,
.
o
„
02.16.01 „
”
,
”
2014 .
.................................................................................................................................. 4
.
1.
........................ 5
1.1.
............................................................................................... 5
1.2.
........................................................................... 6
1.3.
................................................................................................................................ 6
1.4.
1 ............................................................................. 7
2.
.................................. 8
2.1.
... 8
2.2.
.......................................................... 9
2.2.1.
........................................................................................... 9
2.2.2.
................................................................ 9
2.2.3.
............................... 9
2.2.4.
................................. 9
2.3.
................................................................................................................... 9
2.4.
....................................... 10
2.7.
................... 10
2.9.
................................................................................................................................ 10
2.10.
2 ................................................................................ 10
3.
3.2.
3.2.3.
(GPS) ............................................................. 11
GPS
...................................................... 11
............................................................... 11
3.2.3.1.
.......................................................................................... 11
3.2.3.2.
.................................................................................. 11
3.2.4.
...................................................... 12
3.5.
GPS ................................................. 12
3.6.
.................................................. 14
3.6.1.
.................................................................................. 15
3.6.2.
......................................................................... 15
3.6.3.
......................................................... 15
3.6.4.
..................................... 17
1
3.6.5.
............................................................................................ 18
3.7.
3 ........................................................................... 18
4.
.
.............................................................................. 20
4.3.
........................................................................................................................ 20
4.4.
....................................................................... 21
4.5.
....... 22
4.5.1.
............................ 22
4.5.2.
..................................................................... 22
4.5.3.
.................................................. 23
4.6.
....................................................................................................... 23
4.8.
4 ........................................................................... 24
5.
. 25
5.2.
................................................................................................................................. 25
5.2.1.
,
.............................................. 26
5.2.2.
,
.......................... 27
5.2.3.
,
) .................................. 28
( 5.2.4.
( -
W-
,
) .................................................. 30
5.2.5.
................................................................................ 31
5.3.
6.
5 ........................................................................... 32
...................................................................................................................... 34
6.1.
................................................ 35
6.2.
......... 36
6.3.
....................................................................................................... 37
6.4.
7.
6 ........................................................................... 39
-
........................ 40
2
7.2.
........................................................................................................................ 43
7.3.
7 ........................................................................... 46
,
...................................................................................................................... 47
8.
8.1.
....................................................................... 47
8.2.
....................................................................................................... 47
8.3.
8.4.
SPSS................................. 48
8 ........................................................................... 55
....................................................................................... 57
................................................................................................................ 61
...................................................................................... 67
................................................................ 68
3
.
,
,
,
.
–
„
–
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.
2011 .,
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13/29.01. 2004
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1980 .,
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7.1. „
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3
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:
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2.
,
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(
3.
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4.
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5.
6.
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7.
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1.
1.1.
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0 – 15
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:
15 – 29
30 – 59
60 – 99
100 – 149
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2.
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1.3.
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6
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20-
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92%
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13/29.01.2004 .
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10
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2.
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8
2.2.
2.2.1.
,
,
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.
2.2.2.
,
,
,
,
.
–
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2.2.3.
,
:
;
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2.2.4.
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,
mQ
Qmin,
.
(mQ)
( Q),
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2.3.
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9
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(
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2
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1980 .
1980 .,
,
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–
,
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,
(
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10
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GPS
WGS84
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(
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3.
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3.2.
GPS
3.2.3.
,
,
10
GPS
,
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3.2.3.1.
,
–
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.
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–
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11
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-
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3.2.4.
.
,
,
–
.
3.5.
GPS
GPS
.
,
,
.
(
)
,
. .
.
,
-
.
GPS
„
–
,
” –
GPS
.
.
(3.1)
4
- XP, YP, ZP
tP.
,
:
A Ax + A f = 0 → Nx + F = 0
T
T
(3.35)
,
(4,4):
12
N −1
Q XX
Q
= Q =  XY
 Q XZ

 Q Xt
Q XY
QYY
QYZ
Q XZ
QYZ
QZZ
QYt
QZt
Q Xt 
QYt 
QZt 

Qtt 
(3.36)
GPS
,
.
,
,
,
,
, . .
,
(
P = kK −1 = k µ 2Q
)
(3.34):
−1
,
(3.38)
–
.
(
)
 s 2Q
.... 0 
 1 1

.... 0 
.....
= k
 .....
.... ....


.... Pn 
 0
 P1 0
0 P
2
P = k
.... ....

