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Optimal Design of Neuro-Mechanical Networks
Linköping University, Department of Management and Engineering, Mechanics. Linköping University, The Institute of Technology.
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Many biological and artificial systems are made up from similar, relatively simple elements that interact directly with their nearest neighbors. Despite the simplicity of the individual building blocks, systems of this type, network systems, often display complex behavior — an observation which has inspired disciplines such as artificial neural networks and modular robotics. Network systems have several attractive properties, including distributed functionality, which enables robustness, and the possibility to use the same elements in different configurations. The uniformity of the elements should also facilitate development of efficient methods for system design, or even self-reconfiguration. These properties make it interesting to investigate the idea of constructing mechatronic systems based on networks of simple elements.

This thesis concerns modeling and optimal design of a class of active mechanical network systems referred to as Neuro-Mechanical Networks (NMNs). To make matters concrete, a mathematical model that describes an actuated truss with an artificial recurrent neural network superimposed onto it is developed and used. A typical NMN is likely to consist of a substantial number of elements, making design of NMNs for various tasks a complex undertaking. For this reason, the use of numerical optimization methods in the design process is advocated. Application of such methods is exemplified in four appended papers that describe optimal design of NMNs which should take on static configurations or follow time-varying trajectories given certain input stimuli. The considered optimization problems are nonlinear, non-convex, and potentially large-scale, but numerical results indicate that useful designs can be obtained in practice.

The last paper in the thesis deals with a solution method for optimization problems with matrix inequality constraints. The method described was developed primarily for solving optimization problems stated in some of the other appended papers, but is also applicable to other problems in control theory and structural optimization.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2012. , 42 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1444
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-76984ISBN: 978-91-7519-900-9 (print)OAI: oai:DiVA.org:liu-76984DiVA: diva2:524028
Public defence
2012-06-01, C3, C-huset, Campus Valla, Linköpings universitet, Linköping, 11:15 (English)
Opponent
Supervisors
Available from: 2012-04-27 Created: 2012-04-27 Last updated: 2017-05-15Bibliographically approved
List of papers
1. Modeling and Optimal Design of Neuro-Mechanical Shape Memory Devices
Open this publication in new window or tab >>Modeling and Optimal Design of Neuro-Mechanical Shape Memory Devices
2012 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 45, no 2, 257-274 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we describe the modeling and optimization of what we refer to as Neuro-Mechanical Shape Memory Devices (NMSMDs). These are active mechanical structures which are designed to take on specific shapes in response to certain external stimuli. An NMSMD is a particular example of a Neuro-Mechanical Network (NMN), a mechanical structure that consists of a network of simple but multifunctional elements. In the present work, each element contains an actuator and an artificial neuron, and when assembled into a structure the elements form an actuated truss with a superimposed recurrent neural network.

The task of designing an NMSMD is cast as an optimization problem in which a measure of the error between the actual and desired shape for a number of given stimuli is minimized. The optimization problems are solved using a gradient based solver, and some numerical examples are provided to illustrate the results from the design process and some aspects of the proposed model.

Place, publisher, year, edition, pages
Springer, 2012
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-67845 (URN)10.1007/s00158-011-0684-1 (DOI)000298500500008 ()
Note
Funding agencies|National Graduate School of Scientific computing (NGSSC)||Swedish Research Council| DNR 2006-6218 |Available from: 2011-04-29 Created: 2011-04-29 Last updated: 2017-12-11Bibliographically approved
2. Optimal Design of Neuro-Mechanical Oscillators
Open this publication in new window or tab >>Optimal Design of Neuro-Mechanical Oscillators
2013 (English)In: Computers & structures, ISSN 0045-7949, E-ISSN 1879-2243, Vol. 119, 189-202 p.Article in journal (Refereed) Published
Abstract [en]

