CN102880786A - Kriging ground settlement time domain monitoring method based on simulated annealing method - Google Patents

Abstract

The invention discloses a Kriging ground settlement time domain monitoring method based on a simulated annealing method. The method comprises the following steps of: extracting monitoring information, performing normal conversion, and determining the dimension scale of equivalent dimension dynamic prediction; dividing time groups, calculating a variable function value which corresponds to each time group, selecting a spherical model as a variable function model, and fitting the variable function model by using the simulated annealing method; and drawing a variable function curve, calculating Kriging weight coefficients, calculating an estimation value of Kriging interpolation at a predicted moment, performing iterative calculation, interpolating and encrypting grids in a time domain, and generating a settlement monitoring result at a quasi monitoring moment. The Kriging ground settlement time domain monitoring method has the advantages that high-accuracy prediction can be performed according to the characteristic of ground settlement data abnormal distribution, the abnormal situation of monitoring points can be effectively and truly reflected, and the phenomenon of falling of a solution into a local extremum caused by high dependence of a linear inversion method result on selection of an initial model can be avoided.

Description

Kriging ground settlement time domain monitoring method based on simulated annealing method

Technical Field

The invention relates to a monitoring model in the field of geographic information, in particular to a kriging ground settlement time domain monitoring method based on a simulated annealing method.

Background

Ground subsidence is a common and increasingly obvious geological phenomenon. The geological change is an environmental geological change caused by regional ground elevation decline, mostly occurs in densely populated and industrially developed cities, and has the advantages of slow generation, long duration, wide damage range and serious damage. The urban ground settlement monitoring is an important means for protecting the lives and properties of people and reducing economic loss, and the analysis and the processing of monitoring data are scientific bases for judging the superiority and inferiority of urban environmental addresses. Therefore, when the city is developed, the settlement condition of the bottom surface of the city must be monitored, the first-hand data can be grasped in time, the observed data can be scientifically analyzed, and the possible hidden dangers can be found in time, so that reasonable prevention and treatment measures can be made to ensure the modernization process of the city. At present, the commonly used monitoring models comprise a deterministic model, a statistical model, an artificial intelligence model and the like, wherein most models are limited to the requirements of the models, and are only suitable for establishing a space monitoring model, and other time monitoring models cannot take into account the randomness and structural characteristics of discrete data, so that the result of model interpolation prediction is always strong and the requirements are difficult to meet in actual engineering.

On the other hand, in the Kriging model, disturbance information is gradually accumulated due to the fact that monitoring data are not normal, so that a variation function cannot truly reflect the distribution characteristics of settlement data, and a traditional variation function fitting model is based on a least square criterion and has an obvious amplification effect on measurement errors when processing data.

Disclosure of Invention

The purpose of the invention is as follows: the invention aims to provide a Kriging ground settlement time domain monitoring method based on a simulated annealing method, which reduces disturbance information accumulation and measurement errors.

The technical scheme is as follows: in order to realize the technical scheme, the Kriging ground settlement time domain monitoring method based on the simulated annealing method comprises the following steps of:

(1) extracting a monitoring time t_iAnd sedimentation data Z_iCarrying out normalization processing, wherein i is 1,2, …, N;

(2) will settle data Z_iCarrying out normalization conversion;

(3) determining the dimension scale of the isopimetric dynamic prediction;

(4) time packets are divided by { t'_mDenotes:

$\left\{t_m^{\′}\right\}=m\×\frac{\mathrm{\Δ}{T}^{\′}}{N_T},m=\mathrm{1,2},...,N_T$

when the time intervals of sampling at each period are relatively uniform,

{t′_m}＝m×T′，m＝1,2,...,N_T

in the formula, T 'is the time interval of determined dimension scale, T' is the shortest time interval of two adjacent time points, N_TIndicates the number of time packets, N_T≥4；

(5) Calculating the logarithmic variation function value corresponding to each time group:

$r*\left(t_m^{\′}\right)=\frac{1}{2N\left(t_m^{\′}\right)}\underset{i=1}{\overset{N\left(t_m^{\′}\right)}{\mathrm{\Σ}}}{[\mathrm{In}\left(Z_i(x_i,y_i)\right)-\mathrm{In}\left(Z_i(x_i+t,y_i+t)\right)]}^2$

in the formula (II), N (t'_m) Representing the number of all monitoring intervals of time interval t, Z_i(x_i,y_i) Is the ith point (x)_i,y_i) Monitoring value of settlement at a certain moment, Z_i(x_i+t,y_i+ t) is a settlement monitoring value of the ith point after t time;

