In integrated deterministic and probabilistic safety analysis (IDPSA),
safe scenarios and prime implicants (PIs) are generated by simulation. In this paper,
we propose a novel postprocessing method, which resorts to a risk-based clustering method
for identifying Near Misses among the safe scenarios. This is important because the possibility
of recovering these combinations of failures within a tolerable grace time allows avoiding
deviations to accident and, thus, reducing the downtime (and the risk) of the system. The
postprocessing risk-significant features for the clustering are extracted from the following: (i)
the probability of a scenario to develop into an accidental scenario, (ii) the severity of the
consequences that the developing scenario would cause to the system, and (iii) the combination of
(i) and (ii) into the overall risk of the developing scenario. The optimal selection of the extracted
features is done by a wrapper approach, whereby a modified binary differential evolution (MBDE) embeds
a
Integrated deterministic and probabilistic safety analysis (IDPSA) attempts to overcome some limitations of deterministic safety analysis (DSA) and probabilistic safety analysis (PSA). The former is solidly founded on the multibarrier and defense-in-depth concepts and aims at verifying the capability of a nuclear power plant (NPP) to withstand a set of postulated design basis accidents (DBA) [
Both DSA and PSA are scenario-based analyses, where scenario selection and definition are done by expert judgment. State of the art of DSA and PSA approaches can provide relevant and important insights into what is already known to be an “issue,” but they are not capable of revealing what, and to what extent, is not known (i.e., scenarios which are not expert-selected in the DSA and PSA inputs), with the risk of neglecting or underestimating potentially dangerous scenarios [
The development and application of IDPSA in practice must meet the challenge of computational complexity, in both model construction and implementation and in postprocessing for the retrieval of the relevant information from the scenario outcomes. The number of dynamic scenario branches generated in IDPSA increases in power law with the number of occurring events and, thus, is much larger than in classical PSA based on event trees (ET) and fault trees (FT). The a posteriori information retrieval (postprocessing) then becomes quite burdensome and difficult [
Postprocessing, in general, consists in classifying the generated dynamic scenarios into safe scenarios and prime implicants (PIs), that is, sequences of events that represent minimal combinations of accident failures necessary for system failure and cannot be covered by more general implicants [
In the literature, several authors introduce the concept of Near Misses as accident precursors [
The postprocessing analysis entails a “Forward” classification of the dynamic scenarios into classes, that is, safe, PIs, and Near Misses and a “Backward” identification of the similarities of the features of the scenarios (i.e., stochastic event occurrence and deterministic process variables values), which characterize the groups of Near Misses among the whole set of safe scenarios.
For the “Forward” classification of the Near Misses sequences, we look at two factors of risk: the probability of occurrence of an undesired event and the severity of the consequence caused by the event [
The optimal features for discerning the Near Misses from the safe scenarios are extracted from the profiles of
The outcomes of this “Forward” classification is, then, interpreted by a “Backward” identification of the similarities of the features of the Near Misses scenarios: the acquired knowledge can be exploited in an online integrated risk monitoring system that can rapidly detect the problem and set up a repair strategy of the occurring failures before the system reaches a fault state.
The proposed approach is illustrated with reference to scenarios occurring in the steam generator (SG) of a NPP [
The paper is organized as follows. In Section
The U-tube steam generator (UTSG) under consideration is sketched in Figure
Schematic of the UTSG [
The reactor coolant enters the UTSG at the bottom and moves upward and then downward in the inverted U-tubes, transferring heat to the secondary fluid before exiting at the bottom. The secondary fluid, the feedwater (
“Swell and shrink” phenomena are also modeled to reproduce the dynamic behavior of the SG: when
The
The incoming water flow rate
Parameters of the UTSG model at different power levels [
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36 | 56 | 63 | 44 | 40 | 40 | 40 |
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13 | 18 | 10 | 4 | 4 | 4 | 4 |
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170 | 56 | 30 | 10 | 8 | 5 | 5 |
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10 | 10 | 10 | 30 | 30 | 30 | 30 |
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10 | 10 | 10 | 10 | 10 | 10 | 10 |
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140 | 140 | 140 | 140 | 140 | 140 | 140 |
The exiting steam-water mass
Combining (
We assume
The goal of the system is to maintain the SG water level at a reference position (
Set point for
A dedicated model has been implemented in SIMULINK to simulate the dynamic response of the UTSG at different
Block diagram representing the SIMULINK model of the SG.
The set of multiple component failures that can occur during the system life are shown in Figure The outlet steam valve can fail stuck at a random time in The safety relief valve can fail stuck at a random time in The communication between the sensor that monitors The PID controller can fail stuck at random times in
It is worth noticing that in the UTSG there are two PID controllers and, thus, two communications between the sensors measuring
Sketch of the failures that can be injected into the system.
Choices and hypotheses for modeling the failures (i.e., the mission time, the number and type of faults, the distributions of failure times, and magnitudes) have been arbitrarily made with the aim of generating multiple failures in the sequences and capturing the dynamic influence of their order, timing, and magnitude. The choice of a mission time (
For realistically treating the dynamic behavior of the UTSG when component failures occur, we go beyond the binary state representation and adopt a multiple value logic (MVL) [ time discretization: we use the labels magnitude discretization:
the steam valve magnitude is indicated as 1, 2, or 3 for failure states corresponding to stuck at 0%, stuck at 50%, and stuck at 150% of the the safety relief valve fails with magnitude indicated as 1, 2, 3, and 4, if it is stuck between the communication between the sensor measuring the PID controller failure magnitude range is discretized into 8 equally spaced magnitude intervals, labelled from 1 to 8, representative of failure states corresponding to discrete intervals of output value belonging to
The values of time and magnitude and order of failure occurrence for each component are included into a sequence vector that represents a scenario. As an example, the sequence vector of Figure
Sequence vector representing a scenario.
The number of possible sequence vectors that arise from the MVL discretization is 100509, each one evolving towards either safe or faulty conditions. To investigate this, a Monte Carlo-driven fault injection engine is used to sample combinations of discrete times and discrete magnitudes of components failures.
The (dynamic) analysis has been performed with respect to the two constant power scenarios, 5%
System configurations.
System |
Failure of the |
Failure of the |
Level sensor-PID controller |
Failure of the |
---|---|---|---|---|
1 | — | — | — | — |
2 | X | — | — | — |
3 | — | X | — | — |
4 | — | — | X | — |
5 | — | — | — | X |
6 | X | X | — | — |
7 | X | — | X | — |
8 | X | — | — | X |
9 | — | X | X | — |
10 | — | X | — | X |
11 | — | — | X | X |
12 | X | X | X | — |
13 | X | X | — | X |
14 | X | — | X | X |
15 | — | X | X | X |
16 | X | X | X | X |
The dynamic analysis shows that the same combination of components failures does not unequivocally lead to only one system end state but rather it depends on when the failures occur and with what magnitude. This is shown in Figure
Histograms for high power level (a) and low power level (b) of the frequencies of occurrence of the end states for each of the 16 system configurations of Table
Figure 1052 seconds (solid line), 1063 seconds (dashed-dotted line).
The two scenarios lead to low and high failure modes, respectively, whereas they would be considered as minimal cuts sets (MCS) in a static reliability analysis presented in Appendix
Example of dynamic system behavior at 80%
Figure magnitude equal to 13% of the nominal magnitude equal to 12% of the nominal 1046 seconds (dashed-dotted line), 1047 seconds (solid line). The PID controller failure is the first failure event along the sequence of events (dashed-dotted line). The safety relief valve failure is the first failure event along the sequence of events (solid line).
