Статті в журналах: "Algebraic estimation method"

1

Beltran-Carbajal, F., R. Tapia-Olvera, A. Valderrabano-Gonzalez, and H. Yanez-Badillo. "An asymptotic and algebraic estimation method of harmonics." Electric Power Systems Research 206 (May 2022): 107771. http://dx.doi.org/10.1016/j.epsr.2022.107771.

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Abouaïssa, H., and V. Iordanova. "Algebraic Methods for Traffic Flow Densities Estimation." Cybernetics and Information Technologies 13, no. 4 (December 1, 2013): 5–17. http://dx.doi.org/10.2478/cait-2013-0049.

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Abstract An estimation approach that allows recovering of the traffic state is proposed in this paper. The method used is based on numerical differentiation, which does not need any integration of differential equations and turns out to be quite robust with respect to perturbations and measurements noises. Numerical simulations, carried-out by using the so-called Cell Transmission Model (CTM) demonstrate the relevance of the proposed on-line estimation scheme.

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3

Kastoris, Dimitris, Kostas Giotopoulos, and Dimitris Papadopoulos. "Neural Network-Based Parameter Estimation in Dynamical Systems." Information 15, no. 12 (December 16, 2024): 809. https://doi.org/10.3390/info15120809.

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Mathematical models are designed to assist decision-making processes across various scientific fields. These models typically contain numerous parameters, the values’ estimation of which often comes under analysis when evaluating the strength of these models as management tools. Advanced artificial intelligence software has proven to be highly effective in estimating these parameters. In this research work, we use the Lotka–Volterra model to describe the dynamics of a telecommunication sector in Greece, and then we propose a methodology that employs a feed-forward neural network (NN). The NN is used to estimate the parameter’s values of the Lotka–Volterra system, which are later applied to solve the system using a fourth-algebraic-order Runge–Kutta method. The application of the proposed architecture to the specific case study reveals that the model fits well to the experiential data. Furthermore, the results of our method surpassed the other three methods used for comparison, demonstrating its higher accuracy and effectiveness. The implementation of the proposed feed-forward neural network and the fourth-algebraic-order Runge–Kutta method was accomplished using MATLAB.

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4

Salmi, Tapio, Esko Tirronen, Johan Wärnå, Jyri-Pekka Mikkola, Dmitry Murzin, and Valerie Eta. "A Robust Method for the Estimation of Kinetic Parameters for Systems Including Slow and Rapid Reactions—From Differential-Algebraic Model to Differential Model." Processes 8, no. 12 (November 27, 2020): 1552. http://dx.doi.org/10.3390/pr8121552.

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Reliable estimation of kinetic parameters in chemical systems comprising both slow and rapid reaction steps and rapidly reacting intermediate species is a difficult differential-algebraic problem. Consequently, any conventional approach easily leads to serious convergence and stability problems during the parameter estimation. A robust method is proposed to surmount this dilemma: the system of ordinary differential equations and nonlinear algebraic equations is converted to ordinary differential equations, which are solved in-situ during the parameter estimation. The approach was illustrated with two generic examples and an example from green chemistry: synthesis of dimethyl carbonate from carbon dioxide and methanol.

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5

Qi, Naixin, Shengxiu Zhang, Lijia Cao, Xiaogang Yang, Chuanxiang Li, and Chuan He. "Fast and robust homography estimation method with algebraic outlier rejection." IET Image Processing 12, no. 4 (April 1, 2018): 552–62. http://dx.doi.org/10.1049/iet-ipr.2017.0254.

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6

Delpoux, R., and T. Floquet. "On-line Parameter Estimation via Algebraic Method: An Experimental Illustration." Asian Journal of Control 17, no. 1 (May 6, 2014): 315–26. http://dx.doi.org/10.1002/asjc.870.

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BALAMETOV, Ashraf B., Elman D. KHALILOV, Afaq K. SALIMOVA, and Tarana M. ISAYEVA. "State Estimation of an AC Overhead Power Line Using the Relinearization Method." Elektrichestvo 4, no. 4 (2021): 17–24. http://dx.doi.org/10.24160/0013-5380-2021-4-17-24.

