Remote Objects Research Articles

Remote Sensing Object Counting Through Regression Ensembles and Learning to Rank

Remote sensing object counting is finding applications in many fields. Global regression is a long-ignored method for object counting, though it needs much less manual annotations than the alternatives. This work revisits global regression and improves it in two ways—one way is by replacing one single regressor with a deep ensemble, the other is by breaking down global regression into two easier and smaller problems: learning to rank (L2R) and linear transformation. To this end, we make a PAC-Bayesian analysis of regression ensembles and give an upper bound for their generalization error, offering new theoretical insight into ensemble learning. We also adapt a ranking metric optimization scheme to suit object counting, elegantly handling the L2R problem with gradient descent. What is more, based on our theoretical perspective, we provide a novel way of building deep regression ensembles, on which the ambiguity constraint is imposed. Then, by incorporating L2R into a deep ensemble, we propose a new counting model called the “ensemble of first-rank-then-estimate networks (eFreeNet).” Our extensive evaluation on six benchmarks shows that eFreeNet exhibits compelling performance across the board while being more annotation-efficient than other methods. Our source code is publicly available at https://github.com/huangyongbobo/eFreeNet.

MashFormer: A Novel Multiscale Aware Hybrid Detector for Remote Sensing Object Detection

Object detection is a critical and demanding topic in the subject of processing satellite and airborne images. The targets acquired in remote sensing imagery are at various sizes, and the backgrounds are complicated, which makes object detection extremely challenging. We address these aforementioned issues in this paper by introducing the MashFormer, an innovative multi-scale aware CNN and Transformer integrated hybrid detector. Specifically, MashFormer employs the transformer block to complement the convolutional neural network (CNN) based feature extraction backbone, which could obtain the relationships between long-range features and enhance the representative ability in complex background scenarios. With the intention of improving the detection performance for objects with multi-scale characteristic, since in remote sensing scenarios, the size of object varies greatly. A multi-level feature aggregation component, incoperate with a cross-level feature alignment module is designed to alleviate the semantic discrepancy between features from shallow and deep layers. To verify the effectiveness of the suggested MashFormer, comparative experiments are carried out with other cutting-edge methodologies using the publicly available High Resolution Remote Sensing Detection (HRRSD) and Northwestern Polytechnical University (NWPU) VHR-10 datasets. The experimental findings confirm the effectiveness and superiority of our suggested model by indicating that our approach has greater mean average precision (mAP) than the other methodologies.

Task Alignment Interaction and Cross-Scale Guided Enhancement for Remote Sensing Object Detection

Task Alignment Interaction and Cross-Scale Guided Enhancement for Remote Sensing Object Detection

POWER SUPPLY INSTALLATION FOR REMOTE RURAL SETTLEMENTS WITH SOLAR THERMOELECTRIC GENERATOR

The analysis of scientific research, which presents thermoelectric technologies based on solar energy, capable of satisfying not only the need for electricity production, but also contribute to energy conservation and environmental protection, is carried out. (Research purpose) The research purpose is developing a structural diagram of an electric power supply installation with thermoelectric generators for remote rural settlements and objects of the agro-industrial complex with a solar concentrator and a solid-state thermal accumulator, calculating the main characteristics of the elements of the proposed installation with a solar thermoelectric generator. (Materials and methods) Conducted a patent search on the websites of the Eurasian Patent Organization, Rospatent and Google Patents. The available calculated dependences were analyzed to determine the main thermal characteristics of the elements of the proposed structural scheme of the power supply installation. The results of theoretical and experimental studies devoted to the development of power supply systems based on thermoelectric generators in combination with photovoltaic panels, solar concentrators and heat pipes have been demonstrated, which allow us to conclude that the creation of solar thermoelectric generators is relevant. (Results and discussion) A design was developed and a description of the operation of an electric power supply unit with a solar thermoelectric generator and heat pipes transmitting thermal energy from a solar concentrator through a solid-state thermal accumulator to a thermoelectric generator was presented. (Conclusions) Proposed a block diagram of the installation of a solar thermoelectric generator for remote settlements in combination with a solid-state heat accumulator and heat pipes that transmit thermal energy from a solar concentrator. Expressions were given for calculating the main thermal characteristics of the elements of the proposed installation with a solar thermoelectric generator (solar concentrator and solid-state thermal accumulator), as well as the efficiency and output electrical power of a thermoelectric power generator.

