Analytical Representation Research Articles

HIERARCHICAL MODEL FOR BUILDING COMPOSITE WEB SERVICES

The current evolution of disseminated computer program frameworks is characterized by a growing adherence to the principles of service-oriented engineering (SOA). Simultaneously, these frameworks are becoming more intricate, with an increasing number of components and more complex data connections between them. This situation underscores the importance of employing mechanisms to unify artifacts in the process of developing composite web services, which govern, among other aspects, the architectural plane of the frameworks under construction. A model for constructing composite web services is suggested as a suitable tool, implemented in accordance with a hierarchical approach, intended for use in designing distributed systems. Model is constructed over an assumption that coordination of the components of a composite web service is carried out in a centralized manner. in accordance with the orchestration model. To implement formalization and obtain, based on analytical representations, the corresponding software implementations, it has been decided to use the DEVS mathematical apparatus. The aspect of software implementation is considered pivotal in determining the feasibility of automating the acquisition of composite web services that operate within the orchestration model. Obtained research results has been interpreted as a conrmation of the eectiveness of this approach on the basis of the scenario of querying the database. Resulting artifacts have been represented with UML notation. The relationship between analytical representations and corresponding software implementations has also been demonstrated. Usage of the DEVS Suite tools has made it possible to visualize the process of simulation - to obtain estimated values of the indexes of the resulting solutions

Pair-distribution function of active Brownian spheres in three spatial dimensions: simulation results and analytical representation

This work provides an analysis of the fully orientation-resolved pair-distribution function of active Brownian spheres in three spatial dimensions based on Brownian dynamics simulations, along with an analytical approximation.

Properties of the entropic risk measure EVaR in relation to selected distributions

Entropic Value-at-Risk (EVaR) measure is a convenient coherent risk measure. Due to certain difficulties in finding its analytical representation, it was previously calculated explicitly only for the normal distribution. We succeeded to overcome these difficulties and to calculate Entropic Value-at-Risk (EVaR) measure for Poisson, compound Poisson, Gamma, Laplace, exponential, chi-squared, inverse Gaussian distribution and normal inverse Gaussian distribution with the help of Lambert function that is a special function, generally speaking, with two branches.

ФОРМИРОВАНИЕ БИЗНЕС-МОДЕЛИ РЫНКА ЛИТИЯ

The purpose of the study is to formulate an analytical representation of the emerging Russian lithium market in the structure of business model templates, allowing for a description of key market elements in the context of the industry under consideration. The sources of the study are data on the state of the global and Russian lithium market, presented in open information and scientific resources. Research procedures were based on the use of systems methodology, comparative analysis methods and forecasting methods. The choice of a template for describing a market business model was determined based on a generalization of existing industry practice. The main result of the study is a compiled representation of the business model in the emerging lithium market within the framework of the Osterwalder-Pigneur “value” approach. The practical focus of this description is considered in terms of the formation of a unified technology for running a lithium business as the basis for the created business model of its ecosystem.

An Efficient Method for Calculating Hysteretic Dry Friction Response of Dynamic Systems Subjected to Combined Harmonic and Random Excitation.

Many examples of dynamic analysis require modelling of dry friction. Often this is represented by a so-called Jenkins element or multiple Jenkins elements in parallel, which is sometimes termed a parallel-series Iwan element. This study considers the case where a system that includes these representations of dry friction are loaded dynamically with a combination of deterministic harmonic and random excitation. This paper presents a new efficient method for predicting the response of systems subject to combined deterministic and random excitation. The method is based on equivalent linearisation and involves averaging across both an ensemble of random responses as well as over a harmonic excitation period. The key novelty in the approach is the use of an auxiliary harmonic term to facilitate an analytical representation of the nonlinear force. This overcomes the challenge of analysing a discontinuous hysteretic nonlinearity in the presence of random excitation. Analytical solutions are presented and it is shown that the proposed approach can predict the approximate response at a significantly reduced computational cost.