0 0
−1
-
0
s 22Q2
.....
0
(
.....
.....
.....
.....
)
−1
0
0
.....
s n2 Qn
(
:




−1 

(3.39)
)
-
0,
.
.
,
.
:
K xy
rxy =
(3.40)
mx m y
GPS
,
:
mΦ2 = mΦ2 1 + mΦ2 2 + 2
m1
m1 –
.
1
PΦ1 PΦ 2
1
PΦ1
1
PΦ 2
mΦ1 mΦ 2
,
(3.41)
; p1
p2 –
:
13
mΦ2 = mΦ2 1 + m Φ2 2 + 2 rΦ1Φ 2 m Φ1 mΦ 2
(3.42)
0,
.
GPS
,
,
.
,
P=Q
−1
:
Q = P −1 ,
(3.43)
(3,3):
 1
 p
1

r
 12
Q =  p1 p 2

 ........
 r1n
 p1 p n
r12
p1 p 2
1
p2
........
r2 n
p2 p n
........
........
........
........
r1n
p1 p n
r2 n
p 2 pn
........
1
pn


  q11 q12
 q
q 22
 =  12
 ..... .....
 q
q2 n
  1n

..... q1n 
..... q2 n 
..... .....  ,

..... q nn 
(3.44)
,
GPS
,
,
-
,
.
,
,
,
-
,
-
Q
.
qii =
1
pii
(3.45)
3.6.
GPS
:
-
,
, . .
;
-
;
;
;
;
.
,
14
,
.
3.6.1.
–
, GPS
.
GPS
.
3.6.2.
–
.
RTK
-
,
.
,
.
3.6.3.
–
.
.
,
.
.
,
:
vind = R − 1 ,
: vind –
v=
n(n − 1)
,
2
(3.51)
;R–
.
:
(3.52)
:v–
;n–
.
( -
3.45).
(R > 2),
,
R
n.
s:
 n (n − 1) 
s=
,
 2(R − 1)
 n (n − 1)

if s = float [ ], else s = int 
+ 0.75  (3.53)
 2(R − 1)

3.2.
,
R
,
n:
15
R
n
3
4
5
6
7
8
9
10
2 (vind)
3
4
5
6
7
8
9
10
3
6
10
15
21
28
36
45
2
4
6
8
11
15
19
23
3
5
6
8
11
13
15
4
5
6
8
10
13
4
5
6
8
10
4
5
7
8
4
6
7
5
6
5
. 3.2.
-
15
30,
.
,
.
, . .
4
(
)
6
.
n
R.
n
k =   +1 ,
R
(3.54)
-
.
s,
,
.
50%.
:
3.8
-
.
3.52
3.53)
n = 21,
7
210
35
(
.
. 3.8.
(
(3.54),
3.9 , ,
3.8
4
),
s = 16.
16
. 3.9.
. 3.9.
. 3.9.
. 3.9.
,
,
,
,
,
.
3.6.4.
–
,
.
,
-
.
(
-
–
):
;
;
– DOP
„
/
”
;
;
–
-
.
(
20
35
)
1 - 2
,
)
(
.
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(
).
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-
GPS
5
.
,
– 10
,
17
50%.
(
),
.
3.6.5.
–
,
,
INdependent EXchange)
,
.
RINEX (Receiver
.
.
3.7.
3
GPS
,
GPS
,
,
,
,
.
,
(
) GPS
.
3
-
95%
GPS
(
GPS
„
,
70
.
”,
.
.
).
,
GPS
,
(3.53)
.
.
,
.
(1 – 2
)
,
,
,
(
)
.
,
,
.
18
,
2.5
,
,
L1,
.
,
0 [8].
,
.
,
,
.
RTK
,
„
”
(
.
,
)
.
,
RINEX
.
,
[2].
-
,
–
3
-
[2].
(
)
,
,
.
,
,
[46].
,
.
,
-
,
.
2 /
„
/
”
,
,
,
.
,
20 – 35
.,
,
,
19
,
(3.52).
.
,
5
,
,
-
,
,
10
.,
.
,
.
5
.
10
(
.
),
.
4.
.
.
.
,
.
GPS
.
,
,
,
.
4.3.
(X, Y, Z)
:
(B, L, H).
X = ( N + H )cos B cos L
Y = ( N + H )cos B sin L ,
[ (
)
(4.8)
]
Z = N 1 − e + H sin B
2
N–
N=
,
a
(4.9)
1 − e 2 sin 2 B
–
,
e2 =
:
a2 + b2
=2f − f2,
2
a
b
.
(4.10)
; f –
(
-
:
,
. 4.5):
–
20
-
Z–
X–
Y–
;
;
,
.
:
X
Y
;
-
;
.
. 4.5.
:
L = arctg
A
( A − a ),
N'
1
k=
,
h 2

