Vector Approximation | ScienceGate

An Eight-Node Hexahedral Finite Element with Rotational DOFs for Elastoplastic Applications

Acta Universitatis Sapientiae Electrical and Mechanical Engineering ◽

10.2478/auseme-2019-0005 ◽

2019 ◽

Vol 11 (1) ◽

pp. 54-66

Author(s):

Ayoub Ayadi ◽

Kamel Meftah ◽

Lakhdar Sedira ◽

Hossam Djahara

Keyword(s):

Mathematical Model ◽

Finite Element ◽

Plastic Zone ◽

Displacement Vector ◽

Small Strain ◽

Benchmark Problems ◽

Plasticity Model ◽

Vector Approximation ◽

Calculation Code

Abstract In this paper, the earlier formulation of the eight-node hexahedral SFR8 element is extended in order to analyze material nonlinearities. This element stems from the so-called Space Fiber Rotation (SFR) concept which considers virtual rotations of a nodal fiber within the element that enhances the displacement vector approximation. The resulting mathematical model of the proposed SFR8 element and the classical associative plasticity model are implemented into a Fortran calculation code to account for small strain elastoplastic problems. The performance of this element is assessed by means of a set of nonlinear benchmark problems in which the development of the plastic zone has been investigated. The accuracy of the obtained results is principally evaluated with some reference solutions.

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Vector approximation method with parameter adaptation and torque control of CSI-fed induction motor

IEEE Transactions on Industry Applications ◽

10.1109/28.395293 ◽

1995 ◽

Vol 31 (4) ◽

pp. 830-840 ◽

Cited By ~ 7

Author(s):

K. Ide ◽

Zhi-Guo Bai ◽

Zi-Jiang Yang ◽

T. Tsuji

Keyword(s):

Induction Motor ◽

Approximation Method ◽

Torque Control ◽

Parameter Adaptation ◽

Vector Approximation

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Meta-Descent for Online, Continual Prediction

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v33i01.33013943 ◽

2019 ◽

Vol 33 ◽

pp. 3943-3950

Author(s):

Andrew Jacobsen ◽

Matthew Schlegel ◽

Cameron Linke ◽

Thomas Degris ◽

Adam White ◽

...

Keyword(s):

Gradient Descent ◽

Large Scale ◽

Time Series Prediction ◽

Real Data ◽

Second Order ◽

Stochastic Gradient Descent ◽

Step Size ◽

Vector Approximation ◽

Prediction Problems ◽

Stationary Problems

This paper investigates different vector step-size adaptation approaches for non-stationary online, continual prediction problems. Vanilla stochastic gradient descent can be considerably improved by scaling the update with a vector of appropriately chosen step-sizes. Many methods, including AdaGrad, RMSProp, and AMSGrad, keep statistics about the learning process to approximate a second order update—a vector approximation of the inverse Hessian. Another family of approaches use meta-gradient descent to adapt the stepsize parameters to minimize prediction error. These metadescent strategies are promising for non-stationary problems, but have not been as extensively explored as quasi-second order methods. We first derive a general, incremental metadescent algorithm, called AdaGain, designed to be applicable to a much broader range of algorithms, including those with semi-gradient updates or even those with accelerations, such as RMSProp. We provide an empirical comparison of methods from both families. We conclude that methods from both families can perform well, but in non-stationary prediction problems the meta-descent methods exhibit advantages. Our method is particularly robust across several prediction problems, and is competitive with the state-of-the-art method on a large-scale, time-series prediction problem on real data from a mobile robot.

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