Object-Centric Masked Image Modeling-Based Self-Supervised Pretraining for Remote Sensing Object Detection

Masked image modeling (MIM) has been proved to be an optimal pretext task for self-supervised pretraining (SSP), which can facilitate the model to capture an effective task-agnostic representation at the pretraining step and then advance the fine-tuning performance of various downstream tasks. However, under the high randomly masked ratio of MIM, the scene-level MIM-based SSP is hard to capture the small-scale objects or local details from complex remote sensing scenes. Then, when the pretrained models capturing more scene-level information are directly applied for object-level fine-tuning step, there is an obvious representation learning misalignment between model pretraining and fine-tuning steps. Therefore, in this article, a novel object-centric masked image modeling (OCMIM) strategy is proposed to make the model better capture the object-level information at the pretraining step and then further advance the object detection fine-tuning step. First, to better learn the object-level representation involving full scales and multicategories at MIM-based SSP, a novel object-centric data generator is proposed to automatically setup targeted pretraining data according to objects themselves, which can provide the specific data condition for object detection model pretraining. Second, an attention-guided mask generator is designed to generate a guided mask for MIM pretext task, which can lead the model to learn more discriminative representation of highly attended object regions than by using the randomly masking strategy. Finally, several experiments are conducted on six remote sensing object detection benchmarks, and results proved that the proposed OCMIM-based SSP strategy is a better pretraining way for remote sensing object detection than normally used methods.

Remote Sensing Object Detection Based on Strong Feature Extraction and Prescreening Network

Remote sensing object detection has been an important and challenging research hotspot in computer vision that is widely used in military and civilian fields. Recently, the combined detection model of CNN and Transformer has achieved good results, but the problem of poor detection performance of small objects still needs to be solved urgently. This letter proposes a deformable DETR-based framework for object detection in remote sensing images. Firstly, Multi-Scale Split Attention (MSSA) is designed to extract more detailed feature information by grouping. Next, we propose Multi-Scale Deformable Prescreening Attention (MSDPA) mechanism in decoding layer, which achieves the purpose of pre-screening, so that the encoder-decoder structure can obtain attention map more efficiently. Finally, the A-D loss function is applied to the prediction layer, increasing the attention of small objects and optimizing the IOU function. We conduct extensive experiments on the DOTA v1.5 dataset and the HRRSD dataset, which show that the reconstructed detection model is more suitable for remote sensing objects, especially for small objects. The average detection accuracy in DOTA dataset has improved by 4.4% (up to 75.6%), especially the accuracy of small objects has raised by 5%.

OPTICAL-ELECTRONIC SYSTEM OF HIGH SPATIAL RESOLUTION WHEN OBSERVING REMOTE OBJECTS

Schematic solutions of an optoelectronic system for obtaining high spatial resolution when observing remote objects are studied, which allow obtaining high resolution of objects in the volume of the observed space, providing high accuracy in determining the coordinates and geometric features of objects in three-dimensional space. A hybrid system is considered for simultaneous registration of the entire set of rays from observed objects in a full solid angle by a high-resolution optical system together with a system for registering sets of different sets of ray directions from objects in the same observed space, which makes it possible to form a set of narrow layers of the observed space in range. To further improve the accuracy of obtaining coordinate and non-coordinate information of the observed objects, the images of narrow layers of space are expanded to the resolution of the first optical registration system by weighted substitution of the detail filters of the discrete wavelet transform. Integration in different digital information ranges is achieved by decomposing the image of the first digital source and each of the set of images of the second digital source into low-frequency and high-frequency components, separate processing of image components based on the principle of weighted summation for each pixel, and the formation of the resulting image. Computational experiments have been carried out showing the effectiveness of the proposed circuit solutions in determining the parameters of objects of interest.