This paper concerns optimization of active mechanical systems capable of exhibiting persistent oscillatory behavior. In part inspired by biological systems possessing similar properties we refer to these systems as neuro-mechanical oscillators. The mathematical model consists of a set of nonlinear ordinary differential equations describing an actuated truss excited by a nonlinear recurrent neural network. An optimization problem is formulated with the goal of adjusting some of the parameters in the system such that when the neural network is subjected to a constant input, one of the nodes in the truss follows a prescribed trajectory in a periodic fashion. Two examples are presented to illustrate the concept, and the corresponding optimization problems are solved numerically.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-67846 (URN)10.1016/j.compstruc.2012.11.018 (DOI)000317171000017 ()
Available from: 2011-04-29 Created: 2011-04-29 Last updated: 2017-12-11Bibliographically approved
3. Optimal Design of Neuro-Mechanical Oscillators with Stability Constraints
Open this publication in new window or tab >>Optimal Design of Neuro-Mechanical Oscillators with Stability Constraints
2015 (English)In: ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, ISSN 0044-2267, Vol. 95, no 6, 620-637 p.Article in journal (Refereed) Published
Abstract [en]

This paper concerns optimal design of so-called Neuro-Mechanical Oscillators (NMOs). An NMO is a new type of bio-inspired mechatronic system which consists of an actuated truss with a recurrent neural network (RNN) superimposed onto it. By choosing the entries of the weight matrix of the RNN, an NMO can be designed, using numerical optimization, to generate pre-specified time-varying motions when subject to certain time-varying input signals. However, to rule out possible dependence of the motion on the initial state of the system as well as convergence into limit cycles, some form of constraints must be imposed on the system's design parameters. To derive such constraints, we investigate under what conditions the influence of the initial state eventually vanishes and the motion becomes completely determined by the input signal. Three sufficient criteria are presented for RNNs, but the possibility of large mechanical deformations most likely rule out global system level results. For sufficiently small deformations, however, local results are obtained, and a numerical example provided in the paper indicates that these can be useful for designing practical systems.

Place, publisher, year, edition, pages
Wiley-VCH Verlagsgesellschaft, 2015
Keyword
Neuro-Mechanical Oscillators; recurrent neural networks; optimal design; convergent systems
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-76981 (URN)10.1002/zamm.201300031 (DOI)000355725900004 ()
Available from: 2012-04-27 Created: 2012-04-27 Last updated: 2015-06-26Bibliographically approved
4. Some Aspects of Optimal Design of Neuro-Mechanical Shape Memory Devices
Open this publication in new window or tab >>Some Aspects of Optimal Design of Neuro-Mechanical Shape Memory Devices
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Neuro-Mechanical Shape Memory Devices (NMSMDs) are a new type of active mechanical systems designed to take on prescribed shapes when subjected to a certain input stimuli. In an earlier paper we derived a mathematical model for NMSMDs and posed an optimization problem for finding system parameters that would result in an NMSMD with a certain desired behavior. The optimization problem was highly nonlinear and non-convex, making it difficult to find good solutions. In this paper, through using a numerical example, we show that these difficulties can be alleviated by a new formulation of the original optimization problem. However, it is also shown that, due to the possible existence of multiple equilibrium points for the governing equations of NMSMDs, solutions to the new optimization problem must be carefully validated.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-76982 (URN)
Available from: 2012-04-27 Created: 2012-04-27 Last updated: 2017-05-15Bibliographically approved
5. A Simple Method for Solving Nonlinear Non-convex Optimization Problems with Matrix Inequality Constraints with Applications in Structural Optimization
Open this publication in new window or tab >>A Simple Method for Solving Nonlinear Non-convex Optimization Problems with Matrix Inequality Constraints with Applications in Structural Optimization
(English)Manuscript (preprint) (Other academic)
Abstract [en]

This paper is about a simple method for solving nonlinear, non-convex optimization problems (NLPs) with matrix inequality constraints. The method is based on the fact that a symmetric matrix is positive semi-definite if and only if it admits a Cholesky decomposition, and works by reformulating the original matrix inequality constrained problem into a standard NLP, for which there are currently many high-quality codes available. Examples of optimization problems involving matrix inequality constraints are relatively frequent in the structural optimization literature, and to illustrate a potential usage of our method we present numerical solutions for weight minimization of trusses subject to compliance and global buckling constraints. Looking ahead, we also see problems involving simultaneous optimization of both structure and control systems being common, and since matrix inequality constrained problems appear frequently in control theory, we believe that the number of applications for codes like the one presented here will continue to grow rapidly.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-76983 (URN)
Available from: 2012-04-27 Created: 2012-04-27 Last updated: 2012-04-27Bibliographically approved

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