Thesis topics

Combination of Linearized and Nonlinear Methods for Tomography

Combination of Linearized and Nonlinear Methods for Tomography

Many structural health monitoring activities employ means of tomography in order to get insights into structures. There is a series of algorithms to perform the tomography which can be mainly categorized into two groups:

Linearized methods (based on first arrival times, fast and robust)

nonlinear methods (based on model inversion, slow and less robust but with higher precission).

The idea for the content of the Master's Thesis is the combination of both methods in order to profit from the advantages of both approaches.

Codes for the two approaches will be provided.

Supervision: I. Reichert, T. Lahmer, M. Schickert (MFPA)

Random field interface for CodeBright FE software

Random field interface for CodeBright FE software

Tasks

  • Usage of existing methods for generating random fields
  • Mapping of random field data to material properties of FE model created with CodeBright FE software
  • Implementation of a automatic interface utilizing a stochastic analysis of a CodeBright FE model using the random field material description
  • Part of research project: Polymorphic uncertainty

 

Suggested qualifications

  • MATLAB
  • Bash scripting
  • Finite element method
  • Stochastics (random fields)


Supervisors

Moment-free Sensitivity Analysis of Engineering Models

Moment-free Sensitivity Analysis of Engineering Models

To assess the influence of model parameters on the model's response, means of sensitivity analysis are applied.

Most of these methods are based on the analysis of the variance.

In this work, techniques shall be studied, which consider the complete distribution of a system's output during a Monte Carlo Simulation. Results are to be compared with variance-based methods.

The choice of the application (engineering model) is according to the students suggestion.

Contact: Prof. Tom Lahmer (tom.lahmer@uni-weimar.de)

Adaption of a 2D thermo-hydro-mechanical finite element code to 3D

Tasks

  • An existing efficient 2D FE thermo-hydro-mechanical code (MATLAB) models the cross section of a gravity dam (THM system).
  • Adaption to a 3D FE code
  • Comparision of the 2D plain strain to a simple 3D models
  • Verification of 3D FE implementation with commercial software
  • Part of research project: Polymorphic uncertainty

 

Suggested qualifications

  • MATLAB
  • Finite element method

 

Supervisors

Application of the GUM for Uncertainty Quantification of Ambient Acceleration Measurements

The Guide to the Assessment of Uncertainties in Measurements (GUM) [1] provides the general concepts and guidelines for uncertainty description and quantification of measurements. These procedures should be applied, in order to develop a quality measure for acquired vibration acceleration signals.

Tasks

    • Study and summary of the relevant sections of the GUM
    • Implementation of the respective Type A and Type B uncertainty Models
    • Uncertainty propagation using Monte-Carlo Methods
    • Application to measured laboratory vibration signals

    Literature

    1. International Organization for Standardization (ISO). Guide to the Expression of Uncertainty
      in Measurement.
      Tech. rep. Geneva: ISO, Oct. 1, 2008.

    Suggested qualifications

      • "Signal Processing": good grade
      • "Stochastics for risk assessment": good grade
      • "Experimental Structural Dynamics": recommended
      • "Structural Dynamics": recommended
      • Intermediate Knowledge of MATLAB or Python

      Supervisors

      Identification of Damping Models from output-only Vibration Data

      The vibration of a mechanical system is governed by stiffness, mass and damping. The latter can be modeled as a viscous, hysteretic or other mechanism [3]. The forward solution of the system is to obtain the forced-vibration response of the system. The inverse solution is to identify system parameters from the system response (and forces) [1].

      Several methods for the identification of damping values from output-only data exist e.g. logarithmic decrement fitting, half-power bandwidth method, random decrement signatures and system-identification methods [2]. Most of them assume viscous damping, with some exceptions e.g. [4].

      In this thesis, a simple method for the identification of viscous and hysteretic damping should be developed and applied.

      Tasks

      • Literature study on damping identification
      • Implementation of a numerical solution for the forward problem for a single-mass oscilator with different damping models
      • Identification of viscous damping from taks 2
      • Identification of hysteretic damping from task 2
      • Identification of hysteretic damping from real measurements

      Literature

      1. Torsten Soderstrom and Petre Stoica. System Identification. Prentice Hall International Series in Systems and Control Engineering. July 1, 1989, p. 612.
      2. A. Kareem and K. Gurley. “Damping in structures: its evaluation and treatment of uncertainty”. In: Journal of Wind Engineering and Industrial Aerodynamics 59.2-3 (Mar. 1996), pp. 131–157.
      3. D. J. Ewins. Modal testing: theory, practice, and application. Vol. Mechanical engineering research studies. Research Studies Press, 2000.
      4. Anela Bajrić and Jan Høgsberg. “Estimation of hysteretic damping of structures by stochastic subspace identification”. In: Mechanical Systems and Signal Processing 105 (May 2018), pp. 36–50.

          Suggested qualifications   

          • "Signal Processing": good grade
          • "Structural Dynamics": good grade
          • "Stochastics for risk assessment": recommended
          • "Experimental Structural Dynamics": recommended
          • Intermediate Knowledge of MATLAB or Python

          Supervisors

          Influence of Inappropriate First Principle Laws in System Identification of Mechanical Structures

          System identification is concerned with building a mathematical model of a system from measurements of the system inputs and outputs [1,2]. In the identification of dynamical systems, usually first principle laws, such as linearity, time-invariance and others are employed to invent parametrizations that describe the behaviour of the systems. These are then estimated by optimization or realization techniques.

