CN113468648A - Dam monitoring data three-dimensional displacement field generation method based on Krigin interpolation - Google Patents
Dam monitoring data three-dimensional displacement field generation method based on Krigin interpolation Download PDFInfo
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Abstract
The invention discloses a dam monitoring data three-dimensional displacement field generation method based on kriging interpolation, which comprises the following steps: the method comprises the steps that dam body monitoring points are arranged, and first monitoring data of a dam are obtained; carrying out abnormal value cleaning on the first monitoring data to obtain second monitoring data; and generating a three-dimensional displacement field by interpolation based on a kriging interpolation method and the second monitoring data, so as to realize the safety performance evaluation of the dam. According to the method, a three-dimensional displacement field on a dam body time domain is obtained by interpolation through a Krigin interpolation method, and the spatial correlation existing in dam body displacement can be considered; the invention can obtain the displacement value of the damaged measuring point of the monitoring equipment, the displacement value when the monitoring equipment is normal but the measured value is unreliable, and the displacement value at any time of any concerned position of the dam body, and estimates the safety state of the dam according to the parameters, thereby greatly improving the reliability.
Description
Technical Field
The invention belongs to the technical field of dam monitoring, and particularly relates to a dam monitoring data three-dimensional displacement field generation method based on Krigin interpolation.
Background
The safety state of the dam service period is a nonlinear dynamic evolution process under the action of multiple factors, and the safety performance of the dam and the foundation structure gradually declines with the passage of time. A dam, in case of a crash, would have catastrophic consequences. With the rapid development of computer technology and safety monitoring means, the adoption of non-engineering measures to reduce the dam operation risk is more and more emphasized, and early warning is an important means for reducing the dam operation risk. The deformation can visually reflect the safety performance of the dam and is an important index of the trend change of the performance of the dam. The accurate acquisition of the deformation of the space-time distribution of the concrete dam is one of the important means for ensuring the long-term service safety of the concrete.
The structural deformation of the dam is continuous, the measuring points on the dam are limited and discrete, and monitoring equipment at some measuring points can be damaged along with the time, so that the monitoring data available on the dam is less for longer time. In addition, the observation data is susceptible to environmental factors in the observation process, and some unreliable data can be generated sometimes by monitoring equipment which operates normally. The local and overall safety performance of the dam structure in service period gradually declines with the passage of time, and in order to evaluate the local or overall safety of the dam, some measuring points are not arranged or the data of the measuring points are unreliable or the displacement of the damaged position of measuring point equipment is needed to be known sometimes.
Therefore, a displacement field of the whole or local space-time distribution of the dam is generated according to the monitoring displacement of a limited number of measuring points on the dam body, so that the safety evaluation analysis of the dam is performed, and the problem concerned by researchers is solved.
Disclosure of Invention
According to the invention, the displacement field of integral or local space-time distribution is generated by a Crimen interpolation algorithm according to the monitoring displacement of a limited number of measuring points on the dam body, so that the safety evaluation analysis of the dam is carried out, and the displacement value of the measuring point damaged by the monitoring equipment is obtained by considering the spatial correlation existing in the dam body displacement.
In order to achieve the purpose, the invention provides the following scheme: a dam monitoring data three-dimensional displacement field generation method based on Kriging interpolation comprises the following steps:
the method comprises the steps that dam body monitoring points are arranged, and first monitoring data of a dam are obtained; carrying out abnormal value cleaning on the first monitoring data to obtain second monitoring data; and generating a three-dimensional displacement field by interpolation based on a kriging interpolation method and the second monitoring data, so as to realize the safety performance evaluation of the dam.
Preferably, the first monitoring data comprises a time dimension, a space dimension;
the dam body monitoring points are uniformly distributed on the dam, the first monitoring data obtained in the time dimension in the same space dimension are continuous distribution data, and the acquisition frequency of the continuous distribution data is the same.
Preferably, the abnormal value cleaning is to calculate the jitter characteristics of the first monitoring data, compare the ratio of the jitter deviation absolute value and the mean square error of the first monitoring data with a preset value based on the Laplace criterion, and remove the abnormal value of which the ratio is greater than the preset value.
