Quasi-periodic Process Research Articles

Neural network energy management strategy for plug-in hybrid electric combine harvesters based on quasi-periodic samples

Energy management strategies are crucial for Plug-in Hybrid Electric Combine Harvester (PHECH). However, many existing approaches rely on rigid, pre-setting rules that struggle to adjust to the PHECH operational conditions. This paper first introduces a power estimation model tailored to the quasi-periodic process of harvester activity. Then, Dynamic Programming (DP) is applied to derive optimal samples of engine power ratio across various scenarios. Building on the samples, a Neural Network (NN) is developed to enhance the strategy's economic and real-time performance. Simulation tests evaluate the proposed algorithm's efficacy and its energy conservation potential. The findings suggest that, compared to fuel-driven harvesters, the NN strategy achieves similar energy cost savings to the DP approach, exceeding 11%, which is better than the Charge Depleting and Charge Sustaining (CDCS) strategy's 7.22% and the MPC-ECMS strategy's 7.87%. Moreover, the NN strategy reduces the time expense to roughly one-fifth of that required by the DP approach.

Long-period modulation of the classical T Tauri star CI Tau

Context. Detecting planets within protoplanetary disks around young stars is essential for understanding planet formation and evolution. However, planet detection using the radial velocity method faces challenges due to the strong stellar activity in these early stages. Aims. We detect long-term periodicities in photometric and spectroscopic time series of the classical T Tauri star (CTTS) CI Tau, and retrieve evidence for inner embedded planets in its disk. Methods. The study conducted photometric and spectroscopic analyses using K2 and Las Cumbres Observatory Global Network light curves, and high-resolution spectra from ESPaDOnS and SPIRou. We focused our radial velocity analysis on a wavelength domain less affected by spot activity. To account for spot effects, a quasi-periodic Gaussian process model was applied to K2 light curve, ESPaDOnS, and SPIRou radial velocity data. Additionally, a detailed bisector analysis on cross-correlation functions was carried out to understand the cause of long-term periodicity. Results. We detect coherent periods at ~6.6d, 9d, ~11.5d, ~14.2d, and ~25.2d, the last of which is seen consistently across all datasets. Bisector analysis of the cross-correlation functions provides strong hints for combined activity-induced and Doppler reflex signals in the radial velocities at a period of 25.2 d. Our analysis suggests that this periodicity is best explained by the presence of a 3.6 ± 0.3 MJup eccentric (e ~ 0.58) planet at a semi-major axis of 0.17 au. Conclusions. We report the detection of a massive inner planet in CI Tau. Our study outlines the difficulty of searching for disk-embedded planets in the inner 0.1 au of young and active systems. When searching for planets in actively accreting stars such as CI Tau, we demonstrate that the primary limitation is stellar activity rather than the precision of RV measurements provided by the instrument.

Data-Driven Modal Decomposition Methods as Feature Detection Techniques for Flow Fields in Hydraulic Machinery: A Mini Review

Cavitation is a quasi-periodic process, and its non-stationarity leads to increasingly complex flow field structures. On the other hand, characterizing the flow field with greater precision has become increasingly feasible. However, accurately and effectively extracting the most representative vibration modes and spatial structures from these vast amounts of data has become a significant challenge. Researchers have proposed data-driven modal decomposition techniques to extract flow field information, which have been widely applied in various fields such as signal processing and fluid dynamics. This paper addresses the application of modal decomposition methods, such as dynamic mode decomposition (DMD), Proper Orthogonal Decomposition (POD), and Spectral Proper Orthogonal Decomposition (SPOD), in cavitation feature detection in hydraulic machinery. It reviews the mathematical principles of these three algorithms and a series of improvements made by researchers since their inception. It also provides examples of the applications of these three algorithms in different hydraulic machinery. Based on this, the future development trends and possible directions for the improvement of modal decomposition methods are discussed.

