Nonlinear forecasting with wavelet neural networks

When the time delay embedding technique (TDET) is employed to predict transient, nonlinear automotive emissions many seconds into the future, it captures general magnitude and timing for conditions it hasn't experienced before, but some details are lost. If the driving inputs to the system are known, and certain characteristic shapes are expected for the response, then those features can be reconstructed. In order to capture the localized frequency details, wavelet coefficients are added to the first layer of a multilayer feedforward neural network. TDET predictions and real emissions are used to train this hybrid network, and then it is asked to reconstruct the details of future emissions when the engine calibration and environment are changed. The method is expected to be implementable online and in plenty of time for anticipatory control efforts.