Optimal Choice of the Regularization Parameter for Direct Identification of Polymers Relaxation Time and Frequency...

Area of Science:

• Polymer Science
• Rheology
• Computational Materials Science

Background:

• Recovering the relaxation spectrum from experimental data is a challenging ill-posed inverse problem.
• Existing methods require specialized identification techniques for accurate polymer characterization.

Purpose of the Study:

• To investigate regularization aspects of Tikhonov regularization for direct relaxation spectra identification.
• To develop and validate new methods for selecting the optimal regularization parameter.

Main Methods:

• Applied Tikhonov regularization to the linear-quadratic optimization task for relaxation spectra identification.
• Investigated the influence of the regularization parameter on spectral model norms and relaxation modulus fit.
• Defined two new multiplicative indices for regularization parameter selection based on trade-offs.

Main Results:

• Derived and solved two new optimal selection problems for the regularization parameter.
• Presented a complete identification algorithm for relaxation spectra.
• Demonstrated the effectiveness of new selection rules with various spectral models.

Conclusions:

• The proposed multiplicative indices offer effective criteria for selecting the optimal regularization parameter.
• The developed algorithm and selection rules enhance the accuracy of polymer relaxation spectrum identification.
• This work provides a robust framework for rheological data analysis.