CN113807011B - Parameter inversion method for coal mining subsidence prediction model based on whale optimization algorithm - Google Patents
Parameter inversion method for coal mining subsidence prediction model based on whale optimization algorithm Download PDFInfo
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Abstract
The invention relates to a whale optimization algorithm-based parameter inversion method for a coal mining subsidence prediction model, which comprises the following steps: s1, initializing parameters required by a whale optimization algorithm to obtain an initial whale population of the algorithm, wherein the required parameters comprise the whale population size N and the maximum iteration number t of the algorithm max Inputting predicted parameters and constructing whale vector whale= [ q tan beta b theta ] within the initialization generation range 0 S 1 S 2 S 3 S 4 ]Wherein the predicted parameters include a dip coefficient q, a dominant impact tangent tan beta, and a mining impact propagation angle theta 0 Horizontal movement coefficient b, inflection point offset s of lower mountain boundary 1 Offset s of inflection point of upper mountain boundary 2 Left mining boundary inflection point offset s 3 And right mining boundary inflection point offset distance s 4 . The parameter inversion method of the coal mining subsidence prediction model based on the whale optimization algorithm has the advantages of high convergence speed, high convergence precision, high local optimizing capability and high global searching capability, can accurately predict the coal mining subsidence parameters, and can effectively prevent and reduce mining subsidenceReduced risk of damage.
Description
Technical Field
The invention belongs to the technical field of coal mining subsidence prediction, and particularly relates to a parameter inversion method of a coal mining subsidence prediction model based on whale optimization algorithm.
Background
The national economy development is not separated from the coal resources, and the national is the largest coal resource country in the world and the largest coal resource consumption country. While coal resources are rapidly mined, a series of mining subsidence occurs due to the wide range of mining working surfaces, the large number of layers and the limited depth. Predicting mining subsidence is a precondition for preventing and reducing the risk of damage to mining subsidence, and it is particularly important to accurately analyze and predict mining subsidence. Accurate parameters and a reliable prediction model can accurately predict the subsidence deformation value of the earth surface, so that the research on an accurate probability integral parameter inversion method has very important significance.
The probability integration method has simple model and accurate predicted result, and is one of the methods which are mature and widely applied in coal mining settlement prediction in China. The predicted parameters of the probability integration method are obtained by inverting the actual measurement data of the surface movement monitoring station, and the inversion method is subjected to the processes of direct inversion, inversion of an experimental design method to inversion of an optimization algorithm and inversion of an intelligent algorithm. Because of the complexity of the probability integral function, the iterative process of the direct inversion method is prone to divergence and is often difficult to implement. The direct inversion result of the linear least square method has higher precision, but incorrect initial value selection is easy to cause parameter calculation failure. The orthogonal experiment design method can better solve the problem of parameter failure caused by improper selection of working face parameters and initial values with any shape according to actual measurement data, however, the factors influencing the probability integral model are many, and the probability integral model is difficult to realize through an algorithm, so that the number of experiments to be designed is large, the labor intensity is high, the efficiency is low, and only the approximate value of the parameters can be obtained; the inversion program of experimental design by using a mode vector method is easy to program, the optimizing capability is strong, the data measured by any working face can be parameterized, however, the solving process can be trapped in a local extremum trap due to the complexity of an error function used for solving parameters, and only a local optimal solution is obtained. The optimization algorithm has poor resistance to coarse interference, strong dependence on initial values and easy sinking into local minima.
Disclosure of Invention
The invention aims to solve the problems and provides a coal mining subsidence prediction model parameter inversion method based on a whale optimization algorithm, which is simple in structure and reasonable in design.
The invention realizes the above purpose through the following technical scheme:
a coal mining subsidence prediction model parameter inversion method based on a whale optimization algorithm comprises the following steps:
s1, initializing parameters required by a whale optimization algorithm to obtain an initial whale population of the algorithm, wherein the required parameters comprise the whale population size N and the maximum iteration number t of the algorithm max Inputting predicted parameters and constructing whale vector whale= [ q tan beta b theta ] within the initialization generation range 0 S 1 S 2 S 3 S 4 ]Wherein the predicted parameters include a dip coefficient q, a dominant impact tangent tan beta, and a mining impact propagation angle theta 0 Horizontal movement coefficient b, inflection point offset s of lower mountain boundary 1 Offset s of inflection point of upper mountain boundary 2 Left mining boundary inflection point offset s 3 And right mining boundary inflection point offset distance s 4 ；
S2, constructing a fitness function and calculating fitness of each whale position in the whale population;
s3, selecting a whale position corresponding to the minimum fitness value based on the fitness of each whale position, and defining the whale position as an initial optimal position of whale;
step S4, updating algorithm parameters and whale group positions based on the initial optimal position of whales and three position updating mechanisms of whales, wherein the three total position updating mechanisms of whales comprise a shrink surrounding mechanism, a spiral position updating mechanism and a random hunting mechanism;
step S5, setting the iteration times t of the algorithm>t max When the time is a termination condition, outputting an optimal solution vector whale after termination best ＝[q tanβ b θ 0 S 1 S 2 S 3 S 4 ]。
As a further optimization scheme of the invention, in the step S2, a fitness function is constructed and the fitness of each whale position in the whale population is calculated, specifically, the mining face information, coordinate data (x, y) of each observation point and corresponding sinking value W in the mining area actual measurement data are read xy0 And a horizontal movement value U xy0 And the whale vector whale= [ q tan beta b theta ] 0 S 1 S 2 S 3 S 4 ]Substituting the estimated value into a calculation formula of the sinkage value and the horizontal movement value of the probability integration method to obtain an estimated value W of the sinkage value of the observation point xy And a horizontal movement value predictive value U xy Based on the measured dip value W xy0 And a horizontal movement value U xy0 Building fitness function f= Σ [ (W) by the sum of squares of differences between the respective prediction values xy -W xy0 ) 2 +(U xy -U xy0 ) 2 ]And determining the fitness of each whale in the whale population according to the fitness function.