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As is well known, dispatch control centers receive information about the electric power system operation mode from a supervisory control and data acquisition system (SCADA) and phasor measurement units (PMU) in the form of remote measurements and remote signals. The remote measurements contain information on the power system operating parameters, and remote signals contain information on the positions of switching equipment. The controlled facility state estimation problem is conventionally solved using iteration methods because the system of state equations is nonlinear in nature. The application of the Kipnis-Shamir method makes it possible to transform the nonlinear system of algebraic equations into a linear system in a non-iterative manner by replacing quadratic state variables, after which the obtained linear system is solved parametrically. By applying a second transformation of variables, the system of algebraic equations is transformed into a second system of linear equations, after which the solution of this system and the quadratic system of linear equations, and, hence, also the initial system of nonlinear equations are found. The application of the non-iterative approach is considered on the example of estimating the state of a 500 kV overhead power line.

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8

Garba, Bashir Danladi, and Sirajo Lawan Bichi. "A hybrid method for solution of linear Volterra integro-differential equations (LVIDES) via finite difference and Simpson’s numerical methods (FDSM)." Open Journal of Mathematical Analysis 5, no. 1 (May 27, 2021): 69–75. http://dx.doi.org/10.30538/psrp-oma2021.0084.

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In this paper, a hybrid of Finite difference-Simpson’s approach was applied to solve linear Volterra integro-differential equations. The method works efficiently great by reducing the problem into a system of linear algebraic equations. The numerical results shows the simplicity and effectiveness of the method, error estimation of the method is provided which shows that the method is of second order convergence.

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9

SIRA-RAMÍREZ, HEBERTT, and MICHEL FLIESS. "AN ALGEBRAIC STATE ESTIMATION APPROACH FOR THE RECOVERY OF CHAOTICALLY ENCRYPTED MESSAGES." International Journal of Bifurcation and Chaos 16, no. 02 (February 2006): 295–309. http://dx.doi.org/10.1142/s0218127406014812.

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In this article, we use a variant of a recently introduced algebraic state estimation method obtained from a fast output signal time derivatives computation process. The fast time derivatives calculations are entirely based on the consequences of using the "algebraic approach" in linear systems description (basically, module theory and non-commutative algebra). Here, we demonstrate, through computer simulations, the effectiveness of the proposed algebraic approach in the accurate and fast (i.e. nonasymptotic) estimation of the chaotic states in some of the most popular chaotic systems. The proposed state estimation method can then be used in a coding–decoding process of a secret message transmission using the message-modulated chaotic system states and the reliable transmission of the chaotic system observable output. Simulation examples, using Chen's chaotic system and the Rossler system, demonstrate the important features of the proposed fast state estimation method in the accurate extraction of a chaotically encrypted messages. In our simulation results, the proposed approach is shown to be quite robust with respect to (computer generated) transmission noise perturbations. We also propose a way to evade computational singularities associated with the local lack of observability of certain chaotic system outputs and still carry out the encrypting and decoding of secret messages in a reliable manner.

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10

Haddar, Maroua, S. Caglar Baslamisli, Riadh Chaari, Fakher Chaari, and Mohamed Haddar. "Road profile identification with an algebraic estimator." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 4 (April 4, 2018): 1139–55. http://dx.doi.org/10.1177/0954406218767470.

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In order to isolate the propagation of unwanted vibrations to passengers and improve vehicle maneuverability, it is common practice to predict road profile roughness in the scope of active suspension design. An algebraic estimator designed for the estimation of the road profile excitation has been investigated in this study based on vehicle dynamics responses. An approximation of road profile excitation by a piecewise constant function has been proposed using the operational calculus method and the differential algebraic theory. The proposed technique allows for the usage of cheap instrumentation with a small number of sensors and employs a straightforward calibration process. Accurate approximation of the road profile was obtained from the measurement of sprung mass and unsprung mass vertical displacements. The performance and robustness of the proposed algebraic predictor is compared with an augmented Kalman estimator. Numerical results are provided to analyze the effectiveness and the limitations of the proposed algorithm for road profile reconstruction. Furthermore, a comparison with real profile was studied.

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11

Gorshkov, K. S., and V. V. Filaretov. "A generalization of Middlebrook's symbolic analysis method for tolerance calculation of electrical circuits." Electronics and Communications 15, no. 5 (March 29, 2010): 60–64. http://dx.doi.org/10.20535/2312-1807.2010.58.5.284542.

