Machine learning with finite impulse response models

An accurate and reliable model is the foundation for analysis, design, and control of a modern automation system. It is often too complicated, too expensive, or too inaccurate to develop these models based on first principles. In recent years, machine learning has made tremendous progress through the usage of data to generate models. Nevertheless, a key drawback is that for the identified models there is no stability guarantee. Thus, within this thesis, methods for identifying both linear and nonlinear systems based on finite impulse response (FIR) models are investigated. These avoid feedback and thus ensure stability.
Linear FIR models offer a compelling advantage due to the interpretability of the impulse response and inherent stability. Recently, novel methods for regularization based on a specifically designed Tikhonov regularization have been proposed. In this contribution these approaches are extended to allow for a better incorporation of existing prior knowledge. The developed method can be employed for order selection and gray-box identification. Its feasibility is demonstrated on numerical benchmarks and on a laboratory example.
Local model networks allow for the extension of linear identification methods to nonlinear systems. Here, the regularization mechanism applied to linear systems is employed to identify local FIR models. Especially for identification problems with a low signal to noise ratio, the method performs significantly better than local model networks with feedback of the output.
Finally, machine learning with convolutional neural networks is investigated. The relation between these and block-oriented nonlinear systems is analyzed. Then, a specific structure of a deep neural network containing FIR models as building blocks is proposed. This structure is equipped with a regularization scheme adopted from linear FIR models for the impulse responses comprised in the neural network. It is shown that the bias-variance trade-off is influenced positively on a benchmark example and achieves state-of-the-art results while additionally the internal impulse responses are smoothed and the stability of the system is guaranteed.