Indirect Measurement of Fractional Impedances
Bibliographic record
Abstract
This thesis investigates the measurement of fractional-order parameters that describe the electrical impedance of tissues and devices without requiring direct impedance measurements. Concepts from fractional calculus are imported to develop fractional circuit theory and derive the voltage and current excited step responses and magnitude responses of the single-dispersion Cole impedance model which is widely used in biomedicine and biology. Using these responses a numerical graph-fitting and non-linear least squares fitting routine have been applied to MATLAB simulations to assess the accuracy of this approach to extract the fractional impedance parameters that describe this model. Experimentally collected data from fruit tissues and ideal Cole models validate these methods. These fractional calculus concepts are further applied to develop the circuit theory to describe the current excited step response and magnitude response of the double-dispersion Cole impedance model. MATLAB and PSPICE simulations of assess the accuracy of this approach to extract the fractional impedance parameters that describe this model. Experimentally collected data from the current-excited step response and voltage excited magnitude response of apples validates these methods. Finally, the fractional circuit theory is applied to develop the expression for the voltage-excited step-response of a fractional model for a supercapacitor which is then used with non-linear least squares method extract the impedance parameters that characterize the model. This method is validated experimentally using results collected from low capacity supercapacitors with manufacturer ratings of 0.33 F, 1 F, and 1.5 F and high capacity supercapacitors with 1500 F and 3000 F manufacturer ratings.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".