Magnetic fields and rotation periods of M dwarfs from SPIRou spectra

ABSTRACT We present near-infrared spectropolarimetric observations of a sample of 43 weakly to moderately active M dwarfs, carried with SPIRou at the Canada–France–Hawaii Telescope in the framework of the SPIRou Legacy Survey from early 2019 to mid-2022. We use the 6700 circularly polarised spectra collected for this sample to investigate the longitudinal magnetic field and its temporal variations for all sample stars, from which we diagnose, through quasi-periodic Gaussian process regression, the periodic modulation and longer-term fluctuations of the longitudinal field. We detect the large-scale field for 40 of our 43 sample stars, and infer a reliable or tentative rotation period for 38 of them, using a Bayesian framework to diagnose the confidence level at which each rotation period is detected. We find rotation periods ranging from 14 to over 60 d for the early-M dwarfs, and from 70 to 200 d for most mid- and late-M dwarfs (potentially up to 430 d for one of them). We also find that the strength of the detected large-scale fields does not decrease with increasing period or Rossby number for the slowly rotating dwarfs of our sample as it does for higher-mass, more active stars, suggesting that these magnetic fields may be generated through a different dynamo regime than those of more rapidly rotating stars. We also show that the large-scale fields of most sample stars evolve on long time-scales, with some of them globally switching sign as stars progress on their putative magnetic cycles.

Multi-scale characteristics investigation of sheet/cloud cavitation

Sheet and cloud cavitation involve the formation of large-scale cavities and microbubbles across a wide range of length scales. In this study, a two-way coupling Eulerian-Lagrangian algorithm was utilized to simulate the cavitating flow around a NACA66 hydrofoil at an incidence of 8 degrees and a cavitation number of 1.2. The large eddy simulation (LES) and volume of fraction (VOF) methods are used to capture the large scale vapor structures in Eulerian frame. Meanwhile, the discrete bubble model (DBM) and simplified Rayleigh-Plesset equation are implied to solve the dynamic of Lagrangian microbubbles smaller than local grid scale. The results indicate that large-scale cavities are periodically shed downstream, influenced alternatively by the re-entrant jet and shock wave mechanisms, resulting in periodic variations of both the number and Sauter mean diameter of microscale bubbles. During the quasi-periodic evolution process of sheet/cloud cavitation, the microbubbles scatter around the large scale cavities where have strong turbulence intensity and high vorticity, and the probability density function of discrete bubble diameter similarly conforms to Gamma distribution with the dominant bubble size between 30 and 70μm. During the growth of an attached cavity, the number density of bubbles follows a power-law scaling with a value of -5/3 on radius. For the other stages, the bubble size spectrum of smaller microbubbles exhibits a -2/3 power-law scaling when the diameter of the microbubble is less than 200 μm. For larger bubbles with a diameter greater than 300 μm, the bubble density is proportional to the bubble radius to the power of -6.

DMPP-4: candidate sub-Neptune mass planets orbiting a naked-eye star

ABSTRACT We present radial velocity measurements of the very bright (V ∼ 5.7) nearby F star, DMPP-4 (HD 184960). The anomalously low Ca ii H&K emission suggests mass-loss from planets orbiting a low activity host star. Periodic radial velocity variability with ∼10 m s−1 amplitude is found to persist over a >4 yr time-scale. Although the non-simultaneous photometric variability in four TESS sectors supports the view of an inactive star, we identify periodic photometric signals and also find spectroscopic evidence for stellar activity. We used a posterior sampling algorithm that includes the number of Keplerian signals, Np, as a free parameter to test and compare (1) purely Keplerian models (2) a Keplerian model with linear activity correlation and (3) Keplerian models with Gaussian processes. A preferred model, with one Keplerian and quasi-periodic Gaussian process indicates a planet with a period of $P_\textrm {b} = 3.4982^{+0.0015}_{-0.0027}$ d and corresponding minimum mass of $m_\textrm {b}\, \textrm {sin}\, i = 12.2^{+1.8}_{-1.9}$ M⊕. Without further high-time resolution observations over a longer time-scale, we cannot definitively rule out the purely Keplerian model with two candidates planets with $P_\textrm {b} = 2.4570^{+0.0026}_{-0.0462}$ d, minimum mass $m_\textrm {b}\, \textrm {sin}\, i = 8.0^{+1.1}_{-1.5}$ M⊕ and $P_\textrm {c} = 5.4196^{+0.6766}_{-0.0030}$ d and corresponding minimum mass of $m_\textrm {b}\, \textrm {sin}\, i = 12.2^{+1.4}_{-1.6}$ M⊕. The candidate planets lie in the region below the lower-envelope of the Neptune Desert. Continued mass-loss may originate from the highly irradiated planets or from an as yet undetected body in the system.

