Systematic process to determine DNBR limit of CHF correlation with repetitive cross-validation technique

Figures & data

Figure 1. Flowchart to optimize CHF correlation with cross-validation technique.

Figure 2. Statistical procedure to yield 95/95 DNBR values.

Table 1. Sensitivity results for data-set split ratio

Data-set split ratio
(training data-set:	The number of	The number of
validation data-set)	training data-set	validation data-set	DNBR limit
80%:20%	208	52	Not available
75%:25%	193	67	1.157
70%:30%	180	80	1.157
65%:35%	167	93	1.158
60%:40%	153	107	1.158

Figure 3. Comparison results with repeated k-fold cross-validation technique and sensitivity check on the number of repetition.

Table 2. Statistics of M/Ps for 1000 cases for five classifications

Distribution of ${\bar{x}}_{\left(M/P\right)}$	Group	No. of case	Average	S.D.
ALL	Training	1000	1.0082	0.0005
	Validation	1000	1.0092	0.0091
Poolability	Poolable	957	1.0085	0.0021
	Non-poolable	43	1.0111	0.0199
	Poolable and
Combined	Non-poolable	1000	1.0085	0.0023

Table 3. Statistics of DNBR values for 1000 cases for five classifications

Distribution of 95/95
DBNR values	Group	No. of case	Average	S.D.
ALL	Training	1000	1.1481	0.0087
	Validation	1000	1.1534	0.0206
Poolability	Poolable	957	1.1466	0.0061
	Non-poolable	43	1.1549	0.0282
	Poolable and
Combined	Non-poolable	1000	1.1469	0.0085

Table 4. M/P statistics of 39th rank out of 1000 DNBR values

Group	No. of data	Average	S.D.	95/95 DNBR limit
Training	193	0.9996	0.0556	–
Validation	67	1.0233	0.0666	–
KCE-1M	260	1.0044	0.0586	1.157
KCE-1Mall	260	1.0081	0.0671	1.128

Table 5. Results of the poolablity 39th rank out of 1000 DNBR values

Case	Test		P-Value	Test Result
39^th rank out of “Combined”	Normality	Training	0.1405	Yes
		Validation	0.0097	No
		All	0.0349	No
	F-test		0.0095	No
	T-test		0.4992	Yes
	Wilcoxon-Mann-Whitney		0.9969	Yes

Figure 4. Average M/Ps distribution for 1000 cases for five classifications.

Figure 5. Distribution of 95/95 DNBR values for 1000 cases for five classifications.

Table 6. Range of variables for 39th rank out of 1000 DNBR values

	Pressure	Local mass flux	Local
Group	(psia)	(Mlbm/hr-ft^2)	quality
Training (39th rank)	1738–2415	0.740–3.717	−0.063–0.284
Validation (39th rank)	1732–2415	0.737–3.678	−0.038–0.295
KCE-1Mall	1731–2415	0.737–3.717	−0.063–0.295

Figure 6. Comparison of predicted CHF and measured CHF.