Plant Tissue Modelling Using Power-Law Filters
Abstract
:1. Introduction
2. Power-Law Filters
2.1. Filters Based on First-Order Mother Functions
2.2. Filters Based on Second-Order Mother Functions
2.3. Power-Law Filter Sections
3. Problem Definition
- The objective function () used by the optimization algorithm is the minimization of the sum of the absolute error between the estimated impedance from the power-law filter and the measured one for each point in the frequency range represented as:
- The number of iterations used in the optimization is 2500 iterations with 60 search agents and 50 independent runs through all the tested samples.
- The search agents search for the best solution in a range defined between a lower (LB) and an upper (UB) boundary defined differently for each filter order. For first-order filters, LB = [, K, ] = [0, 0, 0] and UB = [1, 1, 1], while for second-order filters LB = [, K, , Q] = [0, 0, 0, 0] and UB = [1, 1, 1 , 10].
4. Results and Discussion
4.1. Models Based on Single Power-Law Filters
4.2. Models Based on Power-Law Filters Sections
Nyquist | Error | |
---|---|---|
Apple | ||
Cucumber | ||
Eggplant | ||
Kiwi | ||
Peach | ||
Pear | ||
Plum | ||
Tomato |
Nyquist | Error | |
---|---|---|
Apple | ||
Cucumber | ||
Eggplant | ||
Kiwi | ||
Peach | ||
Pear | ||
Plum | ||
Tomato |
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Parameters | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
Samples | ||||||||||
Single Filter | LP | Apple | - | 0.6846 | - | - | - | - | ||
Cucumber | - | 0.4248 | - | - | - | - | ||||
Eggplant | - | 0.4122 | - | - | - | - | ||||
Kiwi | - | 0.6058 | - | - | - | - | ||||
Peach | - | 0.4896 | - | - | - | - | ||||
Pear | - | 0.5634 | - | - | - | - | ||||
Plum | - | 0.6807 | - | - | - | - | ||||
Tomato | - | 0.5851 | - | - | - | - | ||||
LP | Apple | 0.6344 | - | - | - | - | ||||
Cucumber | 0.4097 | - | - | - | - | |||||
Eggplant | 0.3628 | - | - | - | - | |||||
Kiwi | 0.6050 | - | - | - | - | |||||
Peach | 0.4896 | - | - | - | - | |||||
Pear | 0.4263 | - | - | - | - | |||||
Plum | 0.4066 | - | - | - | - | |||||
Tomato | 0.5419 | - | - | - | - | |||||
BP | Apple | 0.6846 | - | - | - | - | ||||
Cucumber | 8.35 | 0.4248 | - | - | - | - | ||||
Eggplant | 16.02 | 0.4122 | - | - | - | - | ||||
Kiwi | 7.53 | 0.6058 | - | - | - | - | ||||
Peach | 9.59 | 0.4896 | - | - | - | - | ||||
Pear | 0.5634 | - | - | - | - | |||||
Plum | 1.35 | 0.6807 | - | - | - | - | ||||
Tomato | 0.5851 | - | - | - | - | |||||
Double Filters | LP & LP | Apple | - | 0.6981 | - | 0.8015 | ||||
Cucumber | - | 0.2987 | - | 0.4459 | ||||||
Eggplant | - | 0.4234 | - | 0.4431 | ||||||
Kiwi | - | 0.5400 | - | 0.6184 | ||||||
Peach | - | 0.7046 | - | 0.4896 | ||||||
Pear | - | 0.6374 | - | 0.4893 | ||||||
Plum | - | 0.9581 | - | 0.7095 | ||||||
Tomato | - | 0.0061 | - | 0.5851 | ||||||
LP & LP | Apple | 0.41 | 0.3617 | 0.32 | 0.4803 | |||||
Cucumber | 0.36 | 0.2479 | 0.033 | 0.4268 | ||||||
Eggplant | 0.42 | 0.3119 | 0.3491 | |||||||
Kiwi | 0.31 | 0.8244 | 0.11 | 0.3812 | ||||||
Peach | 0.016 | 0.3298 | 0.44 | 0.3366 | ||||||
Pear | 0.049 | 0.4399 | 0.34 | 0.4024 | ||||||
Plum | 0.084 | 0.3535 | 0.36 | 0.3985 | ||||||
Tomato | 0.24 | 0.3418 | 0.35 | 0.3833 | ||||||
LP & AP | Apple | - | 0.6847 | 0 | - | 0.84 | 0.0310 | |||
Cucumber | - | 0.4248 | 0 | - | 0.0087 | |||||
Eggplant | - | 0.4122 | 0 | - | 0.4148 | |||||
Kiwi | - | 0.6057 | 0 | - | 0.053 | 0.0028 | ||||
Peach | - | 0.4896 | 0 | - | 0.0749 | |||||
Pear | - | 0.5638 | 0 | - | 0.0003 | |||||
Plum | - | 0.6807 | 0 | - | 0.0844 | |||||
Tomato | - | 0.5858 | 0 | - | 0.0001 | |||||
LP & BP | Apple | - | 0.6187 | 3.89 | 0.8543 | |||||
Cucumber | - | 0.4241 | 7.95 | 0.4335 | ||||||
Eggplant | - | 0.4342 | 4.46 | 39.33 | 0.4003 | |||||
Kiwi | - | 0.5376 | 0.35 | 0.9375 | ||||||
Peach | - | 0.5069 | 1.39 | 63.72 | 0.4339 | |||||
Pear | - | 0.6352 | 1.83 | 0.6393 | ||||||
Plum | - | 0.6311 | 8.92 | 0.8769 | ||||||
Tomato | - | 0.5851 | 1.04 | 0.9668 | ||||||
BP & AP | Apple | - | 0.6847 | 0 | - | 0.84 | 0.0003 | |||
Cucumber | - | 0.4248 | 0 | - | 0.0087 | |||||
Eggplant | - | 0.4122 | 0 | - | 0.4148 | |||||
Kiwi | - | 0.6057 | 0 | - | 0.053 | 0.0002 | ||||
Peach | - | 0.4896 | 0 | - | 0.0749 | |||||
Pear | - | 0.5638 | 0 | - | 0.0003 | |||||
Plum | - | 0.6807 | 0 | - | 0.0008 | |||||
Tomato | - | 0.5858 | 0 | - | 0.0001 |
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Gadallah, S.I.; Ghoneim, M.S.; Elwakil, A.S.; Said, L.A.; Madian, A.H.; Radwan, A.G. Plant Tissue Modelling Using Power-Law Filters. Sensors 2022, 22, 5659. https://doi.org/10.3390/s22155659
Gadallah SI, Ghoneim MS, Elwakil AS, Said LA, Madian AH, Radwan AG. Plant Tissue Modelling Using Power-Law Filters. Sensors. 2022; 22(15):5659. https://doi.org/10.3390/s22155659
Chicago/Turabian StyleGadallah, Samar I., Mohamed S. Ghoneim, Ahmed S. Elwakil, Lobna A. Said, Ahmed H. Madian, and Ahmed G. Radwan. 2022. "Plant Tissue Modelling Using Power-Law Filters" Sensors 22, no. 15: 5659. https://doi.org/10.3390/s22155659
APA StyleGadallah, S. I., Ghoneim, M. S., Elwakil, A. S., Said, L. A., Madian, A. H., & Radwan, A. G. (2022). Plant Tissue Modelling Using Power-Law Filters. Sensors, 22(15), 5659. https://doi.org/10.3390/s22155659