Design and Development of a Multi-Sided Tabletop Augmented Reality 3D Display Coupled with Remote 3D Imaging Module

This paper proposes a tabletop augmented reality (AR) 3D display paired with a remote 3D image capture setup that can provide three-dimensional AR visualization of remote objects or persons in real-time. The front-side view is presented in stereo-3D format, while the left-side and right-side views are visualized in 2D format. Transparent glass surfaces are used to demonstrate the volumetric 3D augmentation of the captured object. The developed AR display prototype mainly consists of four 40 × 30 cm2 LCD panels, 54% partially reflective glass, an in-house developed housing assembly, and a processing unit. The capture setup consists of four 720p cameras to capture the front-side stereo view and both the left- and right-side views. The real-time remote operation is demonstrated by connecting the display and imaging units through the Internet. Various system characteristics, such as range of viewing angle, stereo crosstalk, polarization perseverance, frame rate, and amount of reflected and transmitted light through partially reflective glass, were examined. The demonstrated system provided 35% optical transparency and less than 4% stereo crosstalk within a viewing angle of ±20 degrees. An average frame rate of 7.5 frames per second was achieved when the resolution per view was 240 × 240 pixels.

A Two-Phase Mass Flow Rate Model for Nitrous Oxide Based on Void Fraction

In the field of space propulsion, self pressurized technology is an example of innovation capable of improving system performances through reduction of volumes and other optimizations. Potential applications are widespread and not limited to the propulsion panorama: from on-orbit maneuvering to in-orbit servicing, from refueling of satellites at the end of life to in situ resource exploitation for missions headed towards remote objects of the solar system. However, important drawbacks have been reported for these systems: modeling of fluids and thermal phenomena is complex, thus preventing accurate performance predictions. As a result, no comprehensive and accurate model capable of describing the dynamics of a self-pressurizing propellant tank has been developed so far. In this context, this paper proposes a two-phase mass flow rate model based on void fraction. N2O has been selected due to its use as a green and self-pressurized propellant for in-space propulsive applications. The aim of this paper is to describe the current mass flow rate models present in the literature for this fluid and compare the new model with the one proposed by Dyer. A model validation is also offered, and a test campaign is mentioned. Finally, preliminary results are shown and discussed: results are then compared with the ones obtained through the Dyer model, in order to retrieve a comprehensive comparison among the two simulation frameworks. Comments on the results are added, showing the improvements as well as the limitations of the proposed framework.

Feasibility of Remotely Monitoring Daily Physical Activity in Individuals with Acquired Brain Injury

<h3>Research Objectives</h3> Wearable physical activity monitors (PAM) are increasingly replacing traditional patient recall questionnaires to monitor physical activity in the community. Remote objective monitoring of physical activity is needed especially in the current times of the Covid-19 pandemic. While PAM are increasingly used in multiple populations, there is no information on the feasibility and challenges of using PAM to remotely monitor physical activity in individuals with acquired brain injury. The main goal of this research is to determine the usability, ease of use and identify challenges of using PAM for remotely monitoring objective physical activity in the community in individuals with acquired brain injury. <h3>Design</h3> Mixed methods research (4-weeks). <h3>Setting</h3> In the community (real-world). <h3>Participants</h3> Ten individuals with acquired-brain-injury (Stroke and TBI). <h3>Interventions</h3> All participants wore three (wrist, ankle, waist) ActiGraph GT9X Link PAM simultaneously for 4-weeks in the community and provided their feedback weekly. <h3>Main Outcome Measures</h3> Usability, ease of use, challenges. <h3>Results</h3> Participants rated all PAM to have good usability on the System Usability Scale. They gave the best possible score on the After Scenario Questionnaire after using the remote data hub which was used daily to transfer the data remotely to the research dashboard. Qualitative content analysis showed that most challenges reported were for wrist PAM and wear attachments were the most challenging aspect of using PAM in this population. <h3>Conclusions</h3> This research helps establish the framework and challenges of using PAM to remotely monitor objective physical activity in the community in individuals with acquired brain injury. Continuous monitoring of physical activity in the community is essential to evaluate the progress and the effect of rehab interventions and for tracking daily physical activity in individuals with acquired brain injury. <h3>Author(s) Disclosures</h3> No conflicts.

On Theoretical Foundations of Aerolimnology: Study of Fresh Water Bodies and Coastal Territories Using Air Robot Equipment

