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Calibration Procedures for Orthogonal Superposition Rheology

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Inverse problem and the pseudoempirical orthogonal function method of solution. 1: Theory.

A Ben-David, B M Herman, J A Reagan

|June 10, 2010

Summary

This summary is machine-generated.

This study introduces pseudo-empirical orthogonal functions to reconstruct data distributions when observations are limited. This method enables accurate function inversion using mathematical models and constraints.

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Area of Science:

Data analysis
Applied mathematics
Scientific modeling

Background:

Empirical orthogonal functions (EOFs) are derived from observed data distributions.
Constructing EOFs requires a substantial library of observations, which is often unavailable.
Mathematical functions can represent distributions when direct observations are scarce.

Purpose of the Study:

To develop an inversion method using pseudo-empirical orthogonal functions (pseudo-EOFs) when observational data is insufficient.
To leverage known mathematical forms of distributions to create a functional library.
To enable function reconstruction from a limited set of mathematical functions.

Main Methods:

Constructing a library of distributions from known mathematical functions.
Developing pseudo-EOFs from this mathematical library.
Employing a linear sum of pseudo-EOFs to represent any distribution.
Implementing an inversion technique with smoothing and positivity constraints.

Main Results:

Demonstrated the feasibility of constructing pseudo-EOFs from mathematical libraries.
Successfully applied the pseudo-EOF method for function inversion without extensive observed data.
Validated the effectiveness of incorporating smoothing and positivity constraints.

Conclusions:

Pseudo-EOFs provide a viable alternative to empirical EOFs when observational data is limited.
The developed inversion method is effective for reconstructing distributions using mathematical models.
The technique offers a robust approach for data analysis in data-scarce scientific domains.