The results from our previous study [
25], where we analyzed three different configurations of the applied excitation current, which generates two different patterns of magnetic flux around our opted MI TD coils, shown in
Figure 1 and
Figure 2. Both of the generated magnetic flux patterns were further divided into cases for further analysis, where, in
Figure 1, we observed blind areas from 80° to 200° and 270° to 20°, which, in total, combined to form 120° + 110° = 230° blind areas. In
Figure 2, we observe blind areas from 110° to 160°, 210° to 260°, 290° to 350°, and 20° to 70°, which, in total, combined to form 200° of blind areas. These blind areas were causing a lot of inaccuracy in the localization of sensor Rx nodes in MI-UWSNs. The main point of concern due to these blind areas was that a lot of power source was wasted.
Additionally, we did not find any MI TD coil configuration by any research group in any study, where one can claim an omni directional magnetic flux or near to omni directional communication around the anchor Tx and sensor Rx coils. We in this study besides, a machine learning-based linear regression technique, to predict localization estimation accuracy in MI-UWSNs. However, had also focused on achieving an omni directional magnetic flux pattern around the MI TD coils. For which a combination of four coils approach at xy plane and an eight coils approach in xyz plane is opted to achieve almost near to omni directional magnetic flux pattern around the communicating coils in MI-UWSNs. The top view of the TD coil is shown in
Figure 6a. Where c1 is denoting coil one, which is at 0°, c2 is denoting coil 2 which is at 40° from c1. c3 denotes coil 3, which is at 80° from c1 and 40° from c2. c4 denotes coil four which is at 120° from c1, 80° from c2 and 40° degree from c3. Do not confuse the aforementioned degrees as degree of computation of magnetic flux. Consider these degrees, as the degree of shift where the new coil will be placed. Which means that all the four coils are separate entities in itself and will have a computation degree of 0° to 360°.
Figure 6b,c) are showcasing the side view of the opted MI TD coil in xy and xy, z planes, respectively.
The New Magneto Inductive Flux Pattern
The pseudo code to generate new flux pattern is given as Algorithm 3. So that one can regenerate the results portrayed in
Figure 7,
Figure 8 and
Figure 9. All these results are obtained in MATLAB. Whereas a first step we have to find out the magneto motive force
M. For which
N is the number of turns,
I is the excitation current applied,
A is the area of the coil. Once this magneto motive force was found out, then we will find the magnetic flux produced by it. The magnetic flux produced by the magneto motive force will consists of two components. Bothe these components will be 90° out of phase to each other. We can call these components the major (
) and minor (
) components. Major component is the one which is along the x axis and has a cos dependency. Minor component is the one which is tangent to the major axis and has a sin dependency. Once holding the plot of major and minor components of the generated magnetic flux on the same polar plot. We will highlight the maximum of both the aforementioned component. Next another coil with the same structural properties is introduced in the simulation environment but it will be 40° out of phase from the coil 1. Two more coils named, coil 3 and coil 4 with same structural properties and each one 40° out of phase from its previous coil are introduced in the simulation environment. Which provided us the magnetic flux pattern around the coil shown in
Figure 7e. Next we had plotted the z component of the magnetic flux. For which the maximum of the xy plane will act as x axis and the z axis will be considered as y axis and the whole process will be repeated. Which will give us the magnetic flux pattern shown in
Figure 8e. As we think that it will be difficult to assume the sketch of both the maximum values in 3D. So for the better understanding of the readers, we had plotted the maximum values of xy and xy, z plane in 3D that are shown in
Figure 9a,b, respectively.