As a further optimization scheme of the invention, the dip value calculation formula is as follows:
W 0 ＝mqcosα
the calculation formula of the horizontal movement value is as follows:
wherein,,
l 3 ＝(D 3 -S 3 -S 4 )
in which W is 0 Represents the maximum subsidence value of the earth surface, alpha is the dip angle of the coal bed, psi represents the offset of any point of the earth surface caused by mining subsidence, the value is the angle of rotating the x-axis forward direction to a designated position in the anticlockwise direction, l 1 、l 3 Calculated lengths of trend and trend, respectively, D 1 、D 3 The trend length and the trend length of the working surface are respectively, and r, r1 and r2 are respectively the main influence radiuses of the trend direction, the downhill direction and the uphill direction, H, H 1 、H 2 The depth is adopted for the main section of the trend, the depth is adopted for the lower boundary of the working face, and the depth is adopted for the boundary of the working face.
As a further optimization scheme of the invention, the mathematical expression of the shrink wrapping mechanism is as follows:
D＝|Cwhale * (t)-whale(t)|
whaleX(t+1)＝whale * (t)-AD
wherein t is the current iteration number, A and C are coefficient vectors, and whale * (t) represents the optimal spatial position of the whale population so far, while (t) represents the spatial position of the current whale population.
As a further optimization scheme of the present invention, the mathematical expression of the coefficient vectors a and C is as follows:
A＝2aR 1 -a
C＝2R 2
wherein: a is a constant whose value decreases linearly from 2 to 0 and whose expression is a=2-2 t/t max ，R 1 、R 2 Are all random vectors ranging from 0,1]。
As a further optimization scheme of the invention, the mathematical expression of the spiral position updating mechanism is as follows:
whale(t+1)＝whale * (t)+de bl cos(2πl)
d＝|whale * (t)-whale(t)|
where b is a constant defining the shape of a spiral, d is the distance between whale and prey, and l is a random number between (-1, 1).
As a further optimization scheme of the invention, the mathematical expression of the random search hunting mechanism is as follows:
D＝|CX rand -whale(t)|
whale(t+1)＝X rand -AD
wherein X is rand Are randomly selected whale individuals in the current population.
The invention has the beneficial effects that:
1) The method has the advantages of high convergence speed, high convergence precision, high local optimizing capability and strong global searching capability, can accurately predict the parameters of coal mining subsidence, and can effectively prevent and reduce the damage risk of mining subsidence;
2) The invention has certain data coarse interference resistance, random error interference resistance and observation point missing interference resistance.
Drawings
FIG. 1 is a flow chart of the inversion probability integration method parameters of the present invention;
FIG. 2 is a schematic diagram of the shrink wrap mechanism of the whale optimization algorithm of the present invention;
FIG. 3 is a schematic diagram of a spiral location update mechanism of the whale optimization algorithm of the present invention;
FIG. 4 is a schematic diagram of the random search hunting mechanism of the whale optimization algorithm of the present invention;
FIG. 5 is an absolute error map and a fitting map of a predicted value and an actual measured value obtained by substituting a parameter inversion result into a probability integration method dip calculation formula;
fig. 6 is an absolute value error diagram and a fitting diagram of a predicted value and an actual measured value obtained by substituting a parameter inversion result into a probability integration method horizontal movement value calculation formula.
Detailed Description
The following detailed description of the present application is provided in conjunction with the accompanying drawings, and it is to be understood that the following detailed description is merely illustrative of the application and is not to be construed as limiting the scope of the application, since numerous insubstantial modifications and adaptations of the application will be to those skilled in the art in light of the foregoing disclosure.
