A comparison of statistical learning approaches for engine torque estimation

Abstract Engine torque estimation has important applications in the automotive industry: for example, automatically setting gears, optimizing engine performance, reducing emissions and designing drivelines. A methodology is described for the on line calculation of torque values from the gear, the accelerator pedal position and the engine rotational speed. It is based on the availability of input-torque experimental signals that are pre-processed (resampled, filtered and segmented) and then learned by a statistical machine learning method. Four methods, spanning the main learning principles, are reviewed in a unified framework and compared using the torque estimation problem: linear least squares, linear and non-linear neural networks and support vector machines. It is found that a non-linear model structure is necessary for accurate torque estimation. The most efficient torque model built is a non-linear neural network that achieves about 2% test normalized mean square error in nominal conditions.

[1]  Jonas Fredriksson,et al.  Cylinder-by-Cylinder Engine Models Vs Mean Value Engine Models for use in Powertrain Control Applications , 1999 .

[2]  David K. Smith,et al.  Mathematical Programming: Theory and Algorithms , 1986 .

[3]  Tomaso A. Poggio,et al.  Regularization Networks and Support Vector Machines , 2000, Adv. Comput. Math..

[4]  R. Babu,et al.  Engine load prediction in off-road vehicles using multi-objective nonlinear identification , 2004 .

[5]  Giorgio Rizzoni,et al.  Event-Based Estimation of Indicated Torque for IC Engines Using Sliding Mode Observers , 1996 .

[6]  Geoffrey E. Hinton,et al.  Learning internal representations by error propagation , 1986 .

[7]  D. Wolpert,et al.  No Free Lunch Theorems for Search , 1995 .

[8]  Tomaso A. Poggio,et al.  Regularization Theory and Neural Networks Architectures , 1995, Neural Computation.

[9]  Samy Bengio,et al.  SVMTorch: Support Vector Machines for Large-Scale Regression Problems , 2001, J. Mach. Learn. Res..

[10]  Taketoshi Sano,et al.  A substitution method for measuring engine output torque — calculation from the combustion pressure wave , 1995 .

[11]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[12]  Larry L. Schumaker,et al.  Topics in Multivariate Approximation , 1987 .

[13]  Tor Arne Johansen,et al.  Engine load prediction in off-road vehicles using multi-objective nonlinear identification , 2004 .

[14]  Kenneth Levenberg.  A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES , 1944 .

[15]  John B. Heywood,et al.  Internal combustion engine fundamentals , 1988 .

[16]  Bernhard Schölkopf,et al.  A tutorial on support vector regression , 2004, Stat. Comput..

[17]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[18]  Nabil G. Chalhoub,et al.  Effects of structural deformations of the crank-slider mechanism on the estimation of the instantaneous engine friction torque , 1999 .

[19]  Volker Krebs,et al.  Nonlinear Torque Control of a Spark Ignition Engine , 2000 .

[20]  Yann Chamaillard,et al.  A simple method for robust control design, application on a non-linear and delayed system: engine torque control , 2004 .

[21]  B. Efron.  Estimating the Error Rate of a Prediction Rule: Improvement on Cross-Validation , 1983 .

[22]  Nira Dyn,et al.  Interpolation of scattered Data by radial Functions , 1987, Topics in Multivariate Approximation.

[23]  Brian D. Ripley,et al.  Pattern Recognition and Neural Networks , 1996 .

[24]  Rolf Isermann,et al.  Model-based control design for IC-engines on dynamometers: The toolbox "Optimot" , 2002 .

[25]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[26]  James L. McClelland,et al.  Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations , 1986 .

[27]  Heekuck Oh,et al.  Neural Networks for Pattern Recognition , 1993, Adv. Comput..