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Research Papers

Convergence Analysis and Experimental Validation of a Fused Numerical/Experimental Active System Optimization Framework

[+] Author and Article Information
Nihar Deodhar

Department of Mechanical Engineering,
University of North Carolina at Charlotte,
Charlotte, NC 28223
e-mail: ndeodhar@uncc.edu

Christopher Vermillion

Mechanical and Aerospace Engineering,
North Carolina State University,
Raleigh, NC 27607
e-mail: cvermil@ncsu.edu

1Present address: GE Transportation, Global Locomotive Operations, Erie, PA 16531.

2Present address: Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27607.

3Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received May 28, 2018; final manuscript received November 12, 2018; published online December 19, 2018. Assoc. Editor: Douglas Bristow.

J. Dyn. Sys., Meas., Control 141(4), 041011 (Dec 19, 2018) (11 pages) Paper No: DS-18-1255; doi: 10.1115/1.4042032 History: Received May 28, 2018; Revised November 12, 2018

This paper presents a convergence analysis and experimental validation of an iterative design optimization framework that fuses numerical simulations with experiments. At every iteration, a G-optimal design generates a set of simulations and experiments that are used to characterize response surfaces. A subset of the experiments termed as the training points are used to fit a combined numerical/experimental response. This numerical response is obtained as a result of numerical model correction via experiments. The quality of fit for this combined response is evaluated using the remaining validation points. Based on the quality of fit, the feasible design space is reduced for a given confidence interval using hypothesis testing. A convergence analysis of the framework quantifies the closeness of the corrected numerical model to the true system as a function of response estimation error. This design optimization framework, along with the convergence result, is validated through an airborne wind energy (AWE) application using a lab-scale water channel setup. The quality of flight is greatly improved by optimizing the center of mass location, pitch angle set point, horizontal and vertical stabilizer areas using an effective experimental infusion as compared to a pure numerically optimized design.

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References

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Deodhar, N. , Vermillion, C. , and Tkacik, P. , 2015, “ A Case Study in Experimentally-infused Plant and Controller Optimization for Airborne Wind Energy Systems,” American Control Conference, Chicago, IL, July 1–3, pp. 2371–2376.
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Deodhar, N. , Deese, J. , and Vermillion, C. , 2018, “ Experimentally Infused Plant and Controller Optimization Using Iterative Design of Experiments—Theoretical Framework and Airborne Wind Energy Case Study,” ASME J. Dyn. Syst. Meas. Control, 140(1), p. 011004. [CrossRef]
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Figures

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Fig. 1

Flowchart detailing the steps involved in the iterative framework. An iteration comprises the optimal design of experiments, execution of the simulations/experiments, estimation of a response surface, improvement of the numerical model, and shrinking of the feasible design space.

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Fig. 2

Full-scale prototype of an Altaeros BAT used during 2013 flight testing [19]

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Fig. 3

Ground-frame and body-frame coordinates, along with key variables used in deriving equations of motion for the BAT

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Fig. 4

Block diagram of the flight controller used to track altitude and attitude set points [18]

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Fig. 6

Side and bottom views of the 1/100-scale BAT model used for testing. The ballast holes provide the ability to modify the center of mass location between iterations.

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Fig. 5

Water channel-based test platform at UNC-Charlotte

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Fig. 10

The top row shows a comparison between heading angle for the numerically optimal configuration and experimentally infused optimum. The bottom row shows a similar comparison between the squared heading angle (the quantity that is directly penalized in the cost function).

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Fig. 11

This figure shows a comparison between roll and zenith angle responses for the numerically optimized design (left) versus the design resulting from the experimentally infused optimization approach (right)

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Fig. 7

The top row shows design points and combined numerical/experimental response for the first iteration. The middle row shows the same plots within the reduced design space at an intermediate iteration. The bottom row shows the significant reduction in design space at the last iteration.

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Fig. 8

Evolution of ||Ĵnum,n−Jtrue|| for two-parameter (top left) and four-parameter (bottom left) optimization. The plots on right show the evolution of the design space as a fraction of the original design space for two- and four-parameter optimizations.

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Fig. 9

Heading angle comparison between the optimum design at the first iteration (top left) and last iteration (bottom left), which shows a significant improvement. Zenith angle shows a slight improvement as well.

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