Equivalent Transformation Research Articles

A new convex model for linear hyperspectral unmixing

Over the past two decades, Minimum Simplex Volume-based (MV) methods for linear hyperspectral unmixing have attracted considerable academic attention due to their robustness in the absence of pure pixels. Within this framework, certain prevalent MV models incorporate a Log-Absolute-Determinant Function (LADF) that operates on a matrix variable Q. In practical applications, the LADF inherently exhibits non-convex characteristics, thus limiting its applicability in real-world scenarios. To address this challenge, this paper employs Tikhonov regularization, combined with a series of equivalent transformations, to construct a positively definite matrix, thereby rendering the corresponding LADF convex. Theoretical foundations linking the newly convexified LADF and the original non-convex function are rigorously established. Experimental validation, conducted on standard hyperspectral benchmark datasets, confirms its efficiency and necessity. Notably, this paper introduces a unified strategy for ensuring convexity in MV models for linear hyperspectral unmixing.

Optimizing DNNs With Partially Equivalent Transformations and Automated Corrections

Optimizing DNNs With Partially Equivalent Transformations and Automated Corrections

Dynamic User-Scheduling and Power Allocation for SWIPT Aided Federated Learning: A Deep Learning Approach

Federated learning (FL) has been considered as a promising paradigm for enabling distributed machine learning (ML) in wireless networks. To address the limited energy capacity of wireless devices, we propose a simultaneous wireless information and power transfer (SWIPT) aided FL, in which one FL server (FLS) co-located at a cellular base station (BS) uses SWIPT to simultaneously broadcast the global model to wireless user-devices (UDs) and provide wireless power transfer to them. The UDs then use the harvested energy to train their local models and further transmit the local models to the FLS for aggregation. To improve the spectrum efficiency, we consider that the UDs form a non-orthogonal multiple access (NOMA) group for simultaneously sending their local models over the same spectrum channel. Taking the UDs' time-varying available energy and channel conditions into account, we propose a dynamic optimization of the UDs-scheduling, the BS's transmit-power allocation, and the UDs' power-splitting factors for SWIPT, with the objective of minimizing the long-term energy consumption while ensuring the FL convergence. The optimization problem, however, is challenging to solve since it is a finite-horizon dynamic programming problem but with an unknown stopping time, and moreover, the action space covers both discrete and continuous variables. To address these difficulties, we first execute a series of equivalent transformations to reduce the number of decision variables and then formulate the problem as a stochastic shortest path problem, based on which we propose an actor-critic deep reinforcement learning algorithm with the proximal policy optimization to efficiently learn the policy that dynamically adjusts the UDs-scheduling for FL as well as the BS's transmit-power for SWIPT. Numerical results validate the effectiveness and performance of our proposed algorithm. The results demonstrate that our proposed algorithm can effectively reduce the long-term energy consumption in comparison with two baseline algorithms.

Mathematical and computer modeling of atmospheric air pollutants transformation with input data refinement

<p>This article addresses the critical issue of harmful impurity dispersion in industrial facility atmospheres, considering point sources and factoring in photochemical changes. Conjugate equations are employed to assimilate pollutant data into the transfer equations' right side. Boundary conditions derive from global models like weather research and forecasting (WRF) and system for integrated modeling of atmospheric composition (SILAM), customized for the unique characteristics of an industrial city's pollutants. To encompass anthropogenic heat sources and surface heterogeneity, the model incorporates differential schemes for the atmospheric boundary layer, transport equations, and impurity transformation equations. Parameters for photochemical transformations, varying with weather and time of day, are derived from Ust-Kamenogorsk. A cloud-based geoinformation system (GIS) is developed for monitoring and forecasting air pollution. It assimilates data sources and accounts for photochemical transformations, enabling visualization of diverse weather and environmental scenarios. The article presents numerical modeling results of impurity spread and transformation influenced by mesometeorological processes, topography, and water resources within a specific city.</p>

Asymptotic stability of a nonlinear energy harvester with mass disturbance undergoing Markovian jump