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This article presents the circuit-algebraic interpretation of the R. D. Middlebrooks formulas for obtaining of the symbolical circuit functions fractional expressions, their generalization and realization in computer program Toleralize for estimation of the tolerance and transformations errors of linear electric networks

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12

Mid, Ernie Che, and Vivek Dua. "Fault Detection in Wastewater Treatment Systems Using Multiparametric Programming." Processes 6, no. 11 (November 20, 2018): 231. http://dx.doi.org/10.3390/pr6110231.

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In this work, a methodology for fault detection in wastewater treatment systems, based on parameter estimation, using multiparametric programming is presented. The main idea is to detect faults by estimating model parameters, and monitoring the changes in residuals of model parameters. In the proposed methodology, a nonlinear dynamic model of wastewater treatment was discretized to algebraic equations using Euler’s method. A parameter estimation problem was then formulated and transformed into a square system of parametric nonlinear algebraic equations by writing the optimality conditions. The parametric nonlinear algebraic equations were then solved symbolically to obtain the concentration of substrate in the inflow, , inhibition coefficient, , and specific growth rate, , as an explicit function of state variables (concentration of biomass, ; concentration of organic matter, ; concentration of dissolved oxygen, ; and volume, ). The estimated model parameter values were compared with values from the normal operation. If the residual of model parameters exceeds a certain threshold value, a fault is detected. The application demonstrates the viability of the approach, and highlights its ability to detect faults in wastewater treatment systems by providing quick and accurate parameter estimates using the evaluation of explicit parametric functions.

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13

Song, Songbai, Yan Kang, Xiaoyan Song, and Vijay P. Singh. "MLE-Based Parameter Estimation for Four-Parameter Exponential Gamma Distribution and Asymptotic Variance of Its Quantiles." Water 13, no. 15 (July 30, 2021): 2092. http://dx.doi.org/10.3390/w13152092.

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The choice of a probability distribution function and confidence interval of estimated design values have long been of interest in flood frequency analysis. Although the four-parameter exponential gamma (FPEG) distribution has been developed for application in hydrology, its maximum likelihood estimation (MLE)-based parameter estimation method and asymptotic variance of its quantiles have not been well documented. In this study, the MLE method was used to estimate the parameters and confidence intervals of quantiles of the FPEG distribution. This method entails parameter estimation and asymptotic variances of quantile estimators. The parameter estimation consisted of a set of four equations which, after algebraic simplification, were solved using a three dimensional Levenberg-Marquardt algorithm. Based on sample information matrix and Fisher’s expected information matrix, derivatives of the design quantile with respect to the parameters were derived. The method of estimation was applied to annual precipitation data from the Weihe watershed, China and confidence intervals for quantiles were determined. Results showed that the FPEG was a good candidate to model annual precipitation data and can provide guidance for estimating design values.

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14

Wang, Mingliang, Bruce Borders, and Dehai Zhao. "Parameter Estimation of Base-Age Invariant Site Index Models: Which Data Structure to Use?" Forest Science 53, no. 5 (October 1, 2007): 541–51. http://dx.doi.org/10.1093/forestscience/53.5.541.

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Abstract Two main approaches to estimating parameters of dominant height curves (derived by algebraic difference approach (ADA) and generalized ADA (GADA)), the dummy variable method and the difference approach (the error-in-variable (EIV) method along with ordinary least-squares (OLS) fits)are compared using second-rotation loblolly pine (Pinus taeda L.) data from a designed experiment. It was found that the EIV method consistently performed better than the dummy variable method, and the two unbiased estimation methods were not necessarily better than the biased OLS differencemethods. In general, the performance of these two approaches was similar in height prediction given site index, but in combination with site index prediction given heights, the difference methods generally performed better. The nonoverlapping forward difference data structure (III), is recommendedto fit difference models.

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15

Gutekunst, Jürgen, Robert Scholz, Armin Nurkanović, Amer Mešanović, Hans Georg Bock, and Ekaterina Kostina. "Fast moving horizon estimation using multi-level iterations for microgrid control." at - Automatisierungstechnik 68, no. 12 (November 18, 2020): 1059–76. http://dx.doi.org/10.1515/auto-2020-0081.

