We solve the problem of recognizing geomagnetic storms from matrix time series of observations with the URAGAN muon hodoscope, using deep learning neural networks. A variant of the neural network software module is selected and its parameters are determined. Geomagnetic storms are recognized using binary classification procedures; a decision-making rule is formed. We estimate probabilities of correct and false recognitions. The recognition of geomagnetic storms is experimentally studied; for the assigned Dst threshold Yᴅ₀=–45 nT we obtain acceptable probabilities of correct and false recognitions, which amount to β=0.8212 and α=0.0047. We confirm the effectiveness and prospects of the proposed neural network approach.

The recognition of local anisotropies of muon fluxes using the functions of normalized variations for matrix observations of the URAGAN hodoscope is considered. Normalized instrument functions are introduced and spatiotemporal filtration is used, which become the basis of computation of the functions of normalized variations. An algorithm of recognition of local anisotropies is implemented. An experimental study of the application of the functions of normalized variations is carried out that confirms the efficiency of the developed algorithm for recognition of local anisotropies of muon fluxes in times series of matrix observations of the URAGAN hodoscope.

We analyzed MLP (Multi-Layer Perceptron) structures for geomagnetic storm recognition based on cosmic ray data. We used observations of the muon hodoscope URAGAN and neutron monitor systems. Variants of MLP structures modifications were implemented. The results of the analysis allowed us to form a structure that provides the optimal correlations for the probabilities of correct and false recognition of geomagnetic storms.

This article describes a method for recognizing sudden commencement events using digital differentiating filters. This method is applied to INTERMAGNET observatory data. Maximum amplitude derivatives for the magnetic components (X, Y, Z) and the total intensity (F) of the geomagnetic field are introduced, and the decision-making rule is formulated. The authors developed a procedure for selecting optimal digital differentiating filters. Estimates of probabilities of correct and false recognition of sudden commencements were obtained. The calculations of the probabilistic characteristics have confirmed the effectiveness of the method.

A method for predicting geomagnetic storms based on the neural network digital processing of joint observations of the URAGAN muon hodoscope and the international system of neutron monitor stations has been proposed. A time series of Dst indices are used. Formulas for extrapolating model estimates of Dst indices have been developed. A fully-connected feed-forward neural network has been used. Prediction decision rule has been implemented. The probability characteristics of geomagnetic storm prediction have been estimated. An experimental study of the prediction method confirmed its effectiveness. It has been shown that the observations of the hodoscope–monitor system increased the probability of correctly predicting geomagnetic storms compared to using each of the observations separately.

Indicator matrices are proposed for the recognition of local anisotropies (LAs) of muon fluxes in time series of matrix observations of the URAGAN hodoscope. Reference and current time intervals are implemented, and confidence intervals are calculated for the mathematical expectations of Poisson observations in these intervals. An anomaly function is formed. Indicator matrices are obtained by comparing the anomaly functions with thresholds. The recognition of local anisotropies by indicator matrices and the decision-making procedure are tested on model and experimental observations. The efficiency of the application of indicator matrices for the recognition of LAs of muon fluxes (MFs) in time series of matrix observations of the URAGAN hodoscope is confirmed.

Muon hodoscope URAGAN (MEPhI, Moscow) with an area of 45 sq. m is capable of real time detection of the tracks of all muons arriving from the upper celestial hemisphere with a high spatial and angular accuracy (1 cm and 1 degree, respectively). The measured angular distribution of the muons flux over a certain period of exposure time and expressed in R.M.S. deviations from an averaged reference matrix and corrected for barometric and temperature effects represents a matrix-muonograph (by analogy with X-ray radiography) of the Earth's atmosphere and near-terrestrial space. Such muonograph contains information on the current variation the flux of cosmic muons associated with modulation processes in the heliosphere, magnetosphere and atmosphere of the Earth. The sequence of muonographs converted to the GSE coordinate system allows one to study in real time the dynamics of cosmic ray anisotropy and to identify in advance geoeffective processes in the heliosphere associated with solar activity. Results of the analysis of the anisotropy of the cosmic ray muon flux at the minima of the 23rd (2009-2010) and 24th (2018-2019) solar cycles are discussed.

Problems of digital processing of Poisson-distributed data time series from various counters of radiation particles, photons, slow neutrons etc. are relevant for experimental physics and measuring technology. A low-pass filtering method for normalized Poisson-distributed data time series is proposed. A digital quasi-Gaussian filter is designed, with a finite impulse response and non-negative weights. The quasi-Gaussian filter synthesis is implemented using the technology of stochastic global minimization and modification of the annealing simulation algorithm. The results of testing the filtering method and the quasi-Gaussian filter on model and experimental normalized Poisson data from the URAGAN muon hodoscope, that have confirmed their effectiveness, are presented.

