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MIMO over-the-air computation (MIMO-AirComp) is a recently proposed technique that leverages the superposition property of the multiple access channel to compute the target multifunction of various applications. This article presents how the MIMO-AirComp principle can be applied to the state estimation problem using distributed sensing data. The representative target function is explicitly formulated as a nomographic function matched to the structure of the multiple access channel with the proper processing function. The proposed framework efficiently computes the target multifunction by coordinating local preprocessing at each node, aggregation through the wireless channel, and postprocessing at the fusion center. We analyze and demonstrate that the proposed approach significantly improves the computation throughput for the distributed estimation application. Specifically, the proposed MIMO-AirComp framework outperforms the conventional separated communication and computation approach when the network system relies on noisy measurements obtained by the densely deployed sensors.

Although various deep learning techniques have been proposed to diagnose industrial faults, it is still challenging to obtain sufficient training samples to build the fault diagnosis model in practice. This paper presents a framework that combines wavelet transformation and transfer learning (TL) for fault diagnosis with limited target samples. The wavelet transform converts a time-series sample to a time-frequency representative image based on the extracted hidden time and frequency features of various faults. On the other hand, the TL technique leverages the existing neural networks, called GoogLeNet, which were trained using a sufficient source data set for different target tasks. Since the data distributions between the source and the target domains are considerably different in industrial practice, we partially retrain the pre-trained model of the source domain using intermediate samples that are conceptually related to the target domain. We use a reciprocating pump model to generate various combinations of faults with different severity levels and evaluate the effectiveness of the proposed method. The results show that the proposed method provides higher diagnostic accuracy than the support vector machine and the convolutional neural network under wide variations in the training data size and the fault severity. In particular, we show that the severity level of the fault condition heavily affects the diagnostic performance.

Fault detection and diagnosis is one of the most critical components of preventing accidents and ensuring the system safety of industrial processes. In this paper, we propose an integrated learning approach for jointly achieving fault detection and fault diagnosis of rare events in multivariate time series data. The proposed approach combines an autoencoder to detect a rare fault event and a long short-term memory (LSTM) network to classify different types of faults. The autoencoder is trained with offline normal data, which is then used as the anomaly detection. The predicted faulty data, captured by autoencoder, are put into the LSTM network to identify the types of faults. It basically combines the strong low-dimensional nonlinear representations of the autoencoder for the rare event detection and the strong time series learning ability of LSTM for the fault diagnosis. The proposed approach is compared with a deep convolutional neural network approach for fault detection and identification on the Tennessee Eastman process. Experimental results show that the combined approach accurately detects deviations from normal behaviour and identifies the types of faults within the useful time.