# Waves, Signals and Systems

The research in waves, signals and systems deals primarily with acoustic and electromagnetic direct and inverse problems, with engineering and industrial applications.

## Our research

The Waves, Signals and Systems (WSS) research group is part of the Department of Physics and Electrical Engineering as well as the Department of Mathematics, at the Faculty of Technology.

Typical application areas are with antennas and wireless communications,

waveguide theory, quantum electrodynamics for optical fibers, flow acoustics, structural dynamics, microwave tomography, electrical impedance tomography, and power engineering. The research is based on mathematical modeling of wave phenomena, mathematical and numerical analysis, statistical signal analysis and optimization.

Presently, our main application areas are with power cables, electromagnetic design, building acoustics, fiber optics, antennas and scattering.

## Projects

### Electromagnetic dispersion modeling and analysis for HVDC power cables

The project aims to develop accurate cable models and related high-resolution fault localization methods for High Voltage Direct Current (HVDC) submarine power cables. The fault localization methods are based on the detection of Partial Discharges (PD), or ''virgin pulses'', caused by dielectric breakdown and electrical shorts.

As a concrete goal, we are aiming to develop a cable model that can be used to monitor and detect faults with a resolution of less than 10 m for a 250.000 m long submarine power cable. Based on accurate wave modeling and transient signal analysis, the ultimate goal is to develop new efficient techniques that can make the critical power delivery infrastructure more reliable and safe. The project involves extensive electromagnetic modeling in combination with estimation theory and optimization theory.

The project is concerned with advanced waveguide modeling issues regarding complicated open structures, periodical and helical structures, waveguide dispersion, material dispersion, spectral problems, step discontinuities, inverse source problems, frequency domain methods, time domain methods, transform methods, Cagniard-DeHoop methods, mode matching, Wiener-Hopf techniques, Finite Element Modeling, integral equations, etc.

We collaborate with ABB AB who is a manufacturer of HVDC cables and Baltic Cable AB who is an owner and operator of a HVDC-link. Both companies provide us with the possibility to validate our methods by performing measurements on their cables and systems.

### Electromagnetic losses in three-phase power cables

The purpose of this project is to develop new theory and techniques to calculate the power losses in three-phase high-voltage power cables. The potential application is with an optimal electromagnetic design of such high-voltage AC cables.

The research comprises a detailed modeling of the electromagnetic losses inside the metal layers of the cables, i.e., the skin effect and the related AC conductor losses, as well as the losses that are associated with induced eddy currents and magnetic hysteresis phenomena inside the metal sheaths and steel armour.

As a first step, the project is concerned with the characterization, measurement and estimation of the electric and magnetic properties of the cable steel armour based on a simple model transformer built on armour steel. One of the challenges is to estimate correctly the conduction properties of the armour in the presence of non-linear hysteresis phenomena in the magnetic steel.

As a second step, new analytical methods and numerical techniques will be developed to determine the natural modes of complicated helical structures such as the power cable. The resulting mode-shapes will then be used to determine the correct current distribution and magnetic flow inside the cable and the associated power losses.

The research is carried out in close collaboration with ABB AB via the SSF mobility project Electromagnetic losses in three-phase power cables, as well as with the SSF project Complex analysis and convex optimization for EM design in a collaboration between the Lund University, Linnaeus University, Stockholms University and KTH.

ABB AB will be supplying relevant information, expertise in high voltage technology as well as access to measurement data based on their power cable systems.

It is expected that the outcome of the project will be an enhanced collaboration and exchange between the industrial and academic partners, as well as an increased understanding regarding the losses in high-voltage power cables, electromagnetic design and optimization.

### Complex analysis and convex optimization for EM design

This is a joint SSF project in applied mathematics between Lund University, Linnaeus University, Stockholms University and KTH and comprises one senior researcher as well as one PhD student from each partner university as well as a number of associated academic and industrial research collaborators.

The project is concerned with the development of mathematical tools to solve fundamental problems in electromagnetic (EM) design of structures such as antennas, filters, phasors, absorbers, and cables. We will mainly work within the fields of complex analysis in one and several variables and convex as well as non-convex optimization.

