Modeling the basin of attraction as a two-dimensional manifold from experimental data: Applications to balance in humans

Zakynthinaki, Maria S.; Stirling, James Robert; Martínez, Carol; Durana, Alfonso López Díaz de; Quintana, Manuel Sillero; Rodríguez-Romo, Gabriel; Molinuevo, Javier Sampedro

doi:10.1063/1.3337690

Cited by 21 publications

(27 citation statements)

References 35 publications

(34 reference statements)

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“…For example, an important requirement for the maintenance of balance during quiet standing is that the center of mass must stay within the base of support located beneath and between the soles of the feet. In mathematical terms the base of support is approximately the basin of attraction for the upright position [30]. A much studied example of the effect of perturbations in the state variables on standing balance is the ankle-hip-step strategy adopted by subjects in response to increasingly large perturbations [31], [32], [33], [34].…”

Section: Discussionmentioning

confidence: 99%

Extension of Stability Radius to Neuromechanical Systems With Structured Real Perturbations

Hajdu

Milton

Insperger

2016

IEEE Trans. Neural Syst. Rehabil. Eng.

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Abstract-The ability of humans to maintain balance about an unstable position in a continuously changing environment attests to the robustness of their balance control mechanisms to perturbations. A mathematical tool to analyze robust stabilization of unstable equilibria is the stability radius. Based on the pseudospectra, the stability radius gives a measure to the maximum change of the system parameters without resulting loss of stability. Here we compare stability radii for a model for human frontal plane balance controlled by a delayed proportional-derivative feedback to two types of perturbations: unstructured complex and weighted structured real. It is shown that 1) narrow stance widths are more robust to parameter variation; 2) stability is maintained for larger structured real perturbations than for unstructured complex perturbations; and 3) the most robust derivative gain to weighted structured real perturbations is located near the stability boundary. It is argued that stability radii can effectively be used to compare different control concepts associated with human motor control.

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Section: Discussionmentioning

confidence: 99%

Extension of Stability Radius to Neuromechanical Systems With Structured Real Perturbations

Hajdu

Milton

Insperger

2016

IEEE Trans. Neural Syst. Rehabil. Eng.

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“…Our procedure was adapted from Zakynthinaki et al [19]. The experiment consisted of leaning in eight distinct directions, where the subject’s initial and final position was standing upright on a force plate with both feet together on the floor and with hands on their hips.…”

Section: Methodsmentioning

confidence: 99%

Basins of attraction in human balance

Smith

Lockhart

Spano

2017

Eur. Phys. J. Spec. Top.

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Falls are a recognized risk factor for unintentional injuries among older adults, accounting for a large proportion of fractures, emergency department visits, and urgent hospitalizations. Human balance and gait research traditionally uses linear or qualitative tests to assess and describe human motion; however, human motion is neither a simple nor a linear process. The objective of this research is to identify and to learn more about what factors affect balance using nonlinear dynamical techniques, such as basin boundaries. Human balance data was collected using dual force plates for leans using only ankle movements as well as for unrestricted leans. Algorithms to describe the basin boundary were created and compared based on how well each method encloses the experimental data points as well as captures the differences between the two leaning conditions.

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“…In dynamical systems, any system that evolves towards a steady state is said to be drawn to an attractor [171]. This idea can be used in the context of continuous optimization, if we consider a local optimum to be a steady state.…”

Section: Basins Of Attractionmentioning

confidence: 99%

Algorithm selection for black-box continuous optimization problems: A survey on methods and challenges

Muñoz

Sun

Kirley

et al. 2015

Information Sciences

177

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a b s t r a c tSelecting the most appropriate algorithm to use when attempting to solve a black-box continuous optimization problem is a challenging task. Such problems typically lack algebraic expressions, it is not possible to calculate derivative information, and the problem may exhibit uncertainty or noise. In many cases, the input and output variables are analyzed without considering the internal details of the problem. Algorithm selection requires expert knowledge of search algorithm efficacy and skills in algorithm engineering and statistics. Even with the necessary knowledge and skills, success is not guaranteed.In this paper, we present a survey of methods for algorithm selection in the black-box continuous optimization domain. We start the review by presenting Rice's (1976) selection framework. We describe each of the four component spaces -problem, algorithm, performance and characteristic -in terms of requirements for black-box continuous optimization problems. This is followed by an examination of exploratory landscape analysis methods that can be used to effectively extract the problem characteristics. Subsequently, we propose a classification of the landscape analysis methods based on their order, neighborhood structure and computational complexity. We then discuss applications of the algorithm selection framework and the relationship between it and algorithm portfolios, hybrid meta-heuristics, and hyper-heuristics. The paper concludes with the identification of key challenges and proposes future research directions.

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Modeling the basin of attraction as a two-dimensional manifold from experimental data: Applications to balance in humans

Cited by 21 publications

References 35 publications

Extension of Stability Radius to Neuromechanical Systems With Structured Real Perturbations

Extension of Stability Radius to Neuromechanical Systems With Structured Real Perturbations

Basins of attraction in human balance

Algorithm selection for black-box continuous optimization problems: A survey on methods and challenges

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