAGE020
representing observation data
Figure 809460DEST_PATH_IMAGE021
Representing the parameter to be estimated
Figure 969046DEST_PATH_IMAGE022
(ii) a Sum the squares of the residuals
Figure 739556DEST_PATH_IMAGE023
Minimum calculation of the parameter to be estimated
Figure 100130DEST_PATH_IMAGE024
The function is:
Figure 956091DEST_PATH_IMAGE025
(8)
and (5) forecasting and reconstructing each IMF component by using the formula (5) to obtain a deformation monitoring prediction value.
Further, the method further includes determining the deformation prediction value by using the root mean square error, as shown in formula (9):
Figure 670100DEST_PATH_IMAGE026
（9）
wherein RMSE is the root mean square error; n is the predicted length;
Figure 560696DEST_PATH_IMAGE027
is an original sequence;
Figure 951226DEST_PATH_IMAGE028
is a predicted sequence.
According to the deformation monitoring method provided by the embodiment of the application, the MEEMD algorithm is introduced to decompose the original monitoring sequence on the basis of the ARMA prediction model, the MEEMD algorithm does not need to select a function base, the method has good adaptivity to the nonlinear unstable sequence, and the problem of mode aliasing in the EMD method is solved. And performing ARMA (autoregressive moving average) fine prediction reconstruction on the decomposed components, constructing a deformation monitoring and forecasting model with higher precision, early warning on engineering detection objects, reducing disasters, and having certain application value in the field of deformation monitoring and disaster forecasting of engineering buildings.
Further, the method further includes determining the deformation prediction value by using the average absolute error, as shown in equation (10):
Figure 294482DEST_PATH_IMAGE029
（10）
wherein AME is the mean absolute error; n is the predicted length;
Figure 671237DEST_PATH_IMAGE030
is an original sequence;
Figure 790240DEST_PATH_IMAGE031
is a predicted sequence.
Further, the method further includes determining the deformation prediction value by using the average absolute percentage error, as shown in formula (11):
Figure 492617DEST_PATH_IMAGE032
（11）
wherein MAPE is the mean absolute percent error; n is the predicted length;
Figure 323170DEST_PATH_IMAGE033
is an original sequence;
Figure 628249DEST_PATH_IMAGE034
is a predicted sequence.
Further, decomposing the deformation monitoring sequence by using an adaptive complete set empirical mode decomposition (CEEMDAN) algorithm comprises:
1) in the original signal
Figure 493437DEST_PATH_IMAGE035
Adding self-adaptive white noise with average value of 0
Figure 101136DEST_PATH_IMAGE036
Of 1 at
Figure 28772DEST_PATH_IMAGE037
The secondary signal can be expressed as:
Figure 278488DEST_PATH_IMAGE038
(12)
wherein i is the number of experiments; using EMD algorithm pair
Figure 732603DEST_PATH_IMAGE039
Decomposing to obtain a first IMF, and then performing summation average calculation on the first IMF to obtain:
Figure 901416DEST_PATH_IMAGE040
(13)
mixing the original signal with
Figure 440982DEST_PATH_IMAGE041
The subtraction yields the residual component:
Figure 963230DEST_PATH_IMAGE042
(14)
2) obtaining the 2 nd order modal component IMF2, and obtaining the residual component
Figure 911332DEST_PATH_IMAGE043
Continuously adding white noise
Figure 860834DEST_PATH_IMAGE044
Forming a new signal to be decomposed:
Figure 153275DEST_PATH_IMAGE045
(15)
Figure 603848DEST_PATH_IMAGE046
a second IMF was obtained:
Figure 298134DEST_PATH_IMAGE047
(16)
original signal and
Figure 418537DEST_PATH_IMAGE048
the subtraction yields the residual component:
Figure 808061DEST_PATH_IMAGE049
(17)
3) repeating the steps 1) and 2) until the signal can not be decomposed any more, thus obtaining
Figure 937691DEST_PATH_IMAGE050
An IMF, primary signal
Figure 220905DEST_PATH_IMAGE051
Can be expressed as:
Figure 902422DEST_PATH_IMAGE052
(18)。
the deformation monitoring method provided by the embodiment of the application adopts Adaptive Complete set Empirical Mode Decomposition (CEEMDAN), the CEEMDAN adds Adaptive white Gaussian Noise in a signal at each Decomposition stage, the total average calculation is immediately carried out after modal components are obtained by Decomposition, the same operation is carried out in the next Decomposition, the reconstruction error is ensured to be 0 under the condition of less average times, and the problems of Noise transmission and modal aliasing can be avoided.
