Research Papers

Evaluating Optimization Strategies for Engine Simulations Using Machine Learning Emulators

[+] Author and Article Information
Daniel M. Probst, Peter K. Senecal

Convergence Science, Inc.,
Madison, WI 53719

Mandhapati Raju

Convergent Science, Inc.,
Madison, WI 53719

Janardhan Kodavasal, Pinaki Pal, Sibendu Som, Ahmed A. Moiz

Argonne National Laboratory,
Argonne, IL 60439

Yuanjiang Pei

Aramco Research Center,
Detroit, MI 48377

Manuscript received April 25, 2019; final manuscript received May 30, 2019; published online June 20, 2019. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(9), 091011 (Jun 20, 2019) (9 pages) Paper No: GTP-19-1208; doi: 10.1115/1.4043964 History: Received April 25, 2019; Revised May 30, 2019

This work evaluates different optimization algorithms for computational fluid dynamics (CFD) simulations of engine combustion. Due to the computational expense of CFD simulations, emulators built with machine learning algorithms were used as surrogates for the optimizers. Two types of emulators were used: a Gaussian process (GP) and a weighted variety of machine learning methods called SuperLearner (SL). The emulators were trained using a dataset of 2048 CFD simulations that were run concurrently on a supercomputer. The design of experiments (DOE) for the CFD runs was obtained by perturbing nine input parameters using a Monte-Carlo method. The CFD simulations were of a heavy duty engine running with a low octane gasoline-like fuel at a partially premixed compression ignition mode. Ten optimization algorithms were tested, including types typically used in research applications. Each optimizer was allowed 800 function evaluations and was randomly tested 100 times. The optimizers were evaluated for the median, minimum, and maximum merits obtained in the 100 attempts. Some optimizers required more sequential evaluations, thereby resulting in longer wall clock times to reach an optimum. The best performing optimization methods were particle swarm optimization (PSO), differential evolution (DE), GENOUD (an evolutionary algorithm), and micro-genetic algorithm (GA). These methods found a high median optimum as well as a reasonable minimum optimum of the 100 trials. Moreover, all of these methods were able to operate with less than 100 successive iterations, which reduced the wall clock time required in practice. Two methods were found to be effective but required a much larger number of successive iterations: the DIRECT and MALSCHAINS algorithms. A random search method that completed in a single iteration performed poorly in finding optimum designs but was included to illustrate the limitation of highly concurrent search methods. The last three methods, Nelder–Mead, bound optimization by quadratic approximation (BOBYQA), and constrained optimization by linear approximation (COBYLA), did not perform as well.

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Fig. 1

Training results for the SuperLearner emulator showing the model coefficients

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Fig. 2

Training results for the SuperLearner emulator showing risk

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Fig. 3

Training results for the SuperLearner emulator showing the predicted versus training merit

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Fig. 4

Training results for the Gaussian process emulator showing the predicted versus training merit

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Fig. 5

Optimization results for the SuperLearner emulator for 100 trials of each optimization method. The median is shown for each method, with the minimum and maximum shown with error bars.

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Fig. 6

Optimization results plotted against the successive evaluations used by each method. The minimum, median, and maximum are shown for each optimization method.

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Fig. 7

PDF calculated for each of the four best performing optimizers (SuperLearner)

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Fig. 8

Optimization results for the Gaussian process emulator for 100 trials of each optimization method. The median is shown for each method, with the minimum and maximum shown with error bars.

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Fig. 9

Optimization results for the Gaussian process emulator. The minimum, median, and maximum are shown for each optimization method.

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Fig. 10

PDF calculated for each of the four best performing optimizers (Gaussian process)



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