Bayesian Optimization of Equilibrium States in Elastomeric Beams

2021 ◽  
pp. 1-36
Author(s):  
David Yoo ◽  
Nathan Hertlein ◽  
Vincent Chen ◽  
Carson Willey ◽  
Andrew Gillman ◽  
...  
Keyword(s):  
Penalty Method ◽  
Vibration Isolation ◽  
Design Space ◽  
Strong Dependence ◽  
Series Representation ◽  
Building Blocks ◽  
Equilibrium States ◽  
Bayesian Optimization ◽  
Stable States ◽  
Beam Shape

Abstract Architected elastomeric beam networks have great potential for energy absorption, multi-resonant vibration isolation, and multi-bandgap elastic wave control, due to the reconfigurability and programmability of their mechanical buckling instabilities. However, navigating this design space is challenging due to bifurcations between mono- and bistable beam designs, inherent geometric nonlinearities, and the strong dependence of buckling properties on beam geometry. To investigate these challenges, we developed a Bayesian optimization framework to control the equilibrium states of an inclined elastomeric beam, while also tuning the energy to transition between these configurations. Leveraging symmetry to reduce the design space, the beam shape is parameterized using a Fourier series representation. A penalty method is developed to include monostable designs in objective functions with dependencies on bistable features, enabling monostable results to still be incorporated in the Gaussian Process surrogate and contribute to the optimization process. Two objectives are optimized in this study, including the position of the second stable equilibrium configuration and the ratio of output to input energy between the two stable states. A scalarized multi-objective optimization is also carried out to study the trade-off between equilibrium position and the energetics of transition between the stable states. The predicted designs are qualitatively verified through experimental testing. Collectively, the study explores a new parameter space for beam buckling, introduces a penalty method to regularize between mono- and bistable domains and provides a library of beams as building blocks to assemble and analyze in future studies.

Bayesian Optimization of Equilibrium States in Elastomeric Beams

2019 ◽  
Author(s):  
David Yoo ◽  
Carson Wiley ◽  
Andrew Gillman ◽  
Vincent Chen ◽  
Abigail Juhl ◽  
...  
Keyword(s):  
Vibration Isolation ◽  
Design Space ◽  
Continuation Method ◽  
Computational Cost ◽  
Computational Design ◽  
Equilibrium States ◽  
Bayesian Optimization ◽  
Single Element ◽  
Element Analysis ◽  
Trade Off

Abstract Architected elastomers have demonstrated great potential for energy absorption, multi-resonant vibration isolation, and multi-bandgap acoustic control, due to the reversibility and programmability of their mechanical instabilities. However, computational design tools are needed to explore the large parameter space that regulates buckling-based mechanical instability behavior. In this study, we develop a machine-learning-based design optimization framework to control equilibrium states of a bistable elastomeric beam, while also regulating the required energy to transition between these configurations. Leveraging symmetry to reduce the design space, the research is performed on a single element, an inclined, slender beam, through a Fourier series parameterization. To evaluate the force-displacement response of the bistable beam, a nonlinear finite element analysis (FEA) with an arc-length continuation method is employed in a commercial FEA tool. Due to the highly non-convex bistability response of the beam in this proposed design space and the computational cost of the FEA analysis, a Bayesian optimization is implemented to promote a better trade-off between the number of function evaluations and rate of convergence. Bayesian optimization depends on several optimization parameters, which are systematically tuned in this study to characterize their role on the optimization process. With the proposed method, the equilibrium displacement and the ratio of output to input energy between stable states can be optimized within a few tens of iterations. A multi-objective optimization is also carried out to study the trade-off between equilibrium position and the energetics to transition between the bistabilities.

A New Adaptive Penalty Method for Constrained Genetic Algorithm and Its Application to Water Distribution Systems

2006 ◽  
Author(s):  
Berge Djebedjian ◽  
Ashraf Yaseen ◽  
Magdy Abou Rayan
Keyword(s):  
Genetic Algorithm ◽  
Penalty Function ◽  
Penalty Method ◽  
Distribution Systems ◽  
Water Distribution ◽  
Optimization Problem ◽  
Water Distribution Systems ◽  
Building Blocks ◽  
Adaptive Penalty ◽  
Adaptive Penalty Method

This paper presents a new adaptive penalty method for genetic algorithms (GA). External penalty functions have been used to convert a constrained optimization problem into an unconstrained problem for GA-based optimization. The success of the genetic algorithm application to the design of water distribution systems depends on the choice of the penalty function. The optimal design of water distribution systems is a constrained non-linear optimization problem. Constraints (for example, the minimum pressure requirements at the nodes) are generally handled within genetic algorithm optimization by introducing a penalty cost function. The optimal solution is found when the pressures at some nodes are close to the minimum required pressure. The goal of an adaptive penalty function is to change the value of the penalty draw-down coefficient during the search allowing exploration of infeasible regions to find optimal building blocks, while preserving the feasibility of the final solution. In this study, a new penalty coefficient strategy is assumed to increase with the total cost at each generation and inversely with the total number of nodes. The application of the computer program to case studies shows that it finds the least cost in a favorable number of function evaluations if not less than that in previous studies and it is computationally much faster when compared with other studies.