When an excitation sinusoidal current is applied to c1. A magnetic flux around the coil is generated which can be found by
. Where
M is the magneto motive force, N and A are number of turns and area of the communicating coils respectively. This generated magneto motive force consists of two parts. One is on the axis of communication at 0° and the other one is the tangential component which is normally 90° out of phase to the communicating axis.
is the calculation of major component of magnetic flux density which is at 0°, and
is the minor component of the generated magnetic flux around the communicating TD coil which is at 90°, and normally it is tangent to major component. In the aforementioned equations
M is the magneto motive force,
r is the distance, where the effect of magnetic flux can be observed. The cube on the distance in the equation indicates that the attenuation factor in MI communication is very high and the MI signal decays rapidly with respect to the increase in distance between Rx and Tx nodes. The magnetic flux pattern that can be seen in
Figure 7a, shows both the major communicating component of the generated magnetic flux around the coil1 (c1) which is denoted with blue and is calculated by
. Whereas the tangential component of the generated magnetic flux around the c1, is denoted with orange and is calculated by
. However, the black line, are the maximum values of the generated magnetic flux, which consist of both major and minor component of c1. The magnetic flux pattern shown in
Figure 7b is obtained when another coil c2 is introduced
Figure 6a. Which is at 40° shifted from the c1
“
see calculus one for graph shifting”. Here the data denoted with yellow is the maximum of the major and minor components of c2. However, the black line, are the maximum values of the generated magnetic flux, which consist of both major and minor component of c1, c2.
Algorithm 3: A Pseudo Code for the Generation of Magnetic Flux Pattern. |
Start |
- 1:
Inputs - 2:
N = number of turns - 3:
I = current applied - 4:
A = area of the coil - 5:
M = NIA magneto motive force - 6:
theta = 0–360 - 7:
theta_rad = convert theta values to radian - 8:
Outputs - 9:
major component of magnetic flux of coil 1 in xy plane - 10:
minor component of magnetic flux of coil 1 in xy plane - 11:
- 12:
Max of major and minor axis - 13:
- 14:
polar plot - 15:
major component of magnetic flux of coil 2 in xy plane - 16:
minor component of magnetic flux of coil 2 in xy plane - 17:
- 18:
Max of major and minor axis - 19:
- 20:
polar plot - 21:
major component of magnetic flux of coil 3 in xy plane - 22:
minor component of magnetic flux of coil 3 in xy plane - 23:
- 24:
Max of major and minor axis - 25:
- 26:
polar plot - 27:
major component of magnetic flux of coil 4 in xy plane - 28:
minor component of magnetic flux of coil 4 in xy plane - 29:
- 30:
Max of major and minor axis - 31:
- 32:
polar plot - 33:
- 34:
max coil 1, coil 2, coil 3, coil 4 in xy plane - 35:
- 36:
polar plot - 37:
major component of magnetic flux of coil1 in xy, z plane - 38:
- 39:
max coil 1, coil 2, coil 3, coil 4 in xy plane - 40:
- 41:
Max of coils at xy plane plus max of coil 1 at z plane - 42:
- 43:
polar plot - 44:
major component of magnetic flux of coil 2 in xy, z plane - 45:
- 46:
max coil 1, coil 2, coil 3, coil 4 in xy plane - 47:
- 48:
Max of coils at xy plane plus max of coil 2 at z plane - 49:
- 50:
polar plot - 51:
major component of magnetic flux of coil 3 in xy, z plane - 52:
- 53:
max coil 1, coil 2, coil 3, coil 4 in xy plane - 54:
- 55:
Max of coils at xy plane plus max of coil 3 at z plane - 56:
- 57:
polar plot - 58:
major component of magnetic flux of coil 4 in xy, z plane - 59:
- 60:
max coil 1, coil 2, coil 3, coil 4 in xy plane - 61:
- 62:
Max of coils at xy plane plus max of coil 4 at z plane - 63:
- 64:
polar plot - 65:
- 66:
theta = max of all coils at xy plane - 67:
- 68:
phi = max of coils at xy plan and z plane - 69:
- 70:
mesh/surf - 71:
end - 72:
end - 73:
end
|
Magnetic flux pattern shown in
Figure 7c is obtained by introducing a 3rd coil c3, which is 80° shifted from c1
and 40° shifted from c2
