Model Order Reduction Techniques with a Posteriori Error Control for Nonlinear Robust Optimization Governed by Partial Differential Equations

Lass, Oliver; Ulbrich, Stefan

doi:10.1137/16m108269x

Cited by 29 publications

(31 citation statements)

References 51 publications

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“…3). The system matrix and right-hand side in (8) are decomposed into fixed submatrices and subvectors multiplied by coefficients that fully inherit the dependence on p. In this way, the submatrices and subvectors need to be assembled only once on beforehand, while the weighting coefficients are promptly computed by evaluating an analytical formula every time the geometry changes.…”

Section: Computation Of Pmsmsmentioning

confidence: 99%

“…In contrast, gradient-based methods typically converge fast, provided that the gradients of the objective and constraint function are given with a sufficient accuracy. Although this can be cumbersome for complicated functions, such preliminary computations are rewarded by a low iteration count of the embracing optimization procedure [8]. The comparably large number of uncertain parameters is efficiently treated by stochastic collocation on a Clenshaw-Curtis sparse grid [17], [18].…”

Section: Introductionmentioning

confidence: 99%

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Robust Optimization of a Permanent-Magnet Synchronous Machine Considering Uncertain Driving Cycles

D'Angelo¹,

Bontinck²,

Schöps³

et al. 2020

IEEE Trans. Magn.

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This work focuses on the robust optimization of a permanent magnet (PM) synchronous machine while considering a driving cycle. The robustification is obtained by considering uncertainties of different origins. Firstly, there are geometrical uncertainties caused by manufacturing inaccuracies. Secondly, there are uncertainties linked to different driving styles. The final set of uncertainties is linked to ambient parameters such as traffic and weather conditions. The optimization goal is to minimize the PM's volume while maintaining a desired machine performance measured by the energy efficiency over the driving cycle and the machine's maximal torque. The magnetic behavior of the machine is described by a partial differential equation (PDE) and is simulated by the finite-element method employing an affine decomposition to avoid reassembling of the system of equations due to the changing PM geometry. The Sequential Quadratic Programming algorithm is used for the optimization. Stochastic collocation is applied to compute moments of stochastic quantities. The robustness of the optimized configurations is validated by a Monte Carlo sampling. It is found that the uncertainties in driving style and road conditions have significant influence on the optimal PM configuration.

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Section: Computation Of Pmsmsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust Optimization of a Permanent-Magnet Synchronous Machine Considering Uncertain Driving Cycles

D'Angelo¹,

Bontinck²,

Schöps³

et al. 2020

IEEE Trans. Magn.

View full text Add to dashboard Cite

show abstract

“…[39], a numerically feasible optimization problem is obtained. Also higher order expansions can be exploited [40], however, in this work only linearizations of the cost function and the constraint are considered:…”

Section: Robust Optimizationmentioning

confidence: 99%

“…However, they can be obtained analogously as described previously. Finally, this approach can be generalized to use a quadratic approximation with respect to P, see [40].…”

Section: Robust Optimizationmentioning

confidence: 99%

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Robust optimisation formulations for the design of an electric machine

Bontinck

Lass

Schöps

et al. 2018

IET Science, Measurement & Technology

Self Cite

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In this paper two formulations for the robust optimization of the size of the permanent magnet in a synchronous machine are discussed. The optimization is constrained by a partial differential equation to describe the electromagnetic behavior of the machine. The need for a robust optimization procedure originates from the fact that optimization parameters have deviations. The first approach, i.e., worst-case optimization, makes use of local sensitivities. The second approach takes into account expectation values and standard deviations. The latter are associated with global sensitivities. The geometry parametrization is elegantly handled thanks to the introduction of an affine decomposition. Since the stochastic quantities are determined by tools from uncertainty quantification (UQ) and thus require a lot of finite element evaluations, model order reduction is used in order to increase the efficiency of the procedure. It is shown that both approaches are equivalent if a linearization is carried out. This finding is supported by the application on an electric machine. The optimization algorithms used are sequential quadratic programming, particle swarm optimization and genetic algorithm. While both formulations reduce the size of the magnets, the UQ based optimization approach is less pessimistic with respect to deviations and yields smaller magnets.

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Optimal control of district heating networks using a reduced order model

Rein

Möhring

Damm

et al. 2020

Optim Control Appl Methods

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SummaryWe study the optimal control of district heating networks using a reduced order model based on a system theoretic description close to the underlying Euler equations. In the presented scenarios, the central task is to limit the maximal feed‐in power occurring as a product of control and state variables. The underlying dynamics of heating networks acting as optimization constraints pose the central computational complexity, prohibiting the determination of an optimal control online. The advection of the injected energy density on the network results in an index‐1, quadratic in state differential algebraic equation, challenging to reduce. The suggested reduced model decreases the computation time of the optimization significantly. The effectiveness of the presented approach is demonstrated for an existing, large‐scale heating network including changes of flux directions.

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Model Order Reduction Techniques with a Posteriori Error Control for Nonlinear Robust Optimization Governed by Partial Differential Equations

Cited by 29 publications

References 51 publications

Robust Optimization of a Permanent-Magnet Synchronous Machine Considering Uncertain Driving Cycles

Robust Optimization of a Permanent-Magnet Synchronous Machine Considering Uncertain Driving Cycles

Robust optimisation formulations for the design of an electric machine

Optimal control of district heating networks using a reduced order model

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