The integration of the methodological basis of several different sciences in interdisciplinary research is a characteristic feature of new mechanisms for solving modern applied problems. The emerging theoretical foundations of aerolimnology, as a new scientific direction, are considered from the point of view of the contribution of three key sciences to it: limnology, informatics and robotics. Classifications of methods and approaches of limnological research, airborne robotic means, and information technologies that are promising for solving problems in the field of aerolimnology are given. The task of the scientific direction of aerolimnology is formulated as the study of the possibilities and limitations of combined methods of remote sensory measurement, robotic sampling and analytical study of the parameters of freshwater ecosystems to monitor and predict the dynamics of their development. Among the main areas of aerolimnological research, the following are distinguished: the construction of orthophotomaps and photogrammetric spatial models of the bottom topography and individual elements of the bottom landscape and coastal zone of various scales; geological and geophysical mapping of the underwater part of the coastal zone; the study of phytoplankton, in particular, the "bloom" of water caused by cyanobacteria; study of distribution and migration of large representatives of hydrofauna; study of temperature fields and processes of redistribution of water masses. The limitations imposed on the use of unmanned aerial vehicles (UAVs) in sampling and monitoring coastal water areas are discussed, primarily weather-climatic, temporal, spatial, and technical. The advantage of using unmanned aerial vehicles in aerolimnology is justified by an increase in the speed of data acquisition, the possibility of approaching hard-to-reach and territorially remote objects, and a decrease in the influence of the human factor. The scientific novelty of the presented research consists in an attempt to integrate interdisciplinary knowledge when using unmanned aerial vehicles and processing the obtained data based on artificial intelligence technologies in the study of limnological objects and processes. The important role of geoinformation systems is noted and examples of maps of shore typification and geomorphology of Lake Ladoga are given, posted on the website of the Center for the Collective Use of Scientific Equipment "North-Western Center for Monitoring and Forecasting the Development of Territories" of the St. Petersburg Federal Research Center of the Russian Academy of Sciences. The main stages of the methodology for conducting aerolimnological studies using interdisciplinary approaches based on limnology, informatics and robotic tools operating in different environments are considered.

MRS-Tex: A Magnetically Responsive Soft Tactile Device for Texture Display

Tactile devices provide an intuitive way for texture display, which allows users to perceive the detailed surface properties of virtual or remote objects. For existing tactile devices that create actual topographical transformations, it remains challenging to render surface textures with high spatial resolution due to the limitation of the size of actuators. To address this challenge, a magnetically responsive soft actuator with a diameter of 1 mm is proposed. Integrating the high-density soft actuator array and a soft membrane bracket, we develop a magnetically responsive soft tactile device (named MRS-Tex) for texture display. When a magnetic field is applied, the magnetic units will sink to form pits, and the soft membrane bracket resists the finger pressure so that users can perceive the rendered surface texture. Thanks to the proposed sunken solution, MRS-Tex is capable of rendering surface textures with millimeter-level resolution (1.5 mm) while providing a sufficient upward holding force. Moreover, we conduct quantitative experiments and two user studies to evaluate the performance of MRS-Tex. Experimental results show that MRS-Tex can generate pits with a depth of more than 0.20 mm, which is sufficient for rendering perceivable surface textures. The average discrimination accuracy of user study can reach up to 82% for both six basic texture patterns and four complex texture patterns.

Multi-Thread AI Cameras Using High-Speed Active Vision System

In this study, we propose a multi-thread artificial intelligence (AI) camera system that can simultaneously recognize remote objects in desired multiple areas of interest (AOIs), which are distributed in a wide field of view (FOV) by using single image sensor. The proposed multi-thread AI camera consists of an ultrafast active vision system and a convolutional neural network (CNN)-based ultrafast object recognition system. The ultrafast active vision system can function as multiple virtual cameras with high spatial resolution by synchronizing exposure of a high-speed camera and movement of an ultrafast two-axis mirror device at hundreds of hertz, and the CNN-based ultrafast object recognition system simultaneously recognizes the acquired high-frame-rate images in real time. The desired AOIs for monitoring can be automatically determined after rapidly scanning pre-placed visual anchors in the wide FOV at hundreds of fps with object recognition. The effectiveness of the proposed multi-thread AI camera system was demonstrated by conducting several wide area monitoring experiments on quick response (QR) codes and persons in nature spacious scene such as meeting room, which was formerly too wide for a single still camera with wide angle lens to simultaneously acquire clear images.