Orbital precession in the restricted three-body problem: Exact representations

Analytical representations for the rate of apsidal precession in the planar elliptical restricted three-body problem are considered in the case when the orbit of the disturbing body is external to the orbit of the test particle. Analytical expressions are compared with numerical data obtained during numerous calculations of the precession rate. An analytical expression is obtained for the apsidal precession velocity in the form of a power series with a parameter equal to the ratio of the semi-major axes of the orbits of the test particle and the disturbing planet. It is shown that the analytical expressions for the velocity of the apsidal precession of the particle are reliable only at distances not close to the instability zone near the orbit of the disturbing planet. Near the Wisdom gap, the linear secular theory stops working. A correction empirical formula is proposed for calculating the apsidal precession rate at relatively high (less than 0.5) eccentricities of the particle and the disturbing planet. The proposed formulas are applied to the description of the precession of orbits in real exoplanetary systems.

Signal modeling of means of tacit information acquisition using spline functions

The article deals with the problem of recognizing signals from systems of unauthorized covert acquisition of confidential information. The general problem of detecting signals from the means of covert information acquisition (CIL) consists in the direct formation of a technique that would allow submitting the detected signal from CIL using the legal data transmission range in an analytical form convenient for further analysis and direct detection of a malicious signal. An analysis of the meaning, signs and properties of the means of covertly obtaining information was carried out, and their unmasking signs were presented. An overview of the methods used to record the detected signals from the means of covert information acquisition in an analytical form convenient for further analysis is carried out. Methods of analytical representation of the detected signal in the form of a composition of continuous functions and in the form of a spline function of two variables were analyzed. In order to increase the effectiveness of signal recognition of means of covert information obtaining, a method of constructing a ZNOI signal in the form of a two-dimensional spline function or a tensor product of two one-dimensional spline spaces is proposed. This method makes it possible to improve the efficiency of recognition of ZNOI signals and its automation. It is shown that an important condition for the recognition of a probable signal of a digital ZNOI is finding the maximum energy of the spectrum, which in turn makes it possible to apply the criteria of mathematical analysis of reaching the extrema of the function. The use of such a mathematical apparatus makes it possible, using the existing technical and software complexes, to automate the process of recognition of ZNOI signals.

Modeling of Rapidly Changing Macroeconomic Processes Based on the Analysis of Jump and Generalized Functions

In recent years, the economies of many countries around the world have been in a situation of intense, rapidly changing, abrupt processes. The current situation urgently requires a change in the economic paradigm in the near future, which leads to the need to develop new conceptual models. The purpose of the article is to develop basic theoretical principles and practical approaches to modeling macroeconomic processes based on the analysis of jump and generalized functions. The objectives of the study are the following: (1) describe the main types of impulse and jump functions using examples from economic theory and practice; (2) perform an analytical representation of impulse and jump functions; (3) select macroeconomic characteristics to analyze rapidly changing processes in the economy; and (4) create models and mechanisms for forecasting impulsive and abrupt changes in the macroeconomy. The approaches to the development of macroeconomic theory and its methods proposed in the article are not associated with the use of evolutionary continuous functions; for example, power functions, which is typical for many canonical macroeconomic models. These approaches do not include management decisions to achieve optimal values of given target functions, which is typical for recursive macroeconomic models of dynamic programming. This article is about formulating the main provisions of macroeconomic theory and its methods, which, with varying degrees of accuracy, could give a forecast about the upcoming possibility of sudden changes (impulse, shock, spasmodic, and others) in the macroeconomic situation. The research methodology is statistical analysis, special methods developed by the author for studying impulse, and jump processes. As a result of this study, the basic principles of modeling macroeconomic theory based on rapid impulse and abrupt changes were formulated, approaches to constructing the tools of this theory were outlined, and problems and tasks for further research were identified.

The thermodynamic properties of diatomic gases. A rigorous analytical approach

The paper reports a closed-form analytical representation of the thermodynamic functions of diatomic molecules in the ground electronic state. For this purpose, analytical formulas for vibrational and rotational partition functions are derived. A rigorous method is proposed for factorizing the vibrational and rotational contributions to the ro-vibrational partition function using an average vibrational quantum number. The behavior of thermodynamic functions as a function of temperature is discussed for carbon monoxide as a test system. The reliability of the analytical method is verified by comparison with experimental data and with the direct summation method, which uses theoretical values of energy levels.

