Exploring the performance of the topological energy method for object and damage detection from noisy and poor...

Area of Science:

• Computational physics and applied mathematics.
• Signal processing and inverse problems.

Background:

• Limited-view data and noise challenge accurate experimental analysis.
• Topological energy computations offer a novel approach to data processing.

Purpose of the Study:

• To evaluate numerical methods based on topological energies for noisy, limited-view data.
• To demonstrate the application of these methods in electromagnetic scattering and acoustic testing.
• To address challenges in non-smooth variational problems within mechanics.

Main Methods:

• Utilizing numerical methods centered on topological energy calculations.
• Processing synthetic and real experimental data with limited views and few frequencies.
• Applying methods to electromagnetic scattering from objects in the Fresnel database.
• Employing acoustic testing on synthetic steel welding joints to detect flaws.

Main Results:

• Successful performance of topological energy-based numerical methods was demonstrated.
• Effective processing of noisy, limited-view data from both synthetic and real experiments.
• Accurate identification of flaws such as air bubbles and inclusions in steel welds.
• Validation of the approach for electromagnetic scattering problems.

Conclusions:

• Numerical methods leveraging topological energies are effective for processing challenging experimental data.
• The study highlights the utility of these methods in practical applications like non-destructive testing.
• Topological energy computations provide a robust framework for inverse problems with limited data.