Descriptions of Entropy with Fractal Dynamics and Their Applications to the Flow Pressure of Centrifugal Compressor

Scale-Fractal Detrended Fluctuation Analysis for Fault Diagnosis of a Centrifugal Pump and a Reciprocating Compressor

Reciprocating compressors and centrifugal pumps are rotating machines used in industry, where fault detection is crucial for avoiding unnecessary and costly downtime. A novel method for fault classification in reciprocating compressors and multi-stage centrifugal pumps is proposed. In the feature extraction stage, raw vibration signals are processed using multi-fractal detrended fluctuation analysis (MFDFA) to extract features indicative of different types of faults. Such MFDFA features enable the training of machine learning models for classifying faults. Several classical machine learning models and a deep learning model corresponding to the convolutional neural network (CNN) are compared with respect to their classification accuracy. The cross-validation results show that all models are highly accurate for classifying the 13 types of faults in the centrifugal pump, the 17 valve faults, and the 13 multi-faults in the reciprocating compressor. The random forest subspace discriminant (RFSD) and the CNN model achieved the best results using MFDFA features calculated with quadratic approximations. The proposed method is a promising approach for fault classification in reciprocating compressors and multi-stage centrifugal pumps.

Coupled Criticality Analysis of Inflation and Unemployment

In this paper, we focus on the critical periods in the economy that are characterized by unusual and large fluctuations in macroeconomic indicators, like those measuring inflation and unemployment. We analyze U.S. data for 70 years from 1948 until 2018. To capture their fluctuation essence, we concentrate on the non-Gaussianity of their distributions. We investigate how the non-Gaussianity of these variables affects the coupling structure of them. We distinguish "regular" from "rare" events, in calculating the correlation coefficient, emphasizing that both cases might lead to a different response of the economy. Through the "multifractal random wall" model, one can see that the non-Gaussianity depends on time scales. The non-Gaussianity of unemployment is noticeable only for periods shorter than one year; for longer periods, the fluctuation distribution tends to a Gaussian behavior. In contrast, the non-Gaussianities of inflation fluctuations persist for all time scales. We observe through the "bivariate multifractal random walk" that despite the inflation features, the non-Gaussianity of the coupled structure is finite for scales less than one year, drops for periods larger than one year, and becomes small for scales greater than two years. This means that the footprint of the monetary policies intentionally influencing the inflation and unemployment couple is observed only for time horizons smaller than two years. Finally, to improve some understanding of the effect of rare events, we calculate high moments of the variables' increments for various q orders and various time scales. The results show that coupling with high moments sharply increases during crises.

Obtaining Information about Operation of Centrifugal Compressor from Pressure by Combining EEMD and IMFE

Based on entropy characteristics, some complex nonlinear dynamics of the dynamic pressure at the outlet of a centrifugal compressor are analyzed, as the centrifugal compressor operates in a stable and unstable state. First, the 800-kW centrifugal compressor is tested to gather the time sequence of dynamic pressure at the outlet by controlling the opening of the anti-surge valve at the outlet, and both the stable and unstable states are tested. Then, multi-scale fuzzy entropy and an improved method are introduced to analyze the gathered time sequence of dynamic pressure. Furthermore, the decomposed signals of dynamic pressure are obtained using ensemble empirical mode decomposition (EEMD), and are decomposed into six intrinsic mode functions and one residual signal, and the intrinsic mode functions with large correlation coefficients in the frequency domain are used to calculate the improved multi-scale fuzzy entropy (IMFE). Finally, the statistical reliability of the method is studied by modifying the original data. After analysis of the relationships between the dynamic pressure and entropy characteristics, some important intrinsic dynamics are captured. The entropy becomes the largest in the stable state, but decreases rapidly with the deepening of the unstable state, and it becomes the smallest in the surge. Compared with multi-scale fuzzy entropy, the curve of the improved method is smoother and could show the change of entropy exactly under different scale factors. For the decomposed signals, the unstable state is captured clearly for higher order intrinsic mode functions and residual signals, while the unstable state is not apparent for lower order intrinsic mode functions. In conclusion, it can be observed that the proposed method can be used to accurately identify the unstable states of a centrifugal compressor in real-time fault diagnosis.

The Fractional View of Complexity

Fractal analysis and fractional differential equations have been proven as useful tools for describing the dynamics of complex phenomena characterized by long memory and spatial heterogeneity [...]

Anomaly Detection in IoT Communication Network Based on Spectral Analysis and Hurst Exponent

Internet traffic monitoring is a crucial task for the security and reliability of communication networks and Internet of Things (IoT) infrastructure. This description of the traffic statistics is used to detect traffic anomalies. Nowadays, intruders and cybercriminals use different techniques to bypass existing intrusion detection systems based on signature detection and anomalies. In order to more effectively detect new attacks, a model of anomaly detection using the Hurst exponent vector and the multifractal spectrum is proposed. It is shown that a multifractal analysis shows a sensitivity to any deviation of network traffic properties resulting from anomalies. Proposed traffic analysis methods can be ideal for protecting critical data and maintaining the continuity of internet services, including the IoT.