Smart analysis of anxiety people and their activities using heterogeneous quasiperiodic process

AbstractThe increase in anxiety levels worldwide can be described as a serious global health threat. Around 500 million people suffer from mental disorders and are suffering from depression, and other mental‐oriented disabilities. The new technological paradigms such as the Internet of Things (IoT) were employed for detecting, and treating these disorders, which are being proposed, developed, and provide new capabilities to detect, assess and care for anxious people. These possibilities lead to several issues that are identified, which relate to patient privacy and confidentiality, security challenges such as data security, and the organization of IoT systems. To rectify these issues, we implement the Smart analysis of anxious people and their activities using Heterogeneous computing with virtual sensing. This system consists of the health application featuring the technique of the internet of things, heterogeneous computing, Cognitive Quasiperiodic motion, and Pentagonal tiling. This system introduces the internet of things‐assisted smart analysis of anxiety against people with their activities. It performs the optimization analysis for improving the levels. The observational results focus on how to deal with the issues which were overcome in the analysis levels of the anxiety disorders, which show that time spent using the heterogeneous computing with the virtual sense proves more accuracy (92.3%), specificity (Degrees of anxiety severity by 20%), precision (Analysis of anxiety stress level by 65%), and recall (Anxiety chances percentile by 65.34%). The proposed model is simulated, and the outcomes are compared with the prevailing methods for evaluating the parameters like accuracy, end‐end‐end delay, energy consumption, network lifetime, and throughput.

Optical and near-infrared stellar activity characterization of the early M dwarf Gl 205 with SOPHIE and SPIRou

Context. The stellar activity of M dwarfs is the main limiting factor in the discovery and characterization of the exoplanets orbiting them, because it induces quasi-periodic radial velocity (RV) variations. Aims. We aim to characterize the magnetic field and stellar activity of the early, moderately active M dwarf Gl 205 in the optical and near-infrared (NIR) domains. Methods. We obtained high-precision quasi-simultaneous spectra in the optical and NIR with the SOPHIE spectrograph and SPIRou spectropolarimeter between 2019 and 2022. We computed the RVs from both instruments and the SPIRou Stokes V profiles. We used Zeeman–Doppler imaging (ZDI) to map the large-scale magnetic field over the time span of the observations. We studied the temporal behavior of optical and NIR RVs and activity indicators with the Lomb-Scargle periodogram and a quasi-periodic Gaussian process regression (GPR). In the NIR, we studied the equivalent width of Al I, Ti I, K I, Fe I, and He I. We modeled the activity-induced RV jitter using a multi-dimensional GPR with activity indicators as ancillary time series. Results. The optical and NIR RVs show similar scatter but NIR shows a more complex temporal evolution. We observe an evolution of the magnetic field topology from a poloidal dipolar field in 2019 to a dominantly toroidal field in 2022. We measured a stellar rotation period of Prot = 34.4 ± 0.5 days in the longitudinal magnetic field. Using ZDI, we measure the amount of latitudinal differential rotation (DR) shearing the stellar surface, yielding rotation periods of Peq = 32.0 ± 1.8 days at the stellar equator and Ppol = 45.5 ± 0.3 days at the poles. We observed inconsistencies in the periodicities of the activity indicators that could be explained by these DR values. The multi-dimensional GP modeling yields an RMS of the RV residuals down to the noise level of 3 m s−1 for both instruments while using Hα and the BIS in the optical and the full width at half maximum (FWHM) in the NIR as ancillary time series. Conclusions. The RV variations observed in Gl 205 are due to stellar activity, with a complex evolution and different expressions in the optical and NIR revealed thanks to an extensive follow-up. Spectropolarimetry remains the best technique to constrain the stellar rotation period over standard activity indicators, particularly for moderately active M dwarfs.