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AbstractAccurate state-estimation is a vital prerequisite for fast feedback control methods such as Nonlinear Model Predictive Control (NMPC). For efficient process control, it is of great importance that the estimation process is carried out as fast as possible to provide the feedback mechanism with fresh information and enable fast reactions in case of any disturbances. We discuss how Multi-Level Iterations (MLI), known from NMPC, can be applied to the Moving Horizon Estimation (MHE) method for estimating the states and parameters of a system described by a Differential Algebraic Equation model. A challenging field of application for the proposed MLI-MHE method are electric microgrids. These push current control approaches to their limits due to the rising penetration of volatile renewable energy sources and the fast electrical system dynamics. We investigate the closed-loop control performance of the proposed MLI-MHE algorithm in combination with an NMPC controller for a realistic sized microgrid as a numerical example.

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16

Wang, Pei, Xiaozheng Gan, Qing Zhang, Guochao Bu, Li Li, Xiuxian Xu, Yaxin Li, Zichu Liu, and Xiangming Xiao. "Analysis of Parameters for the Accurate and Fast Estimation of Tree Diameter at Breast Height Based on Simulated Point Cloud." Remote Sensing 11, no. 22 (November 19, 2019): 2707. http://dx.doi.org/10.3390/rs11222707.

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Terrestrial laser scanning (TLS) is a high-potential technology in forest surveys. Estimating the diameters at breast height (DBH) accurately and quickly has been considered a key step in estimating forest structural parameters by using TLS technology. However, the accuracy and speed of DBH estimation are affected by many factors, which are classified into three groups in this study. We adopt an additive error model and propose a simple and common simulation method to evaluate the impacts of three groups of parameters, which include the range error, angular errors in the vertical and horizontal directions, angular step width, trunk distance, slice thickness, and real DBH. The parameters were evaluated statistically by using many simulated point cloud datasets that were under strict control. Two typical circle fitting methods were used to estimate DBH, and their accuracy and speed were compared. The results showed that the range error and the angular error in horizontal direction played major roles in the accuracy of DBH estimation, the angular step widths had a slight effect in the case of high range accuracy, the distance showed no relationship with the accuracy of the DBH estimation, increasing the scanning angular width was relatively beneficial to the DBH estimation, and the algebraic circle fitting method was relatively fast while performing DBH estimation, as is the geometrical method, in the case of high range accuracy. Possible methods that could help to obtain accurate and fast DBH estimation results were proposed and discussed to optimize the design of forest inventory experiments.

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17

Guler, Demet Cilden, Ece S. Conguroglu, and Chingiz Hajiyev. "Single-Frame Attitude Determination Methods for Nanosatellites." Metrology and Measurement Systems 24, no. 2 (June 27, 2017): 313–24. http://dx.doi.org/10.1515/mms-2017-0023.

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AbstractSingle-frame methods of determining the attitude of a nanosatellite are compared in this study. The methods selected for comparison are: Single Value Decomposition (SVD), q method, Quaternion ESTimator (QUEST), Fast Optimal Attitude Matrix (FOAM) − all solving optimally the Wahba’s problem, and the algebraic method using only two vector measurements. For proper comparison, two sensors are chosen for the vector observations on-board: magnetometer and Sun sensors. Covariance results obtained as a result of using those methods have a critical importance for a non-traditional attitude estimation approach; therefore, the variance calculations are also presented. The examined methods are compared with respect to their root mean square (RMS) error and variance results. Also, some recommendations are given.

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18

Wei, Yan-Qiao, Da-Yan Liu, Chang-Chun Hua, and Cong Zhang. "Online algebraic disturbance estimation method for linear systems with noisy state measurements." Journal of the Franklin Institute 362, no. 1 (January 2025): 107442. https://doi.org/10.1016/j.jfranklin.2024.107442.

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19

RASHIDINIA, J., and ALI PARSA. "SEMI-ORTHOGONAL SPLINE SCALING FUNCTIONS FOR SOLVING HAMMERSTEIN INTEGRAL EQUATIONS." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 03 (May 2011): 427–43. http://dx.doi.org/10.1142/s0219691311004134.

