A Method for Handling Uncertainty in Evolutionary Optimization With an Application to Feedback Control of Combustion

• Published in: IEEE transactions on evolutionary computation Vol. 13; no. 1; pp. 180 - 197
• Main Authors: Hansen, N., Niederberger, A.S.P., Guzzella, L., Koumoutsakos, P.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-02-2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive control; Algorithms; Applied sciences; Automatic control; Combustion; Computer Science; Continuous cycle engines: steam and gas turbines, jet engines; Controllers; Convergence; Covariance matrix; Covariance matrix adaptation; Engines and turbines; evolutionary algorithms (EAs); Evolutionary computation; Exact sciences and technology; Feedback control; gain-delay control; gas turbines; Handling; Internal combustion engines: gazoline engine, diesel engines, etc; Machine Learning; Materials handling; Mathematical models; Mechanical engineering. Machine design; On-line systems; Online; Optimization; Optimization methods; Studies; Testing; thermo acoustic instabilities; Uncertainty; gain-delay control; Motor fuel injection; Evolutionary algorithm; Delay control; Quantization; Feedback regulation; Combustion; Modeling; Optimization; Fuel injector; Uncertain system; evolutionary algorithms (EAs); Covariance matrix adaptation; gas turbines; H infinite control; Non stationary condition; Covariance matrix; Experimental study; thermoacoustic instabilities; Operating conditions; Closed feedback; Engineering design; Design process; Combustion chamber; Genetic algorithm; Instability; Thermoacoustic effect; Internal combustion engine; Gas turbine; Building process
• ISSN: 1089-778X; 1941-0026
• DOI: 10.1109/TEVC.2008.924423

We present a novel method for handling uncertainty in evolutionary optimization. The method entails quantification and treatment of uncertainty and relies on the rank based selection operator of evolutionary algorithms. The proposed uncertainty handling is implemented in the context of the covariance matrix adaptation evolution strategy (CMA-ES) and verified on test functions. The present method is independent of the uncertainty distribution, prevents premature convergence of the evolution strategy and is well suited for online optimization as it requires only a small number of additional function evaluations. The algorithm is applied in an experimental setup to the online optimization of feedback controllers of thermoacoustic instabilities of gas turbine combustors. In order to mitigate these instabilities, gain-delay or model-based H infin controllers sense the pressure and command secondary fuel injectors. The parameters of these controllers are usually specified via a trial and error procedure. We demonstrate that their online optimization with the proposed methodology enhances, in an automated fashion, the online performance of the controllers, even under highly unsteady operating conditions, and it also compensates for uncertainties in the model-building and design process.