(6) selecting a spherical model as a variation function model, fitting the variation function model by adopting a simulated annealing method, and drawing a variation function curve;

(7) calculating Kriging weight coefficient:

λ＝K^-1M，

wherein, $K=\left[\begin{array}{ccccc}{\mathrm{\γ}}_{11}& {\mathrm{\γ}}_{12}& \·\·\·& {\mathrm{\γ}}_{1n}& 1\\ {\mathrm{\γ}}_{21}& {\mathrm{\γ}}_{22}& \·\·\·& {\mathrm{\γ}}_{21}& 1\\ \·\·\·& \·\·\·& \·\·\·& \·\·\·& \·\·\·\\ {\mathrm{\γ}}_{n1}& {\mathrm{\γ}}_{n1}& \·\·\·& {\mathrm{\γ}}_{\mathrm{nn}}& 1\\ 1& 1& 1& 1& 0\end{array}\right],$ $M=\left[\begin{array}{c}{\stackrel{\‾}{\mathrm{\γ}}}_{1p}\\ {\stackrel{\‾}{\mathrm{\γ}}}_{2p}\\ \·\·\·\\ {\stackrel{\‾}{\mathrm{\γ}}}_{\mathrm{np}}\\ 1\end{array}\right];$

(8) calculating an estimated value of Kringing interpolation at the predicted time:

$Z*\left(X_0\right)={\∑}_{i=1}^n{\mathrm{\λ}}_{i}Z\left(X_i\right)$

(9) and (5) repeating the steps (4) to (8), interpolating and encrypting the grids on the time domain, and generating a settlement monitoring result at the quasi-monitoring moment.

In the Kriging time domain monitoring model, monitoring data presents obvious non-normality, firstly, an actual measurement value of a polynomial fitting reference moment is used as an approximate value of a true value, the actual measurement value is subtracted from the actual measurement value, then BOX-COX conversion is carried out on the difference value, and finally a data sequence conforming to normal distribution is formed. The normalization in the step (2) comprises the following specific steps:

(201) fitting the measured value of the reference time as an approximate value of the true value by using a polynomial;

(202) the fitting value is differed from the measured value;

(203) and performing BOX-COX conversion on the difference value to finally form a data sequence conforming to normal distribution.

The specific method for BOX-COX conversion comprises the following steps:

$y^r=\left\{\begin{array}{c}\frac{y^{r-1}}{\mathrm{\λ}},r\≠0\\ \mathrm{Iny},r=0\end{array}\right.$

wherein r is a variable parameter estimated from raw data; y is a family of transformations.

The invention adopts an equal-dimensional dynamic prediction mode, ensures the time correlation and reduces the disturbance information accumulation. Namely, the monitoring data is continuously updated, the old data is deleted, and meanwhile, the dimension scale of the data is ensured to be unchanged. The dimension scale is determined according to the actual situation, and the dimension scale in the step (3) is 8-15.

The method selects the ground settlement amount as the regional variable, has the characteristics of slow growth, long duration, wide influence range, complex cause mechanism and the like, is easily influenced by uncertain factors such as local building construction, temporary underground water extraction, sudden geological destruction and the like, enables the monitoring result to be easy to be abnormal, and provides a measure for taking the natural logarithm of the regional variable in order to reduce the influence of the factors. Therefore, as a further optimization of the present invention, the function value of the variation function corresponding to each time group calculated in step (5) is taken from the natural logarithm:

$r*\left(t_m^{\′}\right)=\frac{1}{2N\left(t_m^{\′}\right)}\underset{i=1}{\overset{N\left(t_m^{\′}\right)}{\mathrm{\Σ}}}{[\mathrm{In}\left(Z_i(x_i,y_i)\right)-\mathrm{In}\left(Z_i(x_i+t,y_i+t)\right)]}^2$

in the formula (II), N (t'_m) Representing the number of all monitoring intervals of time interval t, Z_i(x_i,y_i) Is the ith point (x)_i,y_i) Monitoring value of settlement at a certain moment, Z_i(x_i+t,y_i+ t) is a settlement monitoring value of the ith point after t time;

the method replaces the traditional least square criterion and utilizes a simulated annealing algorithm to fit a spherical function model. The spherical model variation function in the step (6) is as follows:

$r\left(t\right)=\left\{\begin{array}{cc}0& t=0\\ C_0+C(\frac{3}{2}\&CenterDot;\frac{t}{a}-\frac{1}{2}\&CenterDot;\frac{t^3}{a^3})& 0<t\&le;a\\ C_0+C& t>a\end{array}\right.,$

wherein, C₀The value of the block gold, the value of the bias base, and a represents the variation range.

