Table 1.
Measurement Instrumentation with Associated Measurands, Uncertainties, and Acquisition Rates under Experimental Conditions
Instrument Measurand Uncertainty Acquisition Rate ADT286 T 0.21°C (RTD), 0.457°C (TC) 2.2–4.6 s (RTD), 1 s (TC) Vantage Pro2
T
w
s
,
p
w
s
, RH0.3°C, 107 Pa, 2% 60 s SP932U-WBI (
x
c
,
y
c
), (
D
4
σ
x
,
D
4
σ
y
) 345 nm, 5% 0.01–0.25 s RPPM
P
R
P
P
M
1.6% 0.1 s IPG photodiode
V
I
P
G
– 0.1 s
Table 2.
Feature and Target Variables Selected for Random Forest Regression
Target Variable Feature Variables
P
t
a
r
g
e
t
V
I
P
G
,
T
w
s
,
p
w
s
,
R
H
w
s
,
T
A
D
T
286
,
G
s
o
u
r
c
e
,
D
4
σ
s
o
u
r
c
e
,
G
s
o
u
r
c
e
′
,
D
4
σ
s
o
u
r
c
e
′
I
t
a
r
g
e
t
V
I
P
G
,
T
w
s
,
p
w
s
,
R
H
w
s
,
T
A
D
T
286
,
G
s
o
u
r
c
e
′
,
D
4
σ
s
o
u
r
c
e
′
G
t
a
r
g
e
t
′
V
I
P
G
,
T
w
s
,
p
w
s
,
R
H
w
s
,
T
A
D
T
286
D
4
σ
′
t
a
r
g
e
t
V
I
P
G
,
T
w
s
,
p
w
s
,
R
H
w
s
,
T
A
D
T
286
Table 3.
Model Performance with Relative Feature Importance for a Subset of Features
Y MAE RMSE OOBE Feature Importance
P
t
a
r
g
e
t
0.0248 kW 0.187 kW 0.0007
V
I
P
G
(
0.47
)
,
D
4
σ
(
0.39
)
,
T
A
D
T
286
(
0.08
)
I
t
a
r
g
e
t
0.0102
k
W
/
c
m
2
0.060
k
W
/
c
m
2
0.0005
V
I
P
G
(
0.61
)
,
T
A
D
T
286
(
0.25
)
G
t
a
r
g
e
t
′
0.00042 cm 0.007 cm 0.0457
T
A
D
T
286
,
R
T
D
(
0.32
)
,
T
A
D
T
286
,
T
C
(
0.46
)
,
V
I
P
G
(
0.03
)
D
4
σ
′
t
a
r
g
e
t
0.0012 cm 0.002 cm 0.0435
T
A
D
T
286
(
0.85
)
,
V
I
P
G
(
0.07
)
Table 4.
Summary of Irradiance, Centroid, and Beam Width Values, with Varying Laser Power and Rayleigh Numbersa
T
1
,
0
/
∘
C
R
a
/
10
6
P
/
k
W
I
s
o
u
r
c
e
/
(
k
W
/
c
m
2
)
I
t
a
r
g
e
t
/
(
k
W
/
c
m
2
)
G
s
o
u
r
c
e
′
/
µ
m
G
t
a
r
g
e
t
′
/
µ
m
D
4
σ
s
o
u
r
c
e
/
c
m
D
4
σ
t
a
r
g
e
t
/
c
m
21 1.44 1.07 0.365 (0.001) 0.362 (0.001) 10.80 17.41 2.708 (0.003) 2.72 (0.003) 41 15.2 0.97 0.331 (0.001) 0.328 (0.001) 12.67 29.39 2.718 (0.003) 2.73 (0.006) 61 28.2 1.01 0.344 (0.001) 0.341 (0.003) 12.37 50.95 2.723 (0.003) 2.74 (0.011) 21 1.42 1.89 0.648 (0.002) 0.643 (0.002) 16.86 28.18 2.705 (0.004) 2.72 (0.005) 41 14.9 1.73 0.588 (0.002) 0.586 (0.003) 18.02 37.69 2.717 (0.004) 2.72 (0.007) 61 28.2 1.94 0.663 (0.002) 0.658 (0.005) 18.79 55.33 2.707 (0.005) 2.72 (0.011) 21 1.37 2.87 0.989 (0.004) 0.985 (0.005) 21.19 35.79 2.698 (0.005) 2.71 (0.007) 41 14.8 2.86 0.987 (0.004) 0.982 (0.006) 23.95 45.34 2.700 (0.005) 2.71 (0.009) 61 28.4 2.88 0.989 (0.004) 0.988 (0.009) 24.62 62.51 2.700 (0.005) 2.70 (0.012) 21 1.37 4.19 1.472 (0.014) 1.468 (0.011) 50.65 52.69 2.677 (0.019) 2.68 (0.010) 41 14.6 4.67 1.647 (0.009) 1.643 (0.015) 33.55 62.10 2.678 (0.007) 2.68 (0.012) 61 28.5 4.76 1.679 (0.008) 1.677 (0.017) 34.94 78.37 2.679 (0.007) 2.68 (0.014) 21 1.29 6.66 2.371 (0.015) 2.379 (0.023) 37.45 62.79 2.662 (0.009) 2.66 (0.013) 41 