Indicated Mean Effective Pressure Estimator Order Determination and Reduction When Using Estimated Engine Statistics

The indicated mean effective pressure (IMEP) is typically used as an engine running quality metric. IMEP depends on cylinder pressure, which is costly to measure, therefore it is useful to estimate IMEP from currently measured crankshaft encoder data. In this paper, the difficulties in developing an optimal linear estimator from acceleration computed from crankshaft rotational speed and cylinder pressure data are discussed, and strategies are presented to reduce these difficulties. Estimating IMEP from crankshaft data requires the determination of which data to use in the estimator. Without this step, the estimator can become unnecessarily complex due the inclusion of strongly correlated data points in the estimator. A strategy to determine the angular location of the acceleration points to use is presented and is shown to greatly reduce the estimator complexity without significantly affecting estimation error. Additionally, while increasing the estimator order usually decreases the estimation error, it will be shown that increasing the estimator order can actually increase the estimation error. This effect is due to uncertainties in the gains of the estimator. These uncertainties in the gains can result from using limited training data to estimate the statistics necessary to compute the gains or when dealing with a nonstationary system. A method of reducing the effect of these uncertainties by optimizing the estimator order based on the number of available training data cycles is developed and demonstrated.