AS-polRI: Analysis of apparent spectral polarization radiant intensity in the midwave infrared band for man-made object detection

Detecting remote man-made objects in mid-infrared band is an important problem in aerial surveillance. Spectral polarization in the midwave infrared (MWIR) hyperspectral band can be a feasible solution but it has been studied less than the visible light band. The conventional degree of linear polarization (DoLP) metric cannot provide physical spectral polarization information because it is defined as a energy-normalized ratio, which leads to incorrect polarization degree in low signal-to-noise ratio in MWIR band. This paper presents a novel physical metric called apparent spectral polarization radiant intensity (AS-polRI) for MWIR spectral polarization in man-made object detection. AS-polRI, measured in Watts per steradian (W/sr), is obtained by integrating the difference between parallel spectral radiance and perpendicular spectral radiance assuming a 1 m2 object area. The proposed AS-polRI is compared with the degree of linear polarization (DoLP) in terms of man-made object detection. Experimental results for various outdoor scenarios and materials validate the usefulness of the proposed AS-polRI.

Research data management for bioimaging: the 2021 NFDI4BIOIMAGE community survey.

Background: Knowing the needs of the bioimaging community with respect to research data management (RDM) is essential for identifying measures that enable adoption of the FAIR (findable, accessible, interoperable, reusable) principles for microscopy and bioimage analysis data across disciplines. As an initiative within Germany's National Research Data Infrastructure, we conducted this community survey in summer 2021 to assess the state of the art of bioimaging RDM and the community needs. Methods: An online survey was conducted with a mixed question-type design. We created a questionnaire tailored to relevant topics of the bioimaging community, including specific questions on bioimaging methods and bioimage analysis, as well as more general questions on RDM principles and tools. 203 survey entries were included in the analysis covering the perspectives from various life and biomedical science disciplines and from participants at different career levels. Results: The results highlight the importance and value of bioimaging RDM and data sharing. However, the practical implementation of FAIR practices is impeded by technical hurdles, lack of knowledge, and insecurity about the legal aspects of data sharing. The survey participants request metadata guidelines and annotation tools and endorse the usage of image data management platforms. At present, OMERO (Open Microscopy Environment Remote Objects) is the best known and most widely used platform. Most respondents rely on image processing and analysis, which they regard as the most time-consuming step of the bioimage data workflow. While knowledge about and implementation of electronic lab notebooks and data management plans is limited, respondents acknowledge their potential value for data handling and publication. Conclusion: The bioimaging community acknowledges and endorses the value of RDM and data sharing. Still, there is a need for information, guidance, and standardization to foster the adoption of FAIR data handling. This survey may help inspiring targeted measures to close this gap.

Easing batch image processing from OMERO: a new toolbox for ImageJ.

The Open Microscopy Environment Remote Objects (OMERO) is an open-source image manager used by many biologists to store, organize, view, and share microscopy images, while the open-source software ImageJ/Fiji is a very popular program used to analyse them. However, there is a lack of an easy-to-use generic tool to run a workflow on a batch of images without having to download them to local computers, and to automatically organize the results in OMERO. To offer this functionality, we have built (i) a library in Java: "Simple OMERO Client", to communicate with an OMERO database from Java software, (ii) an ImageJ/Fiji plugin to run a macro-program on a batch of images from OMERO and (iii) a new set of Macro Functions, "OMERO Macro extensions", dedicated to interact with OMERO in macro-programming. The latter is intended for developers, with additional possibilities using tag criteria, while the "Batch OMERO plugin" is more geared towards non-IT scientists and has a very easy to use interface. Each tool is illustrated with a use case.

Solar–Wind System for the Remote Objects of Railway Transport Infrastructure

The article deals with adding the power of a local object to a solar–wind system when consuming electricity from the grid within the power limit. The parameter’s calculation technique for the different values of degree of power increase was considered. The load schedule, the electricity consumption, use of installed power, boundary conditions of generation, and ensuring energy balance were taken into account. Furthermore, data from the renewable source’s generation archive for the location of the object were used. The control of the power consumed by the object was carried out on the taken values of added and total load power with binding to photovoltaic generation. The added power reference on some time intervals was carried out according to the actual renewable generation power value. This increases the degree of use of the battery capacity and energy from renewable sources. The reference of the added power with the state of battery charge formation was carried out according to the forecast. One cycle of deep battery discharge at the evening peak was used to extend the battery life. For the accepted conditions with the average monthly values of renewable energy sources generation with an increase in power by 1.6 times, there was a decrease in electricity consumption by 1.57–4 times.