1 + e ' 
 N' 
Z 1 + e' 2 ,
tgBo =
,
X 2 +Y2
B = arctg (k .tgB )
h=
Y
,
X
a2 − b2
e' =
,
b2
A 2 = X 2 + Y 2 + Z 2 1 + e' 2 ,
N '2 = X 2 + Y 2
(
( )
+ Z (1 + e' ) ,
2 2
2
’–
)
(4.11)
.
,
(a, f)
.
,
,
,
,
.
4.4.
,
,
.
21
,
:
-
-
;
-
;
-
;
–
.
,
.
,
.
(x,y):
x = f x (a, e, B, L )
,
y = f y (a, e, B, L )
fx, fy
–
(4.12)
:
,
–
/
,
.
,
4.5.
.
–
.
GPS
,
d − s = (d − s ') + (s '− s ) ,
(d-s’)
:
(4.13)
, (s’-s)
.
4.5.1.
–
,
,
,
. . d = s’
5
,
:
(d − s ') = 0
(4.14)
4.5.2.
–
-
.
-
,
,
22
500 – 1000 .
5000
,
.
4.5.3.
–
,
–

(s '− s ) = − H m − H o s +  H m − H o
Rm
 Rm
Hm =
Hi
Hi + Hk
,
2
Hk –
.
2

 s ,

(4.20)
H o = H izh = 0,
(4.21)
; Ho = 0
.
Ho = 0,
-
.
,
.
4.6.
GPS
.
,
–
.
–
.
2
:
1.
–
,
.
2.
,
.
;
,
.
.
(x1,y1)
(x2, y2),
,
:
23
2
2
 ∂f 
 ∂f 
mx2 =  x  mx21 +  x  m 2y1
 ∂x1 
 ∂y1 
,
2
2
 ∂f 
 ∂f 
m y2 =  y  mx21 +  y  m 2y1
 ∂x1 
 ∂y1 
(fx, fy)
.
(4.25)
,
4
4.8.
GPS
-
.
,
GPS
.
,
,
,
,
.
,
WGS-84,
,
.
,
.
,
,
.
,
(1-2
),
,
,
.
,
–
.
,
.
-
,
.
,
(
.
2
, GPS
.
)
-
,
,
.
24
,
,
GPS
.
,
.
GPS
.
,
.
5.
,
,
.
(
2),
-
–
.
,
,
.
,
, . .
–
.
,
.
-
.
.
GPS
3
,
,
.
5.2.
–
(control points)
,
.
325
,
,
(X, Y, Z).
5.2.1.
,
,
.
.
.
,
.
.
,
,
d.
,
:
d=
(∆X
2
)
+ ∆Y 2 + ∆ Z 2 ,
X,
Y
(5.14)
Z
.
md =
m∆ X =
(m
2
Xo
(m
2
∆X
mX, mY
mZ
+ mX j
∆Y
2
) ,m
=
:
)
+ m∆ Y + m∆ Z ,
2
(m
2
Yo
2
+ mY j
mXo, mYo, mZo, mXj, mYj
2
(5.15)
) ,m
=
∆Z
mZj
.
(m
.
2
Zo
+ mZ j
2
),
:
(5.16)
.
,
.
,
-
[29].
-
3 (
),
50%
/
2/
,
,
, . .
.
(
4),
:
∆ = t∆ ,
(5.17)
26
t
12 (
4
=0.95, t
3
3
,
.
6
)
).
2.19 (
3,
,
95%, t = 2.463.
-
6,
:
n
M =
∑m
i =1
2
d
,
n
(5.18)
m
,
ne
.
,
:
d ≤ ∆ (5.19)
.
,
.
2,
(
).
5.2.2.
,
,
.
,
3
,
.
,
.
,
,
(
6–
4.3).
-
4,
1.4
.
(
4,
4.4),
,
(
(
4,
2
)
4.5).
,
(
. 5.14)
0.1
,
5.2:
27
(∆N
d =
2
N, E
)
+ ∆E 2 + ∆H 2 ,
(5.20)
H
,
,
,
.
4,
(m
md =
2
∆N
5.15:
+ m∆E + m∆H
2
2
4.6,
)
(5.21)
,
(
5.2).
( -
5.17, 5.18
5.19),
.
-
(
2
).
5.2.3.
,
( -
W-
)
„
”
.
,
,
,
.
,
– -
,
,
.
:
-
, . .
;
;
,
. .
.
-
,
.
.
28
5.1 [88],
.
W
0.001
3.29
5.91
4.24
1D
2D
3D
. 5.1.
0.01
2.58
3.81
2.83
0.05
1.96
2.42
1.89
.
e
.
ij:
σ = J * Qij * J ,
J–
2
ij
T
(5.22)
, Qij –
i
j.
,
Qi
σ

