Thomas Haag

Stability Analysis of Time-Delay Systems With Incommensurate Delays Using Positive Polynomials

We present a new stability condition for linear time-delay systems (TDS) with multiple incommensurate delays based on the Rekasius substitution and positive polynomials. The condition is checked by testing the positivity of multivariate polynomials in certain domains. For this purpose, we propose two alternative algorithms based on linear programming and sum of squares methods, respectively. The efficiency and accuracy of the algorithms is compared in an example to alternative stability conditions taken from the literature.

Experimental and numerical investigation of the dynamics in spatial fluid‐filled piping systems

Hydraulic piping systems, such as fluid‐filled break and fuel pipes in automotive applications, undergo strong acoustic excitation due to pressure pulsations of pump and valve operation. By fluid‐structure coupling the sound transmission within the pipe may lead to a structural excitation of other car components causing excessive noise levels or even structural failure. In order to obtain a complete and reliable understanding of the wave propagation and vibration phenomena in spatial piping systems, a test rig is presented, consisting of a pressure source and a fluid‐filled break pipe with an attached target structure. With this experimental setup, it is possible to quantify the acoustic sound transmission and to examine the dynamic behavior by transfer functions. The experimental results are compared with harmonic and transient finite element simulations employing efficient model order reduction techniques for the fluid‐structure coupled system. This research focuses on the identification of hydraulic resonances and the optimal mounting of the fluid‐filled break pipe in order to minimize the structure‐borne sound induced on the target structure.

Comprehensive Modeling of Uncertain Systems Using Fuzzy Set Theory

Non-determinism in structural mechanics is ubiquitious. Whenever a mathematical model of a real world engineering system is developed, simplification techniques are employed which lead to systematic errors in the modeling procedure. The fuzzy arithmetical approach which is presented in this chapter is designed to handle epistemic uncertainties, as those systematic errors are also termed, in numerical simulations by the use of fuzzy numbers. The approach consists of the transformation method which is designed to compute fuzzy-valued output quantities and an inverse fuzzy arithmetical method which additionally determines the fuzzy-valued model parameters on the basis of measurement data in a second step. Additionally, a kind of a sensitivity analysis is provided along with a criterion to assess the quality of different competing mathematical models.

Model Assessment Using Inverse Fuzzy Arithmetic

A general problem in numerical simulations is the selection of an appropriate model for a given real system. In this paper, the authors propose a new method to validate, select and optimize mathematical models. The presented method uses models with fuzzy-valued parameters, so-called comprehensive models, that are identified by the application of inverse fuzzy arithmetic. The identification is carried out in such a way that the uncertainty band of the output, which is governed by the uncertain input parameters, conservatively covers a reference output. Based on the so identified fuzzy-valued model parameters, a criterion for the selection and optimization is defined that minimizes the overall uncertainty inherent to the model. This criterion does not only consider the accuracy in reproducing the output, but also takes into account the size of the model uncertainty which is necessary to cover the reference output.

Comparison of Different Stability Conditions for Linear Time-Delay Systems with Incommensurate Delays

Abstract We compare different stability conditions for linear time-delay systems with multiple incommensurate, time-invariant delays. In total, nine sufficient stability conditions are taken from the literature and implemented in MATLAB. All of them guarantee asymptotic stability if all delays τk are smaller than a bound. The different conditions are then tested on nine examples which have served as benchmark examples in various earlier publications. The different conditions are compared with each other with respect to computational effort and maximal achievable bound, for which asymptotic stability is guaranteed.

Physical implementation of immersive boundary conditions in acoustic waveguides

The physical implementation of so-called immersive boundary conditions (IBCs) allows the construction of anechoic chambers, where wavefield reflections from the boundary of a physical domain, such as a wave propagation laboratory, are actively suppressed by emitting a secondary wavefield at the domain boundary that destructively interferes with the reflected waves. Moreover, IBCs enable immersive wave propagation experimentation by linking the wave propagation in the physical domain with the propagation in a numerical domain enclosing the physical domain. In this case, IBCs correctly account for all wavefield interactions between both domains, including higher-order scattering. The physical implementation of IBCs is achieved by densely populating the boundary surrounding the physical domain with transducers that enforce the necessary boundary conditions. The signals required at the injection boundary are predicted with the help of a secondary surface of transducers that record the wavefield on a surface slightly inside the physical domain. The recorded wavefield is extrapolated to the boundary by evaluating a Kirchhoff-Helmholtz integral in real-time using an FPGA-enabled data acquisition, computation and control system. Here, we present results of the active suppression of broadband boundary reflections in 1D and 2D acoustic waveguides.The physical implementation of so-called immersive boundary conditions (IBCs) allows the construction of anechoic chambers, where wavefield reflections from the boundary of a physical domain, such as a wave propagation laboratory, are actively suppressed by emitting a secondary wavefield at the domain boundary that destructively interferes with the reflected waves. Moreover, IBCs enable immersive wave propagation experimentation by linking the wave propagation in the physical domain with the propagation in a numerical domain enclosing the physical domain. In this case, IBCs correctly account for all wavefield interactions between both domains, including higher-order scattering. The physical implementation of IBCs is achieved by densely populating the boundary surrounding the physical domain with transducers that enforce the necessary boundary conditions. The signals required at the injection boundary are predicted with the help of a secondary surface of transducers that record the wavefield on a surface s...

Numerical simulations of acoustic cloaking in a real laboratory that deploys immersive boundary conditions

Immersive boundary conditions (IBCs) act as a wavefield injection method that couples a physical wave propagation experiment to an arbitrary virtual domain. They allow novel, real-time applications for acoustic wave experimentation such as interactions between physical and virtual domains, broadband cloaking, and holography. The implementation of IBCs relies on actively injecting a particular wavefield on the boundary of the physical domain from a dense array of transducers. The injected wavefield must honour the real-world physical and the virtual or computational domains. To calculate the required inputs, a dense array of recording transducers inside the boundary is used from which the future wavefield arriving at the source transducers can be predicted using a discretised Kirchhoff-Helmholtz integral. Whereas IBCs are effectively exact for purely numerical applications, a physical implementation in a laboratory suffers from limitations mainly associated with spatial and temporal discretization issues and the imprint of the electrical devices such as transfer functions or radiation characteristics of transducers. We present a comprehensive numerical sensitivity study of a cloaking experiment in a 2D acoustic waveguide. This defines physical limitations of real-world IBCs, and systematic errors introduced due to subsampling of the recording and injection surfaces and to radiation characteristics of the transducers.