The low power scenarios also present dynamic effects, as shown in Figure
Figure
Hereafter, without loss of generality, among the system configurations of Table
Example of dynamic system behavior at 5%
The Near Misses identification is here treated as a classification problem, in which Near Misses are sorted out from the safe scenarios, among the whole set of accidental transients simulated. In practice, the PIs are first identified among the whole set of 100509 possible scenarios and, then, the Near Misses are separated out among the remaining safe scenarios.
A PI is a set of variables that represents a minimal combination of accident component failures necessary for system failure and cannot be covered by a more reduced implicant [
The PIs identification among the whole set of 100509 possible scenarios is performed by means of the visual interactive method presented in [
Once the (1255) PIs for the SG high level failure mode have been identified, they are removed from the set of all possible scenarios, which is left with 64381 safe scenarios. For the identification of Near Misses among these, we resort to their definition as sequences of failure events that indeed keep the system in a safe condition but endangered (i.e., a quasifault system state). To this aim, we introduce a risk-based characterization of these remaining scenarios, calculating their associated risk, at each time instant
In this view, we build a functional relationship such that
Probability function
The consequence
Matrix representation of the intensity coefficient
By so doing, the available 64381 remaining safe scenarios are fully described at each time instant solid line: the PID controller fails at 100 (s) with magnitude 4 and the safety relief valve fails at 190 (s) with magnitude 2; dashed-dotted line: the safety relief valve fails at 100 (s) with magnitude 1, the communication between the sensor measuring
It is worth analysing the behavior of
Probability
The identification of the Near Misses is treated as an unsupervised classification problem and addressed by clustering, where (i) the number of clusters is unknown and (ii) the features that enable the best clustering according to the risk-based characteristic profiles of mean value: peak value: standard deviation: root mean square: skewness: kurtosis:
where
We resort to a wrapper framework [
Wrapper approach for optimal feature subset selection based on a MBDE optimization algorithm and a
The CH index for a number
The optimal features selection provides as best features the standard deviation of
The
Clustering results.
Once the Near Misses for the SG high level failure mode have been identified by clustering, we can search for similarities among them in terms of their multiple value sequences, that is, order and timing of event occurrences and deterministic process variables values. This “Backward” approach can lead us to finding the minimum conditions, that is, minimum
List of the Pareto-optimal
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Steam valve failure time | Steam valve failure magnitude | Steam valve failure order | Safety valve failure time | Safety valve failure magnitude | Safety valve failure order | Sensor-PID failure time | Sensor-PID failure magnitude | Sensor-PID failure order | PID failure time | PID failure magnitude | PID failure order |
---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0 | 0 | 0 | 2 | 3 | 1 | 4 | 1 | 2 | 4 | 3 | 3 |
2 | 3 | 1 | 4 | 1 | 2 | 3 | 1 | 1 | 2 | 1 | 4 | 1 |
3 | 3 | 1 | 4 | 2 | 2 | 3 | 2 | 1 | 1 | 2 | 4 | 2 |
4 | 3 | 1 | 3 | 2 | 2 | 2 | 4 | 1 | 4 | 1 | 4 | 1 |
5 | 3 | 1 | 4 | 3 | 3 | 3 | 2 | 1 | 2 | 1 | 4 | 1 |
6 | 3 | 2 | 4 | 1 | 2 | 2 | 1 | 1 | 3 | 1 | 4 | 1 |
7 | 3 | 2 | 4 | 2 | 3 | 1 | 2 | 1 | 2 | 3 | 3 | 3 |
8 | 4 | 1 | 3 | 3 | 2 | 2 | 4 | 1 | 4 | 2 | 4 | 1 |
9 | 4 | 2 | 3 | 1 | 3 | 2 | 0 | 0 | 0 | 1 | 3 | 1 |
10 | 4 | 2 | 4 | 2 | 1 | 3 | 2 | 1 | 1 | 2 | 4 | 2 |
11 | 4 | 2 | 3 | 4 | 2 | 2 | 0 | 0 | 0 | 4 | 4 | 1 |
12 | 4 | 2 | 4 | 4 | 2 | 3 | 2 | 1 | 1 | 4 | 4 | 2 |
Pareto front for the cluster of Near Misses.
The coverage can be verified by, first, identifying the most similar characteristics of the sequence vectors belonging to the Near Misses cluster with the Pareto set scenarios
The most similar characteristics can be computed by coverage vectors (one for each scenario belonging to
Coverage vector computation by Hamming distance.
Table the failure of the communication between the sensor monitoring the the failure of the PID controller with magnitude belonging to
A SCP can, thus, be solved for verifying that these latest characteristics are the minimum set of stochastic event occurrences and deterministic process variables values of
List of coverage vectors for each scenario belonging to the Pareto set
|
Steam valve failure time | Steam valve failure magnitude | Steam valve failure order | Safety valve failure time | Safety valve failure magnitude | Safety valve failure order | Sensor-PID failure time | Sensor-PID failure magnitude | Sensor-PID failure order | PID failure time | PID failure magnitude | PID failure order |
---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 11.4 | 11.4 | 11.4 | 8.1 | 30.4 | 0.6 | 25.3 |
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46.4 | 1.2 | 1.5 | 0.6 |
2 | 30.1 | 44.3 | 27.1 | 1.2 | 19.9 | 38 | 19.6 |
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46.4 | 68.1 |
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3 | 30.1 | 44.3 | 27.1 | 8.1 | 19.9 | 38 | 22.3 |
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14.2 | 27.4 |
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14.2 |
4 | 30.1 | 44.3 | 42.2 | 8.1 | 19.9 | 19.9 | 25.3 |
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12.7 | 68.1 |
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5 | 30.1 | 44.3 | 27.1 | 28 | 30.4 | 38 | 22.3 |
|
46.4 | 68.1 |
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6 | 30.1 | 36.1 | 27.1 | 1.2 | 19.9 | 19.9 | 19.6 |
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13.9 | 68.1 |
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7 | 30.1 | 36.1 | 27.1 | 8.1 | 30.4 | 0.6 | 22.3 |
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46.4 | 3.3 | 1.5 | 0.60 |
8 | 52.4 | 44.3 | 42.2 | 28 | 19.9 | 19.9 | 25.3 |
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12.7 | 27.4 |
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9 | 52.4 | 36.1 | 42.2 | 1.2 | 30.4 | 19.9 | 13 | 13 | 13 | 68.1 | 1.5 |
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10 | 52.4 | 36.1 | 27.1 | 8.1 | 9.04 | 38 | 22.3 |
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14.2 | 27.4 |
|
14.2 |
11 | 52.4 | 36.1 | 42.2 | 51.2 | 19.9 | 19.9 | 13 | 13 | 13 | 1.2 |
|
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12 | 52.4 | 36.1 | 27.1 | 51.2 | 19.9 | 38 | 22.3 |
|
14.2 | 1.2 |
|
14.2 |
In this paper, a risk-based clustering approach for Near Misses identification has been proposed. The approach includes a risk-based feature selection task, where by each safe scenario it is described in terms of probability, consequence, and overall risk. The optimal features set is identified by a wrapper approach based on the combination of a MBDE algorithm with
The application of the approach to a case study of IDPSA of a UTSG has shown the possibility of retrieving relevant information for risk monitoring.
For a static reliability analysis of the UTSG, we conservatively assume that component failures occur at the beginning of the scenario, with magnitudes equal to their extreme (either maximum or minimum) plausible values [
Possible system configurations to be considered in the static reliability analysis with constant power profile.
