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Analysis, Control, and Design Optimization of Engineering Mechanics Systems
Umeå University, Faculty of Science and Technology, Department of Computing Science.
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis considers applications of gradient-based optimization algorithms to the design and control of some mechanics systems. The material distribution approach to topology optimization is applied to design two different acoustic devices, a reactive muffler and an acoustic horn, and optimization is used to control a ball pitching robot.

Reactive mufflers are widely used to attenuate the exhaust noise of internal combustion engines by reflecting the acoustic energy back to the source. A material distribution optimization method is developed to design the layout of sound-hard material inside the expansion chamber of a reactive muffler. The objective is to minimize the acoustic energy at the muffler outlet. The presence or absence of material is represented by design variables that are mapped to varying coefficients in the governing equation. An anisotropic design filter is used to control the minimum thickness of materials separately in different directions. Numerical results demonstrate that the approach can produce mufflers with high transmission loss for a broad range of frequencies.

For acoustic devices, it is possible to improve their performance, without adding extended volumes of materials, by an appropriate placement of thin structures with suitable material properties. We apply layout optimization of thin sound-hard material in the interior of an acoustic horn to improve its far-field directivity properties. Absence or presence of thin sound-hard material is modeled by a surface transmission impedance, and the optimization determines the distribution of materials along a “ground structure” in the form of a grid inside the horn. Horns provided with the optimized scatterers show a much improved angular coverage, compared to the initial configuration.

The surface impedance is handled by a new finite element method developed for Helmholtz equation in the situation where an interface is embedded in the computational domain. A Nitschetype method, different from the standard one, weakly enforces the impedance conditions for transmission through the interface. As opposed to a standard finite-element discretization of the problem, our method seamlessly handles both vanishing and non-vanishing interface conditions. We show the stability of the method for a quite general class of surface impedance functions, provided that possible surface waves are sufficiently resolved by the mesh.

The thesis also presents a method for optimal control of a two-link ball pitching robot with the aim of throwing a ball as far as possible. The pitching robot is connected to a motor via a non-linear torsional spring at the shoulder joint. Constraints on the motor torque, power, and angular velocity of the motor shaft are included in the model. The control problem is solved by an interior point method to determine the optimal motor torque profile and release position. Numerical experiments show the effectiveness of the method and the effect of the constraints on the performance.

Place, publisher, year, edition, pages
Umeå: Umeå University , 2016. , 58 p.
Series
Report / UMINF, ISSN 0348-0542 ; 16.13
Keyword [en]
Topology optimization, Helmholtz equation, acoustic impedance, anisotropic filter, thin structures, finite element method, Nitsche-type method, interface problem, Optimal control, adjoint method
National Category
Computer Science
Research subject
Computing Science
Identifiers
URN: urn:nbn:se:umu:diva-119978ISBN: 978-91-7601-497-4 (print)OAI: oai:DiVA.org:umu-119978DiVA: diva2:926016
Public defence
2016-05-30, MA121, MIT-huset. Umeå universitet, Umeå, 10:15 (English)
Opponent
Supervisors
Available from: 2016-05-09 Created: 2016-05-03 Last updated: 2017-04-11Bibliographically approved
List of papers
1. Interior layout topology optimization of a reactive muffler
Open this publication in new window or tab >>Interior layout topology optimization of a reactive muffler
2016 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 53, no 4, 645-656 p.Article in journal (Refereed) Published
Abstract [en]

This article presents a material distribution method that is tailored to the interior design of reactive mufflers. Such devices are typically acoustically small, except in the length direction, and their interior consists of a combination of pipes, expansions, contractions, and Helmholtz resonators. In order to design the interior layout using material distribution optimization, it is necessary to be able to resolve thin sound-hard materials as well as thin sheets with a given acoustic impedance, such as perforated plates, and manage small channels to Helmholtz resonators. We develop a method that uses an anisotropic design filter in combination with a fine mesh in order to control the minimum thickness separately in different directions. A two-stage post processing procedure is used to control openings to resonators, and embedded thin impedance surfaces are modeled by a mortar-element method. Numerical results demonstrate that the approach can produce mufflers with high transmission loss for a broad range of frequencies. The optimized mufflers include components that resemble combinations of expansion chambers, cylindrical pipes, and Helmholtz resonators.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2016
Keyword
Topology optimization, Reactive muffler, Acoustic impedance, Mortar functions, Anisotropic filter
National Category
Computational Mathematics
Identifiers
urn:nbn:se:umu:diva-119972 (URN)10.1007/s00158-015-1317-x (DOI)000373023800001 ()
Available from: 2016-05-03 Created: 2016-05-03 Last updated: 2017-10-04Bibliographically approved
2. A Nitsche-type Method for Helmholtz Equation with an Embedded Acoustically Permeable Interface
Open this publication in new window or tab >>A Nitsche-type Method for Helmholtz Equation with an Embedded Acoustically Permeable Interface
Show others...
2016 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 304, 479-500 p.Article in journal (Refereed) Published
Abstract [en]

We propose a new finite element method for Helmholtz equation in the situation where an acoustically permeable interface is embedded in the computational domain. A variant of Nitsche's method, different from the standard one, weakly enforces the impedance conditions for transmission through the interface. As opposed to a standard finite-element discretization of the problem, our method seamlessly handles a complex-valued impedance function Z that is allowed to vanish. In the case of a vanishing impedance, the proposed method reduces to the classic Nitsche method to weakly enforce continuity over the interface. We show stability of the method, in terms of a discrete Gårding inequality, for a quite general class of surface impedance functions, provided that possible surface waves are sufficiently resolved by the mesh. Moreover, we prove an a priori error estimate under the assumption that the absolute value of the impedance is bounded away from zero almost everywhere. Numerical experiments illustrate the performance of the method for a number of test cases in 2D and 3D with different interface conditions. 