Example 1
As shown in FIG. 1, the parameter inversion method of the coal mining subsidence prediction model based on the whale optimization algorithm comprises the following steps:
s1, initializing parameters required by a whale optimization algorithm to obtain an initial whale population of the algorithm, wherein the required parameters comprise the whale population size N and the maximum iteration number t of the algorithm max Inputting predicted parameters and constructing whale vector whale= [ q tan beta b theta ] within the initialization generation range 0 S 1 S 2 S 3 S 4 ]Wherein the predicted parameters include a dip coefficient q, a dominant impact tangent tan beta, and a mining impact propagation angle theta 0 Horizontal movement coefficient b, lower mountain edgeOffset s of boundary inflection point 1 Offset s of inflection point of upper mountain boundary 2 Left mining boundary inflection point offset s 3 And right mining boundary inflection point offset distance s 4 ；
Wherein the dip coefficient q, the principal influencing tangent tan beta, and the mining influencing propagation angle theta 0 The horizontal movement coefficient b and the inflection point offset distances S1, S2, S3, S4 are the 8 main predicted parameters of the probability integration method, and these predicted parameters are determined by the geological mining conditions of the working face, and are different for different mining areas, and the predicted parameters of specific mining areas are fixed.
The initialization algorithm is realized as follows:
function whale＝chushihua
globa1 BO bh N
whale＝ones(N,8)；
for i=1:n%% one hundred initial whales (100,8)
wha1e1＝B0+bh.*(ones(1,8)*(-1)+rand(1,8)*2)；
% random whales generated by initialization are b1=b0-bh within the range of [ B1, B2 ]; b2 =b0+bh
whale(i,:)＝wha1e1；
end
S2, constructing a fitness function and calculating fitness of each whale position in the whale population;
specifically, the mining face information, coordinate data (x, y) of each observation point and corresponding sinking value W in the actual measurement data of the mining area are read xy0 And a horizontal movement value U xy0 And the whale vector whale= [ q tan beta b theta ] 0 S 1 S 2 S 3 S 4 ]Substituting the estimated value into a calculation formula of the sinkage value and the horizontal movement value of the probability integration method to obtain an estimated value W of the sinkage value of the observation point xy And a horizontal movement value predictive value U xy Based on the measured dip value W xy0 And a horizontal movement value U xy0 Building fitness function f= Σ [ (W) by the sum of squares of differences between the respective prediction values xy -W xy0 ) 2 +(U xy -U xy0 ) 2 ]Determination of whale population based on fitness functionFitness of each whale.
The dip value calculation formula is:
W 0 ＝mqcosα
the calculation formula of the horizontal movement value is as follows:
wherein,,
l 3 ＝(D 3 -S 3 -S 4 )
in which W is 0 Represents the maximum subsidence value of the earth surface, alpha is the dip angle of the coal bed, psi represents the offset of any point of the earth surface caused by mining subsidence, the value is the angle of rotating the x-axis forward direction to a designated position in the anticlockwise direction, l 1 、l 3 Calculated lengths of trend and trend, respectively, D 1 、D 3 The trend length and the trend length of the working surface are respectively, and r, r1 and r2 are respectively the main influence radiuses of the trend direction, the downhill direction and the uphill direction, H, H 1 、H 2 The depth is adopted for the main section of the trend, the depth is adopted for the lower boundary of the working face, and the depth is adopted for the boundary of the working face.
The data reading algorithm of the mining area measured data is realized as follows:
function readfile
global gs M m a qxtwj gm x y gczsink gczmobilek fikc bh BO H B1 B2 D1 D3 HX
[filenamel,pathnamel]＝uigetile('*.txt','pick a file for read’)；
fidl＝fopen(strcat(pathnamel,filenamel),'rt'):
if(fidl＝-1)
msgbox('choose a wrong file for read','Warning','warn')；
return；
end
gs＝fscanf(fidl,'％f',1)；
M＝fscanf(fidl,'％f',1)；
m＝fscanf(fidl,'％f',1)；
a＝fscanf(fidl,'％f',1)；
qxfwj＝fscanf(fidl,'％f',1)；
gm＝fscanf(fidl,'％f',1)；
q＝fscanf(ridl,'％f',1)；
tanB＝fscanf(fidl,'％f',1)；
b＝fscanf(fidl,'％f',1)；