Examples of the experiments
The experimental data are derived from the peripheral earth surface monitoring data of the Caoshi station in Guiyang subway No. 3 line, 36-stage monitoring data in the period from 2 month and 3 days in 2020 to 5 month and 1 day in 2020 are selected, and the deformation trend of the later 6 stages is predicted by using the data of the first 30 stages, so that one earth surface settlement monitoring point DBC68-01 and two pile top horizontal monitoring points ZQS-73 and ZQS90-01 are predicted. Firstly, decomposing a deformation sequence into IMF components by using MEEMD, then predicting each component by using an ARMA model, superposing the predicted values of each component to obtain a later 6-stage predicted value, and carrying out inspection by using the actually measured monitoring data of the later 6 stages. The specific displacement variation of the 3 monitoring points is shown in the attached figure 1, and the earth surface around the monitoring points is obviously in a descending trend.
As shown in FIG. 2, FIG. 2 shows the decomposition result of the ZQS90-01 monitor point deformation sequence into 4 IMF components and 1 residual term through the MEEMD algorithm.
As shown in the attached figure 3, the attached figure 3 shows the comparison of the prediction effects of ZQS90-01 monitoring point single ARMA model and the MEEMD-ARMA combined model of the invention, and as can be seen from the figure, the predicted value error of the single ARMA model is larger, but the prediction of the MEEMD-ARMA combined model is more stable and accords with the actual deformation trend.
The attached table 1 shows the comparison between forecast data of the MEEMD-ARMA combined model at the 6 th stage after the monitoring point of ZQS90-01 and actual data, and it can be seen that the absolute errors of the forecast values are better than 2 mm, the relative errors are less than 6%, and the absolute errors are matched with the actual values and are within the acceptable range.
The attached table 2 shows the precision analysis of the deformation prediction of 3 monitoring points, and it can be seen that the prediction precision obtained by a single ARMA model is poor, and the prediction trend of the MEEMD-ARMA combined model is close to the actual deformation trend. The prediction accuracy of the 3 monitoring points is improved, the root mean square error is respectively reduced by 36.92%, 43.2% and 7.42%, the average absolute error is respectively reduced by 40.37%, 41.09% and 10.21%, the average absolute error percentage is respectively reduced by 39.45%, 39.69% and 12.33%, and the deformation monitoring and forecasting requirements are basically met.
Attached watch
Figure 638297DEST_PATH_IMAGE068
ZQS90-01 monitoring point forecast result
Figure DEST_PATH_IMAGE069
Attached table 2 comparison of prediction indexes of deformation trend of monitoring points
Figure 679940DEST_PATH_IMAGE070
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and should not be taken as limiting the invention, but rather the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the present invention.

Claims (8)

1. A deformation monitoring and forecasting method is characterized by comprising the following steps:
s1: acquiring a deformation monitoring sequence;
s2: decomposing the deformation monitoring sequence to obtain a plurality of mode function IMF components and residual items;
s3: predicting through an ARMA (autoregressive moving average) model based on the plurality of modal function components and the residual items to obtain a deformation prediction value of each modal function component;
s4: and determining deformation trend based on the deformation prediction values of the modal function components.
2. The method of claim 1, wherein the decomposing the deformation monitoring sequence comprises:
and decomposing the deformation monitoring sequence by adopting an improved empirical mode decomposition (MEEMD) algorithm or decomposing the deformation monitoring sequence by adopting a self-adaptive complete set empirical mode decomposition (CEEMDAN) algorithm.
3. The method of claim 2, wherein the decomposing the deformation monitoring sequence using the improved empirical mode decomposition (MEEMD) algorithm comprises:
two groups of Gaussian white noises with equal absolute values and opposite signs are constructed
Figure 896633DEST_PATH_IMAGE002
Adding the two groups of white noises into the deformation monitoring sequence to obtain two groups of new sequences, namely:
Figure 548195DEST_PATH_IMAGE004
(1)
Figure 796773DEST_PATH_IMAGE006
(2)
to pair
Figure 926403DEST_PATH_IMAGE008
Respectively carrying out Ensemble Empirical Mode Decomposition (EEMD) algorithm decomposition to obtain two groups of intermediate IMF components
Figure 475196DEST_PATH_IMAGE010
Taking the average value to obtain the following formula:
Figure 32080DEST_PATH_IMAGE012
(3)
and then performing Empirical Mode Decomposition (EMD) algorithm decomposition on the obtained product to obtain a final decomposition result:
Figure 33534DEST_PATH_IMAGE014
(4)
in the formula (I), the compound is shown in the specification,
Figure 950543DEST_PATH_IMAGE016
in order to be the final IMF component,
Figure 353842DEST_PATH_IMAGE018
are residual terms.
