| 21. |
- 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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| 22. |
- Nordebo, Sven, et al.
(författare)
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Data fusion for electromagnetic and electrical resistive tomography based on maximum likelihood
- 2011
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Ingår i: International Journal of Geophysics. - : Hindawi Limited. - 1687-885X .- 1687-8868. ; 2011
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents a maximum likelihood based approach to data fusion for electromagnetic (EM) and electrical resistive (ER) tomography. The statistical maximum likelihood criterion is closely linked to the additive Fisher information measure, and it facilitates an appropriate weighting of the measurement data which can be useful with multiphysics inverse problems. The Fisher information is particularly useful for inverse problems which can be linearized similar to the Born approximation. In this paper, a proper scalar product is defined for the measurements and a truncated Singular Value Decomposition (SVD) based algorithm is devised which combines the measurement data of the two imaging modalities in a way that is optimal in the sense of maximum likelihood. As a multiphysics problem formulation with applications in geophysics, the problem of tunnel detection based on EM and ER tomography is studied in this paper. To illustrate the connection between the Green's functions, the gradients and the Fisher information, two simple and generic forward models are described in detail regarding two-dimensional EM and ER tomography, respectively.
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| 23. |
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| 24. |
- Nordebo, Sven, et al.
(författare)
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Data fusion for reconstruction algorithms via different sensors in geophysical sensing
- 2011
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Ingår i: Journal of Geophysics and Engineering. - 1742-2140 .- 1742-2132. ; 8:3, s. 54-60
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Tidskriftsartikel (refereegranskat)abstract
- Abstract in UndeterminedInformation fusion via multimodal inverse problems and different sensors is addressed using a Fisher information analysis approach. The Fisher information measure is inherently additive, and it facilitates an appropriate weighting of the measurement data that is statistically optimal and can hence be useful with reconstruction algorithms in geophysical sensing. Given that there exists proper knowledge about the sensor noise statistics, correlations and spectral contents, as well as a correct forward model, the Fisher information is a natural measure of information because it is closely linked to the statistical maximum likelihood principle. To illustrate the concept of data correlation based on statistical Fisher information analysis, two simple and generic examples are employed in electrical resistivity and electromagnetic tomography, which are motivated by geophysical applications, such as tunnel detection. The examples demonstrate that a properly weighted data fusion can be of crucial importance for an ill-posed multimodal inverse problem.
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| 25. |
- 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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| 26. |
- 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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| 27. |
- Nordebo, Sven, et al.
(författare)
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Fisher information analysis in electrical impedance tomography
- 2013
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Ingår i: Journal of Geophysics and Engineering. - : Institute of Physics (IOP). - 1742-2132 .- 1742-2140. ; 10:6, s. Article ID: 064008-
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Tidskriftsartikel (refereegranskat)abstract
- This paper provides a quantitative analysis of the optimal accuracy and resolution in electrical impedance tomography (EIT) based on the Cramér–Rao lower bound. The imaging problem is characterized by the forward operator and its Jacobian. The Fisher information operator is defined for a deterministic parameter in a real Hilbert space and a stochastic measurement in a finite-dimensional complex Hilbert space with a Gaussian measure. The connection between the Fisher information and the singular value decomposition (SVD) based on the maximum likelihood (ML) criterion (the ML-based SVD) is established. It is shown that the eigenspaces of the Fisher information provide a suitable basis to quantify the trade-off between the accuracy and the resolution of the (nonlinear) inverse problem. It is also shown that the truncated ML-based pseudo-inverse is a suitable regularization strategy for a linearized problem, which exploits sufficient statistics for estimation within these subspaces. The statistical-based Cramér–Rao lower bound provides a complement to the deterministic upper bounds and the L-curve techniques that are employed with linearized inversion. To this end, electrical impedance tomography provides an interesting example where the eigenvalues of the SVD usually do not exhibit a very sharp cut-off, and a trade-off between the accuracy and the resolution may be of practical importance. A numerical study of a hypothetical EIT problem is described, including a statistical analysis of the model errors due to the linearization.
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| 28. |
- Nordebo, Sven, et al.
(författare)
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Fisher information analysis in microwave tomography
- 2009
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Ingår i: The Third International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP09). - 9781424451807 ; , s. 217-220
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Konferensbidrag (refereegranskat)
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| 29. |
- Nordebo, Sven, et al.
(författare)
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Fisher information for inverse problems and trace class operators
- 2012
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Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 53:12
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Tidskriftsartikel (refereegranskat)abstract
- This paper provides a mathematical framework for Fisher information analysis forinverse problems based on Gaussian noise on infinite-dimensional Hilbert space. The covariance operator for the Gaussian noise is assumed to be trace class, andthe Jacobian of the forward operator Hilbert-Schmidt. We show that the appropriatespace for defining the Fisher information is given by the Cameron-Martin space. This is mainly because the range space of the covariance operator always is strictlysmaller than the Hilbert space. For the Fisher information to be well-defined, it is furthermore required that the range space of the Jacobian is contained in the Cameron-Martin space. In order for this condition to hold and for the Fisher information tobe trace class, a sufficient condition is formulated based on the singular values ofthe Jacobian as well as of the eigenvalues of the covariance operator, together withsome regularity assumptions regarding their relative rate of convergence. An explicit example is given regarding an electromagnetic inverse source problem with “external”spherically isotropic noise, as well as “internal” additive uncorrelated noise.
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| 30. |
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