sita＝fscanf(fidl,'％f',1)；
sl＝fscanf(fidl,'％f',1)；
s2＝fscanf(fidl,'％f',1)；
s3＝fscanf(fidl,'％f',1)；
s4＝fscanf(fidl,'％f',1)；
B0＝[q,tanB,b,sita,s1,s2,s3,s4]；
bh(1,1)＝fscanf(fidl,'％f',1)；
bh(1,2)＝fscanf(fidl,'％f',1)；
bh(1,3)-fscanf(fidl,'％f',1)；
bh(1,4)＝fscanf(fidl,'％f',1)；
bh(1,5)＝fscanf(fidl,'％f',1)；
bh(1,6)＝fscanf(fidl,'％f',1)；
bh(1,7)＝fscanf(fidl,'％f',1)；
bh(1,8)＝fscanf(fidl,'％f',1)；
b1 =b0-bh; b2 =b0+bh; % lower and upper limits
X0＝[]；
YO＝[]；
HO＝[]；
for c＝1:1:8
Xl＝fscanf(fidl,'％f',1)；
Y1＝fscanf(fidl,'％f',1)；
H1＝fscanf(fidl,'％f',1)；
if(X1(1,1)＝＝0&&Y1(1,1)＝＝0&&H1(1,1)＝＝-1)
break；
else
X0＝[X0,X1]；
YO＝[YO,Y1]；
H0＝[H0,H1]；
end
end
H=mean (HO); % depth of production
HX＝max(H0)；HS＝min(H0)；
D3 =sqrt (X0 (1, 2) -X0 (1, 1)) ++2 (Y0 (1, 2) -Y0 (1, 1)) ++2; % trend of
D1 =sqrt (X0 (1, 4) -X0 (1, 1)) ++ (Y0 (1, 4) -Y0 (1, 1)) -2; % tendency
coordinatesk＝fscanf(fidl,'％f',[6,M])；
coordinatesk＝coordinatesk'；
coordinates＝coordinatesk(:,2:3)；
Xi＝coordinates(:.1)；
Yi＝coordinates(:,2)；
x＝(Xi-X0(1,1))*cos(qxfwj/180*pi)+(Yi-Y0(1,1))*sin(qxfwj/180*pi)；
y＝(Yi-Y0(1,1))*cos(qxfwj/180*pi)-(Xi-X0(1,1))*sin(qxfwj/180*pi)；
gczsink＝coordinatesk(:,4)；
gczmobilek＝coordinatesk(:,5)；
fik＝coordinatesk(:,6)；
The construction of the fitness function and the algorithm for obtaining the fitness value are as follows:
function Wzj＝fdifference(wha1e)
globa1 M gczsink gczmobi1ek
% M is the number of observation points, gczsink is the measured dip value, gczmobilek is the measured horizontal movement value
sj=1 ength (whale); % sj is the number of whales
Wzj＝zeros(sj,M)；
Uxy＝zeros(sj,M)；
for i=1:sj% i-th whale, M observation points
q＝wha1e(i,1)；
tanB＝wha1e(i,2)；
b＝wha1e(i,3)；
sita＝wha1e(i,4)；
s1＝wha1e(i,5)；
s2＝wha1e(i,6)；
s3＝wha1e(i,7)；
s4＝wha1e(i,8)；
Wzj (i,:) =sink (q, tanB, b, sita, s1, s2, s3, s 4); % parameter substitution, calculating dip value predicted value
Uxy (i,:) =mobi 1e (q, tanB, b, sita, s1, s2, s3, s 4); % parameter substitution, horizontal movement value prediction value
end
fitness＝zeros(100,M)；
fitnessk＝zeros(100,M)；
for i＝1:sj
fitness(i,:)＝Wzj(i,:)-gczsink'；
fitnessk(i,:)＝Uxy(i,:)-gczmobi1ek'；
end
fitness＝sum(fitness.*fitness,2)；
fitnessk＝sum(fitnessk.*fitnessk,2)；
fitness＝fitness+fitnessk；
fitness=fitness; % fitness function
Wzj＝cat(2,Wzj,Uxy)；
Wzj(:,2*M+1)＝fitness(:,1)；
% 0:M column using the expected dip value of i whale, column M:2M horizontal movement value,% 2M:2M+1 column fitness value
The implementation process of the algorithm of the probability integration method dip value is as follows:
function w=sink (q, tanB, b, sita, s1, s2, s3, s 4)% s1s2 trend s3s4 trend
global D1 D3 H a m M HX HS x y
W＝ones(M,1)；
r＝H/tanB；
r1=hx/tanB; % mountain down
r2=hs/tanB; % mountain climbing
w0＝-m*q*cos(a/180*pi)；
L＝(D1-s1-s2)*sin((sita+a)/180*pi)/sin(sita/180*pi)；
Ca= (HX-s 1 sin (a/180 pi)) -s1 cos (a/180 pi); % ca is originally H1
x1＝x；
y1＝y；
Wy1=w0/2 (erf (pi 0.5 (y1+ca)/r 1) +1); % semi infinite exploitation w (y+C' A)
Wy2=w0/2 (erf (pi 0.5 (y1+ca-L)/r 2) +1); % semi infinite mining w (y+CA-L)
Wy＝Wy1-Wy2；
W＝500*Wy.*(erf(pi^0.5*(x1-s3))/r)-erf((pi^0.5*(x1+s4-D3))/r)；
W＝W'；
end
The implementation process of the algorithm for calculating the horizontal movement value of the probability integration method is as follows:
function Uxy＝mobi1e(q,tanB,b,sita,s1,s2,s3,s4)
globa1 D3 D1 H HX HS m a fik x y
% D3 is the trend length of the working face, D1 is the trend length of the working face, H is the depth of the main section, HX is the depth of the lower boundary of the working face
% HS is the depth of the upper boundary of the working face, m is the thickness of the coal seam, a is the inclination angle of the coal seam, fik is the offset of the ground surface point caused by mining
% x, y is coordinate data
r1=hx/tanB; % mountain down
r2＝HS/tanB；
r＝H/tanB；
L＝(D1-s1-s2)*sin(sita+a)/180*pi)/sin(sita/180*pi)；
CA＝(HX-s1*sin(a/180*pi))*cot(sita/180*pi)-s1*cos(a/180*pi)；
W0＝-m*q*cos(a/180*pi)；
% trend main section
x1＝x；
y1＝y；
wx1=w0/2 (erf (sqrt (pi) ×1-s 3)/r) +1; % trend of
wx2＝w0/2*(erf(sqrt(pi)*(x1-D3+s4)/r)+1)；
wx＝wx1-wx2；
wy1=w0/2 (erf (sqrt (pi) (y1+ca)/r 1) +1); % tendency
wy2＝W0/2*(erf(sqrt(pi)*(y1+CA-L)/r2)+1)；
wy＝wy1-wy2；
ux1＝b*W0*exp(-pi*(((x1-s3)/r).^2))；
ux2＝b*W0*exp(-pi*((x1-D3+s4)/r).^2)；
ux＝ux1-ux2；
uy1＝b*W0*exp(-pi*((y1+CA)/r1).^2))；
uy2＝b*W0*exp(-pi*((y1+CA-I)/r2).^2)；
uy＝(uy1+wy1*cot(sita/180*pi))-(uy2+wy2*cot(sita/180*pi))；
