Table1: Cuboid Geometry Enclosure for the Switched Mode Power Supply
Table 2
knob turns in the controller
voltage of the motor (V)
3
1
4
2
5
3
6
4
7
5
8
6
9
7
10
8
Table2: The Controller Knob is Turned and the Corresponding Voltage Obtained for the Motor
Table 3
Voltage
12V DC
Diameter
26 mm
Speed
18000 rpm
Shaft type
Round type
Shaft length
12 mm
Shaft Diameter
2.3 mm
Total body length
5.7 cm
Current
1.2 A
Table3: Parameters of the Motor
Table 4
length (cm)
width (cm)
height (cm)
31
30
0.5
Table4: Geometry of the Acrylic Slab
Table 5
length (cm)
width (cm)
height (cm)
1
1.5
0.5
Table5: Geometry of the Switch
Table 6
α
1.56E+14
8.70E+13
6.20E+13
5.00E+13
4.10E+13
3.60E+13
3.20E+13
3.16E+13
Table6:α Values for the Theory to Obtain the Current in the Motor
Table 7
Armature voltage = 0.2 V
Armature current = 0.61 A
Armature resistance = 0.32 ohm
Table 7: DC Voltage, Armature Current and Armature Resistance. The Motor Shaft do not Rotate at the Low DC Voltage
Table 8
V (volt)
Ia (A)
Power (W)
RA(ohm)
Eb (V)
Ke (V/(rad/s))
ω(rad/s)
speed (rpm)
Torque (Nm)
1
0.64
0.64
0.32
0.7952
0.0064
124.25
1187.102
0.004096
2
0.71
1.42
0.32
1.7728
0.0064
277
2646.497
0.004544
3
0.76
2.28
0.32
2.7568
0.0064
430.75
4115.446
0.004864
4
0.82
3.28
0.32
3.7376
0.0064
584
5579.618
0.005248
5
0.85
4.25
0.32
4.728
0.0064
738.75
7058.121
0.00544
6
0.89
5.34
0.32
5.7152
0.0064
893
8531.847
0.005696
7
0.92
6.44
0.32
6.7056
0.0064
1047.75
10010.35
0.005888
8
1.04
8.32
0.32
7.6672
0.0064
1198
11445.86
0.006656
Table8: Parameters of the device
Table 9
rpm
rad/s
18000
1884.96
Table9: Speed and Angular Velocity of the Shaft. The Applied Voltage to the DC Motor is 12 V
Table 10
voltage (V)
electric field (V/m)
concentration (mM)
1
-17.6
9200
2
-35.1
5100
3
-52.7
3600
4
-70.2
2900
5
-87.8
2400
6
-105.3
2100
7
-122.81
1900
8
-140.4
1850
Table10: Simulation Parameters to Model the Motor
Table 11
Trial 1
Trial 2
Trial 3
Trial 4
voltage (V)
current (A)
voltage (V)
current (A)
voltage (V)
current (A)
voltage (V)
current (A)
1
0.64
1
0.65
1
0.64
1
0.64
2
0.71
2
0.72
2
0.71
2
0.72
3
0.76
3
0.77
3
0.78
3
0.78
4
0.82
4
0.83
4
0.81
4
0.82
5
0.85
5
0.87
5
0.88
5
0.86
6
0.89
6
0.93
6
0.94
6
0.92
7
0.92
7
0.96
7
1.03
7
1
8
1.04
8
1.08
8
1.12
8
1.14
Table11: Current-Voltage Characteristics for the DC Motor Having Rollers. Trial 1, Trial 2, Trial 3 and Trial 4 are the Four Repeats
Table 12
voltage(V)
current(A)
Power(W)
1
0.64
0.64
1
0.64
0.64
1
0.64
0.64
1
0.64
0.64
1
0.64
0.64
1
0.64
0.64
1
0.64
0.64
Table12: Train data 1 Used for Data Driven in the Neural Network.