System |
Failure of the |
Failure of the |
Level sensor-PID controller |
Failure of the |
---|---|---|---|---|
1 | — | — | — | — |
2 | X | — | — | — |
3 | — | X | — | — |
4 | — | — | X | — |
5 | — | — | — | X |
6 | X | X | — | — |
7 | X | — | X | — |
8 | X | — | — | X |
9 | — | X | X | — |
10 | — | X | — | X |
11 | X | X | X | — |
12 | X | X | — | X |
To identify the system MCS, the different system configurations of Table
Fault tree for the high level failure mode.
The analysis of the low level failure mode provides different MCSs at different
(a)
Fault tree for the low level failure mode at low power.
At 80%
(a)
Fault tree for the low level failure mode at high power.
See Table
Near Miss |
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1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 4 | 1 |
2 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 4 | 2 |
3 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 2 | 1 | 4 | 1 |
4 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 1 | 1 | 2 | 4 | 2 |
5 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 1 | 2 | 2 | 4 | 1 |
6 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 1 | 1 | 3 | 4 | 2 |
7 | 0 | 0 | 0 | 0 | 0 | 0 | 4 | 1 | 2 | 2 | 4 | 1 |
8 | 0 | 0 | 0 | 2 | 2 | 2 | 4 | 1 | 3 | 2 | 4 | 1 |
9 | 0 | 0 | 0 | 2 | 3 | 1 | 4 | 1 | 2 | 4 | 3 | 3 |
10 | 0 | 0 | 0 | 2 | 4 | 2 | 4 | 1 | 3 | 1 | 4 | 1 |
11 | 0 | 0 | 0 | 3 | 2 | 3 | 3 | 1 | 2 | 1 | 4 | 1 |
12 | 0 | 0 | 0 | 3 | 3 | 3 | 1 | 1 | 1 | 1 | 4 | 2 |
13 | 0 | 0 | 0 | 3 | 3 | 3 | 1 | 1 | 2 | 1 | 4 | 1 |
14 | 0 | 0 | 0 | 3 | 3 | 3 | 2 | 1 | 2 | 1 | 4 | 1 |
15 | 0 | 0 | 0 | 3 | 3 | 3 | 2 | 1 | 2 | 2 | 4 | 1 |
16 | 0 | 0 | 0 | 3 | 3 | 2 | 3 | 1 | 3 | 1 | 4 | 1 |
17 | 0 | 0 | 0 | 3 | 3 | 2 | 4 | 1 | 3 | 1 | 4 | 1 |
18 | 0 | 0 | 0 | 3 | 4 | 3 | 1 | 1 | 1 | 2 | 4 | 2 |
19 | 0 | 0 | 0 | 3 | 4 | 3 | 3 | 1 | 2 | 1 | 4 | 1 |
20 | 0 | 0 | 0 | 4 | 2 | 2 | 0 | 0 | 0 | 4 | 4 | 1 |
21 | 0 | 0 | 0 | 4 | 2 | 3 | 2 | 1 | 2 | 1 | 4 | 1 |
22 | 0 | 0 | 0 | 4 | 2 | 3 | 3 | 1 | 2 | 1 | 4 | 1 |
23 | 0 | 0 | 0 | 4 | 2 | 3 | 4 | 1 | 2 | 1 | 4 | 1 |
24 | 0 | 0 | 0 | 4 | 3 | 2 | 0 | 0 | 0 | 1 | 4 | 1 |
25 | 0 | 0 | 0 | 4 | 3 | 2 | 0 | 0 | 0 | 2 | 4 | 1 |
26 | 0 | 0 | 0 | 4 | 3 | 3 | 2 | 1 | 1 | 2 | 4 | 2 |
27 | 0 | 0 | 0 | 4 | 3 | 3 | 3 | 1 | 2 | 2 | 4 | 1 |
28 | 0 | 0 | 0 | 4 | 3 | 2 | 4 | 1 | 3 | 1 | 4 | 1 |
29 | 0 | 0 | 0 | 4 | 4 | 2 | 0 | 0 | 0 | 1 | 4 | 1 |
30 | 0 | 0 | 0 | 4 | 4 | 2 | 0 | 0 | 0 | 2 | 4 | 1 |
31 | 0 | 0 | 0 | 4 | 4 | 3 | 1 | 1 | 1 | 1 | 4 | 2 |
32 | 0 | 0 | 0 | 4 | 4 | 3 | 1 | 1 | 2 | 1 | 4 | 1 |
33 | 0 | 0 | 0 | 4 | 4 | 3 | 1 | 1 | 1 | 2 | 4 | 2 |
34 | 0 | 0 | 0 | 4 | 4 | 3 | 2 | 1 | 2 | 1 | 4 | 1 |
35 | 0 | 0 | 0 | 4 | 4 | 3 | 2 | 1 | 1 | 2 | 4 | 2 |
36 | 0 | 0 | 0 | 4 | 4 | 3 | 3 | 1 | 2 | 3 | 4 | 1 |
37 | 0 | 0 | 0 | 4 | 4 | 3 | 4 | 1 | 2 | 1 | 4 | 1 |
38 | 0 | 0 | 0 | 4 | 4 | 3 | 4 | 1 | 2 | 2 | 4 | 1 |
39 | 1 | 1 | 3 | 1 | 2 | 2 | 1 | 1 | 4 | 1 | 4 | 1 |
40 | 2 | 1 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 4 | 1 |
41 | 2 | 1 | 3 | 0 | 0 | 0 | 1 | 1 | 2 | 1 | 4 | 1 |
42 | 2 | 1 | 3 | 2 | 2 | 2 | 0 | 0 | 0 | 2 | 4 | 1 |
43 | 2 | 1 | 2 | 2 | 2 | 3 | 3 | 1 | 4 | 1 | 4 | 1 |
44 | 2 | 1 | 4 | 2 | 4 | 2 | 2 | 1 | 3 | 1 | 3 | 1 |
45 | 2 | 1 | 3 | 2 | 4 | 4 | 2 | 1 | 2 | 1 | 4 | 1 |
46 | 2 | 1 | 3 | 3 | 2 | 4 | 2 | 1 | 2 | 1 | 4 | 1 |
47 | 2 | 1 | 2 | 3 | 2 | 3 | 4 | 1 | 4 | 1 | 4 | 1 |
48 | 2 | 1 | 3 | 3 | 3 | 4 | 2 | 1 | 2 | 1 | 4 | 1 |
49 | 2 | 1 | 2 | 3 | 3 | 3 | 3 | 1 | 4 | 1 | 4 | 1 |
50 | 2 | 1 | 3 | 3 | 4 | 4 | 1 | 1 | 2 | 1 | 4 | 1 |
51 | 2 | 1 | 2 | 3 | 4 | 3 | 3 | 1 | 4 | 1 | 4 | 1 |