Kepler-102: Masses and Compositions for a Super-Earth and Sub-Neptune Orbiting an Active Star

Radial velocity (RV) measurements of transiting multiplanet systems allow us to understand the densities and compositions of planets unlike those in the solar system. Kepler-102, which consists of five tightly packed transiting planets, is a particularly interesting system since it includes a super-Earth (Kepler-102d) and a sub-Neptune-sized planet (Kepler-102e) for which masses can be measured using RVs. Previous work found a high density for Kepler-102d, suggesting a composition similar to that of Mercury, while Kepler-102e was found to have a density typical of sub-Neptune size planets; however, Kepler-102 is an active star, which can interfere with RV mass measurements. To better measure the mass of these two planets, we obtained 111 new RVs using Keck/HIRES and Telescopio Nazionale Galileo/HARPS-N and modeled Kepler-102's activity using quasiperiodic Gaussian process regression. For Kepler-102d, we report a mass upper limit M d < 5.3 M ⊕ (95% confidence), a best-fit mass M d = 2.5 ± 1.4 M ⊕, and a density ρ d = 5.6 ± 3.2 g cm−3, which is consistent with a rocky composition similar in density to the Earth. For Kepler-102e we report a mass M e = 4.7 ± 1.7 M ⊕ and a density ρ e = 1.8 ± 0.7 g cm−3. These measurements suggest that Kepler-102e has a rocky core with a thick gaseous envelope comprising 2%–4% of the planet mass and 16%–50% of its radius. Our study is yet another demonstration that accounting for stellar activity in stars with clear rotation signals can yield more accurate planet masses, enabling a more realistic interpretation of planet interiors.

Analysis of quasi-periodic space-time non-separable processes to support decision-making in medical monitoring systems

In many decisionsupport systemsthere are processedchaotic spatial-time processes which are non-separable and quasi-periodic. Some examples of such systemsareepidemic spreading, population development, fire spreading, radio wave signals, image processing, information encryption, radio vision, etc. Processes in these systems have periodic character, e.g. seasonal fluctuations(epidemic spreading, population development), harmonic fluctuations (pattern recognition, image processing),etc. In simulation block the existing systems use separable process models which are presented as multiplication of spatialand temporal parts and are linearized. This significantly reduces the quality of spatial-time non-separable processes. The quality model building of chaotic spa-tial-time non-separable processwhich is processed by decisionsupport systemis necessary for getting of learning set. Itis really complicated especially if the random process is formed. The implementation ensemble of chaotic spatial-time non-separable process requires high costs what causes reduction of the system efficiency. Moreover, in many cases the implementation ensemble of spatial-time processes is impossible to get. In this workthemathematical model of a quasi-periodic spatial-time non-separable process has been developed. Based on it the formation method of this process has been developed and investigated. The epidemic spreading pro-cessed was presented as an example.

МОДЕЛИ СИСТЕМ КВАЗИПЕРИОДИЧЕСКИХ ПРОЦЕССОВ НА ОСНОВЕ ЦИЛИНДРИЧЕСКИХ И КРУГОВЫХ ИЗОБРАЖЕНИЙ

The behavior of objects in many practical situations has a quasiperiodic character - the presence of noticeable periodicity with random variations of quasiperiods. For example, noise and vibration of an aircraft engine, hydroelectric unit, seasonal and daily fluctuations in atmospheric temperature, etc. In this case, the object can have several parameters, therefore the object is described by a system of several time series, that is, several random processes. The emerging monitoring tasks (assessing the state of an object and its forecast) require setting a model of such a system of processes and identifying it for a particular object based on the results of its observations. In this paper, to represent a quasi-periodic process, an autoregressive model is used in the form of sweeps of several cylindrical or circular images along a spiral. Choosing the values of a small number of parameters of this model, one can describe and simulate a wide class of systems of quasiperiodic processes. The problem of identifying a model is considered, that is, determining the values of its parameters at which it, in a certain sense, best corresponds to the actually observed process. This problem is solved using a pseudo-gradient adaptive procedure, the advantage of which is its real-time operation with low computational costs.