Table 13
voltage(V)
current(A)
Power(W)
8
0
8.32
8
0
8.32
8
0
8.32
8
0
8.32
8
0
8.32
8
0
8.32
8
0
8.32
Table13: Test Data Given to Predict the Test Current Using Our Data Driven Neural Network
Table 14
voltage(V)
predict voltage(V)
residual(R)
residual(R2)
current(A)
predict current (A)
residual(R)
residual(R2)
8
8.29
0.29
0.0841
1.04
0.768
0.272
0.074
8
8.26
0.26
0.0676
1.04
0.767
0.273
0.0745
8
8.36
0.36
0.1296
1.04
0.728
0.312
0.0973
8
8.26
0.26
0.0676
1.04
0.775
0.265
0.0702
8
8.24
0.24
0.0576
1.04
0.7.41
0.299
0.0894
8
8.24
0.24
0.0576
1.04
0.762
0.278
0.0772
8
8.28
0.28
0.0784
1.04
0.772
0.268
0.0718
Table14: Comparison of Experiments Voltage, Current with the Predicted Results from Data Driven in the Neural Network
Table 15
Power (W)
predict power (W)
residual(R)
residual(R2)
8.32
8.03
0.29
0.0841
8.32
8.08
0.24
0.0576
8.32
8.09
0.23
0.0529
8.32
8.03
0.29
0.0841
8.32
8.09
0.23
0.0529
8.32
8.09
0.23
0.0529
8.32
8.03
0.29
0.0841
Table15: Comparison of Experiments Obtained Power with the Predicted Power in Watts from the Data Driven in the Neural Network
Table 16
Voltage
current(A)
ɛr
1
0.64
3
1
0.64
3
1
0.64
3
1
0.64
3
1
0.64
3
1
0.64
3
1
0.64
3
Table16: Train Data 1 used for Physics Informed Theory in the Neural Network
Table 17
voltage(V)
current(A)
ɛ r
8
0
3
8
0
3
8
0
3
8
0
3
8
0
3
8
0
3
8
0
3
Table17: Test Data Set for Physics Informed Theory in the Neural Network
Table 18
voltage(V)
predict voltage(V)
residual(R)
residual(R2)
current(A)
predict current(A)
residual(R)
residual(R2)
8
7.93
0.07
0.0049
1.04
0.964
0.076
0.0058
8
7.92
0.08
0.0064
1.04
0.941
0.099
0.0098
8
7.84
0.16
0.0256
1.04
0.935
0.105
0.011
8
7.89
0.11
0.0121
1.04
0.923
0.117
0.014
8
7.92
0.08
0.0064
1.04
0.980
0.06
0.0036
8
7.97
0.03
0.0009
1.04
0.963
0.077
0.006
8
7.94
0.06
0.0036
1.04
0.931
0.109
0.012
Table18: Comparison Between the Provided and Physics Informed Theory in the Neural Network for the Voltage; Current. the Residual and Square of the Residual are Calculated
Table 19
ɛr
predictɛr
residual(R)
residual(R2)
3
3.01
0.01
1e-4
3
2.96
0.04
0.0016
3
3.02
0.02
0.0004
3
2.94
0.06
0.0036
3
2.97
0.03
0.0009
3
2.97
0.03
0.0009
3
3.03
0.03
0.0009
Table19: Comparison of Provided and Physics Informed Theory in the Neural Network, Relative Permittivity. The Residual and Square of the Residual are Calculated
Table 20
voltage(V)
current(A)
gas constant (J/mol K)
1
0.64
8.3
1
0.64
8.3
1
0.64
8.3
1
0.64
8.3
1
0.64
8.3
1
0.64
8.3
1
0.64
8.3
Table20: Train Data 1 Used for Physics Informed Partial Differential Equations in the Neural Network
Table 21
voltage(V)
current(A)
gas constant (J/molK)
8
0
8.3
8
0
8.3
8
0
8.3
8
0
8.3
8
0
8.3
8
0
8.3
8
0
8.3
Table21: Test Data Set for Physics Informed Partial Differential Equation in the Neural Network
Table 22
voltage(V)
predict voltage(V)
residual(R)
residual(R2)
current(A)
predict current(A)
residual(R)
residual(R2)
8
7.81
0.19
0.036
1.04
0.97
0.07
0.0049
8
7.79
0.21
0.044
1.04
0.95
0.09
0.0081
8
7.74
0.26
0.068
1.04
0.99
0.05
0.0025
8
7.75
0.25
0.063
1.04
0.92
0.12
0.0144
8
7.78
0.22
0.048
1.04
0.95
0.09
0.0081
8
7.71
0.29
0.084
1.04
0.94
0.1
0.01
8
7.72
0.28
0.079
1.04
0.92
0.12
0.0144
Table 22: Comparison of Provided and Physics Informed Partial Differential Equation in the Neural Network for the Voltage; Current. The Residual and Square of the Residual are Calculated
Table 23
gas constant (J/mol K)
predict gas constant (J/molK)
residual (R)
residual (R2)
8.3
8.47
0.17
0.0289
8.3
8.38
0.08
0.0064
8.3
8.47
0.17
0.0289
8.3
8.43
0.13
0.0169
8.3
8.46
0.16
0.0256
8.3
8.50
0.2
0.04
8.3
8.40
0.1
0.01
Table 23: Comparison of the Provided and Physics Informed Partial Differential Equation in the Neural Network for the Gas Constant. The Residual and Square of the Residual are Calculated