52 | 2 | 1 | 3 | 4 | 1 | 4 | 2 | 1 | 2 | 1 | 4 | 1 |
53 | 2 | 1 | 3 | 4 | 3 | 4 | 1 | 1 | 2 | 1 | 4 | 1 |
54 | 2 | 1 | 2 | 4 | 3 | 4 | 3 | 1 | 3 | 1 | 4 | 1 |
55 | 2 | 1 | 2 | 4 | 3 | 4 | 4 | 1 | 3 | 1 | 4 | 1 |
56 | 2 | 1 | 2 | 4 | 4 | 3 | 0 | 0 | 0 | 1 | 4 | 1 |
57 | 2 | 2 | 3 | 3 | 4 | 4 | 1 | 1 | 2 | 1 | 4 | 1 |
58 | 2 | 2 | 3 | 4 | 4 | 4 | 2 | 1 | 2 | 1 | 4 | 1 |
59 | 3 | 1 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 4 | 1 |
60 | 3 | 1 | 3 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 4 | 2 |
61 | 3 | 1 | 3 | 0 | 0 | 0 | 1 | 1 | 2 | 1 | 4 | 1 |
62 | 3 | 1 | 3 | 0 | 0 | 0 | 2 | 1 | 2 | 1 | 3 | 1 |
63 | 3 | 1 | 3 | 0 | 0 | 0 | 2 | 1 | 2 | 1 | 4 | 1 |
64 | 3 | 1 | 3 | 0 | 0 | 0 | 2 | 1 | 2 | 2 | 4 | 1 |
65 | 3 | 1 | 4 | 1 | 2 | 3 | 1 | 1 | 2 | 1 | 4 | 1 |
66 | 3 | 1 | 4 | 2 | 2 | 2 | 2 | 1 | 3 | 2 | 4 | 1 |
67 | 3 | 1 | 4 | 2 | 2 | 3 | 2 | 1 | 1 | 2 | 4 | 2 |
68 | 3 | 1 | 3 | 2 | 2 | 2 | 4 | 1 | 4 | 1 | 4 | 1 |
69 | 3 | 1 | 4 | 2 | 3 | 3 | 2 | 1 | 2 | 1 | 4 | 1 |
70 | 3 | 1 | 4 | 2 | 4 | 3 | 1 | 1 | 2 | 1 | 4 | 1 |
71 | 3 | 1 | 4 | 2 | 4 | 2 | 3 | 1 | 3 | 1 | 4 | 1 |
72 | 3 | 1 | 3 | 3 | 1 | 4 | 2 | 1 | 2 | 1 | 4 | 1 |
73 | 3 | 1 | 2 | 3 | 1 | 3 | 3 | 1 | 4 | 1 | 4 | 1 |
74 | 3 | 1 | 3 | 3 | 1 | 4 | 3 | 1 | 2 | 1 | 4 | 1 |
75 | 3 | 1 | 2 | 3 | 1 | 3 | 4 | 1 | 4 | 1 | 4 | 1 |
76 | 3 | 1 | 2 | 3 | 2 | 3 | 0 | 0 | 0 | 1 | 4 | 1 |
77 | 3 | 1 | 3 | 3 | 2 | 4 | 2 | 1 | 2 | 1 | 4 | 1 |
78 | 3 | 1 | 4 | 3 | 2 | 3 | 2 | 1 | 2 | 1 | 4 | 1 |
79 | 3 | 1 | 2 | 3 | 2 | 4 | 3 | 1 | 3 | 1 | 4 | 1 |
80 | 3 | 1 | 3 | 3 | 2 | 4 | 3 | 1 | 2 | 2 | 4 | 1 |
81 | 3 | 1 | 3 | 3 | 2 | 2 | 4 | 1 | 4 | 1 | 4 | 1 |
82 | 3 | 1 | 2 | 3 | 3 | 3 | 0 | 0 | 0 | 1 | 4 | 1 |
83 | 3 | 1 | 4 | 3 | 3 | 3 | 2 | 1 | 2 | 1 | 4 | 1 |
84 | 3 | 1 | 3 | 3 | 3 | 4 | 3 | 1 | 2 | 1 | 4 | 1 |
85 | 3 | 1 | 4 | 3 | 3 | 2 | 3 | 1 | 3 | 1 | 4 | 1 |
86 | 3 | 1 | 3 | 3 | 3 | 2 | 4 | 1 | 4 | 1 | 4 | 1 |
87 | 3 | 1 | 2 | 3 | 4 | 3 | 0 | 0 | 0 | 1 | 4 | 1 |
88 | 3 | 1 | 3 | 3 | 4 | 4 | 1 | 1 | 2 | 1 | 4 | 1 |
89 | 3 | 1 | 4 | 3 | 4 | 3 | 2 | 1 | 2 | 1 | 4 | 1 |
90 | 3 | 1 | 2 | 3 | 4 | 4 | 3 | 1 | 3 | 1 | 4 | 1 |
91 | 3 | 1 | 2 | 3 | 4 | 3 | 4 | 1 | 4 | 1 | 4 | 1 |
92 | 3 | 1 | 3 | 4 | 1 | 4 | 1 | 1 | 1 | 1 | 4 | 2 |
93 | 3 | 1 | 3 | 4 | 1 | 4 | 2 | 1 | 2 | 1 | 4 | 1 |
94 | 3 | 1 | 2 | 4 | 1 | 3 | 4 | 1 | 4 | 1 | 4 | 1 |
95 | 3 | 1 | 3 | 4 | 2 | 4 | 2 | 1 | 2 | 1 | 4 | 1 |
96 | 3 | 1 | 3 | 4 | 2 | 4 | 2 | 1 | 2 | 2 | 4 | 1 |
97 | 3 | 1 | 3 | 4 | 2 | 4 | 3 | 1 | 2 | 1 | 4 | 1 |
98 | 3 | 1 | 3 | 4 | 2 | 4 | 3 | 1 | 2 | 2 | 4 | 1 |
99 | 3 | 1 | 3 | 4 | 3 | 4 | 1 | 1 | 2 | 1 | 4 | 1 |
100 | 3 | 1 | 3 | 4 | 3 | 4 | 3 | 1 | 2 | 1 | 4 | 1 |
101 | 3 | 1 | 3 | 4 | 3 | 4 | 3 | 1 | 2 | 2 | 4 | 1 |
102 | 3 | 1 | 2 | 4 | 3 | 4 | 4 | 1 | 3 | 2 | 4 | 1 |
103 | 3 | 1 | 2 | 4 | 4 | 3 | 0 | 0 | 0 | 1 | 4 | 1 |
104 | 3 | 1 | 3 | 4 | 4 | 4 | 1 | 1 | 1 | 1 | 4 | 2 |
105 | 3 | 1 | 3 | 4 | 4 | 4 | 2 | 1 | 2 | 1 | 4 | 1 |
106 | 3 | 1 | 3 | 4 | 4 | 4 | 2 | 1 | 2 | 2 | 4 | 1 |
107 | 3 | 1 | 3 | 4 | 4 | 4 | 3 | 1 | 2 | 1 | 4 | 1 |
108 | 3 | 1 | 2 | 4 | 4 | 4 | 4 | 1 | 3 | 1 | 4 | 1 |
109 | 3 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 4 | 1 |
110 | 3 | 2 | 3 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 4 | 2 |
111 | 3 | 2 | 3 | 0 | 0 | 0 | 1 | 1 | 2 | 1 | 4 | 1 |
112 | 3 | 2 | 2 | 0 | 0 | 0 | 3 | 1 | 3 | 1 | 4 | 1 |
113 | 3 | 2 | 2 | 0 | 0 | 0 | 4 | 1 | 3 | 1 | 4 | 1 |
114 | 3 | 2 | 4 | 1 | 2 | 2 | 1 | 1 | 3 | 1 | 4 | 1 |
115 | 3 | 2 | 3 | 2 | 3 | 2 | 0 | 0 | 0 | 1 | 4 | 1 |
116 | 3 | 2 | 4 | 2 | 3 | 1 | 2 | 1 | 2 | 3 | 3 | 3 |
117 | 3 | 2 | 3 | 2 | 3 | 2 | 3 | 1 | 4 | 1 | 4 | 1 |