Qi = σ Ei Ni
σ E H
 i i
2
Ei
Qj:
σEN
σ N2
σNH
i
σEH
σNH
σ H2
i
i
i
 σ E2
j

Q j = σ E j N j
σ
 E jH j


i i 

i 
i
i
i
σE N
σ N2
σN H
j
j
j
j
j


j j 

j 
σE H
σN H
σ H2
j
j
(5.23)
,
d( i
σ

σ Ei Ni
σ E H
Qij =  i i
 0
 0

 0
2
Ei
j :
σEN
σ N2
σNH
i
i
i
i
i
σEH
σNH
σ H2
i
i
i
i
i
0
0
0
0
0
0
0
0
0
0
0
0
σ E2
σE N
σE H
j
σE N
σ N2
σN H
j
j
j
j
j
j
j
j
j
0 

0 
0 

σ E jH j 
σ N jH j 

σ H2 j 
5.20)
(5.24)
:
 ∂d
J =
 ∂E
 i
∂d
∂N i
∂d
∂H i
∂d
∂E j
∂d
∂N j
∂d
∂H j


 ,

(5.25)
:
Ei − E j
∂d
∂d
=−
=
;
∂Ei
∂E j
d
3
Ni − N j
Hi − H j
∂d
∂d
∂d
∂d
=−
=
=−
=
(5.26)
; ∂H i
∂N i
∂N j
d
∂H j
d
:
29
T=
d
(5.27)
σ ij
<
3D
–
,
>
3D
–
.
5.2.4.
,
( -
)
5.2.3.
.
,
.
,
.
.
,
:
dH ij = H j − H i ,
Hj
σ
2
dH
Hi
=σ +σ
2
i
(5.28)
.
:
dH
2
j
(5.29)
:
,
W=
dH
(5.30)
σ dH
,
5.1.
> W
< W
–
1D
1D.
W
-
(x
d = ∆x 2 + ∆y 2 =
j
:
− xi ) + ( y j − yi )
2
,
2
(5.31)
:
(
)
(
)
(
∆x ∆y
 ∆x 
 ∆y 
σ =   σ x2i + σ x2j + 2
σ xi yi + σ xij \ yij \ +   σ y2i + σ y2j
d d
 d 
 d 
,
2
2
d
T2 D =
d
> T
2D
)
(5.32)
:
(5.33)
σd
T
2
2D
-
< T
2D
–
,
.
5.1.
30
5.2.5.
,
.
(2005)
.
,
:
∆X io = X io − X mo
∆Yi o = Yi o − Ymo
(5.34)
∆Z io = Z io − Z mo ,
Xmo, Ymo
Zmo
,
Xio, Yio
Zio
.
:
[∆X ] = 0
[∆X .∆X ] = min
o
i
o
i
(5.35)
o
i
,
.
-
(
)
.
:
-
,
Xmo, Ymo
Zmo –
;
-
(
-
),
.
-
Xmj,
Ymj
Zmj;
Xm, Ym
∆X m = X − X
j
m
Zm
∆Ym = Yi j − Ymo
∆Z m = Z i − Z
j
:
o
m
(5.36)
o
m
,
:
31
X ij
Yi j
Zi
(1)
(1)
j (1)
= X i j + ∆X m
X mj
= Yi o + ∆Ym
Ymj
(1)
(1)
j (1)
= Z io + ∆Z m
Zm
= X mo
= Ymo
(5.37)
= Z mo
:
∆X i jo = X i j
∆Yi jo = Yi j
∆Z i jo = Z i
(1)
(1)
j (1)
− X io
− Yi o
(5.38)
− Z io
),
(
.
:
∆ ≤ 2 ∆ ,
(5.39)
–
,
:
∆ = a 2 + (b × R )
2
(5.40)
,
–
,
(5
), b –
R –
.
,
∆ ( X ,Y , Z )
=
:
∆ 3
∆ = σ x2 + σ y2 + σ z2
-
(5.41)
,
(5.39),
,
,
,
.
.
5.3.
5
5.7
5-
.
,
.
,
,
,
(
-
.
2-
,
,
Zlat
6
6- )
4 5.
,
32
. .
50%
,
.
6-
,
28-
:
,
.
,
(
5
),
,
,
.
,
,
,
;
95%
5.2.3.
5.2.4.
13,
4
5, 4
5
-
,
.
.
,
,
< 1.4
,
;
-
,
3
(11
-
23
– 13%.
-
13 ),
(
265-
1.4
–
-
-
,
).
4 .
4
5
,
,
-
.
,
. .
(
),
,
;
-
,
–
,
-
.
2,
Zlat
.
.
,
.
(
5
)
33
,
.
,
(
)
.
.
:
6
(
,
3.8
Zlat,
)
;
,
,
–
.
2- , 4-
81% (22
27
2-
).
5-
.
-
5- ,
5
-
,
Zlat
4
6- ,
5.
.
6.
-
,
,
.
,
.
.
±5
,
(
3, . 3.7
).
.
34
,
.
6.1.
III
,
6.1,
.
Sokkia SDL30
1.0
/
.
2
.
. 6.1
,
(
5.2.6.
5,
),
,
,
0.81 – 1.54
/
, . .
.
±3.4
,
401, 501 601.
–
.
,
10-40
/
,
,
95% (
,
2.1
∆H min 10
=
= 5mm
t
2
∆ H min
= 2 m H2 ⇒ m H i =
≈ 3.54 mm
t 2
):
m ∆H ≤
(6.1)
m∆2H
(6.2)
35
6.2.
Leica,
Thales Pro Mark 3,
4 /
System 900
/
3/
/
,
20
,
10
10 .
3,
3.6
3.6.3.
6.2:
. 6.2.
GPS
17
,
14.11.2009 .,
6
6.
.
(3.52),
,
136
,
(
3.53):
 n (n − 1)

