Bengt Lundberg and Torsten Söderström, Uppsala University

These web pages provide the requested information about the project.
The aim is to give some background for the evaluation of the area
Signals and Systems within TFR.

Introduction

This project (doss 271, dnr 98-137) is a continuation of the project “Efficient techniques for estimating physical parameters in distributed dynamic systems” (doss 271, dnr 96-212). The two projects have been carried out in co-operation between three research groups of Uppsala University. The Department of Systems and Control, represented by Professor Torsten Söderström, Professor Bengt Carlsson and Graduate Student Magnus Mossberg, has brought expertise in estimation theory and system identification to the project. The Solid Mechanics Group, represented by Professor Bengt Lundberg, Senior Lecturer Urmas Valdek and Graduate Student Lars Hillström, has contributed with knowledge concerning waves in solids, measurement techniques, and experimental facilities. The Department of Scientific Computing, finally, represented by Associate Professor Leif Abrahamsson, has provided skill concerning numerical methods. The two graduate students have had frequent contacts with each other during the course of their work, and the project group as a whole has met for discussions of problems and results approximately once per month. The co-operation has resulted in a common basis of knowledge and concepts which is highly useful.

Systems and Control

Information Technology undertakes theoretical and applied research in automatic control, signal processing and systems analysis. In the theoretical field we look for development and analysis (mathematical and statistical) of new methods with significant value for practical applications. As a sign of the industrial relevance of our activities, six PhD's have left the department during the 90's for work at Ericsson Radio Systems AB. The department has a rich international net of contacts and partners for joint research. In spring 2000, the staff comprised 4 full professors, 1 adjunct professor, 3 associated professors (one vacant) and 17 PhD students. The scientific output is dominated by work in signal processing, system identification and estimation. The total work since 1995 includes 16 licentiate theses, 9 PhD theses, 6 books, 16 book chapters, 170 Journal papers, and 156 conference papers.

Solid Mechanics

The research concerns theoretical and experimental studies of impact, waves and vibrations. Through support of 4 projects since 1993, TFR has been the main source of funding. During 1999-2000, the research has concerned: (i) Identification of viscoelastic materials by wave propagation methods (TFR), (ii) Vibration control by smart materials (Volvo Research Foundation), (iii) A new configuration for Split Hopkinson Bar tensile testing (FOA) and (iv) Vibrations in carpenter hammers (Bahco Carpentry Tools). In spring 2000, the staff comprised 1 full professor and 1 senior lecturer. The number of graduate students was 6 (1 internal, 5 external). Two graduate students obtained PhD’s in 1996 and 1998, and one will defend his PhD thesis in December 2000. The published work since 1995 includes 4 licentiate theses, 2 PhD theses and about 20 journal papers.

Scientific Computing

Information Technology has research activities in numerical methods, parallel algorithms and image analysis. There are several research groups in numerical analysis. The work on the present project was carried out within the wave simulation group. The goal of its research is to develop, analyse and apply high order finite difference methods for wave propagation problems. Areas of application are wave phenomena in fluids, solids and electromagnetics. An important part of this research is supported by TFR. The group has a staff of 2 full professors, 3 assistant professors, 1 senior lecturer, and 9 PhD students. The scientific output since 1995 includes four PhD theses, 25 journal papers and 15 conference proceedings.

Results achieved

The aim has been, and is, to reinforce and extend our previous work in the area of identification of viscoelastic materials by wave propagation methods. Our main achievements so far are as follows.

For an isotropic linearly viscoelastic material there are two independent material functions of frequency which characterise the material, e.g., the complex modulus and the complex Poisson ratio. Most of our work has concerned the complex modulus, but results have been obtained also for the complex Poisson’s ratio. Laboratory tests with polypropylene and polymethyl methacryalate have been carried out by generating extensional waves in rod specimens (2nd order PDE) and flexural waves in beam specimens (4th order PDE). For identification of the complex modulus, these tests required a minimum of 3 and 5 independent measurements, respectively. Parametric and non-parametric identification methods were used in conjunction with frequency as well as time domain analyses. The methods developed are independent of boundary conditions. Therefore they can be used for in situ tests of elements in structures with properties which need not be known.