Preferably, the jitter characteristic formula is:
di＝2yi-(yi+1+yi-1)
wherein, yiThe measured value is the ith monitoring data;
the ratio of the absolute value of the jitter deviation of the ith measured value to the mean square error is qiThe formula is as follows,
Preferably, the interpolating and generating a three-dimensional displacement field based on the kriging interpolation method and the second monitoring data includes:
obtaining a distance and a half-variance between the second monitoring data based on the same time dimension;
performing data model fitting based on a half variance function and the distance to obtain a functional relation between the half variance and the distance;
acquiring the half-variance of the dam body monitoring point and the non-dam body monitoring point based on the functional relation;
and generating a three-dimensional displacement field based on the kriging interpolation method and the half-variance interpolation to realize the safety performance evaluation of the dam.
Preferably, in the data model fitting process based on the half-variance function and the distance, the data model includes a spherical model, an exponential model, a gaussian model and a cubic model.
Preferably, the formula of the half-variance between the second monitoring data is:
wherein h is xiAnd xi+ h distance between two points, n1(h, t) is the logarithm of points at a distance h, y (x)iT) and y (x)i+ h, t) each being xiAnd xiMonitor displacement value at time t at + h.
Preferably, the dam monitoring data three-dimensional displacement field generation method further comprises the steps of predicting the displacement value of any point of the dam by calculating the root mean square error between the predicted value and the actual value based on the adjacent point of the any point of the dam, and realizing the safety state evaluation of the dam by the displacement value of the any point of the dam.
Preferably, the displacement value of any point of the dam is expressed by the following formula:
λiand (i ═ 1, 2.., n) is an optimal coefficient obtained by solving a kriging equation system.
Compared with the prior art, the invention discloses the following technical effects:
(1) according to the method, a three-dimensional displacement field on a dam body time domain is obtained by interpolation through a Krigin interpolation method, and the spatial correlation existing in dam body displacement can be considered;
(2) the invention can obtain the displacement value of the damaged measuring point of the monitoring equipment;
(3) the invention can obtain the displacement value when the monitoring equipment is normal but the measured value is unreliable;
(4) the method can obtain the displacement value of the dam body at any concerned position at any moment, and is used for evaluating the safety of the dam.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
FIG. 1 is a schematic flow chart of a method according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Referring to fig. 1, the invention provides a dam monitoring data three-dimensional displacement field generation method based on kriging interpolation, which includes:
the method comprises the steps that dam body monitoring points are arranged, and first monitoring data of a dam are obtained; carrying out abnormal value cleaning on the first monitoring data to obtain second monitoring data; and generating a three-dimensional displacement field by interpolation based on a kriging interpolation method and the second monitoring data, so as to realize the safety performance evaluation of the dam.
The first monitoring data comprises a time dimension and a space dimension;
the dam body monitoring points are uniformly distributed on the dam, the first monitoring data obtained in the time dimension in the same space dimension are continuous distribution data, and the acquisition frequency of the continuous distribution data is the same.
And the abnormal value cleaning is to calculate the jitter characteristic of the first monitoring data, compare the ratio of the jitter deviation absolute value and the mean square error of the first monitoring data with a preset value based on the Laplace criterion, and remove the abnormal value of which the ratio is greater than the preset value.
The jitter characteristic formula is as follows:
di＝2yi-(yi+1+yi-1)
wherein, yiThe measured value is the ith monitoring data;
the ratio of the absolute value of the jitter deviation of the ith measured value to the mean square error is qiThe formula is as follows,
The interpolation based on the kriging interpolation method and the second monitoring data generates a three-dimensional displacement field, and the method comprises the following steps:
obtaining a distance and a half-variance between the second monitoring data based on the same time dimension;
performing data model fitting based on a half variance function and the distance to obtain a functional relation between the half variance and the distance;
acquiring the half-variance of the dam body monitoring point and the non-dam body monitoring point based on the functional relation;
and generating a three-dimensional displacement field based on the kriging interpolation method and the half-variance interpolation to realize the safety performance evaluation of the dam.
In the process of fitting the data model based on the half-variance function and the distance, the data model comprises a spherical model, an exponential model, a Gaussian model and a cubic model.
The formula of the half-variance between the second monitoring data is as follows:
wherein h is xiAnd xi+ h distance between two points, n1(h, t) is the logarithm of points at a distance h, y (x)iT) and y (x)i+ h, t) each being xiAnd xiMonitor displacement value at time t at + h.
