Modern internal combustion engines utilize sophisticated control units to precisely time the ignition of fuel during each engine cycle. Ignition timing has a major influence on critical engine performance characteristics such as efficiency and emissions. Researchers aiming to improve engine performance are able to collect detailed data on hundreds of engine cycles using instruments that capture multiple parameters at high temporal resolution. Working with researchers from the University of Michigan Department of Mechanical Engineering, CSCAR Director Kerby Shedden used functional regression techniques to quantify the uncertainty in the relationship between crank angle and the oxygen concentration in the combustion chamber. Modern functional data analysis techniques have been developed by statisticians over the past twenty years to improve the analysis of data whose conditional means or quantiles follow continuous functional relationships. Techniques involving penalized regression in function spaces have largely supplanted unwieldy classical methods for analyzing functional data such as parametric nonlinear regression.