n (n − 1)
v=
= 136 baselines ⇒ s = int 
+ 0.75  ≈ 23
2
 2(R − 1)

,
- 3.54,
,
2
3.
58
(174
5
1,
2
3,
2
23
(6.3)
4
1,
10,
),
(3
):
n
=   +1 ≈ 4
R
(6.4)
.
(
,
)
5
.
36
-
6.2,
.
(N,E)
H
.
6.3.
.
–
,
,
.
,
.
18
28
(
).
,
-
1
:
-
5
-
(
-
7–
9
–
5);
(
17 –
;
21 –
-
);
801
901 –
.
–
,
,
.
(
101
901)
-
–
411
511.
–
,
,
(
),
.
:
. .
dH = H ik − H io
2
mdH
= mH2 k + mH2 o
i
dH –
i
,
.
(6.5)
i
; Hik –
i
;
o
i
–
;
37
mdH –
. . .
0
- ; mHik
- mHi –
. . .
.
,
d = dH GPS − dH LEV
. . .
2
2
md2 = mdH
GPS + m
dH LEV
:
,
(6.6)
d –
GPS
GPS
LEV
(dH )
. . .
(dH
); md –
. . .
GPS (mdHGPS)
,
(mdHGPS)
;
:
n
pdi =
c
,
md2i
µ=
n–
1 n
pdi d i2
∑
2 n i =1
c=
∑m
2
di
1
n
,
(6.7)
.
(6.8)
–
,
(
).
6.3,
.
6.4.
–
цикъл
25.02.2010 - цикъл 6
16.04.2010 - цикъл 8
12.06.2010 - цикъл 10
23.07.2010 - цикъл 11
08.08.2010 - цикъл 12
19.10.2010 - цикъл 14
13.11.2010 - цикъл 15
………………………..
20.07.2011 - цикъл 22
15.09.2011 - цикъл 23
14.10.2011 - цикъл 24
19.11.2011 - цикъл 25
11.12.2011 - цикъл 26
14.01.2012 - цикъл 27
19.02.2012 - цикъл 28
LEV
d
-1.60
-3.80
1.20
-3.90
-0.80
-4.50
-5.40
……..
-8.20
-9.30
-12.00
-12.60
-12.00
-13.90
-14.50
801
dGPS
-3.20
-8.00
-6.10
-1.55
-2.22
-10.50
-7.10
………..
-13.80
-16.30
-13.50
-16.90
-13.60
-19.50
-10.80
d
-1.60
-4.20
-7.30
2.35
-1.42
-6.00
-1.70
………
-5.60
-7.00
-1.50
-4.30
-1.60
-5.60
3.70
mdmid=
901
d
dGPS
4.72 1.0 -1.40 -1.20
5.58 0.7 -3.40 -5.50
5.09 0.9 1.90
-5.30
5.47 0.8 -2.50 -1.20
4.32 1.2 0.00
-2.20
4.78 1.0 -4.00 -5.40
4.50 1.1 -4.70 -3.40
……… …… ………. ………
5.38 0.8 -6.00 -10.10
4.42 1.2 -6.40 -10.70
4.22 1.3 -7.90 -8.10
4.60 1.1 -8.80 -9.50
4.70 1.0 -8.40 -8.00
5.07 0.9 -9.80 -12.90
4.77 1.0 -10.50 -6.50
mdi
4.8
pdi
mm
LEV
d
0.20
-2.10
-7.20
1.30
-2.20
-1.40
1.30
………
-4.10
-4.30
-0.20
-0.70
0.40
-3.10
4.00
mdi
pdi
4.45
5.40
4.83
5.08
3.90
4.55
4.33
………
5.07
4.36
4.33
4.51
4.50
4.81
4.37
1.0
0.7
0.9
0.8
1.4
1.0
1.1
…..
0.8
1.1
1.1
1.0
1.0
0.9
1.1
mdmid=
4.5
mm
38
6.4.
6
.
28
.
27
17.06.2009 – 19.02.2012 .,
.
,
18
.
:
-
,
,
– -
.
6.2.
;
,
6.3.
. . . –
, . .
6.4,
;
39
-
-
„
”
,
;
-
,
:
o
3
-
–
3,
(
3.7),
o
;
,
;
-
o
,
-
,
-
–
,
(
0.6
);
,
o
;
GPS
o
,
;
o
,
.
7.
,
„
”
,
,
3
.
,
,
„
-
”.
,
,
:
40
ε x 
 