Uxy＝1000*(ux.*wy.*cos(fik/180*pi)+uy.*wx.*sin(fik/180*pi))./W0；
Uxy＝Uxy'；
end％Uxy(1,122)
S3, selecting a whale position corresponding to the minimum fitness value based on the fitness of each whale position, and defining the whale position as an initial optimal position of whale;
the whale position leader_pos with the lowest fitness value is selected as the initial target game or optimal position.
Step S4, updating algorithm parameters and whale group positions based on the initial optimal position of whales and three position updating mechanisms of whales, wherein the three total position updating mechanisms of whales comprise a shrink surrounding mechanism, a spiral position updating mechanism and a random hunting mechanism;
when |A| <1, assuming that the target prey or the whale close to the optimal solution is the current optimal position, the new positions of other whales can be arbitrarily defined between the current position and the optimal position, and the mathematical expression of the contraction surrounding mechanism is as follows:
D＝|Cwhale * (t)-whale(t)|
whaleX(t+1)＝whale * (t)-AD
wherein t is the current iteration number, A and C are coefficient vectors, and whale * (t) represents the optimal spatial position of the whale population so far, while (t) represents the spatial position of the current whale population.
As shown in fig. 3, the mathematical expression of the spiral position update mechanism is:
whale(t+1)＝whale * (t)+de bl cos(2πl)
d＝|whale * (t)-whale(t)|
where b is a constant defining the shape of a spiral, d is the distance between whale and prey, and l is a random number between (-1, 1).
As shown in fig. 4, the mathematical expression of the random search hunting mechanism is:
D＝|CX rand -whale(t)|
whale(t+1)＝X rand -AD
wherein X is rand Are randomly selected whale individuals in the current population.
The algorithm realization process for updating the algorithm parameters and searching the optimal solution vector is as follows:
format 1ong；close a11；clear；clc
tic
globa1 BO bh B1 B2 M N
pd=8; % problem dimension (number of decision variables)
N=100; % group (whale) Scale
readfile
whale＝chushihua；
Wzj＝fdifference(wha1e)；
tmax=300; % maximum number of iterations (tmax)
for t＝1:tmax
for i=1:n% cyclic operation% update position and memory for each individual multi-dimension
j1＝(wha1e(i,:)>＝B1)；j2＝(wha1e(i,:)<＝B2)；
if(j1+j2)＝＝16
whale (i,:) =whale (i,:); % problematic, original algorithm correction & improvement algorithm mapping rules
else
whale(i,:)＝B0+bh.*(ones(1,8)*(-1)+rand(1,8)*2)；
Random number update whale position in% production range
end
fit＝Wzj(:,2*M+1)；
fitleader＝min(fit)；
best＝find(fit＝＝fitleader)；
Leader_pos＝whale(best(1),:)；
% whale with minimal fitness as target prey or near optimal solution
end
a＝2-t*(2/tmax)；
R1＝rand()；
A＝2*a*R1-a；
C＝2*R1；
b＝7.5；
1＝2*(rand()-0.5)；
p=rand (); % parameter update
for j=1:size (whale, 2)% performing a circular operation on the individual multi-dimensions of each whale
if p<0.5
if abs (A) <1% shrink wrap mechanism
D_Leader＝abs(C*Leader_pos(j)-wha1e(i,j))；
whale(i,j)＝Leader_pos(j)-A*D_Leader；
elseif abs (a) > = 1% random search mechanism
x_rand＝whale(randperm(100,1),:)；
D_x_rand＝abs(C*X_rand(j)-whale(i,j))；
whale(i,j)＝X_rand(j)-A*D_X_rand；
end
elseif p > = 0.5% spiral location update mechanism
Wzj =fdi office (whale); adaptability assessment of% New solutions
fit= Wzj (: 2×m+1); % fitness of new position
wzbest＝find(fit＝＝min(fit))；
whale_best=whale (wzbest (1):); % find the best position for whale
toc
Step S5, setting the iteration times t of the algorithm>t max When the time is a termination condition, outputting an optimal solution vector whale after termination best ＝[q tanβ b θ 0 S 1 S 2 S 3 S 4 ]。
It should be noted that, the robustness of the WOA parameter inversion model is verified by designing simulation experiments from three aspects of data coarse interference resistance, random error interference resistance and observation point missing interference resistance;
the maximum dip point and the inflection point in the measured data are respectively increased by 0.1w and 0.15w (w is the maximum dip value), and 10 simulation tests are carried out on the dip value after the increase of the coarse difference, and the average value of inversion results and the relative error compared with the design value are shown in the following table 1.