ПСЕВДОГРАДИЕНТНЫЙ АЛГОРИТМ ИДЕНТИФИКАЦИИ ДВАЖДЫ СТОХАСТИЧЕСКОГО ЦИЛИНДРИЧЕСКОГО ИЗОБРАЖЕНИЯ

Nowadays image processing problems are becoming increasingly important due to development of the aerospace Earth monitoring systems, radio and sonar systems, medical devices for early diagnosis, etc. However, the most of the image processing works deals with images defined on rectangular two-dimensional grids or grids of higher dimension. In some practical situations images are set on a cylinder, for example images of pipeline sections, blood vessels, rotary parts, etc. The peculiarity of the domain for specifying such images requires its consideration in their models and processing algorithms. The article deals with autoregressive models of cylindrical images and gives some expressions of the correlation function depending on the autoregression parameters are given. To represent heterogeneous images with random heterogeneities, ‘doubly stochastic’ models are used in which one or more images control the parameters of resulted image. The spiral scan of a cylindrical image can be considered as a quasiperiodic process due to the correlation of image rows. The article proposes the pseudogradient algorithms for the modal identification. The statistical modeling proves these algorithms give good model identification.

Recurrence quantification analysis of São Francisco River flow: hydrological alterations caused by the construction of Sobradinho dam

We investigated how the construction of the Sobradinho dam and reservoir affected the daily streamflow of the São Francisco River, using the method of Recurrence plot (RP) and Recurrence quantification analysis (RQA) which serves to visualize and quantify the recurrences of the states in the phase space of the dynamic system. We analyzed daily streamflow time series recorded in the fluviometric station Juazeiro that is located downstream of the Sobradinho dam, for the periods before (1943-1972) and after (1980-2009) the dam construction. We observed that in the natural regime, before the dam construction, the streamflow dynamics shows characteristics of periodic and quasi-periodic process, indicated by the checkerboard patterns in RP. After the dam construction, streamflow dynamics exhibit sudden changes indicated by white bands in RP, and become less predictable, less complex, and remain s in certain laminar states for shorter periods, indicated by the decrease of the values of RQA parameters.

Modeling the Quasiperiodic Radial Velocity Variations of γ Draconis

Abstract γ Draconis, a K5III star, showed radial velocity (RV) variations consistent with a 10.7 Jupiter mass planet from 2003 to 2011. After 2011, the periodic signal decayed, then reappeared with a phase shift. Hatzes et al. suggested that γ Dra’s RV variations could come from oscillatory convective modes, but did not fit a mathematical model. Here we assess whether a quasi-periodic Gaussian process—appropriate when spots with finite lifetimes trace underlying periodicity—can explain the RVs. We find that a model with only one quasiperiodic signal is not adequate: we require a second component to fit the data. The best-fit model has quasi-periodic oscillations with P 1 = 705 days and P 2 = 15 days. The 705 day signal may be caused by magnetic activity. The 15 day period requires further investigation.