Muon flux intensity modulation (MFIM) recognition is a relevant solar-terrestrial physics problem. The MFIM discussed are due to geoeffective solar coronal mass ejections. The necessary observations are carried out using a computerized muon hodoscope (MH) URAGAN developed by NRNU MEPhI, registering muon fluxes intensity. In the MH, the number of muons falling on its aperture per unit time is counted. MH matrix data time series are formed, in which angular and temporal modulations take place due to MH design features, athmospheric disturbances and noises, the values of which significantly exceed the MFIM values. The MFIM recognition method based on the mathematical apparatus of indicator matrices (IM) and spatial-temporal filtering is proposed. The time series of MH matrix data, consisting of a set of Poisson processes corresponding to azimuthal and zenithal elements of MH matrices, are considered. A reference time span is assigned where MFIM are known to be missing. For it, matrices of estimates of mathematical expectations are calculated and, taking into account the Poisson property, the matrices of reference confidence intervals are calculated. Next, the current time sections are formed, on which the matrices of the current confidence intervals are calculated. Based on the comparison of the matrices of the reference and current confidence intervals, the current matrices of anomalies are formed, which are compared with the specified threshold matrix. Thresholds exceedings correspond to anomalous events. Binary IM are formed: ones correspond to anomalous events, zeros correspond to the absence of anomalies. Recognition is to analyze IM sequence and identify areas of non-zero elements condensation that lead to the conclusion that there are significant MFIM. To reduce the recognition errors, the space-time IM filtering has been developed. MFIM recognition technique, based on the use of IM time series with spatial-temporal filtering has been tested on model and experimental MH data. Testing on the generated time series of model Poisson MH matrix data with model MFIM confirmed the conclusion about the possibility of MFIM recognition by the proposed method with a decrease level of 3-4%. Application of spatial-temporal filtering made it possible to recognize MFIM with decreases with a level half as much. Testing on the formed experimental matrix MH data time series with model MFIM led to a conclusion that it is possible to recognize MFIM with the magnitudes of decreases almost commensurate with the decreases for the case of model MH data. The proposed MFIM recognition method based on indicator matrices for MH observation data allows optimization of parameters and can be successfully applied to solve problems of MFIM recognition and early diagnostics of geomagnetic storms.

A method for elimination of periodical diurnal, annual, and 27-day and 11-year solar variations in the matrix observations of the URAGAN muon hodoscope was developed. The analysis of the parameters of these variations in the time and frequency domains was performed. Two-dimensional bandpass filtering of sequences of muon hodoscope matrix observations was implemented. The structure of a two-dimensional filter is developed, based on the operation of elementwise matrix multiplications and additions. Examples of eliminating variations in the URAGAN muon hodoscope matrix observations are discussed.

A way of detecting local anisotropies of the muon flux using the matrix-form data of the URAGAN hodoscope (MEPhI) is proposed. Confidence intervals for estimating the matrix-data mathematical expectations in observations with reference and sliding data-sampling periods are selected, indicator functions are constructed, and a procedure for space–time filtering is developed. The results are presented from a search for local anisotropy in the muon flux recorded in the matrix-form data of the URAGAN hodoscope.

The problem of the hardware response function calculation for the URAGAN hodoscope (MEPhI) is analyzed. The simpli ed hodoscope model is developed for which the response function is found out analytically. It is shown that the presence of non-detecting intervals (gaps between detectors) leads to the response function that includes azimuthal dependence. A numerical procedure of the response function calculation is developed for the URAGAN hodoscope. The result is in correlation with the averaged matrix data from the hodoscope. The application of response function analyses to detecting of reduced muon ux areas is demonstrated. Further re nement of response function calculation is discussed.

The method of two-dimensional filtering of modulated matrix data sequences is proposed. The structure of a two-dimensional filter based on operations of element-by-element matrix multiplications is developed. An application of the two-dimensional filtering of the URAGAN muon hodoscope matrix data sequence for the elimination of muon flux diurnal modulations is discussed.

Cross-correlation between observation matrixes of the URAGAN muon hodoscope and the Dst index was studied. Functions of total intensity and anomaly were introduced. The results of calculations of cross-correlations on 2D diagrams were considered. It was shown that time periods with increased geomagnetic activity were almost always preceded by time periods with increased values of the modulus of the Pearson correlation coefficient.