Accelerated Microwave Design Optimization With Tuning Space Mapping

Koziel, Slawomir; Meng, Jingke; Bandler, J.W.; Bakr, Mohamed H.; Cheng, Qingsha S.

doi:10.1109/tmtt.2008.2011313

Cited by 89 publications

(74 citation statements)

References 36 publications

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“…As an alternative optimal control strategy, the technique of space-mapping could be used. Developed for the use of microwave filter designs, see [37], the optimal control algorithm is based on the idea of two given models: an accurate but complex model and a simpler but inexact model. The optimization is done exclusively on the level of the simple model, whereas the crucial part is to find a mapping of the complex model to the simple model, the so-called spacemapping.…”

Section: Outlook and Future Researchmentioning

confidence: 99%

Optimal Control of Isometric Muscle Dynamics

Rockenfelle¹,

Götz²

2015

j.math.fund.sci.

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Abstract. We use an indirect optimal control approach to calculate the optimal neural stimulation needed to obtain measured isometric muscle forces. The neural stimulation of the nerve system is hereby considered to be a control function (input) of the system 'muscle' that solely determines the muscle force (output). We use a well-established muscle model and experimental data of isometric contractions. The model consists of coupled activation and contraction dynamics described by ordinary differential equations. To validate our results, we perform a comparison with commercial optimal control software.Keywords: biomechanics; inverse dynamics; muscle model; optimal control, stimulation. 0 B IntroductionMathematical models for everyday phenomena often ask for a control or input such that a system reacts in an optimal or at least in a desired way. Whether finding the optimal rotation of a stick for cooking potatoes on the open fire such that the potato has a desired temperature, see [1], or computing the optimal neural stimulation of a muscle such that the force output is as close as possible to experimentally measured data. Typical examples for biomechanical optimal control problems occur in the calculation of goal directed movements, see [2][3][4] and in robotics [5]. Concerning huge musculoskeletal systems, the load sharing problem of muscle force distribution has to be solved using optimal control [6,7]. The most common application for solving the load sharing problem is the inverse dynamics of multi-body systems (MBS) as in [8,9]. The aim is to approximate observed multi-body trajectories by a forward simulation. The problem occurs to find a set of muscle activations such that the muscle forces resulting from the MBS simulation are similar to the measured ones.Considering a general optimal control problem there is a process described by a vector of state variables which has to be influenced by control variable u ∈ within a time interval [t 0 , t 1 ] such that a given objective function ℑ( , u) is minimized subject to the model equations. These model equations can be either ordinary differential equations (ODE), partial differential equations (PDE) or differential algebraic equations (DAE). Additional constraints on the control Optimal Control of Isometric Muscle Dynamics 13 variable as well as the state variable itself can be imposed. The corresponding general optimal control problem reads as follows:For solving this minimization problem we introduce an adjoint (or costate) variable λ which operates as a penalty function, if the ODE or DAE are not fulfilled. The optimized control variable u * is found at the saddle point of the Lagrangian ℒ.Almost exclusively in biomechanical literature, the problem in Eq. (1) is solved by the technique of first discretize then optimize also known as direct method. Therefore ℑ as well as the ODE/DAE constraints are discretized on a given time grid resulting in a huge non-linear program (NLP), see [1,[10][11][12]. For solving such NLPs, several efficient solvers have been desig...

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Section: Outlook and Future Researchmentioning

confidence: 99%

Optimal Control of Isometric Muscle Dynamics

Rockenfelle¹,

Götz²

2015

j.math.fund.sci.

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“…The SBO techniques might be particularly efficient with the physics-based low-fidelity models such as space mapping [25,27] or simulation-based tuning [29]. However, the area of application of these methods is limited to the problems where fast circuit equivalents are readily available, e.g., in the case of microstrip filters [25][26][27].…”

Section: 3mentioning

confidence: 99%

“…In SBO, the optimization burden is shifted to a surrogate model, computationally cheap representation of the optimized structure. There are two basic approaches to build the surrogate model: (i) approximation of the high-fidelity model data (using, e.g., neural networks [16,17], support-vector regression [18,19], fuzzy systems [20,21], Cauchy approximation [22], or kriging [23,24]), and (ii) suitable correction of a physics-based low-fidelity model (e.g., space mapping (SM) [25][26][27], tuning [28,29]). Approximation models are quite versatile; however, they also require large sets of training data which are normally acquired with substantial computational effort.…”

Section: Introductionmentioning

confidence: 99%

Rapid antenna design optimization using shape-preserving response prediction

Kozieł¹,

Ogurtsov²,

Szczepański³

2012

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. An approach to rapid optimization of antennas using the shape-preserving response-prediction (SPRP) technique and coarsediscretization electromagnetic (EM) simulations (as a low-fidelity model) is presented. SPRP allows us to estimate the response of the high-fidelity EM antenna model, e.g., its reflection coefficient versus frequency, using the properly selected set of so-called characteristic points of the low-fidelity model response. The low-fidelity model, corrected by means of SPRP, is subsequently used to predict the optimal design. The design process is cost efficient because most operations are performed on the low-fidelity model. Performance of our technique is demonstrated using a dielectric resonator antenna and two planar wideband antenna examples. In all cases, the optimal design is obtained at a cost corresponding to a few high-fidelity simulations of the antenna under design.

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“…Conventionally, antenna design relies on optimizing the geometric shape of an initial layout. That is, the design parameters of an antenna structure are first identified, and their values are fine-tuned via trial-and-error approaches, genetic algorithms (GAs) [1,2], particle swarm optimization (PSO) [3,4], space mapping [5], or artificial neural networks (ANN) [6]. However, such approaches may fail to produce a satisfactory design if the detailed initial guess is incorrect.…”

Section: Introductionmentioning

confidence: 99%

A Building-Block Favoring Method for the Topology Optimization of Internal Antenna Design

Chen

2015

International Journal of Antennas and Propagation

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This paper proposes a new design technique for internal antenna development. The proposed method is based on the framework of topology optimization incorporated with three effective mechanisms favoring the building blocks of associated optimization problems. Conventionally, the topology optimization of antenna structures discretizes a design space into uniform and rectangular pixels. However, the defining length of the resultant building blocks is so large that the problem difficulty arises; furthermore, the order of the building blocks becomes extremely high, so genetic algorithms (GAs) and binary particle swarm optimization (BPSO) are not more efficient than the random search algorithm. In order to form tight linkage groups of building blocks, this paper proposes a novel approach to handle the design details. In particular, a nonuniform discretization is adopted to discretize the design space, and the initialization of GAs is assigned as orthogonal arrays (OAs) instead of a randomized population; moreover, the control map of GAs is constructed by ensuring the schema growth based on the generalized schema theorem. By using the proposed method, two internal antennas are thus successfully developed. The simulated and measured results show that the proposed technique significantly outperforms the conventional topology optimization.

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Accelerated Microwave Design Optimization With Tuning Space Mapping

Cited by 89 publications

References 36 publications

Optimal Control of Isometric Muscle Dynamics

Optimal Control of Isometric Muscle Dynamics

Rapid antenna design optimization using shape-preserving response prediction

A Building-Block Favoring Method for the Topology Optimization of Internal Antenna Design

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