Activation Function Dynamic Averaging as a Technique for Nonlinear 2D Data Denoising in Distributed Acoustic Sensors  
[PERSON]  
1 General Physics Department, Applied Mathematics and Mechanics Faculty, Perm National Research Polytechnic University, Prospekt Komsomsomsdsky 29, 614990 Perm, Russia 12 Perm Federal Research Center of the Ural Branch of the Russian Academy of Sciences (PFRC UB RAS), 13a Lenin St., 614000 Perm, Russia; [EMAIL_ADDRESS]  
[PERSON]  
22 Department of Electrical Engineering, University of O  
frequency and spatial coordinate. Together with other reflectometric methods that study slowly changing physical quantities in new materials and structures [17; 18; 19; 20], distributed acoustic sensors for flaw detection problems form a complete understanding of the object's behavior in a wide range of external conditions [21; 22]. Thus, in [21], distributed acoustic monitoring was used to study the operating regimes of a gas turbine. The nature of useful data and noise visually largely coincides with the images obtained in [13; 14]. The authors of [22] used DAS to study the spectral composition of self-oscillations of aircraft structures. Similar problems frequently arise in various fields of science and technology and are often solved by acoustic emission sensors [23; 24; 25]. However, this type of sensor has its own limitations. One of them is the inability to monitor the entire object, since in most of their technical implementations, these sensors are pointwise. As stated in [26], the detection of small details and flaws can be quite easily carried out with pointwise sensors, whereas it is not suitable for studying the whole mechanism assembled from such elements. Tested objects constructed from individual simple elements have a much higher probability of failure than these individual elements. To study such breakdowns, pointwise sensors are not applicable. Thus, some of distributed sensors were purpose-built to study the acoustic emissions of whole machines and assemblies [26; 27; 28]. Since the characteristic frequencies of acoustic emissions are much higher than those used by typical DAS, it was necessary to extend the frequency response of optoelectronic systems. Various effective approaches have been used for this: studied area frequency domain transition (since a continuous signal is used, the time between the pulses no longer limits the upper acoustic frequency) [29]; the use of fiber Bragg gratings (each grating in the fiber can be interrogated as a separate sensor) [30; 31]; the use of pulses with different laser frequencies (allows one not to wait for the previous pulse comeback to send a new one--the maximum recording frequency of 80 kHz was reached for a fiber length of 5 km) [32]. These and other hardware approaches have efficiently extended the DAS frequency response range. However, the pervasion of the technology in new industries has put forward a new requirement--commercial availability. The reduction in system component requirements has helped to decrease their cost, but it has revealed a number of other problems. One of them is signal-to-noise ratio (SNR) degradation when using simpler and more affordable narrow-band laser setups [33; 34]. This problem seems to be serious for the applications posed above, since one or another frequency component may have insufficient amplitude and will be identified as noise. The solution proposed in the same paper utilizes digital signal processing methods. In most state-of-the-art commercial DAS systems, the obtained data are interpreted by means of artificial intelligence [35; 36; 37]. This is explained by the fact that the nature of the recorded signal is characterized by multifrequency, and its shape and spectral composition do not have clear identification criteria. Most neural network methods are based on the principle of a \"black box\", inside of which neural connections are formed. But it is highly desirable to use a well-formalizable and understandable methodological apparatus to solve the problems of flaw detection.