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We developed a new numerical procedure based on the quadratic semi-orthogonal B-spline scaling functions for solving a class of nonlinear integral equations of the Hammerstein-type. Properties of the B-spline wavelet method are utilized to reduce the Hammerstein equations to some algebraic equations. The advantage of our method is that the dimension of the arising algebraic equation is 10 × 10. The operational matrix of semi-orthogonal B-spline scaling functions is sparse which is easily applicable. Error estimation of the presented method is analyzed and proved. To demonstrate the validity and applicability of the technique the method applied to some illustrative examples and the maximum absolute error in the solutions are compared with the results in existing methods.20,25,27,29

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20

Sabrine, Bedoui, Belhadj Brahim Anis, Elloumi Salwa, and Benhadj Braiek Naceur. "On the synthesis of a polynomial controller for enlarging the stability domain for nonlinear discrete system." Transactions of the Institute of Measurement and Control 42, no. 10 (January 10, 2020): 1834–39. http://dx.doi.org/10.1177/0142331219897456.

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This paper aims to propose an algebraic method for estimating the stability region for nonlinear discrete systems. The main contribution is the improvement of an existing technique to enlarge the initial stability region in which the asymptotic stability is guaranteed. To deal with the maximization issue, a state feedback controller is proposed to extend the largest estimation of attraction domain of nonlinear polynomial discrete systems. The proposed approach is illustrated and validated on an isothermal stirred tank reactor.

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21

Mojahedfar, M., Abolfazl Tari, and S. Shahmorad. "A computational method for time fractional partial integro-differential equations." Journal of Applied Analysis 26, no. 2 (December 1, 2020): 315–23. http://dx.doi.org/10.1515/jaa-2020-2013.

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AbstractIn this paper, a class of time fractional partial integro-differential equations (FPIDEs) with initial conditions is studied. Some operational matrices are used to reduce a FPIDE problem to a system of algebraic equations with special properties. The resulted system is solved to give an approximate solution to the problem. Error estimation is also discussed for the approximate solution. Finally, some numerical examples are given to show the accuracy of the proposed method.

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22

Yüzbaşı, Şuayip. "A Laguerre Approach for the Solutions of Singular Perturbated Differential Equations." International Journal of Computational Methods 14, no. 04 (April 18, 2017): 1750034. http://dx.doi.org/10.1142/s0219876217500347.

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In this paper, a Laguerre method is presented to solve singularly perturbated two-point boundary value problems. By means of the matrix relations of the Laguerre polynomials and their derivatives, original problem is transformed into a matrix equation. Later, we use collocation points in the matrix equation and thus the considered problem is reduced to a system of linear algebraic equations. The solution of this system gives the coefficients of the desired approximate solution. Also, an error estimation based on the residual function is introduced for the method. The Laguerre polynomial solution is improved by using this error estimation. Finally, error estimation and residual improvement are illustrated by examples and comparisons are given with other methods.

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23

Al-Jazzar, Saleh O., Zoubir Hamici, and Sami Aldalahmeh. "Two-Dimensional AOA Estimation Based on a Constant Modulus Algorithm." International Journal of Antennas and Propagation 2017 (2017): 1–6. http://dx.doi.org/10.1155/2017/3214021.

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We propose a two-dimensional (2D) angle of arrival (AOA) estimator using the algebraic constant modulus algorithm (ACMA). This algorithm was originally introduced to estimate the one-dimensional (1D) AOA. An extension to estimate and automatically pair the elevation and azimuth angles for different sources is derived and proved in this paper. The ACMA method factorises a matrix into two different matrices; one is of constant modulus and contains the azimuth AOA information; however the second was previously ignored. In this paper we will prove that this second matrix contains the elevation AOA information. Thus, 2D AOA estimation is proved possible using the ACMA method. Simulation results are presented to illustrate the proposed method’s performances under different conditions.

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24

Roether, F. "Improved Identification of Mechanical Multibody Systems From Discrete-Time Data. Differential Identification of Linear Mechanical Systems." Journal of Dynamic Systems, Measurement, and Control 109, no. 2 (June 1, 1987): 140–45. http://dx.doi.org/10.1115/1.3143831.