Previous methods have had poor accuracy near critical frequencies for the complex modulus and in particular its imaginary part which is related to damping. These critical frequencies correspond to situations with an integral multiple of a half wave length between measurement sections. A substantial improvement of the accuracy has been achieved through increased numbers and smart configurations of strain gauges, and improved identification techniques. The increased number of sensors leads to over-determined systems of equations, which has proved to be advantageous, while the smart configuration of them has the beneficial effect that the distance between the strain gauges of any pair is not critical at the same frequency as the distance between the strain gauges of any other pair. In this way, it has been possible to practically eliminate the critical frequencies in the range of frequency of interest.

Extensional waves result in inaccuracy of the complex modulus at low frequencies (in our tests, below a few hundred Hertz) as their wave lengths, approximately inversely proportional to frequency, become very long compared with the distances between the sensors. As flexural waves have wave lengths which are approximately inversely proportional to the square root of frequency, it turns out that they permit acceptable accuracy at lower frequencies (in our tests, down to a few tens of Hertz) with the same size of specimen. In this way, the useful frequency range has been expanded by about a decade in the low-frequency end.

The time-domain method developed has the advantage of being applicable to materials with non-linear as well as linear viscoelastic behaviour. However, attempts to generate extensional waves with amplitude levels high enough for a significantly non-linear response from the materials tested have proved to be more difficult than we had expected. So far, these attempts have resulted in broken specimens.

A method for estimation of state in non-uniform elastic or viscoelastic beams has been developed. This method allows stresses , particle velocity, energy flux etc. to be determined from a sufficient number of measurements of strains or accelerations. If the material of the beam is known, a minimum of 4 independent measurements are needed. Otherwise, a minimum of 5 independent measurements are needed for simultaneous material identification and state estimation.

For extensional waves, we have developed simulation models which can be used to evaluate different kinds of experiments. A thorough statistical analysis of the accuracy of the estimated material parameters has been undertaken. Expressions for the standard deviation, and its frequency dependence, of the estimated complex modulus have been derived. This has given us important tools for evaluation of the quality of the determined material functions or parameters and for the planning of various experimental set-ups.

Besides from two PhD theses (one of them in preparation), the project has so far generated results, most of which we have summarised in papers for journals and conferences. We have published in different types of journals and conferences, so as to reach both the solid mechanics community (which should have an interest in the results from a mechanics and application point of view), and the systems and control community (where the system identification aspects are more in the focus). These considerations are manifested in the following list of five selected publications:

Hillström L., Mossberg M. and Lundberg B. Identification of complex modulus from measured strains on an impact-loaded bar using least squares. Journal of Sound and Vibration 230(3), 689-707 (1999)

Hillström L. and Lundberg B. Analysis of elastic flexural waves in non-uniform beams from measurement of strains or accelerations. Accepted for publication in Journal of Sound and Vibration (2000)

Mossberg M., Hillström L. and Abrahamsson L.Parametric identification of viscoelastic materials from time and frequency domain data. Submitted to Inverse Problems in Engineering (2000)

Mossberg M., Hillström L. and Söderström T. Non-parametric identification of viscoelastic materials from wave propagation experiments. Accepted for publication in Automatica (2000)

Mossberg M., Hillström L. and Söderström T. Identification of viscoelastic materials. In Proc. 12th IFAC Symp. System Identification. Santa Barbara, CA, USA, June 21-23 2000

Impact and limitations

It is not easy to estimate the scientific and industrial impact of our on-going research. However, we are hopeful that ideas generated and methods developed in the project will give rise to continued research in the field of solid mechanics as well as of systems and control. As far as our own research is concerned, we have recently proposed a continuation project to TFR which is based on ideas and “loose ends” from the present project. We are also hopeful that methods developed in the project will find use in industry through our publications as well as our industrial contacts.

Although we are satisfied with the research achievements within the project, there are factors that dampen and hinder fruitful activities. The more these factors can be rectified, the better the chances will be for continued fruitful research.

Faculty funding of research and PhD education has been decreased, slowly but steadily, on an annual basis for many years. This is serious as, e.g., it undermines our possibilities to provide a high-quality course program for our PhD students. Another consequence is that the time for basic non-project based research is decreasing and now tends to be quite limited.

Recruitment of PhD students is now becoming harder than in the past, even if we have successfully doubled the number of PhD students in a few years time. Now there are many interesting options for students graduating with an engineering degree, both in industry and at universities, and the competition for good PhD students is becoming harder and harder. The situation is no doubt positive for many individuals, at least on a short time horizon, but may become crucial for the PhD education in the long run.