ε = ε y 
ε 
 z
γ xy 
 
γ = γ yz 
γ 
 xz 
(7.5)
U,V
W,
.
:
∂U
∂x
∂V
εy =
∂y
∂W
εz =
∂z
∂U ∂V
+
∂y
∂x
∂V ∂ W
=
+
∂z
∂y
∂W ∂U
=
+
∂x
∂z
γ xy =
εx =
γ yz
γ xy
(7.6)
,
[24].
,
Tε =
:
εx
1
γ yx
2
1
γ xy
2
1
γ xz
2
-
εy
1
γ yz
2
1
γ zx
2
1
γ zy
2
(7.7)
εz
:
ε n = ε x λ + ε y µ + ε zν + γ xy λµ + γ yz µν + γ zxνλ
,
:
2
2
ε n = ε x λ + ε y µ + γ xy λµ
–
,
V '−V
e=
,
V
V–
,
2
2
2
(7.8)
XY,
(7.9)
:
(7.10)
V’ –
.
dx, dy
e = (1 + ε x )(1 + ε y )(1 + ε z )
dz,
XYZ,
:
(7.11)
,
(
10
-3
-
),
7.11
2
:
,
41
e = εx +εy +εz
(7.12)
,
:
e
xy
= εx +εy
e yz = ε y + ε z
(7.13)
e = εx +εz
xz
,
,
,
,
:
(ε x − ε n )λ + 1 γ yx µ + 1 γ zxν
=0
2
1
1
γ xy λ + (ε y − ε n )µ + γ zyν = 0
2
2
1
1
γ xz λ + γ yz µ + (ε z − ε n )ν = 0
2
2
2
(7.14)
:
λ + µ +ν = 1
,
2
2
2
(7.15)
,
:
(ε x − ε n )λ + 1 γ yx µ + 1 γ zxν
2
2
1
1
det γ xy λ + (ε y − ε n )µ + γ zyν = 0
2
2
1
1
γ xz λ + γ yz µ + (ε z − ε n )ν
2
2
(7.16)
,
n,
:
ε − J 1ε n2 + J 2ε n − J 3 = 0 ,
3
n
(7.17)
Jn
:
J1 = ε x + ε y + ε z
J 2 = A11 + A22 + A33
(7.18)
J 3 = det (Tε )
XY
,
,
.
:
ε − J 1ε n + J 2 = 0 ,
2
n
(7.19)
42
Jn
:
J1 = ε x + ε y
(7.20)
J 2 = det (Tε )
:
γ xy
,
εx −εy
tan 2Θ =
(7.21)
.
7.2.
.
–
)
411
9(
-
,
101
901
2(
–
-
)
511.
6,
401
501
-
.
,
.
7.8,
n–
x, y , z ,
(7.7);
, , –
:
;
xy
,
yz
,
xz
–
–
.
6 (
.
(7.8)
)
6 (
),
,
,
.
,
(
„
”
4, 5
6
„
901).
101
” – 1, 2
3.
5
4,
.
6
,
411
511
, . .
.
43
7
1,
2,
3,
5,
6,
411
,
511.
.
,
,
,
,
,
(
101
901).
3 (
)
,
.
5/14.11.2009 .,
25/19.11.2011 .
11/23.07.2010
4
5
., 19/23.04.2011 .
.
,
.
N
point
101
201
301
401
501
601
701
801
901
εxx,
.10-3
-0.06
0.01
0.02
0.07
0.06
0.06
0.03
-0.03
-0.06
цикъл 25/19.11.2011
εyy,
εzz,
γxy,
γyz,
γxz,
mεxx
mεzz
m γxz
-3 mεyy
-3
-3 m γxy
-3 m γyz
.10
10
10
10
10-3
0.02 0.03 0.01 -6.81 0.35 -0.03 0.01 -0.12 0.22 1.79 0.52
0.01 0.02 0.00 -2.86 0.20 -0.04 0.01 0.47 0.22 0.51 0.33
0.02 0.02 0.00 -2.32 0.24 0.06 0.01 0.02 0.35 0.29 0.41
0.02 0.02 0.01 2.06 0.41 0.07 0.01 -0.56 0.07 -1.28 0.20
0.01 0.01 0.01 2.04 0.31 0.06 0.02 -0.41 0.09 -1.07 0.13
0.01 0.00 0.01 1.14 0.09 0.03 0.02 -0.14 0.14 -0.86 0.16
0.00 0.00 0.00 0.14 0.06 0.00 0.01 0.17 0.04 -0.22 0.09
0.01 -0.01 0.02 -2.79 0.29 -0.05 0.02 0.53 0.43 1.01 0.29
0.01 0.01 0.03 -3.68 0.65 -0.06 0.03 0.30 0.79 1.56 0.46
Изчисляване на обемните деформации в цикъл 25/19.11.2011г.
me
0.35
0.20
0.24
0.41
0.31
0.09
0.06
0.29
0.65
44
2D представяне на повърхнината на обемните деформации в цикъл 25/19.11.2011г.
H
N
E,
,
,
.
.
,
NE,
(7.13)
(7.19).
цикъл 25/19.11.2011
N
εxx,
εyy,
εmin,
εmax,
Θ,
γxy,
mεxx