SL-RI: Integration of supervised learning in robots for industry 5.0 automated application monitoring

Robotic technology holds a significant role within the realm of smart industries, wherein all functionalities are executed within real-time systems. The verification of robot operations is a crucial aspect in the context of Industry 5.0. To address this requirement, a distinctive design methodology known as SL-RI is proposed. This article aims to establish the significance of incorporating robots in the Industry 5.0 framework through analytical representations. In the context of this industrial monitoring system, the implementation of a supplementary algorithm is essential for effective management, as it enables the robots to acquire knowledge through the analysis and adaptation of restructured commands. The analytical model of robots is designed to accurately monitor the precise position and accelerations of robots, resulting in full-scale representations with minimal error conditions. The uniqueness of the proposed method in robotic monitoring system is related to the application process that is directly applied in Industry 5.0 by using various parametric cases where active movement of robots are monitored with rotational matrix representations. In this type of representations the significance relies in the way to understand the full movement of robots across various machines and its data handling characteristics that provides low loss and error factors.

Software for processing of long-term strength data of materials by use of edwards curves

A description of the developed software for saving and analyzing data on high-temperature deformation and long-term strength of metallic materials is provided. The open source Laravel web framework was chosen to implement in the application. The Voyager solution is used together with it as a graphical interface for interacting with the database. A JavaScript programming language solution using Canvas technology is used to build plots. Basic classes and components are described. With the help of diagrams of use cases, the possibility of using the web application in the engineering practice of data processing of experimental high-temperature creep and fracture studies is shown. An approach and an algorithm for approximating long-term strength curves of general appearance, including different types of failure, using Edwards curves are proposed. With their use, an analytical nonlinear expression for the functional dependence between the time to failure and the failure stress was obtained. Approximations of various types of the long-term strength curve corresponding to the processes of accumulation of damage in the material by various types of physical mechanisms are discussed. The undesirable possibility of obtaining an overestimated value of the time to failure in the case of small and medium stress values without using information on the areas of intergranular failure, failure due to oxidation or corrosion, and overaging on the long-term strength curve is demonstrated. The use of the developed software, approach and method of analytical representation of the functional dependence of the values of failure stress on time in the evolution equation for the damage parameter allows you to carry out refined calculations of structural elements operating under high-temperature load conditions

Orientation Quaternion Norm Correction in SINS Algorithms: Calculation Normalization Schemes and Their Efficiency

The problem of correcting the norm of the computed orientation quaternion in the algorithms for the operation of strapdown inertial navigation systems is considered. Two existing approaches to the correction process are considered, the first approach is to normalize the rotation quaternion at the computation cycle, the second approach is to normalize the resulting quaternion. 5 well-known calculation schemes for norm correction are given. To simulate the test motion, we used an analytical quaternion kinematic rotation model based on a sequence of three rotations corresponding to the Krylov angles. The case of linear dependence of elementary rotation angles on time is considered. The model provides analytical representation of the projections of the angular velocity vector of the rigid body on the associated axes and the corresponding quasi-coordinates on the calculation cycle. The results of numerical simulation of the reference motion for a given set of frequencies are presented as dependences of the projections of the angular velocity vector of the rigid body on time and the constructed trajectories in the configuration space of the orientation parameters.
 To determine the rotation quaternion on a cycle, the Miller algorithm was used, which makes it possible to obtain an increase in the orientation vector based on ideal information from the angular velocity sensors in the form of quasi-coordinates. The transformation into a rotation quaternion occurs with the help of the corresponding expansions of the trigonometric functions of the true rotation angle (modulus of the orientation vector) in a series.
 Based on a numerical experiment, it is shown that the best result of correcting the norm of the calculated quaternion in the sense of the minimum error of the norm is given by one of the finite normalization schemes, for which there is no division operation and ensures the stability of the norm correction in time. The results of numerical simulation of the model rotational motion of a rigid body and the development of schemes for correcting the norm of the calculated orientation quaternion are presented.
 Keywords: orientation quaternion, Miller's orientation algorithm, SINS, norm error, computational drift, analytical reference model, quasi-coordinates, numerical simulation.