Table 24
voltage (V)
current (A)
theory current (A)
residual (R)
residual (R2)
1
0.64
0.642148
0.002148
4.61E-06
2
0.71
0.716242
0.006242
3.9E-05
3
0.76
0.765638
0.005638
3.18E-05
4
0.82
0.823267
0.003267
1.07E-05
5
0.85
0.843848
0.006152
3.78E-05
6
0.89
0.889128
0.000872
7.6E-07
7
0.92
0.922059
0.002059
4.24E-06
8
1.04
1.040609
0.000609
3.71E-07
Table 24: Comparison Between the Device Experiments with the Theory. We Calculate the Residual and the Square of the Residual
Table 25
voltage (V)
current (A)
simulation current(A)
residual (R)
residual (R2)
1
0.64
0.638572
0.001428
2.04E-06
2
0.71
0.707982
0.002018
4.07E-06
3
0.76
0.749628
0.010372
0.000108
4
0.82
0.805156
0.014844
0.00022
5
0.85
0.83292
0.01708
0.000292
6
0.89
0.874566
0.015434
0.000238
7
0.92
0.923153
0.003153
9.94E-06
8
1.04
1.027268
0.012732
0.000162
Table 25: Device Experiments and Partial Differential Equations Simulations. We Calculate the Residual and the Square of the Residual
Table 26
V(volt)
Ia (A)
Power (W)
RA(ohm)
Eb (V)
Ke (V/(rad/s))
ω(rad/s)
speed (rpm)
Torque (Nm)
1
0.64
0.64
0.32
0.7952
0.0064
124.25
1187.102
0.004096
2
0.71
1.42
0.32
1.7728
0.0064
277
2646.497
0.004544
3
0.76
2.28
0.32
2.7568
0.0064
430.75
4115.446
0.004864
4
0.82
3.28
0.32
3.7376
0.0064
584
5579.618
0.005248
5
0.85
4.25
0.32
4.728
0.0064
738.75
7058.121
0.00544
6
0.89
5.34
0.32
5.7152
0.0064
893
8531.847
0.005696
7
0.92
6.44
0.32
6.7056
0.0064
1047.75
10010.35
0.005888
Table 26: Train Set Parameters of the Device
Table 27
V(volt)
Ia (A)
Power (W)
RA(ohm)
Eb (V)
Ke (V/(rad/s))
ω(rad/s)
rpm
Torque (Nm)
8
0
8.32
0.32
7.6672
0.0064
1198
11445.86
0.006656
Table27: Test Set Device Parameters
Table 28
Armature current (A)
Predict current (A)
Variance R2
Root Mean Square Error
1.04
1.3
0.0676
0.26
Table28: Predict Current with the Device Parameters
Figure3: The Circuit Diagram Having the Armature Current, Resistance, Voltage, Load DC Motor and Back Electromotive Force
FIGURE 4
Figure4: Schematic of Data Driven Neural Network
FIGURE 5
Figure5: Schematic of Physics from theory informed in the neural network
FIGURE 6
Figure 6: Schematic of Physics from Partial Differential Equations Informed in the Neural Network
FIGURE 7
Figure 7: Comparison Between the Experiments, Theory and Simulations Current–Voltage Characteristics of the Motor. The Simulations Include Partial Differential Equations and Data Driven Neural Networks.
FIGURE 8
Figure 8: Comparison Between the Experiments and Neural Network Simulations of the Current– Voltage Characteristics. The Simulations Include the Physics from Theory Informed in the Neural Network and Partial Differential Equations and Data Driven Neural Networks. The Voltage of the Switched Mode Power Supply and Controller are Measured as 12.25 V in Our Experiments.
FIGURE 9
Figure9: Comparison of the Voltage of the Motor Between Experiment and Data Driven Neural Network
FIGURE 10
Figure10: Power Obtained from the Experiments and Predict Results from Data Driven in the Neural Network.
FIGURE 11
Figure11: Comparison of the Voltage of the Motor Between Experiments and Physics Informed Theory in the Neural Network
FIGURE 12
Figure12: Relative Permittivity Prediction from Physics Informed Theory in the Neural Network
FIGURE 13
Figure13: Comparison of the Voltage of the Motor Between Experiments and the Physics Informed Partial Differential Equation in the Neural Network
FIGURE 14
Figure14: Gas Constant Prediction from Physics Informed Partial Differential Equation in the Neural Network
FIGURE 15
Figure15: Schematic of Data Driven Neural Network for Parameters of the Device
Tables at a glance
Figures at a glance