-3
-3 mεyy
-3
-3
-3 m γxy
point .10
.10
10
10
[deg]
10
101
-0.03 0.02 0.01 0.00 -0.02 0.01 -0.0363 0.0662 0.75
201
0.01 0.00 0.00 0.00 0.00 0.00 -0.0505 0.0253 0.78
301
0.02 0.01 0.01 0.00 -0.01 0.01 -0.0791 0.0385 359.22
401
0.02 0.01 0.00 0.00 0.01 0.01 -0.1206 0.0299 0.78
501
-0.01 0.00 0.00 0.00 -0.01 0.00 -0.0965 0.0282 0.78
601
-0.02 0.00 0.01 0.00 0.01 0.00 -0.0690 0.0113 0.78
701
-0.01 0.00 0.00 0.00 0.01 0.00 -0.0264 0.0049 0.75
801
0.01 0.01 -0.06 0.02 -0.02 0.02 -0.0345 0.0730 0.78
901
0.03 0.02 0.00 0.07 0.04 0.05 -0.0408 0.0929 0.78
Изчисляване на площните деформации в цикъл 25/19.11.2011г.
me
0.002
0.002
0.008
0.006
0.010
0.008
0.001
0.003
0.003
45
2D
25/19.11.2011 .
7.3.
7
4
,
5
.
.
,
.
,
.
.
–
.
5
,
,
,
, . .
.
46
,
.
,
-
,
.
8.
,
,
,
,
.
,
.
.
8.1.
,
,
.
,
,
“
”.
.
.
-
,
.
.
Y.
Y
X.
,
.
,
.
8.2.
X1, X2,….,Xn
Y
.
47
.
–
,
,
. .
,
:
y = f ( x1 , x2 ,..., xn ; a1 , a2 ,...an ) ,
f–
, ai –
.
(8.1)
,
:
X1, X2,…., Xn
;
Y
Y
.
8.3.
-
SPSS
,
,
.
.
6 /
(
),
(N, E, H)
,
25.02.2010 – 19.02.2012
,
–
/
.
,
101 – 901,
(
F11
F91,
).
,
(
:
,
),
–
1
.
.
–
,
,
.
8.2
,
.
,
.
:
1.
,
48
,
.
9/
/
,
.
1.1.
:
,
0.7).
(
,
-
.
.
,
,
.
,
,
.
,
0.05 (Sig.< 0.05)
.
,
,
95%.
0.05 (
0.10), Sig.
,
.
,
8.3,
„ ”
„ ”
:
101
201
301
401
501
601
701
801
901
weight_mat
weight_water
move_H
move_E
move_N
F(
)
8.2.
,
„
”
„
”
.
,
7
401
801
901
-
.
101 –
–
,
.
„
F51 – F71
”,
.
–
/
(
7.4
).
49
1.2.
,
.
, . .
.
8.4:
0.
–
,
8.4.
-
–
.
,
,
KMO
,
0.5
, . .
“
101
N,E
Determin
KMO
Bartlet
H
Determin
KMO
Bartlet
.
201
301
401
501
”.
601
701
801
901
0.004
0.615
0.000
0.016
0.696
0.000
0.017
0.637
0.000
0.011
0.636
0.000
0.000
0.670
0.000
0.000
0.743
0.000
0.000
0.826
0.000
0.037
0.694
0.000
0.035
0.718
0.000
0.004
0.734
0.000
0.006
0.525
0.000
0.012
0.571
0.000
0.002
0.753
0.000
0.000
0.676
0.000
8.3
0.000
0.837
0.000
0.001
0.709
0.000
0.019
0.693
0.000
0.028
0.697
0.000
-
,
.
2.
–
.
,
.
8.5,
–
.
„Total Variance Explained”
.
100 %,
2
90%,
,
,
.
„Factor Matrix”
.
,
.
-
,
-
,
.
0.5,
.
,
50
„
”
,
-
–
.
„Rotated Factor Matrix”
.
,
.
,
.
,
,
Varimax
,
„
”
.
.
3.
(
) –
,
dH, dE
weight_water).
3.1.
:
•
dN,
(dF, weight_mat,
,
.
.
•
•
.
,
.
•
,
.
.
-
95%
•
ANOVA)
•
:
,
F
< 0.05;
R2
R
-
•
•
•
(
1
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(
SPSS
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:
(
.
);
-
.
,
.
51
.
.
,
.
3.2.
8.6
8.7,
–
.
(dH, dE
dN)
(dF, weight_mat,
.
weight_water),
dH = b0 + b1dE + b2 dN + b3 dF + b4 weight _ mat + b5 weight _ water
(8.13)
(
8.6).
-
:
:
