Future Trend Forecast by Empirical Wavelet Transform and Autoregressive Moving Average

Abstract

In engineering and technical fields, a large number of sensors are applied to monitor a complex system. A special class of signals are often captured by those sensors. Although they often have indirect or indistinct relationships among them, they simultaneously reflect the operating states of the whole system. Using these signals, the field engineers can evaluate the operational states, even predict future behaviors of the monitored system. A novel method of future operational trend forecast of a complex system is proposed in this paper. It is based on empirical wavelet transform (EWT) and autoregressive moving average (ARMA) techniques. Firstly, empirical wavelet transform is used to extract the significant mode from each recorded signal, which reflects one aspect of the operating system. Secondly, the system states are represented by the indicator function which are obtained from those normalized and weighted significant modes. Finally, the future trend is forecast by the parametric model of ARMA. The effectiveness and practicality of the proposed method are verified by a set of numerical experiments.

Correlation Coefficient‐Based Information Criterion for Quantification of Dependence Characteristics in Hydrological Time Series

“…When 𝐴𝐴 𝐴𝐴→ ∞ , the model order determined by AIC cannot converge to the true value according to the probability theory (Fishler et al, 2002). In order to obtain consistent estimation, Akaike (Wang et al, 2018) and Schwarz (Yang et al, 2021) proposed BIC according to the Bayesian principle:…”

Entropy algorithms for detecting incipient damage in high-rise buildings subjected to dynamic vibrations

“…Entropy is known as a nonlinear measurement capable of describing the randomness encountered in a time signal (Shannon, 1948). For this reason, it has been applied in different fields for detecting and quantifying the changes in the waveforms of signals such as vibrations, electroencephalograms, and electrocardiograms, among other signals (Acharya et al, 2018;Figlus, 2019;Wang et al, 2018aWang et al, , 2018bWu et al, 2018). Hence, if these changes are related to the structural dynamic of a civil structure, then the entropy value can be a suitable indicator for determining the condition of a civil structure.…”

“…The continuous advances in the field of SHM have allowed the use of diverse vibration-based signal processing methods for evaluating the health condition of civil structures, with the Fourier transform and its variation called the frequency response function (Demetgul et al, 2015;Rafiei and Adeli, 2018), multiple signal classification (Amezquita-Sanchez et al, 2017;Zhong et al, 2014), and time-series models (Rezaiee-Pajand et al, 2018;Wang et al, 2018aWang et al, , 2018b the most commonly used. In general, these techniques have presented some advances for monitoring the current state of a structure; however, they present diverse drawbacks for extracting patterns or features capable of evaluating the health condition of a civil structure correctly.…”

“…In the last few years, entropy, a powerful nonlinear measurement, has been introduced in different fields such as neuroscience (Li et al, 2018a(Li et al, , 2018bWang et al, 2018aWang et al, , 2018b, monitoring of electrical machines (Wu et al, 2018), monitoring of gearboxes (Figlus, 2019), cardiac diseases (Acharya et al, 2018;Kumar et al, 2016), and the health monitoring of simple beams of few structural elements (Diao et al, 2018;Moreno-Gomez et al, 2018), among other fields. Entropy provides a measure of data randomness encountered in a nonlinear and nonstationary time signal (Shannon, 1948), making it an appropriate tool for detecting damage in civil structures because the measured signals can vary according to damage and its severity encountered in the civil structure, thus producing a change in the entropy value.…”

Mono-Component Feature Extraction for Condition Assessment in Civil Structures Using Empirical Wavelet Transform

“…It is highly favorable for the processing and interpretation of non-stationary and complex signals. This method has been applied to process signals in various areas like biomedical, wind, earthquake, and mechanical engineering [18,19,20,21,22,23,24,25,26,27]. Kedadouche et al [28] conducted a comparative study between EMD and EWT, showing that EWT outperforms EMD on mode estimation and computation time.…”