Stochastic mass has exerted a profound impact on the dynamics of the systems characterized by light mass and compact volume. This work delves into the asymptotic stability with probability one of a variable mass energy harvester. Firstly, the Gaussian white noise with Markovian jump is coupled to model the inherent randomness and discreteness of stochastic mass. Then, we have established an approximate dimensionless system based on an equivalent transformation. Using the stochastic averaging method, the averaged Itô stochastic differential equation of the amplitude within the approximated system is derived. With the linearization, we have deduced the largest Lyapunov exponent for the linearized equation. Furthermore, the necessary and sufficient condition for achieving asymptotic stability of the nonlinear energy harvester is proposed approximately by managing the largest Lyapunov exponent be negative. The study systematically dissects the effects of stochastic mass and Markovian jump on the asymptotic stability with probability one of a nonlinear energy harvester. Under the disturbance of stochastic mass, with the increase of linear stiffness, the stability of the system will change nonlinearly. Moreover, the stability regions of the nonlinear energy harvester under varying transition matrices and stochastic mass noise intensities are thoroughly given. The findings and conclusions presented in this paper have a certain theoretical significance for the management of the system stability in engineering practical.

Model and solution of sustainable bi-level emergency commodity allocation based on type-2 fuzzy theory

The allocation of emergency commodities is very important for efficient emergency response after a disaster. In this study, a sustainable multi-objective bi-level emergency commodity allocation model is established, providing a practical emergency commodity allocation strategy for humanitarian supply chains. First, type-2 fuzzy variables are used to describe uncertain transportation costs and handle them based on the conditional value-at-risk (CVaR) theory of type-2 fuzzy variables. Second, Karush-Kuhn–Tucker (KKT) conditions with complementary constraints are used, auxiliary variables are introduced, and global criteria are applied to achieve the equivalent transformation of the model. Finally, with the Wenchuan earthquake in China in 2008 as an example, we prove the necessity of introducing the CVaR for risk measurement and the practicability of using type-2 fuzzy variables to describe uncertain parameters by comparing this scenario with a risk-neutral situation and the proposed model with a model based on type-1 fuzzy theory. The novelties of this study include considering both the government and suppliers are decision-makers, exploiting CVaR to measure tail risk and using type-2 fuzzy theory to transform uncertain parameters. The contributions of this study include considering sustainability during the rescue process and proposing a CVaR formula based on type-2 theory.

A multiattribute financial time series forecast model based on double hierarchy fuzzy linguistic term set

Based on the double hierarchy linguistic term sets (DHLTS), a novel forecasting model is proposed considering both the internal fluctuation rules and the external correlation of different time series. The innovative aspects of this model consist of: (i) It can expresses more internal fluctuation and external correlation information, providing guarantees for improving the predictive performance of the model. (ii) The equivalent transformation function of DHLTS reduces the fuzzy granularity and improves the prediction accuracy. (iii) The application of similarity measures can extract the closest rules from historical states based on the distance operators of DHLTS. In addition, experiments on TAIEX considering the impact of the U.S. stock market and other data show that the model has good predictive performance.

Asynchronous Dissipative Control of Discrete-Time Fuzzy Markov Jump Systems With Dynamic State and Input Quantization

A numerically tractable two-step approach based on backtrack and optimization searches is proposed for asynchronous quantized dissipative control of discrete-time fuzzy Markov jump systems (DFMJSs) under the networked control framework. The asynchrony of modes between the plant and controller is described by a hidden Markov model. Both dynamic state and input quantization are considered. The dynamic zooming factors of the quantizers are designed as piecewise functions with respect to their arguments to avoid division by zero. A fuzzy asynchronous quantized controller is devised to make sure that the closed-loop system is stochastically stable and strictly <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(\mathcal {Q},\mathcal {S},\mathcal {R})$</tex-math></inline-formula> - dissipative via using a quadratic Lyapunov function and equivalent matrix transformations. Then, the iterative two-step approach is used to determine the optimal dissipativity level and the corresponding control gain and quantization parameters. Analysis and control synthesis for DFMJSs without quantization are also presented, covering some previous results as special cases. Finally, a single-link robot arm system and another numerical example are utilized to validate the present asynchronous dissipative control approaches for the quantization and non-quantization cases, respectively.

