Robust identification of nonlinear dynamic systems using Design of Experiment

Abstract

Modern combustion engines are becoming increasingly complex, with more control variables, to meet the newest emissions regulations and improve the dynamic torque characteristics. However, the large number of control variables presents a challenge for the calibration process. The effects of all control variables and their interactions on the engine characteristics should be quantified in an accurate way to be able to derive the best control strategies aiming to minimise fuel consumption and emissions while generating the desired torque within acceptable time delays. Design of Experiment DoE methods have been used successfully to cope with the difficulties related to the characterisation of the underlying process in the presence of a large number of control variables. DoE provides experiment design methods aiming to reduce the number of measurements needed while ensuring the best quality of information related to a given optimisation criterion.In this paper a procedure is proposed to derive global dynamic models based on dynamic neural networks. The selection of the training data is derived by a D-optimality criterion to enhance the model quality. This ensures a reduction of the amount of measurement data needed for the training and hence an acceleration of the training process. It also improves the model quality by reducing the uncertainty on the model parameters. 1 1 (6) The matrix J J T is usually bad conditioned and its inversion can lead to numeric problems. The iteration is then improved leading finally to the Levenberg-Marquardtiteration [7], [8]:

Simulation-based sensitivity and worst-case analyses of automotive electronics

“…It has strong statistical background. It can control simulations of parameterized systems, for various verification purposes: screening [14], sensitivity analysis [7], for robust design [1], for multi-objective optimization [13].…”