14.9 6.56 2.325 (0.016) 2.338 (0.026) 39.66 69.45 2.663 (0.009) 2.66 (0.015) 61 28.6 6.73 2.402 (0.015) 2.424 (0.028) 38.99 78.86 2.665 (0.008) 2.65 (0.016) 21 1.23 9.62 3.437 (0.023) 3.469 (0.036) 71.22 54.63 2.644 (0.009) 2.63 (0.014) 41 14.4 9.48 3.422 (0.026) 3.465 (0.045) 37.97 66.53 2.646 (0.011) 2.63 (0.018) 61 28.6 9.57 3.455 (0.022) 3.506 (0.046) 40.60 78.92 2.645 (0.009) 2.63 (0.018) 21 1.13 12.55 4.529 (0.030) 4.576 (0.053) 30.85 50.16 2.632 (0.009) 2.62 (0.016) 41 14.3 12.57 4.591 (0.030) 4.640 (0.063) 34.48 61.97 2.635 (0.009) 2.59 (0.022) 61 28.6 12.55 4.564 (0.031) 4.649 (0.069) 72.31 73.58 2.626 (0.009) 2.60 (0.020) 21 0.998 15.32 5.634 (0.065) 5.757 (0.075) 27.74 46.90 2.622 (0.025) 2.59 (0.017) 41 14.1 15.42 5.664 (0.041) 5.810 (0.094) 26.27 50.17 2.619 (0.010) 2.58 (0.019) 61 28.7 15.46 5.705 (0.044) 5.864 (0.105) 28.03 62.03 2.614 (0.011) 2.58 (0.024) 21 0.953 17.24 6.277 (0.061) 6.411 (0.089) 22.02 33.35 2.620 (0.020) 2.59 (0.019) 41 14.2 17.27 6.341 (0.037) 6.516 (0.092) 20.98 40.64 2.613 (0.008) 2.57 (0.019) 61 28.6 17.44 6.434 (0.043) 6.638 (0.110) 24.65 60.77 2.609 (0.009) 2.57 (0.022) 21 0.749 18.23 6.663 (0.091) 6.778 (0.096) 25.88 43.77 2.618 (0.032) 2.60 (0.019) 41 14.0 18.24 6.736 (0.080) 6.943 (0.101) 42.53 42.69 2.612 (0.025) 2.58 (0.019) 61 28.4 18.40 6.762 (0.045) 6.966 (0.123) 23.37 61.39 2.607 (0.009) 2.57 (0.024) 21 0.572 19.35 7.091 (0.042) 7.200 (0.099) 19.60 29.47 2.614 (0.008) 2.60 (0.018) 41 14.0 19.24 7.059 (0.040) 7.232 (0.105) 20.80 38.48 2.610 (0.008) 2.73 (0.007) 61 28.1 19.27 7.071 (0.042) 7.290 (0.125) 20.90 52.66 2.609 (0.008) 2.57 (0.023)
a Fluctuations appear in parenthesis.
Table 5.
Summary of Mean and Fluctuation Temperature Probe Values Above the First Hot Plate with Varying Laser Power and Rayleigh Numbersa
k
(
T
1
,
3
¯
)
/
T
1
,
0
/
∘
C
R
a
/
10
6
P
/
k
W
T
1
,
1
/
∘
C
T
1
,
2
/
∘
C
T
1
,
3
/
∘
C
T
1
,
4
/
∘
C
n
o
(
T
1
,
3
¯
)
/
10
−
3
μ
(
T
1
,
3
¯
)
/
µ
P
a
s
(
m
W
/
m
K
)
21 1.44 1.07 19.87 (0.0182) 19.74 (0.0133) 19.82 (0.0141) 19.88 (0.0207) 2.660 18.14 25.70 41 15.2 0.97 23.25 (0.1161) 22.70 (0.0981) 21.43 (0.0053) 21.63 (0.0226) 2.645 18.22 25.83 61 28.2 1.01 24.23 (0.2741) 22.16 (0.1055) 22.77 (0.1172) 22.30 (0.0794) 2.627 18.31 25.99 21 1.42 1.89 19.94 (0.0200) 19.76 (0.0145) 19.91 (0.0083) 20.02 (0.0152) 2.659 18.15 25.71 41 14.9 1.73 23.02 (0.0999) 22.55 (0.0978) 21.42 (0.0080) 21.56 (0.0124) 2.645 18.22 25.83 61 28.2 1.94 23.94 (0.1913) 22.22 (0.1031) 22.64 (0.0526) 22.24 (0.0810) 2.628 18.28 25.93 21 1.37 2.87 20.23 (0.0207) 20.08 (0.0150) 19.96 (0.0108) 20.10 (0.0154) 2.659 18.15 25.71 41 14.8 2.86 22.86 (0.1074) 22.38 (0.0703) 21.37 (0.0191) 21.54 (0.0219) 2.645 18.22 25.82 61 28.4 2.88 124.37 (0.2538) 22.62 (0.1781) 22.71 (0.0865) 22.08 (0.0678) 2.628 