MS-YOLO: Object Detection Based on YOLOv5 Optimized Fusion Millimeter-Wave Radar and Machine Vision

Millimeter-wave radar and machine vision are both important means for intelligent vehicles to perceive the surrounding environment. Aiming at the problem of multi-sensor fusion, this paper proposes the object detection method of millimeter-wave radar and vision fusion. Radar and camera complement each other, and radar data fusion in machine vision network can effectively reduce the rate of missed detection under insufficient light conditions, and improve the accuracy of remote small object detection. The radar information is processed by mapping transformation neural network to obtain the mask map, so that radar information and visual information in the same scale. A multi-data source deep learning object detection network (MS-YOLO) based on millimeter-wave radar and vision fusion was proposed. Homemade datasets were used for training and testing. This maximized the use of sensor information and improved the detection accuracy under the premise of ensuring the detection speed. Compared with the original YOLOv5 (the fifth version of the You Only Look Once) network, the results show that the MS-YOLO network meets the accuracy requirements better. Among the models, the large model of MS-YOLO has the highest accuracy with an mAP reaching 0.888. The small model of MS-YOLO has good accuracy and speed, and the mAP reaches 0.841 while maintaining a high frame rate of 65 fps.

YOLO-DSD: A YOLO-Based Detector Optimized for Better Balance between Accuracy, Deployability and Inference Time in Optical Remote Sensing Object Detection

Many deep learning (DL)-based detectors have been developed for optical remote sensing object detection in recent years. However, most of the recent detectors are developed toward the pursuit of a higher accuracy, but little toward a balance between accuracy, deployability and inference time, which hinders the practical application for these detectors, especially in embedded devices. In order to achieve a higher detection accuracy and reduce the computational consumption and inference time simultaneously, a novel convolutional network named YOLO-DSD was developed based on YOLOv4. Firstly, a new feature extraction module, a dense residual (DenseRes) block, was proposed in a backbone network by utilizing a series-connected residual structure with the same topology for improving feature extraction while reducing the computational consumption and inference time. Secondly, convolution layer–batch normalization layer–leaky ReLu (CBL) ×5 modules in the neck, named S-CBL×5, were improved with a short-cut connection in order to mitigate feature loss. Finally, a low-cost novel attention mechanism called a dual channel attention (DCA) block was introduced to each S-CBL×5 for a better representation of features. The experimental results in the DIOR dataset indicate that YOLO-DSD outperforms YOLOv4 by increasing mAP0.5 from 71.3% to 73.0%, with a 23.9% and 29.7% reduction in Params and Flops, respectively, but a 50.2% improvement in FPS. In the RSOD dataset, the mAP0.5 of YOLO-DSD is increased from 90.0~94.0% to 92.6~95.5% under different input sizes. Compared with the SOTA detectors, YOLO-DSD achieves a better balance between the accuracy, deployability and inference time.

Use of Hybrid Photovoltaic Systems with a Storage Battery for the Remote Objects of Railway Transport Infrastructure

The use of a grid-tied photovoltaic system with a storage battery to increase the power of objects of railway transport infrastructure above the limit on consumption from the grid with the possibility of energy saving is considered. The methods of analysis of energy processes in photovoltaic systems with a storage battery are used. They are added via the processing of archival data of power generation of a photovoltaic battery and computer modeling results. A technique of system parameter calculation to increase the power according to the given load schedule of the object at constant and maximum possible degree of power increasing is developed. The values of the average monthly generation of a photovoltaic battery at the location point of the object based on archival data are used. The principle of the control of power, consumed from the grid, according to the given values of the added and total load is developed. Using the basic schedule of added load power in connection with the graph of photovoltaic battery generation allows reducing the installed power of the storage battery. The additional reduction in the installed power of the photovoltaic and storage batteries is possible at the corresponding choice of the degree of power load increasing. The joint formation of current schedules with reference to the added power value and state of charge of the battery according to the short-term forecast of the generation of a photovoltaic battery is proposed. The value of added power at certain intervals of time is set according to the graph of actual generation of the photovoltaic battery, which contributes to the maximum use of its energy. With the average monthly generation of a photovoltaic battery in the spring–autumn period, the discharge of the battery during the hours of the morning load peak is not used. This reduces the number of deep discharge cycles and extends the battery life. The description of energy processes in steady-state conditions for the daily cycle of system functioning is formalized. On this basis, a mathematical model is developed in MATLAB with an estimation of the costs of electricity consumed from the grid. When modeling, archival data are used for days when the generation of a photovoltaic battery over time intervals is close to average monthly values. This makes it possible to evaluate the effectiveness of system management under conditions close to real during the year.