Bernhard Brandstätter

Particle swarm optimization - mass-spring system analogon

A concept for the optimization of nonlinear cost functionals, occurring in electrical engineering applications, using particle swarm optimization (PSO) is proposed. PSO is a stochastic optimization technique, whose stochastic behavior can be controlled very easily by one single factor. Additionally, this factor can be chosen to end up with a deterministic strategy, that does not need gradient information. The PSO concept is quite simple and easy to implement (just a few code lines are needed). In this paper, an analogy between the movement of a swarm member and a mass-spring system is developed and tested against other stochastic algorithms. It will be shown how infeasible regions in the parameter space can be treated efficiently and, finally, the particular PSO implementation is used to optimize problems occurring in electrical engineering.

Numerical solution of the general 3D eddy current problem for magnetic induction tomography (spectroscopy)

Magnetic induction tomography (MIT) is used for reconstructing the changes of the conductivity in a target object using alternating magnetic fields. Applications include, for example, the non-invasive monitoring of oedema in the human brain. A powerful software package has been developed which makes it possible to generate a finite element (FE) model of complex structures and to calculate the eddy currents in the object under investigation. To validate our software a model of a previously published experimental arrangement was generated. The model consists of a coaxial coil system and a conducting sphere which is moved perpendicular to the coil axis (a) in an empty space and (b) in a saline-filled cylindrical tank. The agreement of the measured and simulated data is very good when taking into consideration the systematic measurement errors in case (b). Thus the applicability of the simulation algorithm for two-compartment systems has been demonstrated even in the case of low conductivities and weak contrast. This can be considered an important step towards the solution of the inverse problem of MIT.

Reconstruction of inhomogeneities in fluids by means of capacitance tomography

Electrical capacitance tomography (ECT) is a technique for reconstructing information about the spatial distribution of the contents of closed pipes by measuring variations in the dielectric properties of the material inside the pipe. In this paper, we propose a method that solves the non‐linear reconstruction problem directly leading to less iterations and higher accuracy than linear back projection algorithms currently in use in most ECT systems.

A FEM‐BEM approach using level‐sets in electrical capacitance tomography

Purpose – For the spatial reconstruction of a two phase flow, as it might occur in a pipe, the main problem has always been the blurring of the resulting images.Design/methodology/approach – In this paper, we present a method where blurring is implicitly avoided by the use of level sets. The level set method describes the iteratively evolving interface between different materials. The underlying field problem is solved with the boundary element method formulated in the region, where the degrees of freedom are present and the finite element method in all other regions.Findings – Finally reconstruction results of an electrical capacitance tomography sensor are presented to show the validity of the method.Originality/value – Presents a method where blurring is avoided by the use of level sets.

Jacobian calculation for electrical impedance tomography based on the reciprocity principle

Electrical impedance tomography is a noninvasive method, which is particularly useful for patient monitoring. For reconstructing the interior of the human body, a finite-element model is established and the inverse problem is solved by means of a Gauss-Newton method, which requires the Jacobian, describing the mapping between voltage distribution on the bodys surface and the conductivity distribution in the interior. The calculation of the Jacobian has to meet an accuracy requirement as well as a minimal processing time requirement. In this paper, the reciprocity principle is applied to meet both requirements leading to good results for the reconstruction.

Adaptive regularization parameter adjustment for reconstruction problems

In reconstruction (i.e., determining the states of a model from measurements of model outputs), one is often forced to search for a regularized solution due to poor sensitivity of model outputs with respect to the model states. The amount of regularization is controlled by the regularization parameter, a scalar value multiplied with the so-called regularization term. The choice of the regularization parameter is crucial for the reconstruction process. In this paper, a new method to estimate the regularization parameter in an adaptive way is proposed. A condition-number based estimate of the regularization parameter for the first iteration step is required to choose the weighting factor for adapting the regularization parameter iteratively. By virtue of controlling the regularization term, a kind of edge preservation can be achieved. The validity of this method will be demonstrated for a capacitance tomography problem, which is solved applying a Gauss-Newton scheme.

Utilizing feedforward neural networks for acceleration of global optimization procedures [SMES problems]

Global optimization in electrical engineering usually requires an enormous amount of CPU time to evaluate the objective function when stochastic methods are used. Approximating the objective function can drastically reduce the computational demands. The use of feedforward neural networks is proposed in this paper and its application is investigated using an unconstrained and a constrained version of the TEAM Workshop problem 22.

Direct estimation of Cole parameters in multifrequency EIT using a regularized Gauss–Newton method

A major drawback of electrical impedance tomography is the poor quality of the conductivity images, i.e., the low spatial resolution as well as large errors in the reconstructed conductivity values. The main reason is the necessity for regularization of the ill-conditioned inverse problem which results in excessive spatial low-pass filtering. A novel regularization method (SMORR (spectral modelling regularized reconstructor)) is proposed, which is based on the inclusion of spectral a priori information in the form of appropriate tissue models (e.g. Cole models). This approach reduces the ill-posedness of the inverse problem, when multifrequency data are available. An additional advantage is the direct reconstruction of the (physiological) tissue parameters of interest instead of the conductivities. SMORR was compared with posterior fitting of a Cole model to the conductivity spectra obtained with a classical iterative reconstruction scheme at various frequencies. SMORR performed significantly better than the reference method concerning robustness against noise in the data.

Fat and hydration monitoring by abdominal bioimpedance analysis: data interpretation by hierarchical electrical modeling

In a previous publication, it was demonstrated that the abdominal subcutaneous fat layer thickness (SFL) is strongly correlated with the abdominal electrical impedance when measured with a transversal tetrapolar electrode arrangement. This article addresses the following questions: 1) To which extent do different abdominal compartments contribute to the impedance? 2) How does the hydration state of tissues affect the data? 3) Can hydration and fat content be assessed independently? For simulating the measured data a hierarchical electrical model was built. The abdomen was subdivided into three compartments (subcutaneous fat, muscle, mesentery). The true anatomical structure of the compartment boundaries was modeled using finite-element modeling (FEM). Each compartment is described by an electrical tissue model parameterized in physiological terms. Assuming the same percent change of the fat fraction in the mesentery and the SFL the model predicts a change of 1,24 /spl Omega//mm change of the SFL compared to 1,1 /spl Omega//mm measured. 42% of the change stem from the SFL, 56% from the mesentery and 2% from changes of fat within the muscle compartment. A 1% increase of the extracellular water in the muscle is not discernible from a 1% decrease of the SFL. The measured data reflect not only the SFL but also the visceral fat. The tetrapolar electrode arrangement allows the measurement of the abdominal fat content only if the hydration remains constant.

Evolution strategy and hierarchical clustering

In most real world optimization problems, one tries to determine the global among some or even numerous local solutions within the feasible region of parameters. Nevertheless, it could be worthwhile to investigate some of the local solutions as well. A most desirable behavior would be that the optimization strategy behaves globally and yields additional information about local minima detected on the way to the global solution. In this paper, a clustering algorithm has been implemented into an extended higher order evolution strategy in order to achieve these goals. Multimodal two-dimensional test problems, namely, Rastrigins function and the 4-parameter die mold press benchmark problem (Takahashi, 1996), are solved using this approach.