Figure 6a. Here the data denoted with yellow is the maximum of the major and minor components of c3. However, the black line, are the maximum values of the generated magnetic flux, which consist of both major and minor component of c1, c2 and c3. Magnetic flux pattern shown in
Figure 7d is obtained by introducing a 4th coil c4, which is 120° shifted from c1
, 80° shifted from c2 and 40° shifted from c3
Figure 6a. Here the data denoted with yellow is the maximum of the major and minor components of c4. However, the black line, are the maximum values of the generated magnetic flux, which consist of both major and minor component of c1, c2, c3 and c4, where every next coil is 40° shifted in comparison to previous coil. In the next
Figure 7e we have combined all the maximum values of the generated magnetic flux around the coils c1, c2, c3, c4, and shown it on the same plot to depict that this is how the magnetic flux will be, when using this new novel MI-TD coil configuration. The explained coil configuration is for xy plane shown with blue color in
Figure 7f. This
Figure 7f is introduced for the better understanding of the reader. The xy plane is colored blue to indicate that we had achieved a communication pattern for xy plane and now we will introduce a z component to our existing structure of the MI-TD coil to make the generated magnetic flux near to omnidirectional.
The z component of the TD coil configuration is same as coil structure opted for xy plane shown in
Figure 6b. So by combining it with the existing coil structure we get a coil structure shown in
Figure 6c. When an excitation current is applied to the coil 1 on z axis called as cz1. We obtained a magnetic flux pattern shown in
Figure 8a, where the blue data is the maximum of cz1′s major component. The reason we are not showing its conventional minor component is, because the whole xy plane is tangent to z plane as can be seen in
Figure 7f. So as xy is the tangential component and all of its values had been founded, discussed and displayed previously in
Figure 7 in this same section. We will simply take the maximum of all the coils on xy plane as a tangential component of each coil present at z plane. Magnetic flux pattern shown in
Figure 8b is obtained by introducing a 2nd coil cz2 which is at 40° shifted from cz1. The blue data is the maximum of cz2, red data is the maximum of all coils at xy plane, and the data shown with black is the maximum of all coils at xy plane and the maximum of two coil introduced in z plane, i.e., cz1, cz2. Magnetic flux pattern shown in
Figure 8c is obtained by introducing a 3rd coil cz3 which is at 80° shifted from cz1 and 40° shifted from cz2. The blue data is the maximum of cz3, red data is the maximum of all coils at xy plane, and the data shown with black is the maximum of all coils at xy plane and the maximum of three coils introduced in z plane, that are cz1, cz2 and cz3. Magnetic flux pattern shown in
Figure 8d is obtained by introducing a 4th coil cz4 which is at 120° shifted from cz1, 80° shifted from cz2 and 40° shifted from cz3. The blue data is the maximum of cz4, red data is the maximum of all coils at xy plane, and the data shown with black is the maximum of all coils at xy plane and the maximum of four coils introduced in z plane, that are cz1, cz2, cz3 and cz4. In
Figure 8e we have plotted the maximum of all coils at xy plane shown with red, and the black line is showing the combination of both the maximum of all the coils at xy planes and maximum of all the coils at z planes. The
Figure 8f is introduced for the better understanding of the reader. The xy plane is colored blue to indicate that we achieved a communication pattern for xy plane, and the z plane is colored yellow to indicate that magnetic flux pattern for z axis is also obtained.
Now, as both the major and minor component of magnetic flux of the opted MI TD coil for UWSNs are obtained, for xy and z plane. We had plotted those points in a 3D plot for the ease of understanding of the reader. The sphere shown in
Figure 9a is obtained by plotting the maximum values of the magnetic flux patterns shown in
Figure 8e. Whereas
Figure 9b on the other hand is the top view of the 3D plot to give the reader a new perspective for understanding the magnetic flux around the MI TD coil.