In Situ Hvem Studies of Electron-Beam-Driven Composition Changes in Thin Film Alloys: Displacement-Rate Gradient Effects

1984 ◽  
Vol 41 ◽  
Author(s):  
P. R. Okamoto ◽  
N. Q. Lam
Keyword(s):  
Thin Film ◽  
Electron Beams ◽  
Strong Dependence ◽  
Rate Of Change ◽  
Displacement Rate ◽  
Beam Diameter ◽  
Beam Shape ◽  
High Voltage Electron Microscopy ◽  
Composition Changes

AbstractIn situ high-voltage electron microscopy (HVEM) observations have shown that the highly-focused electron beams normally employed for HVEM irradiation experiments can cause large chemical composition changes in the irradiated zone of thin film alloys during elevated temperature irradiations. The driving force for the process comes primarily from the radial gradients in displacement rates generated by the beam. Hence, the rate of change in composition exhibits a strong dependence not only on the temperature and beam intensity, but also on the spatial characteristics of the beam profile. This dependence on beam shape and size poses previously unrecognized problems, particularly for HVEM studies of the effects of dose-rate on radiation-induced phenomena that are sensitive to alloy composition. Moreover, composition changes driven by radial gradients in the displacement- rate occur at increasingly rapid rates as the beam diameter is reduced. Hence, at higher voltages, beam-induced composition changes occurring during analysis may become a serious problem, even at relatively low temperatures, for microchemical analysis techniques, such as EDX and EELS, which employ far smaller diameter electron beams than those used for irradiation purposes in the HVEM.

scholarly journals A Novel AES Cryptographic Core Highly Resistant to Differential Power Analysis Attacks

2009 ◽  
Vol 4 (1) ◽  
pp. 29-35
Author(s):  
Felipe Ghellar ◽  
Marcelo Lubaszewski
Keyword(s):  
Power Analysis ◽  
Design Space Exploration ◽  
Design Space ◽  
Space Exploration ◽  
Building Blocks ◽  
Advanced Encryption Standard ◽  
Side Channel ◽  
Performance Constraints ◽  
Mathematical Properties ◽  
Rijndael Algorithm

In this work, we present a novel core implementation of the Advanced Encryption Standard with an integrated countermeasure against side channel attacks, which can theoretically increase the complexity of a DPA attack by a factor of 240. This countermeasure is based on mathematical properties of the Rijndael algorithm, and retains compatibility with the published Standard. The entire system was designed from the ground up to allow the reutilization of the building blocks in many different combinations, thus providing for design space exploration. Synthesis results show that the protected core can perfectly meet the performance constraints of currently used smart cards.

scholarly journals Matching, Stability, and Vibration Analysis of Nonlinear Suspension System for Truck Cabs

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Fuxing Yang ◽  
Leilei Zhao ◽  
Yuewei Yu ◽  
Changcheng Zhou
Keyword(s):  
Dynamic Simulation ◽  
Vibration Isolation ◽  
Design Space ◽  
Ride Comfort ◽  
Suspension System ◽  
Installation Space ◽  
Vibration Excitation ◽  
Cab Suspension ◽  
Simulation Results ◽  
The Stability

To improve comfort, a nonlinear suspension system is proposed on the basis of the nonlinear vibration isolation theory and the installation space of the cab suspension system for trucks. This system is suitable for all-floating cabs. For easy matching and design, the static and stability characteristics of the suspension system were analyzed, respectively, and the boundary condition for the stability of the system was given. Moreover, the cab simulation model was established, and the dynamic simulation was conducted. The stability analysis shows that the smaller the vibration excitation of the cab system, the higher its stability is. The dynamic simulation results show that the acceleration of the cab with the nonlinear suspension system is effectively suppressed; the dynamic deflection of the suspension is kept within a certain range, and the design space of the suspension stroke can be effectively utilized. Compared with the traditional linear suspension system, the nonlinear suspension system has better vibration isolation characteristics and can effectively improve ride comfort.