Place, publisher, year, edition, pages
Elsevier, 2016
Keyword
Helmholtz equation, Finite Element method, Nitsche's method, interface problem, surface wave, Gårding inequality
National Category
Computational Mathematics
Identifiers
urn:nbn:se:umu:diva-119977 (URN)10.1016/j.cma.2016.02.032 (DOI)000374506600020 ()
Available from: 2016-05-03 Created: 2016-05-03 Last updated: 2017-05-08Bibliographically approved
3. Layout optimization of thin sound-hard material to improve the far-field directivity properties of an acoustic horn
Open this publication in new window or tab >>Layout optimization of thin sound-hard material to improve the far-field directivity properties of an acoustic horn
2017 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 55, no 3, 795-808 p.Article in journal (Refereed) Published
Abstract [en]

To improve the far-field directivity properties of a given mid-range acoustic horn, previously designed by shape optimization to exhibit almost ideal transmission properties in the frequency range 1.6–9.05 kHz, we apply layout optimization of thin sound-hard material in the interior of the horn. The purpose of the optimization is to place scattering material to prevent the sound intensity to increasingly be concentrated, with increasing frequency, along the horn axis. Absence or presence of thin sound-hard material is modeled by an equivalent surface transmission impedance, and the optimization algorithm determines the distribution of air or sound-hard material along a “ground structure” in the form of a grid inside the horn. The surface impedance is numerically handled using a newly developed finite-element formulation that allows exact enforcement of a vanishing impedance, corresponding to air, which would not be possible using a standard formulation. Horns provided with the optimized scatterers show a much improved angular coverage, compared to the initial configuration, with beam widths that exceed 60 ∘ uniformly over the operational frequency range, without destroying the good transmission properties of the initial horn.

Keyword
Layout optimization, Helmholtz equation, Thin structures, Interface problem, Acoustic impedance
National Category
Computer Systems
Identifiers
urn:nbn:se:umu:diva-119973 (URN)10.1007/s00158-016-1536-9 (DOI)000398114200004 ()
Funder
Swedish Research Council, 621-2013-3706
Available from: 2016-05-03 Created: 2016-05-03 Last updated: 2017-05-12Bibliographically approved
4. On the use of thin structures to control the far-field properties of an acoustic device
Open this publication in new window or tab >>On the use of thin structures to control the far-field properties of an acoustic device
2016 (English)Report (Other academic)
Abstract [en]

This work presents a sensitivity analysis for topology optimization of thin structures inside an acoustic horn in order to improve its far-field directivity properties. The objective function gradient is computed using an adjoint-based method, a well-known approach in the design optimization community due to its ability to compute the design sensitivities when there is a large number of design variables. The accuracy of the computed gradient is verified numerically against a first order finite difference approximation. The report also covers the matrix representations of the far-field pattern evaluation and the variational problem with an interface condition to model the thin structures. 

Place, publisher, year, edition, pages
Umeå: Department of Computing Science, Umeå University, 2016. 19 p.
Series
Report / UMINF, ISSN 0348-0542 ; 16.12
National Category
Computer Systems
Identifiers
urn:nbn:se:umu:diva-119975 (URN)
Available from: 2016-05-03 Created: 2016-05-03 Last updated: 2016-08-24Bibliographically approved
5. State constrained optimal control of a ball pitching robot
Open this publication in new window or tab >>State constrained optimal control of a ball pitching robot
2013 (English)In: Mechanism and machine theory, ISSN 0094-114X, E-ISSN 1873-3999, Vol. 69, 337-349 p.Article in journal (Refereed) Published
Abstract [en]

We present a method for offline optimal control of a two-link ball pitching robot with the aim of throwing a ball as far as possible. The pitching robot is connected to a motor via a non-linear torsional spring at the shoulder joint. The elbow joint is passive and loaded with a linear torsional spring. We model the system based on an Euler–Lagrange formulation. Constraints on the motor torque and power as well as the angular velocity of the motor shaft are included in the model. By using an interior point method with gradients supplied by a discrete adjoint method, we numerically solve the resulting constrained control problem of finding the optimal piecewise constant motor torque profile and release position. Numerical experiments illustrate the effectiveness of our strategy as well as the effect of the constraints on the objective. In our experiments, the optimal motor torque gives rise to motions comprising an initial backswing; a transition, where the elbow spring accumulates potential energy; and finally a fast acceleration phase leading up the ball release.

Place, publisher, year, edition, pages
Elsevier, 2013
Keyword
Motion planning, Optimal control, Underactuated system, Adjoint method
National Category
Computational Mathematics Robotics
Identifiers
urn:nbn:se:umu:diva-80313 (URN)10.1016/j.mechmachtheory.2013.06.009 (DOI)000323358600021 ()
External cooperation:
Available from: 2013-09-16 Created: 2013-09-16 Last updated: 2017-12-06Bibliographically approved

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