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For x ij
,if it has p evaluate grades and evaluation grade
space denoted by U, then U ={c 1 ,c 2 , … ,c p }, if c k is
"higher" than c k+1 , denoted by c k > c k+1 (k=1,2,…,p-1) .
In the drilling risk evaluation, the evaluation grade can be
divided into 5 grades,i.e. low risk, lower risk, medium
risk, higher risk, high risk. The evaluation set is as
follows: {c 1 ,c 2 ,c 3 ,c 4 ,c 5 }={ low risk, lower risk, medium
risk, higher risk, high risk }. Suppose μ =
ijk μ ( xij
∈ c
k )
indicates measured value x ij
has the degree of evaluation
level c k ,Then μ is called to be unascertained measure
function, measure for short. Calling the matrix:
⎡μi11 μi 12
L μi 1p
⎤
⎢
⎥
μi21 μi22 μi2
p
( μ
⎢ L
ijk ) =
⎥
m×
p ⎢ M M M M ⎥
⎢
⎥
⎢⎣μim 1
μim2
L μimp
⎥⎦
is single-index evaluation matrix.
2) Structure unascertained measure function :
Geological factor includes two second-level indexes. In
order to evaluate facilitately and make evaluation results
more accurate, take representative data of each indicator
as a classification criteria of evaluation level. See Table 2.
Single-index measure functions of two indexes of
geological factor like Figure 2 and Figure3 respectively.
In addition to geological factors, the indexes contained
in engineering factors are qualitative factors, using
experts scoring method to determine risk value of each
index. Approach is to get indexes assignment interval
[0,100] and numbers in interval indicate security status of
indexes, moreover the higher score standing for higher
level of security. Inserting four points in the interval
[0,100], thus the interval is divided into five risk levels,
i.e. low risk, lower risk, medium risk, higher risk, high
risk. See Table 3. Single-index measure function of
engineering factors like Figure 4.
According to the characteristics of specific issues as
well as variation degree of state ,we can assume different
curves ,for example linear, quadratic curve, sine curve or
exponential etc. ,to construct the specific expression of
measure function .
3) Multi-index measure:Suppose that w j indicates
important degree of I relative to other index, that
j
is to be weight of index I j
.If μik
satisfies: 0 ≤ μ ik
≤ 1 ,
m
μ = ∑ w μ , μ
ik
is unascertained measure,
ik j ijk
j=
1
⎡ μ11 μ12 L μ1
p ⎤
⎢
⎥
μ
21
μ
22
μ
2 p
( μ
⎢ L
ik ) =
⎥
n×
p ⎢ M M M M ⎥
⎢
⎥
⎢⎣
μ
n1 μ
n2 L μ
np ⎥⎦
is multi-index measure matrix of comprehensive
evaluation.
4) Confidence criteria for identification:In order to
make final evaluation results of object evaluated,
introduce the evaluation criteria of "confidence".
Suppose λindicate confidence(takeλ=0.6 or 0.7),
k
⎛
⎞
k0
= min ⎜k: ∑ μl
> λ, k = 1, 2, L,
p⎟
⎝ l=
1
⎠
then judge drilling safety belonging to kth evaluation
grade[4-6].
IV. PRACTICAL APPLICATION
Taking Yanchang Oilfield 21 Well as an example,
unascertained measure model is adopted to evaluate
comprehensively. The type of this well is straight,
designedd well depth is 2776m.
Engineering factors x2 contains eight indicators.
Through expert analysis of engineering factor of this well,
measured values of eight indicators is gained. See Table 4.
Substituting index values into single-index measure
function of Figure 4. For example, x21=82 is substituted
1
into the equation y = ( x−85)
and gain that
75 −85
index measure value is 0.3, that is, safety degree of well
profile belonging to c3 is 0.3, then according to
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