The simulated annealing method comprises the following steps:

(601) initializing variogram model parameters C₀C, a, determining the parameter variation range and calculating the objective function value E (C)₀,C,a)；

(602) For current model C₀C, a perturbing to generate a new model parameter C₀', C', a ', calculating the objective function value E' (C)₀′,C′,a′)；

Model perturbation adopts the temperature-dependent Cauchy distribution proposed by Ingber (1989) to generate a new model, which is specifically as follows:

m_i′＝m_i+y_i(B_i-A_i)，

yi＝Tsgn(μ-0.5)[(1+1/T)^|2μ-1|-1]，

in the formula, m_iIs the ith variable in the current model; mu is [0,1 ]]Uniformly distributed random numbers; [ A ]_i,B_i]Is m_iAnd requires m after disturbance_i∈[A_i,B_i](ii) a sgn is a sign function;

(603) determining Δ E ═ E' (C)₀′,C′,a′)-E(C₀C, whether a) is less than 0, if so, the new model parameter C₀', C ', a ' are received, otherwise, reception is performed according to the probability P;

$P={[1-\frac{(1-h)\mathrm{\&Delta;E}}{T}]}^{\frac{1}{1-h}}$

where T represents temperature and h is a constant other than 1.

(604) When model parameters are received, set C₀=C₀′、C=C′、a=a′；

(605) Slowly reducing the temperature T, iterating according to an annealing mechanism, and outputting an optimal value of a variation model parameter; wherein, the annealing mechanism is as follows:

$T\left(k\right)=T_0{a}^{k^{1/N}}$

in the formula, T₀Is the initial temperature; k is the number of iterations; n is a given constant, typically 1 or 2; a is usually 0.7. ltoreq. a.ltoreq.1.

Has the advantages that: the Kriging ground settlement time-domain monitoring method based on the simulated annealing method can predict the non-normal distribution characteristic of ground settlement data with high precision, effectively reflect the abnormal conditions of the monitoring points truly, and adopt an equal-dimensional dynamic prediction mode to ensure time correlation and reduce disturbance information accumulation; preventing error amplification. The simulated annealing method can find a global optimal solution without solving the partial derivative of the objective function and solving a large matrix equation set, is easy to add constraint conditions, and can avoid the condition that the solution falls into a local extreme value due to the fact that the result of the linear inversion method strongly depends on the selection of an initial model.

Drawings

Fig. 1 is a general flow chart of the present invention.

Detailed Description

The present invention will be further described with reference to the accompanying drawings.

Referring to fig. 1, the method for monitoring time domain of Kriging ground settlement based on simulated annealing of the present invention includes the following steps:

(1) extracting a monitoring time t_iAnd sedimentation data Z_iPerforming normalization processing, wherein i =1,2, …, N;

(2) will settle data Z_iCarrying out normalization conversion, and specifically comprising the following steps:

(201) fitting the measured value of the reference time as an approximate value of the true value by using a polynomial;

(202) the fitting value is differed from the measured value;

(203) and performing BOX-COX conversion on the difference value to finally form a data sequence conforming to normal distribution.

The specific method for BOX-COX conversion comprises the following steps:

$y^r=\left\{\begin{array}{c}\frac{y^{r-1}}{\mathrm{\&lambda;}},r\&NotEqual;0\\ \mathrm{Iny},r=0\end{array}\right.$

wherein r is a variable parameter estimated from raw data; y is a family of transformations.

(3) Determining a dimension scale of the equal-dimension dynamic prediction, wherein the dimension scale is 8-15;

(4) time divisionGrouped, with { t'_mDenotes:

$\left\{t_m^{\&prime;}\right\}=m\&times;\frac{\mathrm{\&Delta;}{T}^{\&prime;}}{N_T},m=\mathrm{1,2},...,N_T$

when the time intervals of sampling at each period are relatively uniform,

{t′_m}＝m×T′，m＝1,2,...,N_T

in the formula, T 'is the time interval of determined dimension scale, T' is the shortest time interval of two adjacent time points, N_TIndicates the number of time packets, N_T≥4；

(5) Calculating the variation function value corresponding to each time group:

