Hybrid Model of Natural Time Series with Neural Network Component and Adaptive Nonlinear Scheme: Application for Anomaly Detection

It is often difficult to describe natural time series due to implicit dependences and correlated noise. During anomalous natural processes, anomalous features appear in data. They have a nonstationary structure and do not allow us to apply traditional methods for time series modeling. In order to solve these problems, new models, adequately describing natural data, are required.

A new hybrid model of a time series (HMTS) with a nonstationary structure is proposed in this paper. The HMTS has regular and anomalous components. The HMTS regular component is determined on the basis of an autoencoder neural network. To describe the HMTS anomalous component, an adaptive nonlinear approximating scheme (ANAS) is used on a wavelet basis. HMTS is considered in this investigation for the problem of neutron monitor data modeling and anomaly detection. Anomalies in neutron monitor data indicate negative factors in space weather. The timely detection of these factors is critically important.

This investigation showed that the developed HMTS adequately describes neutron monitor data and has satisfactory results from the point of view of numeric performance. The MSE model values are close to 0 and errors are white Gaussian noise. In order to optimize the estimate of the HMTS anomalous component, the likelihood ratio test was applied. Moreover, the wavelet basis, giving the least losses during ANAS construction, was determined. Statistical modeling results showed that HMTS provides a high accuracy of anomaly detection. When the signal/noise ratio is 1.3 and anomaly durations are more than 60 counts, the probability of their detection is close to 90%. This is a high rate in the problem domain under consideration and provides solution reliability of the problem of anomaly detection in neutron monitor data. Moreover, the processing of data from several neutron monitor stations showed the high sensitivity of the HMTS. This shows the possibility to minimize the number of engaged stations, maintaining anomaly detection accuracy compared to the global survey method widely used in this field.

This result is important as the continuous operation of neutron monitor stations is not always provided. Thus, the results show that the developed HMTS has the potential to address the problem of anomaly detection in neutron monitor data even when the number of operating stations is small. The proposed HMTS can help us to decrease the risks of the negative impact of space weather anomalies on human health and modern infrastructure.

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Citation: Mandrikova, O.; Mandrikova, B. Hybrid Model of Natural Time Series with Neural Network Component and Adaptive Nonlinear Scheme: Application for Anomaly Detection. Mathematics 2024, 12, 1079. https://doi.org/10.3390/math12071079