A Study of the Multi-Stability in a Non-Rigid Stacked Miura-Origami Cellular Mechanism

2021 ◽  
Author(s):  
Jiayue Tao ◽  
Suyi Li
Keyword(s):  
Building Blocks ◽  
Cellular Mechanism ◽  
Unit Cell ◽  
Torsional Stiffness ◽  
Engineering Systems ◽  
Stable States ◽  
Cellular Solid ◽  
Nonlinear Mechanical ◽  
Material Systems ◽  
Stable Structures

Abstract Multi-stable structures have gathered extensive interest because they can provide a broad spectrum of adaptive functions for many engineering systems. Especially, origami sheets with a translational periodicity can be stacked and assembled to form a multi-stable cellular solid, which has emerged as a promising platform to design functional structures. This paper investigates the multi-stability characteristics of a non-rigid stacked Miura-origami mechanism consisting of Miura-ori sheets and accordion-shaped connecting sheets, focusing on the elemental unit cell. A nonlinear mechanical model based on the barhinge approach is established to quantitatively study the unit cell’s multi-stability with intentionally relaxed rigid-folding conditions. Results show that only two stable states are achievable in the unit cell with enforced rigid-folding kinematics. However, if one relaxes the rigid-folding conditions and allows the facet to deform (i.e. non-rigid folding), four stable states are reachable in the unit cell if the crease torsional stiffness of the connecting sheets becomes sufficiently larger than that of the Miura-ori sheets, or the stress-free folding angle deviates away from 0°. A close examination of the potential energy composition of the non-rigid unit cell provides a detailed principle underpinning the multi-stability. By showing the benefits of exploiting facet compliance, this study can become the building blocks for origami-based structures and material systems with a wider variety of novel functionalities.

Introduction

2020 ◽  
pp. 1-4
Author(s):  
Gabriel Gellner ◽  
Kevin S. McCann ◽  
Emily J. Champagne
Keyword(s):  
Disease Ecology ◽  
Matrix Theory ◽  
Stage Structure ◽  
Building Blocks ◽  
System Structure ◽  
Stable States ◽  
Theoretical Ecology ◽  
Novel Theory ◽  
Large Growth ◽  
Population Interactions

This book continues the authoritative and established edited series of theoretical ecology books initiated by Robert May which helped pave the way for ecology to become a more robust theoretical science, encouraging the modern biologist to better understand the mathematics behind their theories. This latest instalment in the Theoretical Ecology series builds on the legacy of its predecessors with a completely new set of contributions. Rather than placing emphasis on historical ideas in theoretical ecology, the editors have encouraged each contribution to: i) synthesize historical theoretical ideas within modern frameworks that have emerged in the last ten to twenty years (e.g., bridging population interactions to whole food webs); ii) describe novel theory that has emerged in the last twenty years from historical empirical areas (e.g., macro-ecology); and iii) cover the booming area of theoretical ecological applications (e.g., disease theory and global change theory). The result is a forward-looking synthesis that will help guide the field through a further decade of development and discovery. Early chapters are collectively more about the building blocks for understanding dynamics of interacting species in time and space, including coexistence, consumer-resource and biological lags, stochasticity, and stage structure. Later, chapters are representative of the study of networks, a large growth area. These include matrix theory, mutualistic networks, community structure, body size and system structure, and network ecology. Novel concepts such as trait-based models and meta-population ecology are then presented. Applied theoretical ecology is then covered by chapters on disease ecology, climate change dynamics, and stable states.

Linkage Problem, Distribution Estimation, and Bayesian Networks

2000 ◽  
Vol 8 (3) ◽  
pp. 311-340 ◽  
Author(s):  
Martin Pelikan ◽  
David E. Goldberg ◽  
Erick Cantú-Paz
Keyword(s):  
Bayesian Networks ◽  
Joint Distribution ◽  
Prior Information ◽  
Linear Time ◽  
Building Blocks ◽  
Bayesian Optimization ◽  
Problem Size ◽  
Bayesian Optimization Algorithm ◽  
Domain Information ◽  
Estimation Of Distributions

This paper proposes an algorithm that uses an estimation of the joint distribution of promising solutions in order to generate new candidate solutions. The algorithm is settled into the context of genetic and evolutionary computation and the algorithms based on the estimation of distributions. The proposed algorithm is called the Bayesian Optimization Algorithm (BOA). To estimate the distribution of promising solutions, the techniques for modeling multivariate data by Bayesian networks are used. The BOA identifies, reproduces, and mixes building blocks up to a specified order. It is independent of the ordering of the variables in strings representing the solutions. Moreover, prior information about the problem can be incorporated into the algorithm, but it is not essential. First experiments were done with additively decomposable problems with both nonoverlapping as well as overlapping building blocks. The proposed algorithm is able to solve all but one of the tested problems in linear or close to linear time with respect to the problem size. Except for the maximal order of interactions to be covered, the algorithm does not use any prior knowledge about the problem. The BOA represents a step toward alleviating the problem of identifying and mixing building blocks correctly to obtain good solutions for problems with very limited domain information.

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