| 1. |
- Gustafsson, Stefan, et al.
(författare)
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Electromagnetic dispersion modeling and measurements for HVDC power cables
- 2014
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Ingår i: IEEE Transactions on Power Delivery. - : IEEE Press. - 0885-8977 .- 1937-4208. ; 29:6, s. 2439-2447
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Tidskriftsartikel (refereegranskat)abstract
- This paper provides a general framework for electromagnetic (EM) modeling, sensitivity analysis, computation, and measurements regarding the wave propagation characteristics of high-voltage direct-current (HVDC) power cables. The modeling is motivated by the potential use with transient analysis, partial-discharge measurements, fault localization and monitoring, and is focused on very long (10 km or more) HVDC power cables with transients propagating in the low-frequency regime of about 0-100 kHz. An exact dispersion relation is formulated together with a discussion on practical aspects regarding the computation of the propagation constant. Experimental time-domain measurement data from an 80-km-long HVDC power cable are used to validate the electromagnetic model, and a mismatch calibration procedure is devised to account for the connection between the measurement equipment and the cable. Quantitative sensitivity analysis is devised to study the impact of parameter uncertainty on wave propagation characteristics. The sensitivity analysis can be used to study how material choices affect the propagation characteristics, and to indicate which material parameters need to be identified accurately in order to achieve accurate fault localization. The analysis shows that the sensitivity of the propagation constant due to a change in the conductivity in the three metallic layers (the inner conductor, the intermediate lead shield, and the outer steel armor) is comparable to the sensitivity with respect to the permittivity of the insulating layer. Hence, proper modeling of the EM fields inside the metallic layers is crucial in the low-frequency regime of 0-100 kHz.
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| 2. |
- Ivanenko, Yevhen, et al.
(författare)
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Passive Approximation and Optimization Using B-Splines
- 2019
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Ingår i: SIAM Journal on Applied Mathematics. - : SIAM PUBLICATIONS. - 0036-1399 .- 1095-712X. ; 79:1, s. 436-458
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Tidskriftsartikel (refereegranskat)abstract
- A passive approximation problem is formulated where the target function is an arbitrary complex-valued continuous function defined on an approximation domain consisting of a finite union of closed and bounded intervals on the real axis. The norm used is a weighted L-p-norm where 1 <= p <= infinity. The approximating functions are Herglotz functions generated by a measure with Holder continuous density in an arbitrary neighborhood of the approximation domain. Hence, the imaginary and the real parts of the approximating functions are Holder continuous functions given by the density of the measure and its Hilbert transform, respectively. In practice, it is useful to employ finite B-spline expansions to represent the generating measure. The corresponding approximation problem can then be posed as a finite-dimensional convex optimization problem which is amenable for numerical solution. A constructive proof is given here showing that the convex cone of approximating functions generated by finite uniform B-spline expansions of fixed arbitrary order (linear, quadratic, cubic, etc.) is dense in the convex cone of Herglotz functions which are locally Holder continuous in a neighborhood of the approximation domain, as mentioned above. As an illustration, typical physical application examples are included regarding the passive approximation and optimization of a linear system having metamaterial characteristics, as well as passive realization of optimal absorption of a dielectric small sphere over a finite bandwidth.
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| 3. |
- Nordebo, Sven, et al.
(författare)
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A Green's function approach to Fisher information analysis and preconditioning in microwave tomography
- 2010
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Ingår i: Inverse Problems in Science and Engineering. - : Informa UK Limited. - 1741-5977 .- 1741-5985. ; 18:8, s. 1043-1063
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Tidskriftsartikel (refereegranskat)abstract
- The Fisher Information Integral Operator (FIO) and related sensitivity analysis is formulated in a variational framework that is suitable for analytical Green's function and gradient-based approaches in microwave tomography. The main application considered here is for parameter sensitivity analysis and related preconditioning for gradient-based quasi-Newton inverse scattering algorithms. In particular, the Fisher information analysis can be used as a basic principle yielding a systematic approach to robust preconditioning, where the diagonal elements of the FIO kernel are used as targets for sensitivity equalization. The infinite-dimensional formulation has several practical advantages over the finite-dimensional Fisher Information Matrix (FIM) analysis approach. In particular, the FIO approach avoids the need of making a priori assumptions about the underlying discretization of the material such as the shape, orientation and positions of the assumed image pixels. Furthermore, the integral operator and its spectrum can be efficiently approximated by using suitable quadrature methods for numerical integration. The eigenfunctions of the integral operator, corresponding to the identifiable parameters via the significant eigenvalues and the corresponding Cramr-Rao bounds, constitute a suitable global basis for sensitivity and resolution analysis. As a generic numerical example, a two-dimensional inverse electromagnetic scattering problem is analysed and illustrates the spectral decomposition and the related resolution analysis. As an application example in microwave tomography, a simulation study has been performed to illustrate the parameter sensitivity analysis and to demonstrate the effect of the related preconditioning for gradient-based quasi-Newton inverse scattering algorithms.
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| 4. |
- Nordebo, Sven, et al.