Non-contact sensing for anomaly detection in wind turbine blades: A focus-SVDD with complex-valued auto-encoder approach

The occurrence of manufacturing defects in wind turbine blade (WTB) production can result in significant increases in operation and maintenance costs of WTBs, reduce capacity factors of wind farms, and occasionally lead to severe and disastrous consequences. Therefore, inspection during the manufacturing process is crucial to ensure consistent fabrication of composite materials. Non-contact sensing techniques, such as Frequency Modulated Continuous Wave (FMCW) radar, are becoming increasingly popular as they offer a full view – cross sectional analysis – of these complex structures during assembly and curing. In this paper, we enhance the quality assurance of WTB manufacturing utilising FMCW radar as a non-destructive sensing modality. Additionally, a novel anomaly detection pipeline is developed that offers the following advantages: (1) We use the analytic representation of the Intermediate Frequency signal of the FMCW radar as a feature to disentangle material-specific and round-trip delay information from the received wave. (2) We propose a novel anomaly detection methodology called focus Support Vector Data Description (focus-SVDD). This methodology involves defining the limit boundaries of the dataset after removing healthy data features, thereby focusing on the attributes of anomalies. (3) The proposed method employs a complex-valued autoencoder to remove healthy features and we introduces a new activation function called Exponential Amplitude Decay (EAD). EAD takes advantage of the Rayleigh distribution, which characterises an instantaneous amplitude signal. The effectiveness of the proposed method is demonstrated through its application to collected data, where it shows superior performance compared to other state-of-the-art unsupervised anomaly detection methods. This method is expected to make a significant contribution not only to structural health monitoring but also to the field of deep complex-valued data processing and SVDD application. The code and dataset will be made publicly available. The code and dataset are available here 11https://github.com/FrusqueGaetan/Focus_SVDD_EAD.

Experimental admittance-based system identification for equivalent circuit modeling of piezoelectric energy harvesters on a plate

Equivalent circuit modeling is a useful tool for piezoelectric energy harvesters to analyze the electromechanical response of the system especially when complex host structure geometries and nonlinear circuits are used in the harvesting systems. Previous studies have used analytical and finite element models to estimate the equivalent circuit model (ECM) of piezoelectric energy harvesters (PEH) on beam- and plate-like structures. However, those methods require accurate analytical and/or numerical representation of the PEH. Here, we present an experimental admittance-based system identification method that allows us to identify the multi-modal ECM without prior knowledge of the host plate's geometry and/or physical properties of the piezoelectric patches. Using the proposed experimental method, we obtain the electromechanical frequency–response admittance of the PEH system at each vibration mode, and thereby, we calculate the equivalent system parameters. Additionally, a novel experimental technique is presented for the identification of the equivalent voltage sources associated with each LCR branch of the ECM. The derived ECM is experimentally validated for single and multiple piezoelectric patch harvesters on a plate. The electrical frequency response of the system has been validated for standard AC and rectifier circuits using SPICE software. Overall, the proposed admittance-based system identification is an accurate and robust method to identify the equivalent system parameters, making it a practical and reliable tool for modeling piezoelectric energy harvesting systems.

ASSESSMENT OF MATERIAL DEFORMATION RESISTANCE IN BLANKS DURING DIRECT EXTRUSION USING THE DIE FORMING METHOD

In this scientific article, two deformation models for analyzing the accumulation of material damage during upsetting and direct extrusion using the die forming method are investigated. Both models include an analytical representation of the deformation trajectory, approximation of the boundary deformation curve, and a damage accumulation model. A three-parameter representation of the boundary deformation curve is applied, utilizing a power-law model and a linear damage accumulation model. The process of direct extrusion is examined by constructing parametric equations for the deformation trajectory. The functional dependence for the stress state indicator involves three constants, while a non-elementary function with a single constant is used for the accumulated deformation, determined using the theory of limit functions. Considering the complexity of trajectories, the use of a power-law accumulation model with a fixed nonlinearity indicator value is justified. The methodology for determining this indicator confirms its positive values less than one for the investigated trajectories, affirming its applicability. Numerical experiments demonstrate an increasing dependence of the limiting deformation with the increase of this indicator, indicating the effectiveness of the model.

