atw 2017-06

atw Vol. 62 (2017) | Issue 6 ı June
RESEARCH AND INNOVATION 410
| | Fig. 2.
Nodalization for the primary system of AP1000.
compared with the results of
LOFTRAN, such as pressure, flow rate
etc. The comparison results show that
RELAP5 has the capability to predict
the system parameters [11] correctly.
Among above these parameters, the
reactor coolant temperature is the
most important parameter for the
PRHRS loop, as shown in Figure 3.
As depicted in Fig. 3, the results of
RELAP5 and LOFTRAN exhibit the
same trend. A similar value of maximum
temperature has been observed
in the two results. During the accident,
however, a difference in the sequence
of events and response of the reactor
control system can lead to a slight
difference in the temperature trend.
This has no significant influence on
the analysis.
3 Calculation methods
3.1 Latin hypercube sampling
Latin Hypercube Sampling (LHS) [16,
17] is an improvement over the traditional
Monte Carlo sampling method.
It can overcome its drawbacks, in that
most of sampled results lie near the
average value. In order to improve the
accuracy of the parameters, therefore,
the method covers the upper and
lower limits of the distributions.
Hence, this method has the ability to
determine any value, as long as the
parameters are known. The steps are
as follows.
(1) For each variable, the probability
distribution is divided into N nonoverlapping
equal probability
interval [0, 1/N], [1/N, 2/N],…,
[(N-1)/N, 1]. This ensures that
the degree of the correlation of
LHS is small.
(2) The random standard normal
sample matrix Z N×n is used to
represent the order of sample
points, and the integer matrix
R N×n is used to record information
regarding the ordering of the
above sample points. Hence,
R ij = k shows that the sequence
of the j th variable in the i th sampling
is k.
(3) According to in each interval, the
cumulative probability function
of each sample point in the Latin
hypercube can be obtained randomly,
as shown in Eq. (1).
(1)
Here, i = 1,..., N and j = 1,..., n.
The function r a n d (0,1) represents
a random number, which is
uniformly distributed in the [0,1]
interval.
(4) In the Latin hypercube, the sampling
points are obtained by the
method of equal probability
change, as shown in Eq. (2).
(2)
Here, φ –1 (.) is the inverse normal
distribution function.
3.2 Grey Relation Method
The Grey Relational Method [8] is a
quantitative technique for comparative
analysis. The basic idea is to determine
the exponent of each factor in
the correlation, according to their
degree of similarity with the geometry
of sequence curve. If the curve is close
for a particular factor, it would have a
high exponent in the correlation. X 0 is
defined as the target parameter, with
k referring to the sequence of the
parameter, denoted as {X 0 (k)}. It is
assumed that there are a total of m
control parameters, and a parameter j
in the same sequence k is called the
comparison sequence, denoted as
{X j (k)} (k = 1,…, N)(j = 1,…, m). In
this correlation, the exponent of each
factor can be obtained by comparing
the tendency of development between
the target and influence parameters.
These steps are shown as follows [18].
(1) The reference and comparison sequences
are normalized, as shown
in Eq. (3).
(3)
(2) The absolute value of difference
between the reference and the
comparison sequences is calculated
as Eq. (4) based on above normalization
results.
(4)
a) Results of RELAP5. b) Results of LOFTRAN.
| | Fig. 3.
Reactor coolant temperature.
(3) Maximum and minimum absolute
values are calculated shown as
Eq. (5)-(6).
(5)
(6)
Research and Innovation
Reliability Analysis on Passive Residual Heat Removal of AP1000 Based on Grey Model ı Qi Shi, Zhou Tao, Muhammad Ali Shahzad, Li Yu and Jiang Guangming