Automatic detection of venous air embolism using transesophageal echocardiography in patients undergoing neurological surgery in the semi-sitting position: a pilot study

Neurological surgery in the semi-sitting position is linked with a pronounced incidence of venous air embolism (VAE) which can be fatal and therefore requires continuous monitoring. Transesophageal echocardiography (TEE) provides a high sensitivity for the intraoperative detection of VAE; however, continuous monitoring with TEE requires constant vigilance by the anaesthesiologist, which cannot be ensured during the entire surgical procedure. We implemented a fully automatic VAE detection system for TEE based on a statistical model of the TEE images. In the sequence of images, the cyclic heart activity is regarded as a quasi-periodic process, and air bubbles are detected as statistical outliers. The VAE detection system was evaluated by means of receiver operating characteristic (ROC) curves using a data set consisting of 155.14 h of intraoperatively recorded TEE video and a manual classification of periods with visible VAE. Our automatic detection system accomplished an area under the curve (AUC) of 0.945 if all frames with visible VAE were considered as detection target, and an AUC of 0.990 if frames with the least severe optical grade of VAE were excluded from the analysis. Offline-review of the recorded TEE videos showed that short embolic events (≤ 2 min) may be overseen when monitoring TEE video manually. Automatic detection of VAE is feasible and could provide significant support to anaesthesiologists in clinical practice. Our proposed algorithm might possibly even offer a higher sensitivity compared to manual detection. The specificity, however, requires improvement to be acceptable for practical application. Trial Registration: German Clinical Trials Register (DRKS00011607).

Smart alarm based on sleep stages prediction.

A sleep inertia after waking up strongly affects the overall mental recovery after sleep. The sleep inertia depends not as much on overall sleep quality but also on the sleep stage in the waking up moment. The fix-time alarming system results in waking up at random sleep stage, which results in frequent sleep inertia. The widely used flow-time alarming systems based on motion detection (actigraphy) reduce but do not eliminate sleep inertia. Such systems do not wake up users in Deep sleep stage, but may instead wake them up in Wake, Light, or REM (Rapid Eyes Movement) stages. Moreover, frequent waking up in the REM stage results in serious psychological issues. We present a smartwatch alarm system that predicts sleep stages and thus produces an alarm call at an easy waking up moment with minimal sleep inertia effect. The sleep stages are predicted using an Encoder-Decoder Recurrent Neural Network model. The rationale of the prediction is that each sleep stages cycling pattern is a continuous quasi-periodic process. Experimental results from over 138 nocturnal sleep periods from 92 respondents show that our system provides 66-70% accuracy for Deep, Light, Wake, REM sleep stages and 71-77% accuracy for 2-classes (Deep/REM vs. Light/Wake stages) prediction classifications. The proposed alarm system wakes up the user at the moment when Easy Wake (Wake/Light) stage is the most probable.

A Survey of Interplanetary Small Flux Ropes at Mercury

Abstract Interplanetary magnetic flux ropes with durations from a few minutes to a few hours have been termed small flux ropes (SFRs). We have built a comprehensive catalog of SFRs at Mercury using magnetometer data from the orbital phase of the MESSENGER mission (2011–2015). In the absence of solar wind plasma measurements, we developed strict identification criteria for SFRs in the magnetometer observations, including force-free field fits for each flux rope. We identified a total of 48 events that met our strict criteria, with events ranging in duration from 2.5 minutes to 4 hr. Using superposed epoch analysis, we obtained the generic SFR magnetic field profile at Mercury. Due to its eccentric orbit, Mercury’s heliospheric distance varies between 0.31 and 0.47 au, a range of ∼0.16 au. This distance is potentially large enough for the SFRs to undergo measurable changes due to distance. Thus, we split the data into two distance bins to look for such changes. We found that the average SFR profile is more symmetric farther from the Sun, in line with the idea that SFRs form closer to the Sun and undergo a relaxation process in the solar wind. Based on this result, as well as the SFR durations and the magnetic field strength fall-off with heliocentric distance, we infer that the SFRs observed at Mercury are expanding as they propagate with the solar wind. We also determined that the SFR occurrence frequency is nearly four times as high at Mercury as for similarly detected events at 1 au. Most interestingly, we found two SFR populations in our data set, one likely generated in a quasi-periodic formation process near the heliospheric current sheet, and the other formed away from the current sheet in isolated events.