118 | 3 | 2 | 3 | 3 | 1 | 4 | 1 | 1 | 1 | 1 | 4 | 2 |
119 | 3 | 2 | 2 | 3 | 1 | 3 | 3 | 1 | 4 | 1 | 4 | 1 |
120 | 3 | 2 | 2 | 3 | 1 | 3 | 4 | 1 | 4 | 1 | 4 | 1 |
121 | 3 | 2 | 3 | 3 | 2 | 4 | 1 | 1 | 1 | 1 | 4 | 2 |
122 | 3 | 2 | 4 | 3 | 2 | 3 | 2 | 1 | 2 | 1 | 4 | 1 |
123 | 3 | 2 | 3 | 3 | 2 | 4 | 3 | 1 | 2 | 1 | 4 | 1 |
124 | 3 | 2 | 2 | 3 | 3 | 3 | 0 | 0 | 0 | 1 | 4 | 1 |
125 | 3 | 2 | 3 | 3 | 3 | 2 | 0 | 0 | 0 | 1 | 4 | 1 |
126 | 3 | 2 | 4 | 3 | 3 | 3 | 1 | 1 | 1 | 1 | 4 | 2 |
127 | 3 | 2 | 3 | 3 | 3 | 4 | 2 | 1 | 2 | 1 | 4 | 1 |
128 | 3 | 2 | 4 | 3 | 3 | 3 | 2 | 1 | 2 | 2 | 4 | 1 |
129 | 3 | 2 | 2 | 3 | 3 | 4 | 3 | 1 | 3 | 1 | 4 | 1 |
130 | 3 | 2 | 3 | 3 | 3 | 4 | 3 | 1 | 2 | 1 | 4 | 1 |
131 | 3 | 2 | 4 | 3 | 3 | 2 | 3 | 1 | 3 | 1 | 4 | 1 |
132 | 3 | 2 | 4 | 3 | 3 | 3 | 3 | 1 | 2 | 1 | 4 | 1 |
133 | 3 | 2 | 3 | 3 | 3 | 4 | 3 | 1 | 2 | 2 | 4 | 1 |
134 | 3 | 2 | 2 | 3 | 3 | 3 | 4 | 1 | 4 | 1 | 4 | 1 |
135 | 3 | 2 | 3 | 3 | 3 | 2 | 4 | 1 | 4 | 1 | 4 | 1 |
136 | 3 | 2 | 3 | 3 | 4 | 4 | 1 | 1 | 2 | 1 | 4 | 1 |
137 | 3 | 2 | 3 | 3 | 4 | 4 | 2 | 1 | 2 | 1 | 4 | 1 |
138 | 3 | 2 | 4 | 3 | 4 | 3 | 2 | 1 | 2 | 1 | 4 | 1 |
139 | 3 | 2 | 2 | 3 | 4 | 3 | 4 | 1 | 4 | 1 | 4 | 1 |
140 | 3 | 2 | 2 | 3 | 4 | 3 | 4 | 1 | 4 | 2 | 4 | 1 |
141 | 3 | 2 | 2 | 4 | 1 | 4 | 3 | 1 | 3 | 1 | 4 | 1 |
142 | 3 | 2 | 2 | 4 | 1 | 4 | 4 | 1 | 3 | 1 | 4 | 1 |
143 | 3 | 2 | 3 | 4 | 2 | 4 | 1 | 1 | 2 | 1 | 4 | 1 |
144 | 3 | 2 | 3 | 4 | 2 | 4 | 3 | 1 | 2 | 1 | 4 | 1 |
145 | 3 | 2 | 3 | 4 | 2 | 4 | 3 | 1 | 2 | 2 | 4 | 1 |
146 | 3 | 2 | 2 | 4 | 2 | 3 | 4 | 1 | 4 | 1 | 4 | 1 |
147 | 3 | 2 | 2 | 4 | 2 | 4 | 4 | 1 | 3 | 1 | 4 | 1 |
148 | 3 | 2 | 3 | 4 | 3 | 4 | 1 | 1 | 1 | 2 | 4 | 2 |
149 | 3 | 2 | 2 | 4 | 3 | 4 | 3 | 1 | 3 | 1 | 4 | 1 |
150 | 3 | 2 | 3 | 4 | 3 | 4 | 3 | 1 | 2 | 1 | 4 | 1 |
151 | 3 | 2 | 3 | 4 | 4 | 4 | 1 | 1 | 1 | 1 | 4 | 2 |
152 | 3 | 2 | 3 | 4 | 4 | 4 | 1 | 1 | 2 | 1 | 4 | 1 |
153 | 3 | 3 | 3 | 2 | 3 | 2 | 4 | 1 | 4 | 1 | 4 | 1 |
154 | 3 | 3 | 4 | 2 | 4 | 3 | 1 | 1 | 2 | 1 | 4 | 1 |
155 | 3 | 3 | 4 | 3 | 3 | 3 | 2 | 1 | 2 | 1 | 4 | 1 |
156 | 3 | 3 | 3 | 3 | 3 | 2 | 3 | 1 | 4 | 1 | 4 | 1 |
157 | 3 | 3 | 4 | 3 | 4 | 3 | 2 | 1 | 2 | 1 | 4 | 1 |
158 | 3 | 3 | 4 | 3 | 4 | 3 | 3 | 1 | 2 | 1 | 4 | 1 |
159 | 4 | 1 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 4 | 1 |
160 | 4 | 1 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 4 | 1 |
161 | 4 | 1 | 3 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 4 | 2 |
162 | 4 | 1 | 3 | 0 | 0 | 0 | 1 | 1 | 2 | 1 | 4 | 1 |
163 | 4 | 1 | 3 | 0 | 0 | 0 | 2 | 1 | 1 | 2 | 4 | 2 |
164 | 4 | 1 | 3 | 0 | 0 | 0 | 2 | 1 | 2 | 2 | 4 | 1 |
165 | 4 | 1 | 3 | 0 | 0 | 0 | 3 | 1 | 2 | 3 | 4 | 1 |
166 | 4 | 1 | 2 | 0 | 0 | 0 | 4 | 1 | 3 | 1 | 4 | 1 |
167 | 4 | 1 | 3 | 0 | 0 | 0 | 4 | 1 | 2 | 1 | 4 | 1 |
168 | 4 | 1 | 3 | 0 | 0 | 0 | 4 | 1 | 2 | 2 | 4 | 1 |
169 | 4 | 1 | 4 | 2 | 2 | 3 | 1 | 1 | 2 | 1 | 4 | 1 |
170 | 4 | 1 | 4 | 2 | 2 | 2 | 3 | 1 | 3 | 2 | 4 | 1 |
171 | 4 | 1 | 4 | 2 | 3 | 3 | 1 | 1 | 2 | 1 | 4 | 1 |
172 | 4 | 1 | 4 | 2 | 4 | 2 | 4 | 1 | 3 | 1 | 4 | 1 |
173 | 4 | 1 | 4 | 3 | 2 | 3 | 1 | 1 | 1 | 1 | 4 | 2 |
174 | 4 | 1 | 3 | 3 | 2 | 2 | 4 | 1 | 4 | 2 | 4 | 1 |
175 | 4 | 1 | 3 | 3 | 3 | 2 | 0 | 0 | 0 | 1 | 4 | 1 |
176 | 4 | 1 | 4 | 3 | 3 | 3 | 1 | 1 | 2 | 1 | 4 | 1 |
177 | 4 | 1 | 4 | 3 | 3 | 3 | 2 | 1 | 2 | 1 | 4 | 1 |
178 | 4 | 1 | 3 | 3 | 4 | 2 | 0 | 0 | 0 | 1 | 4 | 1 |
179 | 4 | 1 | 4 | 3 | 4 | 3 | 1 | 1 | 1 | 1 | 4 | 2 |
180 | 4 | 1 | 4 | 3 | 4 | 3 | 2 | 1 | 2 | 2 | 4 | 1 |
181 | 4 | 1 | 4 | 3 | 4 | 3 | 3 | 1 | 2 | 1 | 4 | 1 |
182 | 4 | 1 | 4 | 3 | 4 | 3 | 3 | 1 | 2 | 2 | 4 | 1 |