In complex analysis, we focus on representation theorems for various combinations of linear, time translational invariant, causal, and passive systems to derive performance bounds for EM systems. Optimization is used to analyze performance bounds and for automated optimal design of EM structures.

The specific mathematical objectives are to: develop representation theorems for causal systems that can be efficiently used to determine physical bounds.

Determine constraints on multi-parameter systems using complex analysis in several variables together with optimization. Characterize optimal and near optimal solutions in a computationally efficient way for large EM structures. Utilize the optimal solution computed using convex optimization for automated design of EM structures.

We have a close collaboration with industry, in particular Ericsson, Sony Mobile, SAAB Dynamics, ABB AB, ABB Corporate Research, RUAG, and ACAB.

### Numerical solution of integral equations

#### Method development

Traditionally, scattering at high frequencies has been dealt with by means of techniques such as GDT or Physical Optics. These analytical or semianalytical solutions have limitations in terms of generality and accuracy.

In recent years, major advances have been made in the form of the Fast Multipole Method (FMM). This method solves the integral equation of the scattering problem by handling the coupling between the basis functions in large scale problems in an efficient way. An aspect that has not gotten the same systematic attention is the inclusion of high frequency asymptotes in the solution.

With essentially Physical optics as a point of departure, an attempt is being made to include gradually more and more information in a scaling that removes much of the rapid variation in the solution and leaves a simpler problem suited for numerical solution. Both analytical solutions and spectral techniques are used.

#### Applications

Wave propagation in terrain can also be investigated with integral equation solvers. Studies of two-dimensional problems have included terrain features and some antenna properties. The long term objective is to be able to compute the impulse response of a radio channel for a given type of modulation.

### Quantum fibre optics

For quantum communication over long distances, the optic fibre is the only practical medium to use. The project deals with the development of quantum models for long optical fibres and the use of these models for simulations. Connection to both fundamental physics and engineering is of interest. The fundamental physical aspects relate to the performance of loop-free tests for Bell's type inequalities. The engineering aspects relate to encrypted communication.

The project is based on classical electromagnetic modelling of open waveguide modes giving an important connection to other waveguide research in the research group. A quantization of the classical description follows and is used for calculations of quantum mechanical correlation functions for photon detection. Of particular interest is how the correlation functions for both single and entangled photons behave in space and time under the influence of material and waveguide dispersion as well as material dissipation and the associated quantum fluctuations. Asymptotic analysis is often valuable to use in the asymptotic radiation zone.

The ultimate goal is partly to get increased fundamental understanding of the quantum optic fibre and partly to get mathematical models with sufficient accuracy to include both dispersion and dissipation with its related fluctuations.

### Sound transmission in waveguides with and without flow

The objective is to find accurate methods for calculating the transmission of sound in acoustic waveguides, ducts, with or without a mean flow. Natural applications are silencers for fans and motors. Mathematically, the formulation is a scattering problem in cylindrical geometry.

The scattering due to two mechanisms are studied: geometry and flow instability. Ducts consisting of straight parts and joined at discontinuities are most conveniently analysed with the Wiener-Hopf method in combination with the Building Block Method also denoted as the cascade technique.

A large class of ducts with a smooth variation of the geometry can be analysed with the following two stage method. First the waveguide is transformed to a straight waveguide converting the variation in geometry to a spatial variation in wave speed. Second the acoustic transmission for this transformed problem is analysed with Fourier and operator methods including a stabilizing splitting technique. Valuable tools in this procedure are efficient algorithms for numerical conformal mappings of waveguides.

A part of the project deals with the generalization to stable mean flows in smooth waveguides. The sudden area expansion is a critical element in silencer design since it incorporates a strong coupling between sound and the mean flow field even at low Mach numbers. For this problem both the geometry and an unstable mean flow is important for the scattering. A model assuming a non-expanding jet with an infinitesimal boundary layer is used and solved with Wiener-Hopf methods. In comparison with experimental results a good agreement is found for relevant Strouhal numbers. The theory predicts, in harmony with experiments, that the absorption due to interaction with flow increases with decreasing Strouhal number. It is proposed to use this effect to attenuate low frequency sound that in general is difficult to attenuate.

