Two-Dimensional Resistance Tomography Using Orthogonal Basis Functions
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Solution Overview
Problem
Traditional two-dimensional resistance tomography methods suffer from low resolution and inefficient use of computing resources due to the reliance on ill-defined mesh problems and poorly placed contact electrodes, leading to non-unique solutions and wasted computational power.
Innovation Solution
Implement an orthogonal basis function approach with strategically placed electrodes and optimized current-voltage pairs to enhance resolution, using polynomial functions and principle component analysis to ensure a maximum number of independent measurements, thereby improving signal-to-noise ratio and reducing computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a large number of periphery contact electrodes are used to increase tomographic image resolution, then measurement precision is improved, but device complexity and computational complexity increase significantly
Solution Approach 1:
The patent applies partial action by using only 8 strategically placed contact electrodes instead of a large number of electrodes. This selective placement at specific positions (0°, 45°, 90°, 135°, 180°, 225°, 270°, 315°) provides sufficient measurement data for high-resolution tomographic imaging without the complexity of using many more electrodes. The principle is demonstrated in the electrode configuration section where exactly 8 electrodes are positioned at specific angular intervals around the resistive elastomer membrane.
Solution Approach 2:
The patent changes the parameter of electrode placement from arbitrary or uniform distribution to specific angular positions (0°, 45°, 90°, 135°, 180°, 225°, 270°, 315°). This parameter optimization ensures that the 8 electrodes provide maximum information for tomographic reconstruction. The orthogonal basis function approach also changes the mathematical parameter space to efficiently process the limited measurements from these 8 electrodes.
2Device complexity
If traditional mesh algorithms are used with limited electrode data, then device complexity is reduced, but measurement precision and solution uniqueness deteriorate
Solution Approach 1:
The patent applies preliminary action by pre-defining an orthogonal basis function set that is specifically tailored to the 8-electrode configuration. The basis functions are constructed beforehand to match the measurement geometry, ensuring that the inverse problem has a unique solution. This preliminary mathematical framework is established before actual measurements are taken, allowing the system to achieve high resolution without complex iterative mesh algorithms.
Solution Approach 2:
The patent substitutes traditional mechanical mesh-based numerical methods with a mathematical basis function approach. Instead of using complex finite element meshes and iterative solvers, the invention uses pre-defined orthogonal polynomial basis functions that directly map the electrode measurements to the resistivity distribution. This substitution simplifies the computational mechanism while improving solution uniqueness and precision.
3Power
If more computational resources are allocated to mesh algorithms, then processing power increases, but computational efficiency decreases due to ill-defined problems
Solution Approach 1:
The patent extracts the essential measurement information from the electrode data by projecting it onto a pre-defined orthogonal basis function set. This extraction process directly computes the resistivity distribution without requiring complex iterative mesh algorithms. By taking out only the necessary information through the basis function projection, the system achieves efficient computation with reduced power requirements while maintaining high productivity.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
Achieves high-resolution tomographic imaging by ensuring unique solutions and efficient use of computational resources, enhancing the accuracy and speed of resistance mapping.
Implementation Method 1
two-dimensional (2-D) and three-dimensional (3-D) tomographic resistance mapping... a resistive elastomer sensing membrane to produce a change in resistance when contact pressure is applied
Data Source
AI summary
The disclosed 2-D and 3-D tomographic resistance imaging method improves tomographic resistance image resolution by adopting an orthogonal basis with the maximum number of elements N to describe the maximum resolution resistivity map ρ(r), where this number of elements N is set according to the number of electrodes Q; by defining the orthogonal basis according to any known constraints in the problem, thereby enhancing the resolution where it is needed; by positioning electrodes to be sensitive to these basis functions; and by choosing current I and voltage V contact electrode pairs that maximize signal-to-noise ratio.