183 | 4 | 1 | 3 | 3 | 4 | 2 | 4 | 1 | 4 | 2 | 4 | 1 |
184 | 4 | 1 | 2 | 4 | 1 | 3 | 0 | 0 | 0 | 1 | 4 | 1 |
185 | 4 | 1 | 2 | 4 | 1 | 3 | 0 | 0 | 0 | 2 | 4 | 1 |
186 | 4 | 1 | 3 | 4 | 1 | 4 | 1 | 1 | 1 | 2 | 4 | 2 |
187 | 4 | 1 | 3 | 4 | 1 | 4 | 2 | 1 | 2 | 1 | 4 | 1 |
188 | 4 | 1 | 3 | 4 | 1 | 4 | 2 | 1 | 2 | 2 | 4 | 1 |
189 | 4 | 1 | 3 | 4 | 1 | 4 | 3 | 1 | 2 | 1 | 4 | 1 |
190 | 4 | 1 | 2 | 4 | 1 | 3 | 4 | 1 | 4 | 1 | 4 | 1 |
191 | 4 | 1 | 3 | 4 | 1 | 4 | 4 | 1 | 2 | 1 | 4 | 1 |
192 | 4 | 1 | 2 | 4 | 1 | 3 | 4 | 1 | 4 | 2 | 4 | 1 |
193 | 4 | 1 | 3 | 4 | 1 | 4 | 4 | 1 | 2 | 3 | 4 | 1 |
194 | 4 | 1 | 2 | 4 | 2 | 3 | 0 | 0 | 0 | 1 | 4 | 1 |
195 | 4 | 1 | 3 | 4 | 2 | 4 | 1 | 1 | 1 | 1 | 4 | 2 |
196 | 4 | 1 | 4 | 4 | 2 | 3 | 1 | 1 | 2 | 1 | 4 | 1 |
197 | 4 | 1 | 3 | 4 | 2 | 4 | 2 | 1 | 2 | 1 | 4 | 1 |
198 | 4 | 1 | 4 | 4 | 2 | 3 | 2 | 1 | 1 | 2 | 4 | 2 |
199 | 4 | 1 | 3 | 4 | 2 | 4 | 2 | 1 | 2 | 2 | 4 | 1 |
200 | 4 | 1 | 3 | 4 | 2 | 4 | 3 | 1 | 2 | 2 | 4 | 1 |
201 | 4 | 1 | 2 | 4 | 2 | 3 | 4 | 1 | 4 | 1 | 4 | 1 |
202 | 4 | 1 | 3 | 4 | 2 | 2 | 4 | 1 | 4 | 1 | 4 | 1 |
203 | 4 | 1 | 3 | 4 | 2 | 4 | 4 | 1 | 2 | 1 | 4 | 1 |
204 | 4 | 1 | 2 | 4 | 2 | 4 | 4 | 1 | 3 | 2 | 4 | 1 |
205 | 4 | 1 | 3 | 4 | 2 | 4 | 4 | 1 | 2 | 2 | 4 | 1 |
206 | 4 | 1 | 4 | 4 | 2 | 2 | 4 | 1 | 3 | 3 | 4 | 1 |
207 | 4 | 1 | 2 | 4 | 3 | 3 | 0 | 0 | 0 | 1 | 4 | 1 |
208 | 4 | 1 | 3 | 4 | 3 | 2 | 0 | 0 | 0 | 1 | 4 | 1 |
209 | 4 | 1 | 4 | 4 | 3 | 3 | 1 | 1 | 1 | 1 | 4 | 2 |
210 | 4 | 1 | 3 | 4 | 3 | 4 | 1 | 1 | 2 | 1 | 4 | 1 |
211 | 4 | 1 | 4 | 4 | 3 | 3 | 1 | 1 | 2 | 1 | 4 | 1 |
212 | 4 | 1 | 3 | 4 | 3 | 4 | 2 | 1 | 2 | 1 | 4 | 1 |
213 | 4 | 1 | 4 | 4 | 3 | 3 | 2 | 1 | 2 | 1 | 4 | 1 |
214 | 4 | 1 | 4 | 4 | 3 | 3 | 2 | 1 | 1 | 2 | 4 | 2 |
215 | 4 | 1 | 3 | 4 | 3 | 4 | 2 | 1 | 2 | 2 | 4 | 1 |
216 | 4 | 1 | 4 | 4 | 3 | 3 | 2 | 1 | 2 | 2 | 4 | 1 |
217 | 4 | 1 | 3 | 4 | 3 | 4 | 3 | 1 | 2 | 1 | 4 | 1 |
218 | 4 | 1 | 3 | 4 | 3 | 4 | 3 | 1 | 2 | 3 | 4 | 1 |
219 | 4 | 1 | 2 | 4 | 3 | 3 | 4 | 1 | 4 | 1 | 4 | 1 |
220 | 4 | 1 | 2 | 4 | 3 | 4 | 4 | 1 | 3 | 1 | 4 | 1 |
221 | 4 | 1 | 3 | 4 | 3 | 2 | 4 | 1 | 4 | 1 | 4 | 1 |
222 | 4 | 1 | 3 | 4 | 3 | 4 | 4 | 1 | 2 | 1 | 4 | 1 |
223 | 4 | 1 | 2 | 4 | 3 | 3 | 4 | 1 | 4 | 2 | 4 | 1 |
224 | 4 | 1 | 3 | 4 | 3 | 4 | 4 | 1 | 2 | 2 | 4 | 1 |
225 | 4 | 1 | 4 | 4 | 3 | 2 | 4 | 1 | 3 | 2 | 4 | 1 |
226 | 4 | 1 | 2 | 4 | 4 | 3 | 0 | 0 | 0 | 2 | 4 | 1 |
227 | 4 | 1 | 3 | 4 | 4 | 4 | 1 | 1 | 1 | 1 | 4 | 2 |
228 | 4 | 1 | 4 | 4 | 4 | 3 | 1 | 1 | 1 | 1 | 4 | 2 |
229 | 4 | 1 | 4 | 4 | 4 | 3 | 1 | 1 | 1 | 2 | 4 | 2 |
230 | 4 | 1 | 3 | 4 | 4 | 4 | 2 | 1 | 2 | 1 | 4 | 1 |
231 | 4 | 1 | 4 | 4 | 4 | 3 | 2 | 1 | 2 | 1 | 4 | 1 |
232 | 4 | 1 | 4 | 4 | 4 | 3 | 2 | 1 | 2 | 2 | 4 | 1 |
233 | 4 | 1 | 3 | 4 | 4 | 4 | 3 | 1 | 2 | 1 | 4 | 1 |
234 | 4 | 1 | 4 | 4 | 4 | 3 | 3 | 1 | 2 | 1 | 4 | 1 |
235 | 4 | 1 | 3 | 4 | 4 | 4 | 3 | 1 | 2 | 3 | 4 | 1 |
236 | 4 | 1 | 3 | 4 | 4 | 4 | 4 | 1 | 2 | 1 | 4 | 1 |
237 | 4 | 1 | 4 | 4 | 4 | 2 | 4 | 1 | 3 | 2 | 4 | 1 |
238 | 4 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 4 | 1 |
239 | 4 | 2 | 3 | 0 | 0 | 0 | 1 | 1 | 2 | 1 | 4 | 1 |
240 | 4 | 2 | 3 | 0 | 0 | 0 | 2 | 1 | 1 | 2 | 4 | 2 |
241 | 4 | 2 | 3 | 0 | 0 | 0 | 2 | 1 | 2 | 2 | 4 | 1 |
242 | 4 | 2 | 3 | 0 | 0 | 0 | 3 | 1 | 2 | 1 | 4 | 1 |
243 | 4 | 2 | 3 | 0 | 0 | 0 | 3 | 1 | 2 | 2 | 4 | 1 |
244 | 4 | 2 | 3 | 0 | 0 | 0 | 4 | 1 | 2 | 1 | 4 | 1 |
245 | 4 | 2 | 2 | 0 | 0 | 0 | 4 | 1 | 3 | 2 | 4 | 1 |
246 | 4 | 2 | 3 | 1 | 3 | 2 | 0 | 0 | 0 | 1 | 3 | 1 |
247 | 4 | 2 | 4 | 2 | 1 | 3 | 2 | 1 | 1 | 2 | 4 | 2 |
248 | 4 | 2 | 4 | 2 | 3 | 2 | 4 | 1 | 3 | 1 | 4 | 1 |
249 | 4 | 2 | 3 | 2 | 4 | 2 | 0 | 0 | 0 | 1 | 4 | 1 |