Deep Reinforcement Learning Based Resource Allocation and Trajectory Planning in Integrated Sensing and Communications UAV Network

In this paper, multi-UAVs serve as mobile aerial ISAC platforms to sense and communicate with on-ground target users. To optimize the communication and sensing performance, we formulate a joint user association, UAV trajectory planning and power allocation problem to maximize the minimum weighted spectral efficiency among UAVs. This paper exploits the centralized and the decentralized deep reinforcement learning (DRL) solutions to solve the sequential decision-making problem. On one hand, we first introduce the centralized soft actor-critic (SAC) algorithm. Then, we explore the equivalent transformation of the optimization objective based on symmetric group, propose the random and the adaptive data augmentation schemes to design the replay memory buffer of SAC, and accordingly propose SAC algorithms assisted by data augmentation to tackle the transformed problem. On the other hand, the multi-agent soft actor-critic (MASAC), a decentralized solution, is also introduced to solve this sequential decision-making problem. The experiment results reveal the effectiveness of the centralized and the decentralized solutions in considered scenarios. Specifically, the SAC assisted by the adaptive scheme significantly outperforms other centralized solutions in the training speed and the weighted spectral efficiency. Meanwhile, the decentralized MASAC algorithm behaves best in the early training speed.

Stress‐hybrid virtual element method on quadrilateral meshes for compressible and nearly‐incompressible linear elasticity

AbstractIn this article, we propose a robust low‐order stabilization‐free virtual element method on quadrilateral meshes for linear elasticity that is based on the stress‐hybrid principle. We refer to this approach as the stress‐hybrid virtual element method (SH‐VEM). In this method, the Hellinger–Reissner variational principle is adopted, wherein both the equilibrium equations and the strain‐displacement relations are variationally enforced. We consider small‐strain deformations of linear elastic solids in the compressible and near‐incompressible regimes over quadrilateral (convex and nonconvex) meshes. Within an element, the displacement field is approximated as a linear combination of canonical shape functions that are virtual. The stress field, similar to the stress‐hybrid finite element method of Pian and Sumihara, is represented using a linear combination of symmetric tensor polynomials. A 5‐parameter expansion of the stress field is used in each element, with stress transformation equations applied on distorted quadrilaterals. In the variational statement of the strain‐displacement relations, the divergence theorem is invoked to express the stress coefficients in terms of the nodal displacements. This results in a formulation with solely the nodal displacements as unknowns. Numerical results are presented for several benchmark problems from linear elasticity. We show that SH‐VEM is free of volumetric and shear locking, and it converges optimally in the norm and energy seminorm of the displacement field, and in the norm of the hydrostatic stress.

Evaluation of the inertia distribution performance for multi-machine power system

Given large-scale modern power systems with inverter-based resources, the frequency stability faces great challenges in the characteristics of the decreasing inertia for the system and the uneven distribution of the inertia. Although several metrics for system inertia performance have been developed, a more generalized inertia evaluation method is still required. This paper proposed an inertia evaluation method for a multi-machine power system considering both the inertia and disturbance distribution. To reflect the dynamic of a more general system, an equivalent homogeneous transformation (EHT) is used in the system frequency response model with heterogeneous parameters. To reveal the inertia distribution under different disturbances scenario, a general inertia (GI) is proposed to evaluate the nodal frequency stability. Finally, the effectiveness of the proposed equivalent homogeneous system and the metric is validated using two test systems: a modified 4-machine 2-area power system and the 5-area 68-bus system. Numerical simulation study reveals that the proposed method can effectively reflect the inertia spatial distribution characteristics.

Optimization model for low-carbon supply chain considering multi-level backup strategy under hybrid uncertainty

When constructing a supply chain, the profit, environmental impact, and hybrid uncertainties the supply chain faces should be considered. This research investigates the problem of low-carbon supply chain design under hybrid uncertainty, where demand is regarded as a stochastic variable, supply and transportation disruptions are regarded as uncertain events, and the coefficient of emission reduction capacity of suppliers is regarded as an uncertain variable. Based on the probability theory and uncertainty theory, a mixed-integer optimization model is constructed to handle the disruption risk by utilizing a multi-level backup strategy and to reduce carbon emissions by investing in suppliers. This model guarantees that manufacturers’ demand is satisfied to a given confidence level, manufacturers prefer to construct a supply chain within the acceptable supply chain risk, the emission reduction investment scheme and the supply decision to manufacturers are determined to maximize the profit of the supply chain. To facilitate the solution, we perform deterministic equivalent transformation of stochastic and uncertainty constraints, linearize the nonlinear constraints, and analyze the mathematical properties of the model. Finally, the validity of the proposed model is verified by case studies. The results show that although the larger the supply levels, that is, the more priority levels of suppliers, the more beneficial it is to improve the reliability, too large supply levels will reduce profits. The reasonable setting of the supply levels can optimize the emission reduction investment scheme. In addition, the confidence level of carbon emission should be set within a certain range to avoid the disparity between profit growth and emission reduction. Finally, the greater the belief degree of disruption or the lower the emission reduction capacity of suppliers, the more significant the effect of a multi-level backup strategy.