Recently, the difference between 2D and 3D ducts has been studied and work is in progress for a generalization to conical geometry, i.e. diffusers, which according to experiments show an interesting acoustic performance.

### Structural dynamics and acoustics with applications to tall wooden buildings

Experience has shown that it can be difficult to build wooden houses with high acoustic performance in the low frequency regime and to build tall wooden houses that resist wind loads.

One reason is that the density of wood is about one tenth of the density of concrete that has been the common building material. Another reason is lack of experience in using wood as building material. For example, existing measurement standards for impact sound insulation developed for houses build in concrete are poorly suited for wooden houses.

The project aims in the first stage to develop simulation tools for the analysis of the dynamics of the structure and the acoustic fields inside rooms at low frequencies for tall wooden houses.

In a second stage these tools are used in developing building elements with improved performance regarding structural dynamics and acoustics. An ultimate goal is to provide knowledge for the development of improved measurement and design standards. The basis for the numerical simulation tool is finite element modelling. Stochastic estimation theory including Bayesian methods is used to handle the, at present large, uncertainties in material and junction properties.

To achieve the project goals, scientists from many disciplines are cooperating such as building physics, acoustics, signal analysis, mathematics and mathematical statistics.

## Conferences and workshops

The Waves, Signals and Systems research group is one of the organizers of the Mathematical Modelling of Wave Phenomena (MMWP) conferences, which have been arranged at Linnaeus University four times.

The conferences present unifying ideas of wave modelling from different disciplines, treating fundamentals as well as applications. Both mechanical and electromagnetic waves together with related signal analysis is considered, including comparisons with quantum waves.

### Previous conferences

- MMWP 2002.pdf
- MMWP 2002 programme.pdf
- MMWP 2005.pdf
- MMWP 2008.pdf
- MMWP 2008 programme.pdf
- MMWP 2008 invitation.pdf
- MMWP 2008 invited contributions.pdf
- MMWP 2008 content.pdf
- MMWP 2008 keynotes.pdf
- MMWP 2008 thematic presentations.pdf
- MMWP 2013.pdf
- MMWP 2013 programme.pdf
- MMWP 2013 presentations part 1.pdf
- MMWP 2013 presentations part 2.pdf
- MMWP 2013 abstracts.pdf
- MMWP 2013 mini-course Stratis.pdf

## Staff

- Andrei Khrennikov Professor
- +46 470-70 87 90
- andreikhrennikovlnuse

- Christian Engström Professor
- +46 470-70 84 61
- +46 70-216 99 42
- christianengstromlnuse

- Joachim Toft Professor
- +46 470-70 84 65
- +46 72-594 13 67
- joachimtoftlnuse

- Magnus Perninge Associate Professor
- +46 470-70 88 33
- magnusperningelnuse

- Pieternella Cijvat Senior lecturer
- +46 470-70 86 42
- +46 72-200 26 19
- elliecijvatlnuse

- Sven Nordebo Professor
- +46 470-70 81 93
- svennordebolnuse

- Sven-Erik Sandström Professor
- +46 470-70 81 35
- sven-eriksandstromlnuse

## Alumni

Within the research area of Waves, Signals and Systems, a number of postdocs and doctoral students have been involved.

### Postdocs

**Gökhan Cinar**

Postdoc in Electromagnetic Theory, 2010-2011

E-mail: gcinar@gmail.com

Current position: Associate Professor of Electromagnetics, Gebze Institute of Technology, Turkey

**Özge Yanaz Cinar**

Postdoc in Mathematics, 2010-2011

E-mail: ozgeyanaz@yahoo.com

Current position: Lecturer in mathematics, Gebze Institute of Technology, Turkey

**Andreas Ioannidis**

Research Assistant in Engineering Physics, 2012-2014

E-mail: aioannidis@snd.edu.gr

Current position: Researcher at Athens University of Economics and Business

### Doctoral Students

**Thomas Biro**

Theoretical Physics, graduated in 2004

Thesis: Electromagnetic wave modelling on waveguide bends, power lines and space plasmas