The dam monitoring data three-dimensional displacement field generation method further comprises the steps of predicting the displacement value of any point of the dam by calculating the root mean square error between a predicted value and an actual value based on the adjacent point of the any point of the dam, and achieving the safety performance evaluation of the dam by the displacement value of the any point of the dam.
The formula of the displacement value of any point of the dam is as follows:
λiand (i ═ 1, 2.., n) is an optimal coefficient obtained by solving a kriging equation system.
Further, the dam monitoring data three-dimensional displacement field generation method based on the kriging interpolation provided by the invention specifically comprises the following steps:
s1, monitoring the space-time dimension establishment; s2, cleaning abnormal values of the monitoring data; s3, generating a three-dimensional displacement field through interpolation; and S4, evaluating the interpolation precision.
The interpolation generation of the three-dimensional displacement field specifically comprises the following steps: based on the measured point data at the same moment, calculating the distance and the half variance pairwise; performing model fitting on the calculated data distribution; selecting a spherical model or an exponential model or a Gaussian model or a cubic model, and calculating the half-variance among all the measuring points according to a fitting result; calculating the half-variance from the unknown point to all the measuring points; solving a kriging equation set to obtain an optimal coefficient; calculating the estimated displacement of the unknown point according to a kriging interpolation formula;
since the structure of the dam is continuous, the displacement monitoring data of the dam is also continuous in both the time dimension and the space dimension. For the same measuring point, the monitoring data should be continuously distributed in time. For the same monitoring project, the monitoring data acquisition frequency of the time dimension should be consistent, that is, the data acquisition time intervals are the same. In the spatial dimension, the distribution of the measurement points should be substantially uniform for the same monitoring item. The distribution density can be determined according to specific monitoring conditions of different dams. After the dam monitoring space-time dimension is established, interpolation supplement of dam monitoring data can be completed.
And for any monitoring measuring point, removing unreliable data according to the Laplace criterion in the time dimension, and cleaning abnormal values of the monitoring data to improve the interpolation precision.
For a particular scope, let yiFor the ith measurement, the jitter characteristic of the measurement can be expressed as di＝2yi-(yi+1+yi-1). By y1～ynN-2 d can be obtainedi. When n is sufficiently large, a test is performed using the Laplace criterionAnd removing the abnormal value. The mean and mean square error of the jitter characteristics of the recorded values are respectively
And sigma, the ratio of the absolute value of the jitter deviation of the ith measured value to the mean square error is qiNamely:
when q isi＞q*When it is determined that the value is an outlier or unreliable value. Determining q is generally based on trial calculations*I.e. q*Is a preset value set according to actual needs.
Further, in step S3, a spatial kriging interpolation is adopted, and the interpolation to generate the three-dimensional displacement field specifically includes:
s31, calculating the distance between every 2 points and the half-variance gamma (h, t) based on the monitoring data of the time t;
wherein h is xiAnd xi+ h distance between two points, n1(h, t) is the logarithm of points at a distance h, y (x)iT) and y (x)i+ h, t) each being xiAnd xiMonitor displacement value at time t at + h.
S32, obtaining a series of (h) after the step S311,γ1)，(h2,γ2)，…，(hn,γn) Point pairing, selecting a proper half-variance function for fitting to obtain a functional relation between the half-variance and the distance;
s33, calculating the half-variance gamma between all the known points according to the fitting result obtained in the step S32ij；
S34, for the unknown point x0Calculate it and all known points xi(i＝1,2,...,n2)(n2As number of measurements) of the measured data pointsi0；
S35, solving a Kriging equation set to obtain an optimal coefficient lambdai(i＝1,2,...,n)；
S36, obtaining the displacement value of any unknown point by a kriging interpolation method, namely
The step S4 specifically includes: and (3) assuming that the displacement value of any measuring point is unknown, predicting the displacement value by using a proximity point, and calculating the root mean square error of the predicted value and the actual value, wherein the smaller the root mean square error is, the higher the interpolation precision is.