Isomorphism Properties of Optimality and Equilibrium Solutions Under Equivalent Information Structure Transformations: Stochastic Dynamic Games and Teams

Isomorphism Properties of Optimality and Equilibrium Solutions Under Equivalent Information Structure Transformations: Stochastic Dynamic Games and Teams

Water-based nanofluid flow and heat transfer in thin film over an unsteady stretching sheet: An entropy analysis

The transfer of thermal energy is intrinsically associated with the generation of entropy. Here, we investigate the entropy generation number in nanofluid thin film flow over a radiated stretching sheet subject to different shapes of titanium oxide and copper nanoparticles in base fluid water. In addition, the impact of the magnetic field, viscous dissipation, and Joule heating were also considered. Using a suitable similarity transformation, the momentum and energy equations that describe the flow are converted into ordinary differential equations. These equations are then solved numerically using bvp4c in MATLAB. Graphs and explanations show how different physical parameters affect the velocity profile, temperature distribution, Nusselt number, skin friction coefficient, entropy generation number, and Bejan number. As the Brinkman number went up, fluid friction and Joule loss caused more entropy generation, but the Bejan number showed the opposite trend. In a certain situation, it is also important to note that as the value of the radiation parameter goes up, the irreversibility of heat transfer becomes more important. In addition, spherically shaped nanoparticles have the lowest entropy among all other forms. Hence, nanoparticles have the ability to reduce the amount of energy lost in any physical process and increase the overall productivity of systems. Understanding the flow and heat transmission within a thin film has many practical applications in industry, including aerodynamic lamination of plastic sheets, wire and fiber coating, food processing, annealing and thinning of copper wires, reactor fluidization, and many more.

Analytical equivalent transformation method for nonlinear stochastic dynamics with multiple noises in high dimensions

In many practical applications, stochastic problems are high dimensionality and multiple noises. The study focuses on developing an analytical approach for processing multi-noise systems in high dimensions, which overcomes the challenge solving stochastic dynamics problems. Applying an analytical equivalent transformation and introducing a new partial differentiation, the author demonstrate a convenient method for obtaining the Fokker–Planck equation corresponding to Langevin dynamics equations for high-dimensional and multi-noise systems. This methodology is applied to analyze the cubic laser model subjected to white noises and the saturation laser model subjected to bounded sine Wiener noise. The results verify the correction, efficiency, and superiority of the method of processing multiple noises in high dimensions. This approach provides a novel framework for solving other practical dynamics problems for high-dimensional and multi-noise systems.

Asynchronous distributed charging protocol for plug-in electric vehicles

The proliferation of plug-in electric vehicles (PEVs) advocates a distributed paradigm for coordinating PEV charging. Unlike existing primal-dual decomposition or consensus methods, this paper proposes a cutting-plane-based distributed algorithm considering a peer-to-peer (P2P) communication network, which enables asynchronous coordination among PEVs. First, an equivalent surrogate model is established by exploiting the duality of the original optimization problem, which masks the private information of individual users by equivalent transformation. Then, a cutting-plane based algorithm is derived to solve the surrogate problem in a distributed manner with intrinsic superiority to cope with various asynchrony. Critical implementation issues, including distributed initialization, distributed cutting-plane generation, and localized stopping criteria, are discussed in detail. Numerical tests on IEEE 37- and 123-node feeders with actual data illustrate that the proposed method is resilient to several asynchronies and admits the plug-and-play operation mode. The proposed methodology is expected to provide an alternative path toward the robust protocol for PEV charging.

Physics in deformable spacetime: Physical laws emerging from the surface minimality principle and the masses of particles