          If the true system shows non-linear behaviour but a linear description is used, a model error is made [4]. This typically happens in practice, when slightly non-linear dynamic systems are identified. This is referred to as linearization at an operating point, which can be tought of as perturbations of the linear system [3].

          In this thesis, the model error in identifying single-degree-of-freedom oscillators with varying non-linearities, should be investigated. The forward problem is to be solved to generate output data from linear, non-linear, and hysteretically damped oscillators. The inverse problem should then be solved using linear, viscous first-principle laws.

          Tasks    

          • Literature Study on the Subject of Linear and Non-linear System Identification
          • Identification of a simulated single-mass, viscous damped oscillator
          • (Identification of a simulated multi degree of freedom, proportionally, viscous damped oscillator)
          • Linear Identification of a non-linear oscillator
          • Linear Identification of a non-proportionally damped oscillator
          • Linear Identification of a hysteretically damped oscillator

          Literature

          1. Torsten Soderstrom and Petre Stoica. System Identification. Prentice Hall International Series in Systems and Control Engineering. July 1, 1989, p. 612.
          2. Lennart Ljung. System identification - theory for the user. Prentice Hall, 1999. 672 pp.
          3. J. Schoukens et al. “Fast approximate identification of non linear systems”. In: IFAC Proceedings Volumes 36.16 (Sept. 2003), pp. 61–66.
          4. Lennart Ljung. “Perspectives on System Identification”. In: IFAC Proceedings Volumes 41.2 (2008), pp. 7172–7184.

              Suggested qualifications

                • "Signal Processing": good grade
                • "Structural Dynamics": good grade
                • "Experimental Structural Dynamics": recommended
                • Intermediate Knowledge of MATLAB or Python

                Supervisors

                Uncertainty Quantification using Evidence Theory in a Simple System Identification Problem

                Uncertainties can be categorized as aleatoric (inherent stochastic effects) and/or epistemic (reducible, incomplete knowlegde) [4]. There exist a variety of theories for modeling these, among which are probability theory, possibility theory and evidence theory . Whereas the latter can model both aleatoric and epistemic uncertainties in a general way [3].

                System identification is concerned with building a mathematical model of a system from measurements of the system inputs and outputs [1]. The bias and variance of the identification however depends on information content of the data, which in turn depends on pre-processing and system parameters [2].


                In this thesis the uncertainties of important user selectable parameters and stochastic system parameters should be modeled using evidence theory. The propagation/quantification through the process of system identification shall be applied using e.g Monte Carlo Simulation. The procedure should be demonstrated in the identification problem of a simple 1-DOF oscillator using simulated system output signals.

                Tasks

                • Literature study on modeling and propagation/quantification of uncertainties
                • Literature study on system identification
                • Single-mass oscillator system identification
                • Modeling of uncertainties on parameters: sample rate, duration, noise level, excitation, etc.
                • Uncertainty quantification/propagation using Monte Carlo Simulations
                • Computation of Belief and Plausibility Functions on the identified system parameters

                Literature

                1. Torsten Soderstrom and Petre Stoica. System Identification. Prentice Hall International Series in Systems and Control Engineering. July 1, 1989, p. 612.
                2. Lennart Ljung. “Perspectives on System Identification”. In: IFAC Proceedings Volumes 41.2 (2008), pp. 7172–7184.
                3. Roland R. Yager and Liping Liu, eds. Classic Works of the Dempster-Shafer Theory of Belief Functions. Springer Berlin Heidelberg, 2008.
                4. Laura P Swiler, Thomas L Paez, and Randall L Mayes. “Epistemic uncertainty quantification tutorial”. In: Proceedings of the 27th International Modal Analysis Conference. 2009.

                Suggested qualifications

                • "Stochastics for risk assessment": good grade
                • "Signal Processing": good grade
                • "Structural Dynamics": exam passed
                • "Experimental Structural Dynamics": recommended
                • Intermediate Knowledge of MATLAB or Python

                    Supervisors

                    Application of Statistical Methods for Vibration-Based SHM

                    Vibration-based SHM is based on the observation of the modal parameters of a structure [1].
                    The identification of structural changes from identified modal parameters can be achieved
                    using statistical/machine-learning methods, taking into account environmental influences  [2].

                    In this thesis, statistical/machine-learning methods should be applied to existing identified
                    modal parameters from 5 years of vibration monitoring data available from a broadcasting tower (see Figure below).

                     Tasks

                    • Literature study into vibration-based SHM
                    • Implementation of two statistical/machine-learning method for detection of changes
                    • Validation using Z24 bridge data
                    • Application to tower monitoring data

                    Literature

                    1. Wei Fan and Pizhong Qiao. “Vibration-based Damage Identification Methods: A Review and Comparative Study”. In: Structural Health Monitoring: An International Journal 10.1 (Apr. 2010), pp. 83–111.
                    2. Charles R. Farrar and Keith Worden. Structural Health Monitoring: A Machine Learning Perspective. John Wiley & Sons, Inc., Dec. 26, 2012. 654 pp.

                        Suggested qualifications

                        • "Stochastics for risk assessment": good grade
                        • "Structural Health Monitoring": exam passed
                        • "Structural Dynamics": recommended
                        • "Signal Processing": recommended
                        • "Experimental Structural Dynamics": recommended
                        • Intermediate Knowledge of MATLAB or Python

                            Supervisors

                            Figure: Modal and environmental parameters acquired at a telecommunication tower