Compared with the prior art, the invention has the beneficial technical effects that:
(1) according to the method, a three-dimensional displacement field on a dam body time domain is obtained by interpolation through a Krigin interpolation method, and the spatial correlation existing in dam body displacement can be considered;
(2) the invention can obtain the displacement value of the damaged measuring point of the monitoring equipment;
(3) the invention can obtain the displacement value when the monitoring equipment is normal but the measured value is unreliable;
(4) the method can obtain the displacement value of the dam body at any concerned position at any moment, and is used for evaluating the safety of the dam.
The above-described embodiments are merely illustrative of the preferred embodiments of the present invention, and do not limit the scope of the present invention, and various modifications and improvements of the technical solutions of the present invention can be made by those skilled in the art without departing from the spirit of the present invention, and the technical solutions of the present invention are within the scope of the present invention defined by the claims.
Claims (9)
1. A dam monitoring data three-dimensional displacement field generation method based on Krigin interpolation is characterized by comprising the following steps:
the method comprises the steps that dam body monitoring points are arranged, and first monitoring data of a dam are obtained; carrying out abnormal value cleaning on the first monitoring data to obtain second monitoring data; and generating a three-dimensional displacement field by interpolation based on a kriging interpolation method and the second monitoring data, so as to realize the safety performance evaluation of the dam.
2. The method for generating dam monitoring data three-dimensional displacement field based on Krigin interpolation as claimed in claim 1,
the first monitoring data comprises a time dimension and a space dimension;
the dam body monitoring points are uniformly distributed on the dam, the first monitoring data obtained in the time dimension in the same space dimension are continuous distribution data, and the acquisition frequency of the continuous distribution data is the same.
3. The method for generating dam monitoring data three-dimensional displacement field based on Krigin interpolation as claimed in claim 1,
and the abnormal value cleaning is to calculate the jitter characteristic of the first monitoring data, compare the ratio of the jitter deviation absolute value and the mean square error of the first monitoring data with a preset value based on the Laplace criterion, and remove the abnormal value of which the ratio is greater than the preset value.
4. The method for generating dam monitoring data three-dimensional displacement field based on Krigin interpolation as claimed in claim 3,
the jitter characteristic formula is as follows:
di＝2yi-(yi+1+yi-1)
wherein, yiThe measured value is the ith monitoring data;
the ratio of the absolute value of the jitter deviation of the ith measured value to the mean square error is qiThe formula is as follows,
5. The method for generating dam monitoring data three-dimensional displacement field based on Krigin interpolation as claimed in claim 2,
the interpolation based on the kriging interpolation method and the second monitoring data generates a three-dimensional displacement field, and the method comprises the following steps:
obtaining a distance and a half-variance between the second monitoring data based on the same time dimension;
performing data model fitting based on a half variance function and the distance to obtain a functional relation between the half variance and the distance;
acquiring the half-variance of the dam body monitoring point and the non-dam body monitoring point based on the functional relation;
and generating a three-dimensional displacement field based on the kriging interpolation method and the half-variance interpolation to realize the safety performance evaluation of the dam.
6. The method for generating dam monitoring data three-dimensional displacement field based on Krigin interpolation as claimed in claim 5,
in the process of fitting the data model based on the half-variance function and the distance, the data model comprises a spherical model, an exponential model, a Gaussian model and a cubic model.
7. The method for generating dam monitoring data three-dimensional displacement field based on Krigin interpolation as claimed in claim 5,
the formula of the half-variance between the second monitoring data is as follows:
wherein h is xiAnd xi+ h distance between two points, n1(h, t) is the logarithm of points at a distance h, y (x)iT) and y (x)i+ h, t) each being xiAnd xiMonitor displacement value at time t at + h.
8. The method for generating dam monitoring data three-dimensional displacement field based on Krigin interpolation as claimed in claim 1,
the dam monitoring data three-dimensional displacement field generation method further comprises the steps of predicting the displacement value of any point of the dam by calculating the root mean square error between a predicted value and an actual value based on the adjacent point of the any point of the dam, and achieving the safety performance evaluation of the dam by the displacement value of the any point of the dam.
9. The method for generating dam monitoring data three-dimensional displacement field based on Krigin interpolation as claimed in claim 8,
the formula of the displacement value of any point of the dam is as follows:
λiand (i ═ 1, 2.., n) is an optimal coefficient obtained by solving a kriging equation system.
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