Development of a mathematical model of conflict between the parties in the implementation of the offset transaction

The object of research of this work is the conflict of interests of the parties in the implementation of offset agreements. One of the most problematic places when implementing offset agreements is that a wide variety of sudden events, force majeure circumstances, etc. can take place – phenomena that can’t be described in detail and predicted with acceptable accuracy in full. In addition, the offset contract is a conflict of interest between the seller and the buyer. During the study, the methods of the humanitarian and natural-scientific approach are used, thanks to which the conflict was given a new interpretation. It is considered as a way of interaction of complex systems. It is shown that the conflict is not a synonym for confrontation, but a way to overcome contradictions and limitations, a way of interaction of complex systems is an inevitable, normal phenomenon. Of course, conflict involves struggle, but, above all, conflict involves interaction. It is shown that the conflict can’t be considered as an optimization task, since with equal resources of the parties, the conflict will be terminated due to the complete depletion of both sides, and with unequal resources, the defeat of the weaker side with a probability of one. Also, the conflict can’t be resolved within the framework of the theory of adaptation. A brief comparative analysis of the possibilities of using varieties of Markov processes and the degree of their adequacy to the real processes of supporting offset transactions at different stages is carried out. A mathematical model of the conflict between the parties is proposed. In the model, the process of conflict development is a branched semi-Markov process, the transitional and final probabilities of which depend on the ratio of resources of the parties. In addition, the conflict represents a sequence of concerted actions of the parties and, in fact, is a controllable quasiperiodic process with elements of stochasticity. The resulting winnings of the parties to the conflict are investigated with varieties of their cooperation and rivalry. The proposed model can be used to model the processes of development and implementation of offset programs and the wins of the parties.

Pseudo-gradient algorithm for identification of doubly stochastic cylindrical image model

Abstract Nowadays, image processing problems are becoming increasingly important due to development of the aerospace Earth monitoring systems, radio and sonar systems, medical devices for early diagnosis etc. But the most of the image processing works deal with images defined on rectangular two-dimensional grids or grids of higher dimension. In some practical situations, images are set on a cylinder. For example, images of a section of pipelines, worms, blood vessel, parts during turning, etc. The peculiarity of the domain for specifying such images requires its consideration in their models and processing algorithms. In the present paper, autoregressive models of cylindrical images are considered, expressions of the correlation function depending on the autoregression parameters are given. To represent heterogeneous images with random heterogeneities, «doubly stochastic» models are used in which one or more images control the parameters of the resulting image. The spiral scan of a cylindrical image can be considered as a quasiperiodic process due to the correlation of image rows. Pseudo-gradient algorithms for the modal identification are proposed. The statistical modeling showed that these algorithms give good model identification.

КРИТЕРИЙ ДЛЯ ПРОВЕРКИ ГИПОТЕЗ О КОВАРИАЦИОННОЙ ФУНКЦИИ СИСТЕМЫ КВАЗИПЕРИОДИЧЕСКИХ ПРОЦЕССОВ, ПРЕДСТАВЛЕННЫХ ЦИЛИНДРИЧЕСКИМИ МОДЕЛЯМИ ИЗОБРАЖЕНИЙ

The generally accepted mathematical model of a wide variety of natural, technical, economic and other objects that exist in time are random processes, for example sea waves, wind, vibrations of engines and hydraulic units, biorhythms, etc. An object is usually described by several parameters, that is a system of random processes or time series. The processes occurring in many objects have a form close to periodic – quasiperiodic, namely there is a periodicity with an element of unpredictability, for example speech sounds, vibrations of various technical objects, daily temperature fluctuations, etc. In order to formulate the problems of processing the quasiperiodic process systems, their mathematical models are required. For this purpose, authors propose models in which the processes are presented in the form of spiral sweeps on autoregressive cylindrical images. A suitable set of parameter values for these models provides a given degree of quasiperiodicity of individual processes and the given covariance relationships between the processes of the system. A criterion is proposed for testing the hypotheses about the correspondence of the observed system of time series to their model of the described type. The authors provide the examples of the application of this criterion with an analysis of the sensitivity to deviations of the model parameters from the expected ones are given.