TABLE 1
Analysis of the data in table 1 shows that after the rough difference of 0.1w and 0.15w is increased, the relative errors of the inversion result are close to but not more than 3% except the parameters b and S, and therefore, the WOA parameter inversion model has certain anti-interference capability in the aspect of the data rough difference.
The dip values of all monitoring points on the simulated working surface trend and trend observation line are sequentially increased by a random error with variances of 10, 20 and 30, and meanwhile, the horizontal movement value is also sequentially increased by a random error with variances of 3, 6 and 9. 10 independent experiments were performed and the mean value of the inversion results and their relative errors are shown in Table 2 below.
TABLE 2
As can be seen from analysis of the data in Table 2, after increasing random errors of different variances, the average value of inversion results of each parameter is less than 5% compared with the design value, except for the inflection point offset distances S1 and S2 and the horizontal movement coefficient b. Therefore, the WOA parameter inversion model has certain random error interference resistance.
Dividing the sinking curve into three areas according to the boundary, inflection point and maximum sedimentation point of the edge of the observation station, randomly deleting 30%, 50% and 70% of monitoring point data for the three areas and deleting all key points (the inflection point and the maximum sinking point are called key points in the text) for the three areas, and performing 10 times of parameter inversion on the simulated working surface data of the deleted observation point to obtain the average value of the result.
TABLE 3 Table 3
As can be seen from the analysis of the data in Table 3, as the number of observation points in each region increases, the average value of the inversion results is compared with the design value, and the relative errors of the other parameters except the inflection point offset distances S1 and S2 are not more than 7%; the relative error of the dip coefficient q is not greatly changed and does not exceed 0.8% except that the area III lacks 70% of the number of observation points; when all key points are missing, the relative error of the parameters q, tan beta and theta 0 is not more than 0.6%, and the relative error of other parameters is not more than 6.5%. Therefore, the model has certain anti-interference capability on the lack of observation points.
Experimental example 1
The invention is applied to the working face engineering example of the first mining area of the second mining area of the bridge to verify the feasibility of the invention.
Based on the measured data of the working face of the Gu Qiaokuang south second mining area 1414 (1), the observation station data of 75 monitoring points on the trend line and 47 monitoring points on the trend line are respectively selected as initial data, 10 times of parameter inversion is performed by adopting the model of the invention under the same condition, and the average value of inversion results and errors in parameter fitting are shown in the following table 4.
TABLE 4 Table 4
| Parameters (parameters) | Parameter range | Inversion result mean value | Error in parameter fitting |
| q | [0.7,1.3] | 1.0594 | 0.1141 |
| tanβ | [1.5,2.5] | 1.9690 | 0.1861 |
| b | [0.05,0.45] | 0.3064 | 0.0693 |
| θ0 | [84,90] | 89.2178 | 0.5762 |
| S1/m | [-20,20] | 5.0899 | 9.2569 |
| S2/m | [-30,10] | -13.7324 | 9.6743 |
| S3/m | [45,85] | 63.2806 | 9.9821 |
| S4/m | [25,65] | 46.8005 | 9.9688 |
The analysis table 4 shows that the middle errors of the parameters q, tan beta, b and theta 0 are not more than 0.6, the middle errors of the parameters of the inflection point offset are less than 10m, and the inversion result is accurate; the result of the inversion of the working face parameters by the model is as follows: q=1.0594, tan β=1.9690, b= 0.3064, θ0= 89.2178 °, s1=5.0899 m, s2= -13.7324m, s3=63.2806m, s4= 46.8005m.
