External Identification of a Reciprocal Lossy Multiport Circuit under Measurement Uncertainties by Riemannian Gradient Descent
The present paper deals with the external identification of a reciprocal, special passive, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>n</mi></mrow></sema...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/16/6/2585 |
| _version_ | 1797612102611894272 |
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| author | Simone Fiori Jing Wang |
| author_facet | Simone Fiori Jing Wang |
| author_sort | Simone Fiori |
| collection | DOAJ |
| description | The present paper deals with the external identification of a reciprocal, special passive, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>n</mi></mrow></semantics></math></inline-formula>-port network under measurement uncertainties. In the present context, the multiport model is represented by an admittance matrix and the condition that the network is ‘reciprocal special passive’ refers to the assumption that the real part of the admittance matrix is symmetric and positive-definite. The key point is to reformulate the identification problem as a matrix optimization program over the matrix manifold <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi mathvariant="normal">S</mi><mo>+</mo></msup><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>)</mo></mrow><mo>×</mo><mi mathvariant="normal">S</mi><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. The optimization problem requires a least-squares criterion function designed to cope with over-determinacy due to the incoherent data pairs whose cardinality exceeds the problem’s number of degrees of freedom. The present paper also proposes a numerical solution to such an optimization problem based on the Riemannian-gradient steepest descent method. The numerical results show that the proposed method is effective as long as reasonable measurement error levels and problem sizes are being dealt with. |
| first_indexed | 2024-03-11T06:37:40Z |
| format | Article |
| id | doaj.art-47c395b62ade4bea949c0f1e8523e4ad |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-11T06:37:40Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-47c395b62ade4bea949c0f1e8523e4ad2023-11-17T10:48:08ZengMDPI AGEnergies1996-10732023-03-01166258510.3390/en16062585External Identification of a Reciprocal Lossy Multiport Circuit under Measurement Uncertainties by Riemannian Gradient DescentSimone Fiori0Jing Wang1Dipartimento di Ingegneria dell’Informazione, Università Politecnica delle Marche (UPM), Via Brecce Bianche, I-60131 Ancona, ItalySchool of Information, Beijing Wuzi University, Fuhe Street, Tongzhou District, Beijing 101149, ChinaThe present paper deals with the external identification of a reciprocal, special passive, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>n</mi></mrow></semantics></math></inline-formula>-port network under measurement uncertainties. In the present context, the multiport model is represented by an admittance matrix and the condition that the network is ‘reciprocal special passive’ refers to the assumption that the real part of the admittance matrix is symmetric and positive-definite. The key point is to reformulate the identification problem as a matrix optimization program over the matrix manifold <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi mathvariant="normal">S</mi><mo>+</mo></msup><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>)</mo></mrow><mo>×</mo><mi mathvariant="normal">S</mi><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. The optimization problem requires a least-squares criterion function designed to cope with over-determinacy due to the incoherent data pairs whose cardinality exceeds the problem’s number of degrees of freedom. The present paper also proposes a numerical solution to such an optimization problem based on the Riemannian-gradient steepest descent method. The numerical results show that the proposed method is effective as long as reasonable measurement error levels and problem sizes are being dealt with.https://www.mdpi.com/1996-1073/16/6/2585system identificationmultiport modelRiemannian manifoldgradient-steepest-descent optimization |
| spellingShingle | Simone Fiori Jing Wang External Identification of a Reciprocal Lossy Multiport Circuit under Measurement Uncertainties by Riemannian Gradient Descent Energies system identification multiport model Riemannian manifold gradient-steepest-descent optimization |
| title | External Identification of a Reciprocal Lossy Multiport Circuit under Measurement Uncertainties by Riemannian Gradient Descent |
| title_full | External Identification of a Reciprocal Lossy Multiport Circuit under Measurement Uncertainties by Riemannian Gradient Descent |
| title_fullStr | External Identification of a Reciprocal Lossy Multiport Circuit under Measurement Uncertainties by Riemannian Gradient Descent |
| title_full_unstemmed | External Identification of a Reciprocal Lossy Multiport Circuit under Measurement Uncertainties by Riemannian Gradient Descent |
| title_short | External Identification of a Reciprocal Lossy Multiport Circuit under Measurement Uncertainties by Riemannian Gradient Descent |
| title_sort | external identification of a reciprocal lossy multiport circuit under measurement uncertainties by riemannian gradient descent |
| topic | system identification multiport model Riemannian manifold gradient-steepest-descent optimization |
| url | https://www.mdpi.com/1996-1073/16/6/2585 |
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