Design of Dynamic Systems using Surrogate Models of Derivative Functions

[+] Author and Article Information
Anand Deshmukh

Graduate Student, University of Illinois at Urbana-Champaign, Urbana, IL 61801

James T. Allison

Assistant Professor, University of Illinois at Urbana-Champaign, Urbana, IL 61801

1Corresponding author.

ASME 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, and the outer loop updates the surrogate model based on optimization results. 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 effectiveness of the proposed method is demonstrated using two simple design examples, followed by a more detailed wind turbine co-design 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.

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