In this work, the study was focused on how deformable spacetime gives rise to physical laws, particularly quantum and special relativity. It was shown that both the Lorentz factor and quantum mechanics can emerge from the dynamical behavior of minimal surfaces in deformable spacetime, where the Möbius transformations prevail rather than the Lorentz transformations. The motion of deformable surfaces under minimality conditions creates a helicoidal pattern, a minimal surface with a metric designated by AdS (anti-de Sitter) space. Its isometry is a catenoid of which metric belongs to dS (de Sitter) space. When the two ends of the helicoid join it becomes a Möbius strip with multi-twists (i.e. windings), the so-called Möbius helicoid. It represents the most elementary mass with the attributes of charge and spin. It was shown that the number of windings increases with velocity according to the Lorentz factor. In other words, the Lorentz factor emerged from the transformation equations between the helicoid and catenoid, and both of them are isometric minimal surfaces. This fact serves as a means of transforming the metrics of the two isometric surfaces in AdS and dS spaces. There is an intimate relation between helicoidal motion, Möbius helicoid, and the Lorentz transformations. The zitterbewegung behavior of Dirac electron can be explained by the internal dynamics of the Möbius helicoid. Instead of using electromagnetic theory which led to the birth of special relativity, one can use the electrical circuit theory for deformable surface dynamics. A master equation was derived by using the resistive, capacitive, and inductive properties of deformable spacetime. The electromagnetic wave, Schrödinger, Klein–Gordon, Dirac, quantum telegrapher, and quantum torsion equations could be easily obtained from this master equation by making some simplifying assumptions for the parameters involved. The existing torsion due to helicoidal motion modifies the energy/mass equation (i.e.E=mc2) of special relativity. The Higgs potential can be obtained from the dynamic potential term of the master equation. Deformable space–time allows the emergence of a rich number of physical laws and relations. The masses of particles were calculated using the Möbius helicoid model for the very elementary structure of mass. The mass of a particle can be visualized as a three-dimensional network of helicoids with relatively higher stability. The stability is particularly associated with the phase changes of the catenoidal structure of the Möbius helicoid and the torsional vibrational modes of windings. Both the phase (or shape) change and/or the increase of the vibrational energies of windings produce a new configuration that represents a new particle. The masses of 187 particles were determined from this mechanism with an accuracy of ±3 MeV. It turned out that excitation energy states which could be expressed in terms of prime number multiples of a precursor mass play an important role in providing relatively higher stability.

Modal analysis for localization of harmonic oscillations in nonlinear pendulum arrays subjected to horizontal excitation

This study aims to clarify the reason for the occurrence of localization of harmonic oscillations when an array of N nonlinear pendulums connected by linear torsion springs is subjected to sinusoidal displacement excitation in the horizontal direction. Modal analysis is used to derive the modal equations of motion, which form an autoparametric system when identical pendulums are connected by identical torsion springs. Van der Pol’s method is applied to the modal equations of motion, and subsequently the expressions for the frequency response curves (FRCs) of the harmonic oscillations are obtained. By using the transformation equation from the modal coordinates to the physical coordinates, the FRCs in the physical coordinates are determined. The FRCs in the modal and physical coordinates for N = 2 and 3 and the backbone curves for N = 2 are shown. The numerical simulation results for N = 10 are also compared in the modal and physical coordinates. When multiple modes appear simultaneously, the summation of these modes provides localization in the physical coordinates. The vector diagram helps to visualize the mechanism of the localization. The effect of array imperfection on the FRCs is also briefly discussed. Furthermore, experimental data confirmed that when localization occurred in a two-pendulum array, the two modes appeared simultaneously.

DIAGNOSIS OF SYSTEMS UNDER CONDITIONS OF SMALL INITIAL DATA SAMPLING

Object of the study is to assess systems state in conditions of a small sample of initial data. Relevance of the problem is as follows. The functioning of a significant number of real objects takes place under conditions of poorly predicted changes in the values of environmental factors affecting system efficiency. The resulting heterogeneity of the results of objects experimental study and the environment of their functioning leads to reduction in sample size. At the same time, the standard requirements regarding the correspondence of the number of experiments and the number of coefficients of regression equation determining system state are not met. Purpose of the study is to develop methods for assessing systems state operating in a changing environment, in conditions of small sample of initial data. Tasks to be solved to achieve the goal: the first is the equivalent transformation of the set of observed initial data forming a passive experiment in aggregate into an active experiment, which corresponds to an orthogonal plan; the second is the construction of a truncated orthogonal representative sub-plan of the general orthogonal plan obtained as a result of solving the first problem. Research methods: statistical methods of experimental data processing, regression analysis, method for solving a triaxial boolean assignment problem. The results obtained: orthogonal representative subplan of the complete factorial experiment being formed makes it possible to calculate a truncated regression equation containing all the influencing factors and their interactions. Analysis of the coefficients of this equation by known methods makes it possible to cut off its insignificant elements.

A class of wide neighborhood interior-point algorithms based on the algebraic equivalent transformation technique with specific functions

A class of wide neighborhood interior-point algorithms based on the algebraic equivalent transformation technique with specific functions