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Research Papers: Design Automation

Design of Dynamic Systems Using Surrogate Models of Derivative Functions

[+] Author and Article Information
Anand P. Deshmukh

Department of Industrial
and Enterprise Systems Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: adeshmu2@illinois.edu

James T. Allison

Department of Industrial
and Enterprise Systems Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: jtalliso@illinois.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 28, 2016; final manuscript received July 16, 2017; published online August 30, 2017. Editor: Shapour Azarm.

J. Mech. Des 139(10), 101402 (Aug 30, 2017) (12 pages) Paper No: MD-16-1673; doi: 10.1115/1.4037407 History: Received September 28, 2016; Revised July 16, 2017

Optimization of dynamic systems often requires system simulation. Several important classes of dynamic system models have computationally expensive time derivative functions, resulting in simulations that are significantly slower than real time. This makes design optimization based on these models impractical. An efficient two-loop method, based on surrogate modeling, is presented here for solving dynamic system design problems with computationally expensive derivative functions. A surrogate model is constructed for only the derivative function instead of the simulation response. Simulation is performed based on the computationally inexpensive surrogate derivative function; this strategy preserves the nature of the dynamic system, and improves computational efficiency and accuracy compared to conventional surrogate modeling. The inner-loop optimization problem is solved for a given derivative function surrogate model (DFSM), and the outer loop updates the surrogate model based on optimization results. One unique challenge of this strategy is to ensure surrogate model accuracy in two regions: near the optimal point in the design space, and near the state trajectory in the state space corresponding to the optimal design. The initial evidence of method effectiveness is demonstrated first using two simple design examples, followed by a more detailed wind turbine codesign problem that accounts for aeroelastic effects and simultaneously optimizes physical and control system design. In the last example, a linear state-dependent model is used that requires computationally expensive matrix updates when either state or design variables change. Results indicate an order-of-magnitude reduction in function evaluations when compared to conventional surrogate modeling. The DFSM method is expected to be beneficial only for problems where derivative function evaluation expense, and not large problem dimension, is the primary contributor to solution expense (a restricted but important problem class). The initial studies presented here revealed opportunities for potential further method improvement and deeper investigation.

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Figures

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Fig. 1

Comparison of conventional SM and DFSM for approximation of simulation-based models

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Fig. 2

The nonconvex, multimodal amplitude response of a DVA (maximum |x1(t)|): (a) surface plot for max |x1(t)|, (b) level sets for max |x1(t)|, and (c) system model schematic

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Fig. 3

Design process using surrogate models of derivative functions. (* corresponds to optimal solutions).

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Fig. 4

Nested codesign formulation

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Fig. 5

Simultaneous codesign formulation

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Fig. 6

Example 1, comparing actual and DFSM solution, time t on x-axis: (a) optimal ξ1(t), (b) optimal ξ2(t), and (c) optimal u(t)

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Fig. 7

Example 2, comparing actual and DFSM solution, time t on x-axis: (a) optimal ξ1(t), (b) optimal ξ2(t), and (c) optimal u(t)

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Fig. 8

Wind turbine with selected variables and states

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