# Presentation: 424693

## Analysis and Design of Multi-Wave Dilectrometer (MWD) for 

**Characterization of Planetary Subsurface Using Finite Element Method**

- Manohar D. Deshpande and Michael E. Van Steenberg
- NASA Goddard Space Flight Center, Greenbelt, MD

- Seventh FEMCI Workshop on Innovative Solutions to Structural Analysis and Test Problems
- Oct. 25-26, 2006

## 1. One of the scientific goals of these missions is to search for water and other 

- _Hopper Mission to Moon/Mar_

- _Rover Mission to Mar_

- 1. One of the scientific goals of these missions is to search for water and other
-     essential materials for human survivability on these planets.
- A simple, light weight, and low power instrument called Multi-Wave
-      Dielectrometer (MWD) if integrated with Rover/Hopper will help in
-      (a) characterizing electrical properties of subsurface Moon/Mar’s soil,
-      (b) understanding geological evolution of subsurface of these planets
-            without digging .
- In this presentation an attempt is made to demonstrate  use of
- Finite Element Procedure to analyze and design proposed
- MWD instrument

_**Introduction:**_

## Multi-Wave Dielectrometer

- _Multi-Wave Dielectrometer_

- _Schematic Diagram of MWD_

- Moon Hopper

## Data Processing 

-              Data Acquisition
- Measure mutual capacitances
-         between all combinations of
-         electrodes.

- Model #1

- Model #2

- Data Processing
- 1. Assume a physical model for
-         stratified medium
- 2. Using FEM modeling, mutual
-      capacitances are estimated as
-      a function of dielectric profile.
- 3. Define error function as
- 4. Using optimization procedure based
-      on gradient based method, Genetic
-      Algorithm (GA), or Neural Network
-     (NN), error is minimized to arrive at
-      a probable dielectric profile.

- FEM Modeling

## Finite Element Procedure for Estimation of Mutual Capacitances:

- Ground Shield

- #1

- #2

- #3

- #4

- Homogeneous/In-homogeneous
- medium

- How are the capacitances defined?
- Let                   and          be the charges collected on electrodes #1,#2, #3, and #4
- when a low frequency voltage       is applied to electrode #1 and other electrodes are grounded.  Then capacitances are defined as
-           ,             ,            ,
- Other capacitances are similarly defined.  In general capacitance
-            is defined as
-  where the charge collected       is given by
-                  being electrical potential
- Conclusion:
- Mutual capacitances can be estimated by solving Laplace’s equation
-  subjected to proper boundary condition dictated by the geometry of MWD instrument.

## Solution of Laplace Equation Using FEM Method

- Laplace Equation:                                                                   (1)
- Electric Field Distribution:                                                       (2)
- Electric energy stored in the structure:
-                                                                                                   (3)
- For 2-D case:  divide the region into triangles (as shown below).
- If                  are the nodal voltages
- then  electric potential  and field over
- the triangle can be written as
- Electric energy stored over the triangle:

## Stored energy over the triangle:

- where

- If there are N triangles, total stored energy:

- The nodal voltages are obtained
-  by minimizing the total energy.
- This minimization yields following
- matrix equation which can be
- solved for nodal potentials.

- Mutual Capacitance:

##  Discretize Geometry 

- Using Commercial CAD Package
-  Discretize Geometry

- Assume Initial Values for
- electrical properties of medium

- Estimate Capacitances Using
- FEM Code

- Measured Values of Capacitances

- Less than desired value

- Stop

- Estimate Gradient

- Update Initial Guess

- Flow Chart for Dielectric Profile Estimation

## Numerical Validation:

- Example 1:

- Geometrical Model

- FEM Model

- Electrode #1

- Electrode #2

- Electrode #3

- Electrode #4

## Comparison of computed values of capacitances with

- earlier published data forward problem

## Inversion/Extraction Procedure: 

- Can we extract a dielectric profile of medium if the capacitances
-  between electrodes embedded in the medium are known?

- Estimation error = 1.4%

- Estimation error = 2.9%

- Estimation error = 1.5%

## Example 2:

## Electrodes

- Ground Shield

- Dimensions in cm

- Electrode Sensor Geometry

- FEM Model

## Example 3:

- Percentage Error
- In estimation= 9.5%

- Percentage Error
- In estimation= 24%

## 80 degrees wide 

- Ground Shield

- 4 Electrodes
- 80 degrees wide

- FEM Model

## Slide 16

## 2. With er2 = 3.5  generate mutual capacitance 

- Layer#1

- Layer#2

- Layer#3

- Example 4:

- 1. Assume that dielectric constants
-     of layer #1,#3, and #4 are known (=1.0)
- 2. With er2 = 3.5  generate mutual capacitance
-     data
- 3. Use the procedure to estimate dielectric
-     constant of layer #2

## 2. With er3 = 3.5  generate mutual capacitance 

- 1. Assume that dielectric constants
-     of layer #1,#2, and #4 are known (=1.0)
- 2. With er3 = 3.5  generate mutual capacitance
-     data
- 3. Use the procedure to estimate dielectric
-     constant of layer #3

## Conclusions:

- 2-Dimensional Finite Element Method has been successfully employed
-      to analyze and design multi-wave dielectrometer to estimate dielectric
-      constants of inhomogeneous medium.
- When the electrodes are evenly distributed in a medium under test
-       the multi-wave dielectrometer predicts the medium constants with
-       accuracy greater than 97%
- When the electrodes are distributed on a plane surface, the region
-       closer to the electrodes are predicted with more accuracy compared
-       to the regions away from the electrodes.

- Future Work:

- In the present formulation dielectrometer boundary was enclosed in a
-       closed metallic ground shield.  However, in a real situation,  ground
-       shielding is only at the top.  We would like to modify our formulation
-       to take into account actual geometry of MWD
- The real MWD is a 3-Dimenional device.  Our ultimate goal is to develop
-       3-D FEM model to analyze these devices.