Substituting the parameter inversion result into a calculation formula of a subsidence value and a horizontal movement value of a probability integration method to obtain an absolute value error map of a predicted value and an actual measurement value and an algorithm implementation process of a fitting map, wherein the process is as follows:
function readfile
c1c；c1ear；
Global gs M m a qxfwj gm x y gczsink gczmobilek fik bh BO H B1 B2 D1 D3 HX HS
[filenamel,pathname1]＝uigetfile('*.txt','pick a file for read')；
fidl＝fopen(strcat(pathname1,filename1),'rt')；
if(fid1＝＝-1)
msgbox('choose a wrong file for read'，Warning'，warn')；
return；
end
gs＝fscanf(fid1,'％f',1)；
M＝fscanf(fidl,'％f',1)；
m＝fscanf(fid1,'％f',1)；
a＝fscanf(fidl,'％f',1)；
qxfwj＝fscanf(fid1,'％f',1)；
gm＝fscanf(fid1,'％f'，1)；
q＝fscanf(fid1,'％f'，1)；
tanB＝fscanf(fid1,'％f',1)；
b＝fscanf(fid1,'％f',1)；
sita＝fscanf(fid1,'9％f',1)；
s1＝fscanf(fid1,'％f'，1)；
s2＝fscanf(fid1,'％f',1)；
s3＝fscanf(fid1,'％f',1)；
s4＝fscanf(fid1,'％f’,1)；
B0＝[q,tanB,b,sita,s1,s2,s3,s4]；
bh(1,1)＝fscanf(fidl,'％f',1)；
bh(1,2)＝fscanf(fid1,'％f',1)；
bh(1,3)-fscanf(fid1,'％f',1)；
bh(1,4)＝fscanf(fid1,'％f',1)；
bh(1,5)＝fscanf(fidl,'％f',1)；
bh(1,6)＝fscanf(fidl,'％f',1)；
bh(1,7)＝fscanf(fid1,'％f',1)；
bh(1,8)＝fscanf(fid1,'％f’，1)；
b1 =b0-bh; b2 =b0+bh; % lower and upper limits
X0＝[]；
Y0＝[]；
HO＝[]；
forc＝1:1:8
X1＝fscanf(fidl,'％f',1)；
Y1＝fscanf(fidl,'9％f',1)；
H1＝fscanf(fidl,'％f',1)；
if(X1(1,1)＝＝0&&Y1(1,1)＝＝0&&H1(1,1)＝＝-1)
break；
else
X0＝[X0,X1]；
Y0＝[Y0,Y1]；
H0＝[H0,H1]；
end
end
H=mean (HO); % depth of production
HX＝max(HO)；HS＝min(H0)；
D3 =sqrt ((x 0 (1, 2) -x0 (1, 1))ζ2 ++ (Y0 (1, 2) -Y0 (1, 1)) -2; % trend of
D1 =sqrt (x 0 (1, 4) -x0 (1, 1)) ++2 (Y0 (1, 4) -Y0 (1, 1)) ++2; % tendency
coordinatesk＝fscanf(fid1,'％f’，[6,M])；
coordinatesk＝coordinatesk'；
coordinates＝coordinatesk(:,2:3)；
Xi＝coordinates(:,1)；
Yi＝coordinates(:,2)；
x＝(Xi-X0(1,1))*cos(qxfwj/180*pi)+(Yi-Y0(1,1))*sin(qxfwj/180*pi)；
y＝(Yi-Y0(1,1))*cos(qxfwj/180*pi)-(Xi-x0(1,1))*sin(qxfwj/180*pi)；
gczsink＝coordinatesk(:,4)；
gczmobilek＝coordinatesk(:,5)；
fik＝coordinatesk(:,6)；
Wicas＝sink(1.059424374,1.968927647,0.306384126,89.21784257,5.089944933,-13.73235163,63.28062924,46.80047898)；
Uicas＝mobile(1.059424374,1.968927647,0.306384126,89.21784257,5.089944933,-13.73235163,63.28062924,46.80047898)；
figure(1)
xfig＝[1:1:122]；
yfig1＝gczsink'；
yfig2＝Wicas；
yfig3＝abs(gczsink'-Wicas)；
[AX]＝plotyx(xfig,yfigl,xfig,yfig3,'plot','bar')；
set (get, (gca, 'xlabe 1'), 'string', 'viewpoint number');
set (get (AX (1), 'Y1 abe'), 'string', 'measured dip/mm');
set (get (AX (2), 'Y1 abe'), 'string', 'absolute error/mm');
set(gca,'xTick'，_0:10:120])；
set(AX(1),'yTick'，[-2000,-1500,-1000,-500,0])；
set(AX(2),'y1im',[O,2000])；
set(AX(2),’yTICK’，[0,500,1000,1500,2000])；
holdon
h1＝p1ot(xfig,Wicas)；
1egend (measured dip value ', ' WOA predicted dip value ', ' absolute error ');
figure(2)
[BX]＝p1otxx(xfig,gczmobilek',xfig,abs(gczmobi1ek'-Uicas),'plot'，’bar')；
set (get, (gca, 'xlabe 1'), 'string', 'viewpoint number');
set (get (BX (1), 'Y1 abe'), 'string', 'measured horizontal movement value/mm');
set (get (BX (2), 'Y1 abe'), 'string', 'absolute error/mm');
set(gca,’xTick',[0:10:120])；
set(BX(1),'yTick'，[-800,-400,0,400,800])；
set(BX(2),'y1im'，[0,2000])；
set(BX(2),'yTICK',[0,500,1000,1500,2000])；
hold on
h2＝p1ot(xfig,Uicas)；
1egend (measured horizontal movement value ', ' WOA predicted horizontal movement value ', ' absolute value error ')
Substituting the inversion result into a dip value algorithm and a horizontal movement value algorithm respectively, solving a dip predicted value and a horizontal movement predicted value of the working surface, comparing the dip predicted value and the horizontal movement predicted value with actual measurement values of the dip predicted value and the horizontal movement predicted value respectively, and drawing absolute value error maps and fitting maps of the dip value and the horizontal movement value shown in fig. 5 and 6.
