Structural optimization considering smallest magnitude eigenvalues: a smooth approximation

Torii, André Jacomel; Faria, Jairo Rocha de

doi:10.1007/s40430-016-0583-x

Cited by 44 publications

(25 citation statements)

References 22 publications

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“…Each eigenvalue needs to be transformed in the order of magnitude to make it within the range of (0, 10). This range is selected based on the existing research on data pre-processing [18,19].…”

Section: An Improved Methods Of Data Pre-processing For Classificationmentioning

confidence: 99%

Big Data Mining Optimization Algorithm Based on Machine Learning Model

Jiao¹

2020

RIA

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In a big data mining optimization algorithm, the classification algorithm plays an important role. At present, there are many popular classification algorithms based on machine learning. Aiming at the problems of existing big data classification algorithms, two improved strategies and implementation methods are proposed in this paper. First of all, before the data training, the orders of magnitude of the original data are normalized to achieve better data pre-processing and classification. Then with the least mean square algorithm and the BP neural network classification algorithm as the basic algorithms, an improved batch learning BP algorithm is designed, based on the rules of batch learning. The experimental results indicate that the improved batch learning BP algorithm can better solve the imbalanced classification problem in big data.

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Section: An Improved Methods Of Data Pre-processing For Classificationmentioning

confidence: 99%

Big Data Mining Optimization Algorithm Based on Machine Learning Model

Jiao¹

2020

RIA

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“…Black curves refer to application of InvIt with initial guess u (0) = 0. Blue curves refer to the choice u (0) =̃, computed by the multilevel method, and the orange ones take into account the effect of the inexact solution of (18) by the preconditioned conjugate gradient with the stopping criterion (17). PInvIt, preconditioned inverse iteration…”

Section: Figurementioning

confidence: 99%

“…Again, the iteration is stopped according to (17), applied to each u i(k) and w i(k) , respectively.…”

Section: Extension To Multiple Load Casesmentioning

confidence: 99%

“…First, eigenvalues are likely to become repeated and the corresponding sensitivities nonsmooth during the optimization . This theoretical difficulty has been extensively studied in the last decades, and several methods have been proposed for computing sensitivities of repeated eigenvalues or for working with smooth functions of them . Other approaches overcome this issue by recurring to methods of semidefinite programming or nonconvex optimization .…”

Section: Introductionmentioning

confidence: 99%

“…11,12 This theoretical difficulty has been extensively studied in the last decades, and several methods have been proposed for computing sensitivities of repeated eigenvalues 13,14 or for working with smooth functions of them. [15][16][17] Other approaches overcome this issue by recurring to methods of semidefinite programming or nonconvex optimization. 12,18,19 A second practical limitation is due to the high computational cost required by the solution of a large eigenvalue problem at each optimization step.…”

Section: Introductionmentioning

confidence: 99%

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Eigenvalue topology optimization via efficient multilevel solution of the frequency response

Ferrari

Lazarov

Sigmund

2018

Numerical Meth Engineering

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Summary The article presents an efficient solution method for structural topology optimization aimed at maximizing the fundamental frequency of vibration. Nowadays, this is still a challenging problem mainly because of the high computational cost required by spectral analyses. The proposed method relies on replacing the eigenvalue problem with a frequency response one, which can be tuned and efficiently solved by a multilevel procedure. Connections of the method with multigrid eigenvalue solvers are discussed in details. Several applications demonstrating more than 90% savings of the computational time are presented as well.

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Simultaneous topology and fastener layout optimization of assemblies considering joint failure

Ambrozkiewicz

Kriegesmann

2020

Numerical Meth Engineering

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This article provides a method for the simultaneous topology optimization of parts and their corresponding joint locations in an assembly. Therein, the joint locations are not discrete and predefined, but continuously movable. The underlying coupling equations allow for connecting dissimilar meshes and avoid the need for remeshing when joint locations change. The presented method models the force transfer at a joint location not only by using single spring elements but accounts for the size and type of the joints. When considering riveted or bolted joints, the local part geometry at the joint location consists of holes that are surrounded by material. For spot welds, the joint locations are filled with material and may be smaller than for bolts. The presented method incorporates these material and clearance zones into the simultaneously running topology optimization of the parts. Furthermore, failure of joints may be taken into account at the optimization stage, yielding assemblies connected in a fail-safe manner.

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Structural optimization considering smallest magnitude eigenvalues: a smooth approximation

Cited by 44 publications

References 22 publications

Big Data Mining Optimization Algorithm Based on Machine Learning Model

Big Data Mining Optimization Algorithm Based on Machine Learning Model

Eigenvalue topology optimization via efficient multilevel solution of the frequency response

Simultaneous topology and fastener layout optimization of assemblies considering joint failure

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