Fractional Dynamics Identification via Intelligent Unpacking of the Sample Autocovariance Function by Neural Networks

Many single-particle tracking data related to the motion in crowded environments exhibit anomalous diffusion behavior. This phenomenon can be described by different theoretical models. In this paper, fractional Brownian motion (FBM) was examined as the exemplary Gaussian process with fractional dynamics. The autocovariance function (ACVF) is a function that determines completely the Gaussian process. In the case of experimental data with anomalous dynamics, the main problem is first to recognize the type of anomaly and then to reconstruct properly the physical rules governing such a phenomenon. The challenge is to identify the process from short trajectory inputs. Various approaches to address this problem can be found in the literature, e.g., theoretical properties of the sample ACVF for a given process. This method is effective; however, it does not utilize all of the information contained in the sample ACVF for a given trajectory, i.e., only values of statistics for selected lags are used for identification. An evolution of this approach is proposed in this paper, where the process is determined based on the knowledge extracted from the ACVF. The designed method is intuitive and it uses information directly available in a new fashion. Moreover, the knowledge retrieval from the sample ACVF vector is enhanced with a learning-based scheme operating on the most informative subset of available lags, which is proven to be an effective encoder of the properties inherited in complex data. Finally, the robustness of the proposed algorithm for FBM is demonstrated with the use of Monte Carlo simulations.

Anomalous Dynamics of QBO Disruptions Explained by 1D Theory With External Triggering

The Quasi-Biennial Oscillation (QBO) is an alternating, descending pattern of zonal winds in the tropical stratosphere with a period averaging 28 months. The QBO was disrupted in 2016, and arguably again in 2020, by the formation of an anomalous easterly shear zone, and unprecedented stagnation and ascent of shear zones aloft. Several mechanisms have been implicated in causing the 2016 disruption, most notably triggering by horizontal eddy momentum flux divergence, but also anomalous upwelling and wave stress. In this paper, the 1D theory of the QBO is used to show how seemingly disparate features of disruptions follow directly from the dynamics of the QBO response to triggering. The perturbed QBO is interpreted using a heuristic version of the 1D model, which establishes that: (1) stagnation of shear zones aloft resulted from wave dissipation in the shear zone formed by the triggering, and (2) ascent of shear zones aloft resulted from climatological upwelling advecting the stagnant shear zones. Obstacles remain in the theory of triggering. In the 1D theory, the phasing of the triggering is key to determining the response, but the dependence on magnitude is less steep. Yet in MERRA-2, there are triggering events only 20% weaker than the 2016 triggering and equal to the 2020 triggering that did not lead to disruptions. Complicating matters further, MERRA-2 has record-large analysis tendencies during the 2016 disruption, reducing confidence in the resolved momentum budget.

Comparative stochastic analysis of the anomalous dynamics of machines under the action of operational defects

The possibility of increasing the confidence of vibroacoustic diagnostics of the technical condition of rotor-type machinery is being investigated. The search for additional sensitive and reliable features is based on the analysis of two-dimensional probability distribution densities of vibration amplitudes. This approach allows to assess the degree and character of the nonlinearity of the machine dynamic model as an oscillatory system. An example of diagnosing the technical condition of a compressor installation is given, showing the possibility of an indirect operational assessment of the accomplished repair. Keywords vibroacoustic diagnostics, nonlinear oscillations, stochastic connection, sliding bearing, defects. [email protected]