4. The method according to claim 3, wherein the predicting by the ARMA model based on the plurality of modal function components and the residual term, and obtaining the deformation prediction value of each modal function component comprises:
establishing ARMA model forecast and design
Figure 816048DEST_PATH_IMAGE020
For monitoring time series for deformation, for arbitrary
Figure 304798DEST_PATH_IMAGE022
Satisfies the following conditions:
Figure 776231DEST_PATH_IMAGE024
(5)
in the formula, p and q are ARMA model orders,
Figure 34037DEST_PATH_IMAGE026
is the variance
Figure 447569DEST_PATH_IMAGE028
The white gaussian noise of (a) is,
Figure 158036DEST_PATH_IMAGE030
a non-zero parameter to be estimated;
the ARMA model is ordered by adopting an AIC criterion, and the AIC function expression is as follows:
Figure 167581DEST_PATH_IMAGE032
(6)
in the formula (I), the compound is shown in the specification,
Figure 545472DEST_PATH_IMAGE034
for noise term variance estimation, L is the highest order, and N is the number of monitoring data samples; finding out p and q by using an AIC criterion to minimize the AIC, wherein the p and q are the optimal models;
and (3) performing parameter estimation by adopting a least square method, and rewriting the formula (5) into a vector form:
Figure 349480DEST_PATH_IMAGE036
(7)
in the formula (I), the compound is shown in the specification,
Figure 812823DEST_PATH_IMAGE038
representing observation data
Figure 875325DEST_PATH_IMAGE040
Representing the parameter to be estimated
Figure 107724DEST_PATH_IMAGE042
(ii) a Sum the squares of the residuals
Figure 348212DEST_PATH_IMAGE044
Minimum calculation of the parameter to be estimated
Figure 33271DEST_PATH_IMAGE046
The function is:
Figure 650198DEST_PATH_IMAGE048
(8)
and (5) forecasting and reconstructing each IMF component by using the formula (5) to obtain a deformation monitoring prediction value.
5. Method for deformation monitoring and forecasting according to claim 4, characterized in that said method is used for monitoring and forecasting
The method also comprises the step of judging the deformation prediction value by adopting the root mean square error, wherein the formula is as follows (9):
Figure 737102DEST_PATH_IMAGE050
（9）
wherein RMSE is the root mean square error; n is the predicted length;
Figure 397760DEST_PATH_IMAGE052
is an original sequence;
Figure DEST_PATH_IMAGE054
is a predicted sequence.
6. Method for deformation monitoring and forecasting according to claim 4, characterized in that said method is used for monitoring and forecasting
The method also comprises the step of judging the deformation prediction value by adopting the average absolute error, wherein the formula is as follows (10):
Figure DEST_PATH_IMAGE056
（10）
wherein AME is the mean absolute error; n is the predicted length;
Figure DEST_PATH_IMAGE058
is an original sequence;
Figure DEST_PATH_IMAGE060
is a predicted sequence.
7. Method for deformation monitoring and forecasting according to claim 4, characterized in that said method is used for monitoring and forecasting
The method further comprises judging the deformation prediction value by adopting the average absolute percentage error, as shown in formula (11):
Figure DEST_PATH_IMAGE062
（11）
wherein MAPE is the mean absolute percent error; n is the predicted length;
Figure DEST_PATH_IMAGE064
is an original sequence;
Figure DEST_PATH_IMAGE066
is a predicted sequence.
8. The method of claim 2, wherein decomposing the deformation monitoring sequence using an adaptive complete-set empirical mode decomposition (CEEMDAN) algorithm comprises:
1) in the original signal
Figure DEST_PATH_IMAGE068
Adding self-adaptive white noise with average value of 0
Figure DEST_PATH_IMAGE070
Of 1 atThe secondary signal can be expressed as:
Figure 787470DEST_PATH_IMAGE074
(12)
wherein i is the number of experiments; using EMD algorithm pair
Figure 994460DEST_PATH_IMAGE076
Decomposing to obtain a first IMF, and then performing summation average calculation on the first IMF to obtain:
Figure 826019DEST_PATH_IMAGE078
(13)
mixing the original signal with
Figure 485670DEST_PATH_IMAGE080
The subtraction yields the residual component:
Figure 444399DEST_PATH_IMAGE082
(14)
2) obtaining the 2 nd order modal component IMF2, and obtaining the residual component
Figure 240317DEST_PATH_IMAGE084
Continuously adding white noise
Figure 993509DEST_PATH_IMAGE086
Forming a new signal to be decomposed:
Figure DEST_PATH_IMAGE088
(15)
Figure DEST_PATH_IMAGE090
a second IMF was obtained:
Figure 592986DEST_PATH_IMAGE092
(16)
original signal and
Figure 355406DEST_PATH_IMAGE094
the subtraction yields the residual component:
Figure 271409DEST_PATH_IMAGE096
(17)
3) repeating the steps 1) and 2) until the signal can not be decomposed any more, thus obtaining
Figure 195503DEST_PATH_IMAGE098
An IMF, primary signal
Figure 564168DEST_PATH_IMAGE100
Can be expressed as:
Figure 108107DEST_PATH_IMAGE102
(18)。
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