18.28 25.92 21 1.37 4.19 20.31 (0.0239) 20.16 (0.0212) 19.95 (0.0112) 20.16 (0.0162) 2.658 18.15 25.71 41 14.6 4.67 22.62 (0.1523) 22.27 (0.1449) 21.38 (0.0292) 21.53 (0.0298) 2.645 18.22 25.82 61 28.5 4.76 24.89 (0.1709) 23.18 (0.1662) 21.85 (0.0420) 21.87 (0.0442) 2.632 18.25 25.88 21 1.29 6.66 20.37 (0.0270) 20.23 (0.0205) 20.03 (0.0207) 20.25 (0.0223) 2.658 18.15 25.72 41 14.9 6.56 22.74 (0.0738) 22.39 (0.0989) 21.35 (0.0076) 21.55 (0.0234) 2.645 18.21 25.82 61 28.6 6.73 24.88 (0.1526) 24.00 (0.3012) 21.85 (0.0859) 21.77 (0.0714) 2.634 18.24 25.86 21 1.23 9.62 20.59 (0.0402) 20.42 (0.0234) 20.23 (0.0259) 20.480 (0.0336) 2.656 18.16 25.73 41 14.4 9.48 22.91 (0.0893) 22.50 (0.0768) 21.43 (0.0283) 21.67 (0.0335) 2.644 18.22 25.83 61 28.6 9.57 25.30 (0.1903) 24.35 (0.2220) 21.98 (0.0368) 21.96 (0.0223) 2.632 18.24 25.87 21 1.13 12.55 20.89 (0.0445) 20.72 (0.0271) 20.56 (0.0233) 20.80 (0.0327) 2.653 18.18 25.76 41 14.3 12.57 22.67 (0.0740) 22.37 (0.0653) 21.49 (0.0349) 21.67 (0.0353) 2.643 18.22 25.83 61 28.6 12.55 25.29 (0.1989) 24.33 (0.2508) 22.02 (0.0343) 22.05 (0.0322) 2.632 18.25 25.88 21 0.998 15.32 21.19 (0.0610) 21.01 (0.0411) 20.83 (0.0393) 21.11 (0.0474) 2.650 18.19 25.78 41 14.1 15.42 23.11 (0.1284) 22.68 (0.1065) 21.62 (0.0374) 21.82 (0.0391) 2.642 18.23 25.84 61 28.7 15.46 25.70 (0.2710) 24.34 (0.2319) 22.20 (0.0107) 22.34 (0.0453) 2.630 18.25 25.89 21 0.953 17.24 21.42 (0.0682) 21.21 (0.0414) 21.02 (0.0383) 21.32 (0.0459) 2.648 18.20 25.80 41 14.2 17.27 23.16 (0.1217) 22.67 (0.0741) 21.81 (0.0491) 22.07 (0.0502) 2.641 18.24 25.86 61 28.6 17.44 26.42 (0.2695) 25.39 (0.2072) 22.47 (0.0271) 22.51 (0.0627) 2.628 18.27 25.91 21 0.749 18.23 21.82 (0.0642) 21.60 (0.0411) 21.46 (0.0408) 21.75 (0.0472) 2.644 18.22 25.83 41 14.0 18.24 23.95 (0.1004) 23.43 (0.1139) 22.09 (0.0336) 22.37 (0.0455) 2.638 18.25 25.88 61 28.4 18.40 25.97 (0.2758) 24.84 (0.1863) 22.81 (0.0525) 22.87 (0.0521) 2.625 18.28 25.94 21 0.572 19.35 22.17 (0.0591) 21.95 (0.0396) 21.82 (0.0407) 21.15 (0.0462) 2.641 18.24 25.86 41 14.0 19.24 24.27 (0.0987) 23.39 (0.0907) 22.41 (0.0543) 22.69 (0.0571) 2.635 18.27 25.91 61 28.1 19.27 26.41 (0.2339) 25.51 (0.2258) 23.01 (0.0240) 23.13 (0.0455) 2.623 18.29 25.95
a Prandtl number is 0.71. Fluctuations appear in parenthesis.
Table 6.
Mean, Standard Deviation, and Maximal Values of Inter-Slice Relative Percentage Temperature Differences
Relative % Difference
Δ
T
11
/
%
Δ
T
12
/
%
Δ
T
13
/
%
Δ
T
14
/
%
Δ
T
21
/
%
Δ
T
22
/
%
Δ
T
23
/
%
Δ
T
24
/
%
Δ
T
31
/
%
Δ
T
32
/
%
Δ
T
33
/
%
Δ
T
34
/
%
Mean −1.30 −0.65 −4.17 −3.43 0.57 0.87 1.73 −0.60 1.88 1.27 0.45 0.42 Standard deviation 3.27 2.75 2.60 3.43 1.52 1.59 2.72 1.93 1.57 0.98 2.30 2.05 absolute Maximum 12.10 10.23 13.15 15.79 7.09 8.42 10.93 7.37 9.88 5.60 7.70 6.43