A limiting factor is the availability of senior researchers. It is difficult to hire new senior faculty members with established research experience. Again, possible candidates for such positions typically face a number of interesting alternatives, also in industry.

It should furthermore be pointed out that the undergraduate teaching at the universities is becoming considerably less well-funded than in the past. Thus, the funding has gradually deteriorated over the last decades. In the past, faculty members mainly involved in undergraduate teaching could have time for some research and possibilities to follow the development in their fields. Today, there is instead a clear risk, and possibly a tendency, that funding and time aimed for research has to be used to carry out undergraduate teaching and compensate for decreased funding, as there are internal and external pressures to keep up the quality of the undergraduate teaching.

A factor that makes us vulnerable is the insufficient infrastructure in terms of secretarial help and maintenance of computers. While so far the service is mostly of high quality, it is often insufficient in volume. A major problem seems to be that there is no room to use faculty funding to pay for the increasing workload, even when both undergraduate teaching and research activities have grown sharply.

PhD Degrees

At the end of the year 2000, the project and its predecessor will have resulted in one PhD degree in systems and control and one in solid mechanics:

M. Mossberg. Identification of Viscoelastic Materials and Continuous-Time Stochastic Systems. PhD thesis, Uppsala University, Department of Systems and Control, Information Technology, May 2000.

L. Hillström. Estimation of States and Identification of Materials in Elastic and Viscoelastic Bars Traversed by Waves. PhD thesis, Uppsala University, The Angstrom Laboratory, Solid Mechanics, December 2000.

Publications 1997-2000 of research supported by TFR

Systems and Control: See separate list.

Solid Mechanics:

Nygren T., Lundberg B. and Andersson L.-E. Dissipation of wave energy in a viscoelastic junction between elastic bars: Dependence on transmission direction. Journal of Sound and Vibration 199, 323-336 (1997)

Nygren T., Andersson L.-E. and Lundberg B. Optimization of elastic junctions with regard to transmission of wave energy. Wave Motion 29, 223-244 (1999)

Nygren T., Andersson L.-E. and Lundberg B.Synthesis of elastic junctions with wave transmission properties of a given junction. Wave Motion 30, 143-158 (1999)

Nygren T., Lundberg B. and Andersson L.-E. Optimisation of viscoelastic junctions with regard to transmission of wave energy. Accepted for publication in Journal of Sound and Vibration (2000)

Hillström L., Mossberg M. and Lundberg B. Least squares determination of complex modulus from measured strains on an impact-loaded bar. Journal of Sound and Vibration 230(3), 689-707 (1999)

Hillström L. and Lundberg B. Analysis of elastic flexural waves in non-uniform beams from measurement of strains or accelerations. Accepted for publication in Journal of Sound and Vibration (2000)

Hillström L., Valdek U. and Lundberg B. Complex modulus and viscoelastic states from multiple measurements on a non-uniform beam traversed by waves. To be submitted for publication in the Journal of Sound and Vibration (2000)

Mossberg M., Hillström L. and Abrahamsson L. Parametric identification of viscoelastic materials from time and frequency domain data. Submitted to Inverse Problems in Engineering (2000)

Mossberg M., Hillström L. and Söderström T. Non-parametric identification of viscoelastic materials from wave propagation experiments. Accepted for publication in Automatica (2000)

Mossberg M., Hillström L. and Söderström T. Identification of viscoelastic materials. In Proc. 12th IFAC Symp. System Identification. Santa Barbara, CA, USA, June 21-23 2000

Scientific Computing:

Muller B. and Jenny P. Convergence acceleration for computing steady-state compressible flow at low Mach numbers. Computers & Fluids 28,951-972 (1999)

Muller B. Low Mach number asymptotics of the Navier-Stokes equations. J. Engineering Math 34, 97-109 (1998)

Jenny P. and Muller B. Rankine-Hugoniot-Riemann solver considering source terms and multidimensional effects. J. Comput. Phys 145, 576-610 (1998)

Nordström J. On flux-extrapolation at supersonic boundaries. Applied Numerical Mathematics 30, 447-457 (1999)

Nordström J. and Carpenter M.H. Boundary and interface conditions for high-order finite-difference methods applied to the Euler and Navier-Stokes equations. J. Comput. Phys. 148, 621-645 (1999)