scholarly journals Multiple Tensor Train Approximation of Parametric Constitutive Equations in Elasto-Viscoplasticity

2019 ◽  
Vol 24 (1) ◽  
pp. 17
Author(s):  
Clément Olivier ◽  
David Ryckelynck ◽  
Julien Cortial
Keyword(s):  
Constitutive Equations ◽  
Surrogate Model ◽  
Reference Model ◽  
Data Representation ◽  
Differential Algebraic Equations ◽  
Constitutive Law ◽  
Algebraic Equations ◽  
Tensor Representation ◽  
Novel Approach ◽  
Parametric Studies

This work presents a novel approach to construct surrogate models of parametric differential algebraic equations based on a tensor representation of the solutions. The procedure consists of building simultaneously an approximation given in tensor-train format, for every output of the reference model. A parsimonious exploration of the parameter space coupled with a compact data representation allows alleviating the curse of dimensionality. The approach is thus appropriate when many parameters with large domains of variation are involved. The numerical results obtained for a nonlinear elasto-viscoplastic constitutive law show that the constructed surrogate model is sufficiently accurate to enable parametric studies such as the calibration of material coefficients.

scholarly journals Multiple Tensor Train Approximation of Parametric Constitutive Equations in Elasto-Viscoplasticity

2018 ◽  
Author(s):  
Clément Olivier ◽  
David Ryckelynck ◽  
Julien Cortial
Keyword(s):  
Constitutive Equations ◽  
Surrogate Model ◽  
Reference Model ◽  
Data Representation ◽  
Differential Algebraic Equations ◽  
Constitutive Law ◽  
Algebraic Equations ◽  
Tensor Representation ◽  
Novel Approach ◽  
Parametric Studies

This work presents a novel approach to construct surrogate models of parametric Differential Algebraic Equations based on a tensor representation of the solutions. The procedure consists in building simultaneously, for every output of the reference model, an approximation given in tensor-train format. A parsimonious exploration of the parameter space coupled with a compact data representation allows to alleviate the curse of dimensionality. The approach is thus appropriate when many parameters with large domains of variation are involved. The numerical results obtained for a nonlinear elasto-viscoplastic constitutive law show that the constructed surrogate model is sufficiently accurate to enable parametric studies such as the calibration of material coefficients.

scholarly journals A Generalized State-Space Aeroservoelastic Model Based on Tangential Interpolation

Aerospace ◽  
2019 ◽  
Vol 6 (1) ◽  
pp. 9 ◽  
Author(s):  
David Quero ◽  
Pierre Vuillemin ◽  
Charles Poussot-Vassal
Keyword(s):  
State Space ◽  
Reference Model ◽  
Differential Algebraic Equations ◽  
Summation Method ◽  
Algebraic Equations ◽  
Minimal Order ◽  
New Approach ◽  
Model Based ◽  
Generalized State Space ◽  
Generalized State

In this work, a new approach for the generation of a generalized state-space aeroservoelastic model based on tangential interpolation is presented. The resulting system of differential algebraic equations (DAE) is reduced to a set of ordinary differential equations (ODE) by residualization of the non-proper part of the transfer function matrix. The generalized state-space is of minimal order and allows for the application of the force summation method (FSM) for the aircraft loads recovery. Compared to the classical rational function approximation (RFA) approach, the presented method provides a minimal order realization with exact interpolation of the unsteady aerodynamic forces in tangential directions, avoiding any selection of poles (lag states). The new approach is applied first for the generation of an aerodynamic model for the bidimensional unsteady incompressible flow in the time domain. Next, an application on the generation of an aeroservoelastic model for loads evaluation of the flutter reduced order assessment (FERMAT) model under atmospheric disturbances is done, showing an excellent agreement with the reference model in the frequency domain. The proposed aeroservoelastic model of minimal order is suited for loads analysis and multivariable control design, and an application to a gust loads alleviation (GLA) strategy is shown.

Control of Closed Kinematic Chains Using A Singularly Perturbed Dynamics Model

2005 ◽  
Vol 128 (1) ◽  
pp. 142-151 ◽  
Author(s):  
Zhiyong Wang ◽  
Fathi H. Ghorbel
Keyword(s):  
Kinematic Chain ◽  
Perturbation Parameter ◽  
Parallel Robot ◽  
Differential Algebraic Equations ◽  
Singularly Perturbed ◽  
Algebraic Equations ◽  
Kinematic Chains ◽  
Novel Approach ◽  
Lyapunov Function Method ◽  
Perturbed Model

In this paper, we propose a novel approach to the control of closed kinematic chains (CKCs). This method is based on a recently developed singularly perturbed model for CKCs. Conventionally, the dynamics of CKCs are described by differential-algebraic equations (DAEs). Our approach transfers the control of the original DAE system to the control of an artificially created singularly perturbed system in which the slow dynamics corresponds to the original DAE when the perturbation parameter tends to zero. Compared to control schemes that rely on solving nonlinear algebraic constraint equations, the proposed method uses an ordinary differential equation (ODE) solver to obtain the dependent coordinates, hence, eliminates the need for Newton-type iterations and is amenable to real-time implementation. The composite Lyapunov function method is used to show that the closed-loop system, when controlled by typical open kinematic chain schemes, achieves asymptotic trajectory tracking. Simulations and experimental results on a parallel robot, the Rice planar Delta robot, are also presented to illustrate the efficacy of our method.

Markov Jump Linear System Analysis of a Microgrid Operating in Islanded and Grid Tied Modes

2020 ◽  
Author(s):  
Gilles Mpembele ◽  
Jonathan Kimball
Keyword(s):  
Monte Carlo ◽  
Power Systems ◽  
Power System ◽  
System Analysis ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Markov Jump ◽  
Numerical Application ◽  
Conditional Moments ◽  
Markov Jump Linear Systems

<div>The analysis of power system dynamics is usually conducted using traditional models based on the standard nonlinear differential algebraic equations (DAEs). In general, solutions to these equations can be obtained using numerical methods such as the Monte Carlo simulations. The use of methods based on the Stochastic Hybrid System (SHS) framework for power systems subject to stochastic behavior is relatively new. These methods have been successfully applied to power systems subjected to</div><div>stochastic inputs. This study discusses a class of SHSs referred to as Markov Jump Linear Systems (MJLSs), in which the entire dynamic system is jumping between distinct operating points, with different local small-signal dynamics. The numerical application is based on the analysis of the IEEE 37-bus power system switching between grid-tied and standalone operating modes. The Ordinary Differential Equations (ODEs) representing the evolution of the conditional moments are derived and a matrix representation of the system is developed. Results are compared to the averaged Monte Carlo simulation. The MJLS approach was found to have a key advantage of being far less computational expensive.</div>

scholarly journals Differential-algebraic systems are generically controllable and stabilizable

2021 ◽  
Author(s):  
Achim Ilchmann ◽  
Jonas Kirchhoff
Keyword(s):  
Algebraic Geometry ◽  
Linear Time ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Algebraic Systems ◽  
Linear Time Invariant ◽  
Survey Article ◽  
Link Type ◽  
Invariant Differential ◽  
Time Invariant

AbstractWe investigate genericity of various controllability and stabilizability concepts of linear, time-invariant differential-algebraic systems. Based on well-known algebraic characterizations of these concepts (see the survey article by Berger and Reis (in: Ilchmann A, Reis T (eds) Surveys in differential-algebraic equations I, Differential-Algebraic Equations Forum, Springer, Berlin, pp 1–61. 10.1007/978-3-642-34928-7_1)), we use tools from algebraic geometry to characterize genericity of controllability and stabilizability in terms of matrix formats.

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