$r*\left(t_m^{\&prime;}\right)=\frac{1}{2N\left(t_m^{\&prime;}\right)}\underset{i=1}{\overset{N\left(t_m^{\&prime;}\right)}{\mathrm{\&Sigma;}}}{[Z_i(x_i,y_i)-Z_i(x_i+t,y_i+t)]}^2$

in the formula (II), N (t'_m) Representing the number of all monitoring intervals of time interval t, Z_i(x_i,y_i) Is the ith point (x)_i,y_i) Monitoring value of settlement at a certain moment, Z_i(x_i+t,y_i+ t) is a settlement monitoring value of the ith point after t time;

preferably, the error amplification caused by abnormal monitoring results can be reduced by taking the natural logarithm:

$r*\left(t_m^{\&prime;}\right)=\frac{1}{2N\left(t_m^{\&prime;}\right)}\underset{i=1}{\overset{N\left(t_m^{\&prime;}\right)}{\mathrm{\&Sigma;}}}{[\mathrm{In}\left(Z_i(x_i,y_i)\right)-\mathrm{In}\left(Z_i(x_i+t,y_i+t)\right)]}^2;$

(6) the method replaces the traditional least square criterion, utilizes a simulated annealing algorithm to fit a spherical function model, and draws a variation function curve;

the spherical model variation function is:

$r\left(t\right)=\left\{\begin{array}{cc}0& t=0\\ C_0+C(\frac{3}{2}\&CenterDot;\frac{t}{a}-\frac{1}{2}\&CenterDot;\frac{t^3}{a^3})& 0<t\&le;a\\ C_0+C& t>a\end{array}\right.,$

wherein, C₀The value of the block gold, the value of the bias base, and a represents the variation range.

The simulated annealing method comprises the following steps:

(601) initializing variogram model parameters C₀C, a, determining the parameter variation range and calculating the objective function value E (C)₀,C,a)；

(602) For current model C₀C, a perturbing to generate a new model parameter C₀', C', a ', calculating the objective function value E' (C)₀′,C′,a′)；

Model perturbation adopts the temperature-dependent Cauchy distribution proposed by Ingber (1989) to generate a new model, which is specifically as follows:

m_i′＝m_i+y_i(B_i-A_i)，

yi＝Tsgn(μ-0.5)[(1+1/T)^|2μ-1|-1]，

in the formula, m_iIs the ith variable in the current model; mu is [0,1 ]]Uniformly distributed random numbers; [ A ]_i,B_i]Is m_iAnd requires m after disturbance_i∈[A_i,B_i](ii) a sgn is a sign function;

(603) determining Δ E ═ E' (C)₀′,C′,a′)-E(C₀C, whether a) is less than 0, if so, the new model parameter C₀', C ', a ' are received, otherwise, reception is performed according to the probability P;

$P={[1-\frac{(1-h)\mathrm{\&Delta;E}}{T}]}^{\frac{1}{1-h}}$

where T represents temperature and h is a constant other than 1.

(604) When model parameters are received, set C₀=C₀′、C=C′、a=a′；

(605) Slowly reducing the temperature T, iterating according to an annealing mechanism, and outputting an optimal value of a variation model parameter;

wherein, the annealing mechanism is as follows:

$T\left(k\right)=T_0{a}^{k^{1/N}}$

in the formula, T₀Is the initial temperature; k is the number of iterations; n is a given constant, typically 1 or 2; a is usually 0.7. ltoreq. a.ltoreq.1.

(7) Calculating Kriging weight coefficient:

λ＝K^-1M，

wherein, $K=\left[\begin{array}{ccccc}{\mathrm{\&gamma;}}_{11}& {\mathrm{\&gamma;}}_{12}& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{\&gamma;}}_{1n}& 1\\ {\mathrm{\&gamma;}}_{21}& {\mathrm{\&gamma;}}_{22}& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{\&gamma;}}_{21}& 1\\ \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;\\ {\mathrm{\&gamma;}}_{n1}& {\mathrm{\&gamma;}}_{n1}& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{\&gamma;}}_{\mathrm{nn}}& 1\\ 1& 1& 1& 1& 0\end{array}\right],$ $M=\left[\begin{array}{c}{\stackrel{\&OverBar;}{\mathrm{\&gamma;}}}_{1p}\\ {\stackrel{\&OverBar;}{\mathrm{\&gamma;}}}_{2p}\\ \&CenterDot;\&CenterDot;\&CenterDot;\\ {\stackrel{\&OverBar;}{\mathrm{\&gamma;}}}_{\mathrm{np}}\\ 1\end{array}\right];$

(8) calculating an estimated value of Kriging interpolation at the predicted time:

$Z*\left(X_0\right)={\&Sum;}_{i=1}^n{\mathrm{\&lambda;}}_{i}Z\left(X_i\right)$

(9) and (5) repeating the steps (1) to (8), interpolating and encrypting the grids on the time domain, and generating a settlement monitoring result at the quasi-monitoring moment.

