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This paper presents three recurrent neural networks to estimate the spectral content of (noisy) periodic waveforms that are common in many engineering processes. The presented (structured) networks, which are based on the recursive discrete Fourier transform, are especially useful in computing high-order derivaties of such waveforms. Unlike conventional differentiating techniques, the proposed networks perform differentiation in the frequency domain and thus are immune to uncorrelated measurement noise. Furthermore, due to moving-average based correlation scheme, which is inherent to the recursive transform, the presented networks can handle composite waveforms without a detailed signal model in the frequency domain. The performance of the proposed network architectures in a number of simulation and experimental cases has also been evaluated in this paper.

This paper presents a general methodology for designing neural networks by using a priori information on the process under study. The approach is especially useful in developing efficient neural networks for the applications where full-scale models are available but too complicated to implement on conventional computer systems. Traditional neural network development techniques are known to have considerable disadvantages, including a tedious (trial-and-error-based) design process and a long training phase for most real world problems. The presented network design paradigm overcomes these well-known shortcomings. The paper also illustrates the method's application to a real-world problem on the estimation of milling forces in an ideal machining process.