Model Summaryb
Std. Error of the
Model
R
R Square
Adjusted R Square
Estimate
a
1
,902
,814
,765
2,09953
a. Predictors: (Constant), LINT(F11), LINT(move_101E), LINT(move_101N),
LINT(weight_water), LINT(weight_mat)
b. Dependent Variable: LINT(move_101H)
-
,
:
b
ANOVA
Sum of
Mean
Model
Squares
df
Square
F
Sig.
1
Regression
366,084
5
73,217
16,610
,000a
Residual
83,752
19
4,408
Total
449,836
24
a. Predictors: (Constant), LINT(F11), LINT(move_101E), LINT(move_101N),
LINT(weight_water), LINT(weight_mat)
b. Dependent Variable: LINT(move_101H)
52
:
Unstandardized
Coefficients
Std.
B
Error
-8,980
1,411
,000
,000
Coefficientsa
Standardized
Coefficients
Model
1 (Constant)
LINT(weight_
mat)
LINT(weight_
,000
,000
water)
LINT(move_10
-,454
,212
1E)
LINT(move_10
-,010
,151
1N)
LINT(F11)
-,016
,195
a. Dependent Variable: LINT(move_101H)
Beta
t
-6,365
-1,028 -2,459
,379
Sig.
,000
,024
95.0% Confidence
Interval for B
Lower
Upper
Bound
Bound
-11,933
-6,027
-,001
,000
1,103
,284
,000
,000
-,315 -2,141
,045
-,898
-,010
-,014
-,066
,948
-,326
,306
-,011
-,081
,936
-,424
,392
,
.
(
)
,
,
dH = b0 + b1dF1 + b2 dF2
dH = b0 + b1dF1
:
(8.14)
(8.15)
(8.14)
(8.15)
.
-
:
Variables Entered/Removedb
Model
Variables Entered
Variables Removed
1
REGR factor score 1 for
.
analysis 1
a. All requested variables entered.
b. Dependent Variable: LINT(move_101H)
Method
Enter
:
Model Summaryb
Model
R
R Square
Adjusted R Square
a
1
,853
,727
,715
a. Predictors: (Constant), REGR factor score 1 for analysis 1
b. Dependent Variable: LINT(move_101H)
Std. Error of the
Estimate
2,31166
53
-
,
:
b
ANOVA
Model
Sum of Squares
df
Mean Square
1
Regression
326,930
1
326,930
Residual
122,907
23
5,344
Total
449,836
24
a. Predictors: (Constant), REGR factor score 1 for analysis 1
b. Dependent Variable: LINT(move_101H)
F
61,179
Sig.
,000a
:
Coefficientsa
Unstandardized
Standardized
Coefficients
Coefficients
B
Std. Error
Beta
-15,412
,462
-3,693
,472
-,853
Model
1
(Constant)
REGR factor score 1
for analysis 1
a. Dependent Variable: LINT(move_101H)
t
-33,335
-7,822
Sig.
,000
,000
:
dH = −15.412 − 3.693dF1
-
–
,
,
0
0.979:
-
,
45
,
:
54
:
,
,
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901
301, 801
501
701
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,
:
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„
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.,
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.,
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, 2012.
– 2013.
68