250 | 4 | 2 | 4 | 3 | 2 | 3 | 1 | 1 | 2 | 1 | 4 | 1 |
251 | 4 | 2 | 4 | 3 | 2 | 2 | 3 | 1 | 3 | 3 | 4 | 1 |
252 | 4 | 2 | 3 | 3 | 2 | 2 | 4 | 1 | 4 | 1 | 4 | 1 |
253 | 4 | 2 | 3 | 3 | 3 | 2 | 0 | 0 | 0 | 1 | 4 | 1 |
254 | 4 | 2 | 4 | 3 | 3 | 3 | 1 | 1 | 1 | 2 | 4 | 2 |
255 | 4 | 2 | 4 | 3 | 3 | 3 | 2 | 1 | 2 | 1 | 4 | 1 |
256 | 4 | 2 | 4 | 3 | 3 | 3 | 3 | 1 | 2 | 1 | 4 | 1 |
257 | 4 | 2 | 3 | 3 | 3 | 2 | 4 | 1 | 4 | 1 | 4 | 1 |
258 | 4 | 2 | 4 | 3 | 3 | 2 | 4 | 1 | 3 | 1 | 4 | 1 |
259 | 4 | 2 | 4 | 3 | 4 | 3 | 1 | 1 | 1 | 1 | 4 | 2 |
260 | 4 | 2 | 4 | 3 | 4 | 3 | 1 | 1 | 1 | 2 | 4 | 2 |
261 | 4 | 2 | 4 | 3 | 4 | 3 | 2 | 1 | 2 | 1 | 4 | 1 |
262 | 4 | 2 | 4 | 3 | 4 | 3 | 3 | 1 | 2 | 1 | 4 | 1 |
263 | 4 | 2 | 2 | 4 | 1 | 3 | 0 | 0 | 0 | 2 | 4 | 1 |
264 | 4 | 2 | 3 | 4 | 1 | 4 | 1 | 1 | 1 | 1 | 4 | 2 |
265 | 4 | 2 | 3 | 4 | 1 | 4 | 3 | 1 | 2 | 1 | 4 | 1 |
266 | 4 | 2 | 2 | 4 | 1 | 4 | 4 | 1 | 3 | 1 | 4 | 1 |
267 | 4 | 2 | 2 | 4 | 1 | 3 | 4 | 1 | 4 | 2 | 4 | 1 |
268 | 4 | 2 | 3 | 4 | 1 | 4 | 4 | 1 | 2 | 2 | 4 | 1 |
269 | 4 | 2 | 3 | 4 | 2 | 2 | 0 | 0 | 0 | 4 | 4 | 1 |
270 | 4 | 2 | 3 | 4 | 2 | 4 | 1 | 1 | 1 | 1 | 4 | 2 |
271 | 4 | 2 | 3 | 4 | 2 | 4 | 1 | 1 | 1 | 2 | 4 | 2 |
272 | 4 | 2 | 4 | 4 | 2 | 3 | 2 | 1 | 1 | 4 | 4 | 2 |
273 | 4 | 2 | 4 | 4 | 2 | 3 | 3 | 1 | 2 | 1 | 4 | 1 |
274 | 4 | 2 | 3 | 4 | 2 | 4 | 3 | 1 | 2 | 2 | 4 | 1 |
275 | 4 | 2 | 3 | 4 | 2 | 4 | 3 | 1 | 2 | 3 | 4 | 1 |
276 | 4 | 2 | 2 | 4 | 2 | 3 | 4 | 1 | 4 | 1 | 4 | 1 |
277 | 4 | 2 | 3 | 4 | 2 | 2 | 4 | 1 | 4 | 1 | 4 | 1 |
278 | 4 | 2 | 3 | 4 | 2 | 4 | 4 | 1 | 2 | 1 | 4 | 1 |
279 | 4 | 2 | 4 | 4 | 2 | 3 | 4 | 1 | 2 | 1 | 4 | 1 |
280 | 4 | 2 | 2 | 4 | 2 | 4 | 4 | 1 | 3 | 2 | 4 | 1 |
281 | 4 | 2 | 3 | 4 | 3 | 2 | 0 | 0 | 0 | 1 | 4 | 1 |
282 | 4 | 2 | 3 | 4 | 3 | 2 | 0 | 0 | 0 | 2 | 4 | 1 |
283 | 4 | 2 | 4 | 4 | 3 | 3 | 1 | 1 | 1 | 1 | 4 | 2 |
284 | 4 | 2 | 3 | 4 | 3 | 4 | 1 | 1 | 2 | 1 | 4 | 1 |
285 | 4 | 2 | 4 | 4 | 3 | 3 | 1 | 1 | 2 | 1 | 4 | 1 |
286 | 4 | 2 | 3 | 4 | 3 | 4 | 2 | 1 | 2 | 1 | 4 | 1 |
287 | 4 | 2 | 4 | 4 | 3 | 3 | 2 | 1 | 2 | 1 | 4 | 1 |
288 | 4 | 2 | 3 | 4 | 3 | 4 | 2 | 1 | 1 | 2 | 4 | 2 |
289 | 4 | 2 | 4 | 4 | 3 | 3 | 2 | 1 | 1 | 2 | 4 | 2 |
290 | 4 | 2 | 4 | 4 | 3 | 3 | 2 | 1 | 2 | 2 | 4 | 1 |
291 | 4 | 2 | 4 | 4 | 3 | 3 | 3 | 1 | 2 | 1 | 4 | 1 |
292 | 4 | 2 | 3 | 4 | 3 | 4 | 3 | 1 | 2 | 2 | 4 | 1 |
293 | 4 | 2 | 2 | 4 | 3 | 4 | 4 | 1 | 3 | 1 | 4 | 1 |
294 | 4 | 2 | 3 | 4 | 3 | 4 | 4 | 1 | 2 | 1 | 4 | 1 |
295 | 4 | 2 | 2 | 4 | 3 | 3 | 4 | 1 | 4 | 2 | 4 | 1 |
296 | 4 | 2 | 2 | 4 | 3 | 4 | 4 | 1 | 3 | 2 | 4 | 1 |
297 | 4 | 2 | 4 | 4 | 3 | 3 | 4 | 1 | 2 | 2 | 4 | 1 |
298 | 4 | 2 | 3 | 4 | 4 | 2 | 0 | 0 | 0 | 1 | 4 | 1 |
299 | 4 | 2 | 2 | 4 | 4 | 3 | 0 | 0 | 0 | 2 | 4 | 1 |
300 | 4 | 2 | 3 | 4 | 4 | 2 | 0 | 0 | 0 | 2 | 4 | 1 |
301 | 4 | 2 | 4 | 4 | 4 | 3 | 1 | 1 | 2 | 1 | 4 | 1 |
302 | 4 | 2 | 4 | 4 | 4 | 3 | 1 | 1 | 1 | 2 | 4 | 2 |
303 | 4 | 2 | 3 | 4 | 4 | 4 | 2 | 1 | 2 | 1 | 4 | 1 |
304 | 4 | 2 | 4 | 4 | 4 | 3 | 2 | 1 | 2 | 1 | 4 | 1 |
305 | 4 | 2 | 4 | 4 | 4 | 3 | 2 | 1 | 1 | 2 | 4 | 2 |
306 | 4 | 2 | 3 | 4 | 4 | 4 | 3 | 1 | 2 | 1 | 4 | 1 |
307 | 4 | 2 | 2 | 4 | 4 | 4 | 4 | 1 | 3 | 1 | 4 | 1 |
308 | 4 | 2 | 3 | 4 | 4 | 2 | 4 | 1 | 4 | 1 | 4 | 1 |
309 | 4 | 2 | 4 | 4 | 4 | 2 | 4 | 1 | 3 | 1 | 4 | 1 |
310 | 4 | 2 | 2 | 4 | 4 | 4 | 4 | 1 | 3 | 2 | 4 | 1 |
311 | 4 | 2 | 3 | 4 | 4 | 2 | 4 | 1 | 4 | 2 | 4 | 1 |
312 | 4 | 3 | 3 | 2 | 4 | 2 | 0 | 0 | 0 | 1 | 4 | 1 |
313 | 4 | 3 | 4 | 2 | 4 | 3 | 2 | 1 | 2 | 1 | 4 | 1 |
314 | 4 | 3 | 4 | 3 | 3 | 2 | 3 | 1 | 3 | 1 | 4 | 1 |
315 | 4 | 3 | 4 | 3 | 3 | 3 | 3 | 1 | 2 | 1 | 4 | 1 |