E-mail: thomas.biro@jth.hj.se

Current position: Senior Lecturer in Mathematics, Jönköping University, Sweden

**Christian Ackren**

Engineering Physics, graduated (Lic) in 2006

Thesis: On a problem related to waves on a circular cylinder with a surface impedance

**Jonas Lundbäck**

Applied Signal Processing, graduated in 2007 (at BTH)

Thesis: On signal processing and electromagnetic modelling, applications in antennas and transmission lines

E-mail: jonas.lundback@ericsson.com

Current position: Senior Specialist, Research Leader at Ericsson, Sweden

**Anders Andersson**

Mathematics, graduated in 2009

Thesis: Numerical conformal mappings for waveguides

E-mail: anders.andersson@jth.hj.se

Current position: Senior Lecturer in Mathematics, Jönköping University, Sweden

**Raisa Khamitova **

Mathematics, graduated in 2009

Thesis: Symmetries and conservation laws

E-mail: raisa.khamitova@bth.se

Current position: Senior Lecturer, Blekinge Institute of Technology, Sweden

**Sara Rydström**

Mathematics, graduated (Lic) in 2010

Thesis: Wave regularization of parameter problems for dynamic beam models

E-mail: sara.rydstrom@power.alstom.com

Current position: Structural Engineer, Alstom Power, Växjö, Sweden

**Oscar Lindhe**

Engineering Physics, 2008-2011

E-mail: oscar.lindhe@combitech.se

Current position: Information Security Consultant, Combitech AB, Växjö, Sweden

**Therese Sjöden**

Engineering Physics, graduated in 2012

Thesis: Sensitivity analysis and material parameter estimation using electromagnetic modeling

E-mail: therese.sjoden@gmail.com

Current position: Volvo CE, Braås, Sweden

**Stefan Gustafsson**

Engineering Physics, graduated in 2015

Thesis: Electromagnetic dispersion modeling and analysis for power cables

E-mail: stefan.h.gustafsson@se.abb.com

Current position: ABB High Voltage Cables, Karlskrona, Sweden

## Collaboration

The Waves, Signals and Systems research group collaborates with a number of partners – both academic associates, internal as well as external, and partners within industry.

### Internal collaborations within Linnaeus University

**International Center for Mathematical Modeling (ICMM)**Andrei Khrennikov

Joachim Toft

**Department of Mechanical Engineering**Andreas Linderholt

Jörgen Olsson

### External academic partners

**Electrical and Information Technology, Lund University, Sweden**

Gerhard Kristensson

Anders Karlsson

Mats Gustafsson

Daniel Sjöberg

**Electromagnetic Engineering, Royal Institute of Technology (KTH), Sweden**

Martin Norgren

Lars Jonsson

**School of Engineering Sciences, Royal Institute of Technology (KTH), Sweden**

Susann Boij

**Signals and Systems, Chalmers, Sweden**

Andreas Fhager

Mikael Persson

**School of Engineering, Jönköping University, Sweden**

Thomas Biro

Anders Andersson

**School of Science and Technology, Middlesex University, London, UK**

Richard Bayford

**Brno University of Technology, the Czech Republic**

Martin Stumpf

**Gebze Institute of Technology, Gebze, Kocaeli, Turkey**

Gökhan Cinar

Özge Yanaz Cinar

**Mathematics and Computer Sciences, Laboratory of Electromagnetic Research, Faculty of Electrical Engineering, Delft University of Technology, the Netherlands**

Dr Adrianus T de Hoop

H A Lorentz, Chair Emeritus Professor

### Industrial collaborators

**ABB AB, High Voltage Cables, Karlskrona, Sweden**

Marc Jeroense

Mats Sjöberg

Stefan Gustafsson

**ABB Corporate Research, Västerås, Sweden**

Dierk Bormann

**Baltic Cable AB, Malmö, Sweden**

Nils Nordtorp

**Alstom Power, Växjö, Sweden**

Per Ranstad

Andreas Back

**Combitech AB, Växjö, Sweden**

Christian Fransson

Kim Fransson

Oscar Lindhe