Analyzing fig. 5 and 6, wherein the absolute value error of the dip value of each observation point is smaller than 300mm, and the absolute value error of the horizontal movement value is smaller than 300mm except for a very small number of observation points; the calculation shows that the error in the fitting of the dip value and the horizontal movement value is 96.68mm, the error in the fitting of the dip value is 61.12mm and is about 3.1% of the maximum dip value, the error in the fitting of the horizontal movement value is 74.91mm and is about 10.5% of the maximum horizontal movement value, and the overall fitting effect is good.
The foregoing examples illustrate only a few embodiments of the invention and are described in detail herein without thereby limiting the scope of the invention. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, which are all within the scope of the invention.
Claims (5)
1. A coal mining subsidence prediction model parameter inversion method based on a whale optimization algorithm is characterized by comprising the following steps:
s1, initializing parameters required by a whale optimization algorithm to obtain an initial whale population of the algorithm, wherein the required parameters comprise the whale population size N and the maximum iteration number of the algorithm
Inputting predicted parameters and constructing whale vector in initialization generation range>
Wherein the expected parameters include dip coefficient q, impact tangent tan beta, and mining impact propagation angle theta 0 Horizontal movement coefficient b, inflection point offset s of lower mountain boundary 1 Offset s of inflection point of upper mountain boundary 2 Left mining boundary inflection point offset s 3 And right mining boundary inflection point offset distance s 4 ；
Step S2, constructing a fitness function and calculating fitness of each whale position in the whale population, wherein the fitness function comprises the following steps: reading mining face information and coordinates of each observation point in mining area actual measurement dataData (x, y) and corresponding dip values
And a horizontal movement value
And vector of whale->
Substituting the predicted value of the sinking value of the observation point into a calculation formula of the sinking value and the horizontal movement value of the probability integration method to obtain the predicted value +.>
And horizontal movement value predictive value +.>
Based on the measured dip value->
And horizontal movement value +.>
Building fitness functions from the sum of squares of differences between the respective prediction values
Determining the fitness of each whale in the whale population according to the fitness function;
the calculation formula of the dip value is as follows:
the calculation formula of the horizontal movement value is as follows:
wherein,,
in which W is 0 Represents the maximum subsidence value of the earth surface, m is the coal seam mining thickness, alpha is the coal seam inclination angle, psi represents the offset of any point of the earth surface caused by mining subsidence, the value is the angle of rotating the x-axis forward direction to a designated position along the anticlockwise direction, and l is 1 、l 3 Calculated lengths of trend and trend, respectively, D 1 、D 3 The trend length and the trend length of the working surface are respectively, and r, r1 and r2 are respectively the influence radiuses of the trend direction, the downhill direction and the uphill direction, H, H 1 、H 2 The depth of the main section and the lower boundary of the working face are respectively set;
s3, selecting a whale position corresponding to the minimum fitness value based on the fitness of each whale position, and defining the whale position as an initial optimal position of whale;
step S4, updating algorithm parameters and whale group positions based on initial optimal positions of whales and three position updating mechanisms of whales, wherein the three position updating mechanisms of whales comprise a shrink surrounding mechanism, a spiral position updating mechanism and a random hunting mechanism;
step S5, setting the iterative times of the algorithm
When the time is the termination condition, the optimal solution vector is output after termination
。
2. The method for inverting parameters of a coal mining subsidence prediction model based on a whale optimization algorithm according to claim 1, wherein the mathematical expression of the shrinkage surrounding mechanism is as follows:
in the method, in the process of the invention,
for the current iteration number, A and C are coefficient vectors,>
representing the optimal spatial position of the whale population up to now,/->
Representing the current spatial location of the whale population.
3. The method for inverting parameters of a coal mining subsidence prediction model based on a whale optimization algorithm according to claim 2, wherein the mathematical expressions of the coefficient vectors a and C are as follows:
wherein:
is a constant whose value decreases linearly from 2 to 0 and whose expression is +.>
，/>
、/>
Are all random vectors ranging from 0,1]。
4. The method for inverting parameters of a coal mining subsidence prediction model based on a whale optimization algorithm according to claim 2, wherein the mathematical expression of the spiral position updating mechanism is as follows:
in the method, in the process of the invention,
to define the constant of the spiral shape, +.>
For the distance between whale and prey, < ->
Is a random number between (-1, 1).
5. The method for inverting parameters of a coal mining subsidence prediction model based on a whale optimization algorithm according to claim 2, wherein the mathematical expression of the random search hunting mechanism is as follows:
in the method, in the process of the invention,
are randomly selected whale individuals in the current population.
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