INVESTIGATION OF STAMPING BY WRAPPING PROCESSES THROUGH MATERIAL DEFORMATION MODELING ANALYSIS

This scientific article addresses the pressing issue of material deformation modeling in the context of stamping by wrapping processes (SWP). The main challenges in the development of these processes include the likelihood of workpiece failure due to insufficient material plasticity and unfavorable stress-strain states, determined by technological process parameters. Thus, effective SWP process development requires the utilization of material deformation modeling. The article indicates that any material deformation model in plastic deformation processes comprises three main elements: Analytical representation of the curve or surface of boundary plastic deformations during stationary deformation: This element describes how the material's plastic deformation changes during stationary deformation with alterations in the invariant stress state indicators. Mathematical model of the deformation path in coordinates of stress state indicators - accumulated plastic deformation. This model determines the path along which material deformation develops with changing stress state indicators and is dependent on accumulated plastic deformation. Damage accumulation model: This element takes into account accumulated damage in the material and can be used to predict workpiece failure. Specifically, the article analyzes the surface of boundary plastic deformations during stationary cold deformation and employs terminology to describe the dependence of accumulated plastic deformation until failure on invariant stress state indicators. The term "stationary deformation" is used to denote material deformation under unchanged values of these indicators.

System of Partial Differential Equations and Analytical Representations of the Weierstrass Sigma Function

System of Partial Differential Equations and Analytical Representations of the Weierstrass Sigma Function

Analytical Representations of Far Fields of Internal Gravity Waves from Local and Nonlocal Perturbation Sources

Analytical Representations of Far Fields of Internal Gravity Waves from Local and Nonlocal Perturbation Sources

PUDT: Plummeting uncertainties in digital twins for aerospace applications using deep learning algorithms

Identifying objects in aircraft monitoring systems poses significant challenges due to the presence of extreme loading conditions. Despite the presence of several sensor units, the transmission of precise data to multiple data units is hindered by an increase in time intervals. Therefore, the suggested methodology is specifically developed for the purpose of generating digital replicas for aeronautical applications, wherein an aero transfer function is correlated with the digital twins. Mapping functions are utilized in the monitoring of diverse parameters that are associated with the identification of objects inside data transmission networks, with the aim of minimizing uncertainty. The suggested system model is enhanced by incorporating analytical representations and deep learning methods, resulting in the provision of zero point twin functionalities. The present study investigates the aforementioned integrated procedure through the analysis of four different situations. In these settings, an aero communication tool box is employed to transform the device configuration into simulation outputs. The results obtained from the comparison of these scenarios reveal that the projected model significantly enhances the maintenance period while minimizing data errors.

Quantitative interpretations of potential fields: from parametric to geostructural recalculations

The relevance. Need to development of an applied algorithm for combined interpretation of heterogeneous geophysical data based on unified physical analogy, focused on solving the inverse problem of potential theory. The wave approximation of the cross-section of mining massif fits into the paradigm of dissipative structuring of nonequilibrium media acts as a special case of the above analogy. The task of the study is to adapt this algorithm to recalculations of both potential and non-potential geofields. In the list of nonpotential geofields the remote sensing data and digital terrain model are the most interesting as the data with non-regulated access. Practical significance of the research is associated with the approbation of a family of algorithms in production projects of both geological and engineering nature. The aim. To minimize the family of equivalent solutions to the inverse problem by mutual verification of heterogeneous models of the anomaly-forming source. The objects. Development of the geofields combined interpretation algorithm and recalculation of geofields in depth for tracing elements of stratification and geological fractures. The methods. Formed by software and algorithmic development, which is based on deterministic analytical representations: computation of Cauchy integral, iterative application of direct solution, spectrum estimation. The results. Reduced to the set of parametric cross-sections derived with recalculations with minimum a priori geological information with final geological consideration. The combination of visualizations of analytical continuation, singular points and results of automated fitting admits the reconstruction of geostructural model of parametric cross-section with significant reliability. Extension of standard methods of quantitative interpretation by means of wave approximations includes quasi-seismic halftone visualizations verifying the mentioned reconstructions.