316 | 4 | 3 | 3 | 3 | 4 | 2 | 0 | 0 | 0 | 1 | 4 | 1 |
317 | 4 | 3 | 4 | 3 | 4 | 3 | 1 | 1 | 2 | 1 | 4 | 1 |
318 | 4 | 3 | 3 | 3 | 4 | 2 | 4 | 1 | 4 | 1 | 4 | 1 |
319 | 4 | 3 | 4 | 3 | 4 | 2 | 4 | 1 | 3 | 1 | 4 | 1 |
320 | 4 | 3 | 3 | 4 | 3 | 2 | 0 | 0 | 0 | 2 | 4 | 1 |
321 | 4 | 3 | 4 | 4 | 3 | 3 | 3 | 1 | 2 | 1 | 4 | 1 |
322 | 4 | 3 | 4 | 4 | 3 | 2 | 4 | 1 | 3 | 2 | 4 | 1 |
323 | 4 | 3 | 3 | 4 | 4 | 2 | 0 | 0 | 0 | 2 | 4 | 1 |
324 | 4 | 3 | 4 | 4 | 4 | 3 | 1 | 1 | 1 | 1 | 4 | 2 |
325 | 4 | 3 | 4 | 4 | 4 | 3 | 1 | 1 | 2 | 1 | 4 | 1 |
326 | 4 | 3 | 4 | 4 | 4 | 3 | 2 | 1 | 2 | 1 | 4 | 1 |
327 | 4 | 3 | 4 | 4 | 4 | 3 | 2 | 1 | 1 | 2 | 4 | 2 |
328 | 4 | 3 | 4 | 4 | 4 | 3 | 2 | 1 | 2 | 2 | 4 | 1 |
329 | 4 | 3 | 4 | 4 | 4 | 3 | 3 | 1 | 2 | 1 | 4 | 1 |
330 | 4 | 3 | 3 | 4 | 4 | 2 | 4 | 1 | 4 | 1 | 4 | 1 |
331 | 4 | 3 | 3 | 4 | 4 | 2 | 4 | 1 | 4 | 2 | 4 | 1 |
332 | 4 | 3 | 4 | 4 | 4 | 3 | 4 | 1 | 2 | 3 | 4 | 1 |
Continuous event tree
Calinski-Harabasz index
Design basis accident
Dynamic event tree
Deterministic safety analysis
Event tree
Fault tree
Integrated deterministic and probabilistic safety analysis
Initiating event
Modified binary differential evolution
Minimal cuts set
Multiobjective optimization problem
Multiple-valued logic
Nuclear power plant
Prime implicants
Probabilistic safety analysis
Set covering problem
Steam generator
Thermal-hydraulics
U-tube steam generator.
Probability that the developing scenario is an accidental scenario
Consequence that the developing scenario can cause to the system
Overall risk of the developing scenario
Time instant
Probability that at time
Consequence that at time
Overall risk of the developing scenario at time
Flow rate of fresh feed-water entering the steam generator
Operating power
Nominal power
Flow rate of dry steam exiting the steam generator
Narrow range steam generator water level
Wide range steam generator water level
Time constant for the
Flow rate of incoming water in steam generator tube bundle region
Time constant for the water mass transportation dynamics
Time constant for the feed-water valve dynamics
Flow rate of steam-water mixture exiting the steam generator tube bundle region
Time constant for the dynamics relating
Constant in the nonminimum phase term of the dynamics relating
Time constant for the
System state
Derivative of system state
Narrow range steam generator water level at a reference position
Automatic reactor trip threshold
Turbine trip threshold
First prealarm automatic reactor trip threshold
First prealarm turbine trip threshold
Second prealarm automatic reactor trip threshold
First prealarm turbine trip threshold
Water flow rate provided by PID controller
Water flow rate removed by safety valve
Mission time
Time steps in MVL discretization
Cumulative probability function of the Gaussian distribution
Mean value of the Gaussian distribution
Standard deviation of the Gaussian distribution
Intensity coefficient
Number of clusters
Index of the profile of
Mean value of the
Peak value of the
Standard deviation of the
Root mean square of the
Skewness of the
Kurtosis of the
Number of scenarios to the training set
Dimension of the set of features
Number of scenarios to the test set
Overall between-cluster variance
Overall within-cluster variance
Number of scenarios assigned to the
Generic scenario
Centroid of the
Mean risk of the clustered scenarios
Time elapsed from the instant at which
Fitness function of the MOP
First objective function of the MOP
Second objective function of the MOP
Sequence vector belonging to the Pareto set of the MOP.
The authors declare no conflict of interests.