The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims (6)

1. A Kriging ground settlement time domain monitoring method based on a simulated annealing method is characterized in that: the method comprises the following steps:

(1) extracting a monitoring time t_iAnd settlement monitoring data Z_iCarrying out normalization processing, wherein i is 1,2, …, N;

(2) will settle data Z_iCarrying out normalization conversion;

(3) determining the dimension scale of the isopimetric dynamic prediction;

(4) time packets are divided by { t'_mDenotes:

when the time intervals of sampling at each period are relatively uniform,

{t′_m}＝m×T′，m＝1,2,...,N_T，

in the formula, T 'is the time interval of determined dimension scale, T' is the shortest time interval of two adjacent time points, N_TIndicates the number of time packets, N_T≥4；

(5) Calculating the variation function value corresponding to each time group:

in the formula (II), N (t'_m) Representing the number of all monitoring intervals of time interval t, Z_i(x_i,y_i) Is the ith point (x)_i,y_i) Monitoring value of settlement at a certain moment, Z_i(x_i+t,y_i+ t) is a settlement monitoring value of the ith point after t time;

(6) selecting a spherical model as a variation function model, fitting the variation function model by adopting a simulated annealing method, and drawing a variation function curve;

(7) calculating Kriging weight coefficient:

λ＝K^-1M，

wherein,

(8) calculating an estimated value of Kringing interpolation at the predicted time:

(9) and (5) repeating the steps (4) to (8), interpolating and encrypting the grids on the time domain, and generating a settlement monitoring result at the quasi-monitoring moment.

2. The Kriging ground settlement time-domain monitoring method based on the simulated annealing method as claimed in claim 1, wherein:

the normalization in the step (2) comprises the following specific steps:

(201) fitting the measured value of the reference time as an approximate value of the true value by using a polynomial;

(202) the fitting value is differed from the measured value;

(203) and performing BOX-COX conversion on the difference value to finally form a data sequence conforming to normal distribution.

3. The Kriging ground settlement time-domain monitoring method based on the simulated annealing method as claimed in claim 1, wherein: and (4) the dimension scale in the step (3) is 8-15.

4. The Kriging ground settlement time-domain monitoring method based on the simulated annealing method as claimed in claim 1, wherein: calculating the variation function value corresponding to each time group in the step (5) by taking the natural logarithm:

in the formula (II), N (t'_m) Representing the number of all monitoring intervals of time interval t, Z_i(x_i,y_i) Is the ith point (x)_i,y_i) Monitoring value of settlement at a certain moment, Z_i(x_i+t,y_i+ t) is the monitored value of the sedimentation at point i after the lapse of time t.

5. The Kriging ground settlement time-domain monitoring method based on the simulated annealing method as claimed in claim 1, wherein: the spherical model variation function in the step (6) is as follows:

wherein, C₀The value of the block gold, the value of the bias base, and a represents the variation range.

6. The Kriging ground settlement time-domain monitoring method based on the simulated annealing method as claimed in claim 1 or 5, wherein: the simulated annealing method in the step (6) comprises the following steps:

(601) initializing variogram model parameters C₀C, a, determining the parameter variation range and calculating the objective function value E (C)₀,C,a)；

(602) For current model C₀C, a perturbing to generate a new model parameter C₀', C', a ', calculating the objective function value E' (C)₀', C ', a '), the perturbation model being:

m_i′＝m_i+y_i(B_i-A_i)，

yi＝Tsgn(μ-0.5)[(1+1/T)^|2μ-1|-1]，

in the formula, m_iIs the ith variable in the current model; mu is [0,1 ]]Uniformly distributed random numbers; [ A ]_i,B_i]Is m_iAnd requires m after disturbance_i∈[A_i,B_i](ii) a sgn is a sign function;

(603) determining Δ E ═ E' (C)₀′,C′,a′)-E(C₀C, whether a) is less than 0, if so, the new model parameter C₀', C ', a ' are received, otherwise, reception is performed according to the probability P;

wherein T represents temperature, h is a constant not equal to 1;

(604) when model parameters are received, set C₀=C₀′、C=C′、a=a′；

(605) Slowly reducing the temperature T, iterating according to an annealing mechanism, and outputting an optimal value of a variation model parameter;

wherein, the annealing mechanism is as follows:

in the formula, T₀Is the initial temperature; k is the number of iterations; n is a given constant; a is usually 0.7. ltoreq. a.ltoreq.1.

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