(författare)
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An adjoint field approach to Fisher information-based sensitivity analysis in electrical impedance tomography
- 2010
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Ingår i: Inverse Problems. - : IOP Publishing. - 1361-6420 .- 0266-5611. ; 26:12
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Tidskriftsartikel (refereegranskat)abstract
- An adjoint field approach is used to formulate a general numerical framework for Fisher information-based sensitivity analysis in electrical impedance tomography. General expressions are given for the gradients used in standard least-squares optimization, i.e. the Jacobian related to the forward problem, and it is shown that these gradient expressions are compatible with commonly used electrode models such as the shunt model and the complete electrode model. By using the adjoint field formulations together with a variational analysis, it is also shown how the computation of the Fisher information can be integrated with the gradient calculations used for optimization. It is furthermore described how the Fisher information analysis and the related sensitivity map can be used in a preconditioning strategy to obtain a well-balanced parameter sensitivity and improved performance for gradient-based quasi-Newton optimization algorithms in electrical impedance tomography. Numerical simulations as well as reconstructions based on experimental data are used to illustrate the sensitivity analysis and the performance of the improved inversion algorithm in a four-electrode measurement set-up.
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| 5. |
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| 6. |
- Nordebo, Sven, et al.
(författare)
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Cylindrical multipole expansion for periodic sources with applications for three-phase power cables
- 2018
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Ingår i: Mathematical methods in the applied sciences. - : Wiley-Blackwell. - 0170-4214 .- 1099-1476. ; 41:3, s. 959-965
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents a c ylindrical multipole expansion for periodic sources with applications for three-phase power cables.It is the aim of the contribution to provide some analytical solutions and techniques that can be useful in the calculation ofcable losses. Explicit analytical results are given for the fields generated by a three-phase helical current distribution andwhich can be computed efficiently as an input to other numerical methods such as, for example , the Method of Moments.It is shown that the field computations are numerically stable at low frequencies (such as 50 Hz) as well as in the quasi-magnetostatic limit provided that sources are divergence-free. The cylindrical multipole expansion is fur thermore usedto derive an efficient analytical model of a measurement coil to measure and estimate the complex valued permeability ofmagnetic steel armour in the presence of a strong skin-effect.
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| 7. |
- Nordebo, Sven, et al.
(författare)
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Electromagnetic dispersion modeling and measurements for HVDC power cables
- 2011
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This paper provides a general framework for electromagnetic modeling, computation and measurements regarding the wave propagation characteristics of High-Voltage Direct Current (HVDC) power cables. The modeling is focused on very long (10 km or more) HVDC power cables and the relevant frequency range is therefore in the low-frequency regime of about 0-100 kHz. An exact dispersion relation is formulated together with a discussion on practical aspects regarding the computation of the propagation constant and the related characteristic impedance. Experimental time-domain measurement data from an 80 km long HVDC power cable is used to validate the model. It is concluded that a single-mode transmission line model is not adequate to account for the mismatch between the power cable and the instrumentation. A mismatch calibration procedure is therefore devised to account for the connection between the measurement equipment and the cable. A dispersion model is thus obtained that is accurate for early times of pulse arrival. To highlight the potential of accurate electromagnetic modeling, an example of high-resolution length-estimation is discussed and analyzed using statistical methods based on the Cramer-Rao lower bound. The analysis reveals that the estimation accuracy based on the present model (and its related model error) is in the order of 100 m for an 80 km long power cable, and that the potential accuracy using a perfect model based on the given measurement data is in the order of centimeters.
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| 8. |
- Nordebo, Sven, et al.
(författare)
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Fisher information analysis and preconditioning in electrical impedance tomography
- 2010
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Ingår i: Journal of Physics: Conference Series 224 (2010), 1742-6588. - : IOP Publishing. - 1742-6596 .- 1742-6588. ; , s. 012057-
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Konferensbidrag (refereegranskat)abstract
- An adjoint field approach is used to formulate a general numerical framework for Fisher information based sensitivity analysis in electrical impedance tomography. General expressions are given for the gradients used in standard least squares optimization, i.e., the Jacobian related to the forward problem, and it is shown that these gradient expressions are consistent with commonly used electrode models such as the shunt model and the complete electrode model. By using the adjoint field formulations together with a variational analysis, it is also shown how the computation of the Fisher information can be integrated with the gradient calculations used for optimization. It is furthermore described how the Fisher information analysis and the related sensitivity map can be used in a preconditioning strategy to obtain a well balanced parameter sensitivity and improved performance for gradient based quasi-Newton optimization algorithms in electrical impedance tomography. Numerical simulations as well as reconstructions based on experimental data are used to illustrate the sensitivity analysis and the performance of the improved inversion algorithm in a four-electrode measurement set-up.
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| 9. |
- Nordebo, Sven, et al.
(författare)
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Fisher information analysis for two-dimensional microwave tomography
- 2007
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Ingår i: Inverse Problems. - : IOP Publishing. - 0266-5611 .- 1361-6420. ; 23:3, s. 859-877
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, a Fisher information analysis is employed to establish some important physical performance bounds in microwave tomography. As a canonical problem, the two-dimensional electromagnetic inverse problem of imaging a cylinder with isotropic dielectric losses is considered. A fixed resolution is analysed by introducing a finite basis, i.e., pixels representing the material properties. The corresponding Cramer-Rao bound for estimating the pixel values is computed based on a calculation of the sensitivity field which is obtained by differentiating the observed field with respect to the estimated parameter. An optimum trade-off between the accuracy and the resolution is defined based on the Cramer-Rao bound, and its application to assess a practical resolution limit in the inverse problem is discussed. Numerical examples are included to illustrate how the Fisher information analysis can be used to investigate the significance of measurement distance, operating frequency and losses in the canonical tomography set-up.
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| 10. |
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