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Fuzzy neural network (FNN) is regarded as a prominent approach in application of time-series modeling. With the capability of fuzzy reasoning, FNN can capture temporal patterns from the time-series samples. However, the existing FNNs may suffer from the temporal pattern distortion because possibly multiscale features cannot be explored sufficiently. To address this problem, a time-aware fuzzy neural network, based on the frequency-enhanced modulation mechanism (FEM-TAFNN), is developed for time-series prediction in this article. First, a Fourier-based decoder is established to extract the multiscale features. This decoder employs the frequency-domain model to orthogonally separate the time-scale features with different frequencies into independent temporal patterns based on the Fourier basis, which prevents the overlap of temporal patterns using time-domain analysis. Second, a frequency-enhanced modulation mechanism is designed to shape fuzzy rules of FNN based on the contribution of different temporal patterns in the frequency spectrum. It enables FEM-TAFNN to modulate out the realistic multiscale temporal patterns. Finally, the proposed FEM-TAFNN is tested on four multiscale time-series datasets. The empirical results confirm its superior prediction performance than other methods.

The model bias caused by input outliers is a dramatic obstacle to the application of models in industrial processes. To cope with this problem, this article proposes a robust modeling method based on frequency reconstructed fuzzy neural network (FRFNN) for industrial process. The robust modeling consists of two parts: One is feature extraction, where a Fourier-based filter is developed with input data denoising. It enables the model to suppress high-frequency input noises and burst outliers. The other one is feature representation that is realized with a FRFNN. The soft margins of membership functions of FRFNN are designed with Fourier estimation of outliers, which have the capability of outlier-tolerant for filtered-residual outliers. Moreover, an adaptive gradient descent algorithm is introduced to update the model parameters. Based on the adaptive learning rate decaying with outliers, this algorithm is insensitive to the bias effect of outliers and also maintains convergence. Finally, the proposed robust modeling method is tested on two real-world industrial datasets with input outliers. The experimental results demonstrate that the proposed robust modeling method can strengthen robustness and achieve superior performance over other previous methods.