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The parameter estimation problem of linear mechanical systems evaluating discrete-time data is considered. In principle it can be solved by the algebraic back-transformation of an estimated discrete time model. This approach means that a-priori-knowledge concerning some physical parameters or zero positions in the matrices of the mechanical system cannot be used. An algorithm is presented which offers a possibility to use this information. It requires initially an approximate discrete-time model-parametrization, generated e.g., with known identification schemes. The new method combines data transformation based on linearized algebraic links between continuous and discrete-time models with a side-constrained instrumental variable estimator. Simulation results from a centrifuge model, illustrating the improved accuracy of the estimates if continuous built-in a-priori information are available.

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25

Pang, Yu Cai, and Chao Zhu Zhang. "A New Method for Angle Estimation in MIMO Radar with Blind Source Separation." Applied Mechanics and Materials 543-547 (March 2014): 2500–2504. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.2500.

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A joint direction of departures (DODs) and direction of arrivals (DOAs) estimation for bistatic MIMO radar with an algebraic method for blind source separation (BSS) is presented. The proposed method has the relative advantage of simplicity. The DODs and DOAs of targets can be solved in closed-form and paired automatically. Moreover, BSS techniques enable this approach to recover the source signals from the mixed signals. Simulation results verify the effectiveness of the method.

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Lv, Lulu, Huifang Chen, Lei Xie, and Kuang Wang. "A Topology Optimization Method for Reducing Communication Overhead in the Kalman Consensus Filter." Applied Sciences 11, no. 15 (July 31, 2021): 7107. http://dx.doi.org/10.3390/app11157107.

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Distributed estimation and tracking of interested objects over wireless sensor networks (WSNs) is a hot research topic. Since network topology possesses distinctive structural parameters and plays an important role for the performance of distributed estimation, we first formulate the communication overhead reduction problem in distributed estimation algorithms as the network topology optimization in this paper. The effect of structural parameters on the algebraic connectivity of a network is overviewed. Moreover, aiming to reduce the communication overhead in Kalman consensus filter (KCF)-based distributed estimation algorithm, we propose a network topology optimization method by properly deleting and adding communication links according to nodes’ local structural parameters information, in which the constraint on the communication range of two nodes is incorporated. Simulation results show that the proposed network topology optimization method can effectively improve the convergence rate of KCF algorithm and achieve a good trade-off between the estimate error and communication overhead.

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27

Ossai, Emmanuel Ogochukwu, and Abimibola Victoria Oladugba. "The Estimation of Missing Values in Rectangular Lattice Designs." Journal of Modern Applied Statistical Methods 17, no. 2 (September 3, 2019): 2–23. http://dx.doi.org/10.22237/jmasm/1567468800.

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<p>Algebraic expressions for estimating missing data when one or more observation(s) are missing in Rectangular lattice designs with repetition were derived using the method of minimizing the residual sum of squares. Results showed that the estimated value(s) were significantly approximate to that of the actual value(s).</p>

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28

Dyvak, Mykola, and Iryna Oliynyk. "Estimation Method for a Set of Solutions to Interval System of Linear Algebraic Equations with Optimized “Saturated Block” Selection Procedure." Computational Problems of Electrical Engineering 7, no. 1 (March 14, 2017): 17–24. http://dx.doi.org/10.23939/jcpee2017.01.017.

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Panteleev, A. V., and A. V. Lobanov. "Gradient Optimization Methods in Machine Learning for the Identification of Dynamic Systems Parameters." Моделирование и анализ данных 09, no. 4 (2019): 88–99. http://dx.doi.org/10.17759/mda.2019090407.

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The article considers one of the possible ways to solve the problem of estimating the unknown parameters of dynamic models described by differential-algebraic equations. Parameters are estimated based on the results of observations of the behavior of the mathematical model. Their values are found as a result of minimizing the criterion that describes the total quadratic deviation of the state vector coordinates from the exact values obtained at measurements at different points in time. The parallelepiped type constraints are imposed on the parameter values. To solve the optimization problem, it is proposed to use gradient optimization methods used in machine learning procedures: the stochastic gradient descent method, the classical moment method, the Nesterov accelerated gradient method, the adaptive gradient method, root mean square propagation method, the adaptive moment estimation method, the adaptive estimation method modification, Nesterov–accelerated adaptive moment estimation method. An example of identification of the parameters of a linear mathematical model describing a change in the characteristics of a chemical process is shown, which demonstrates the comparative effectiveness of the optimization methods of the selected group. The methods used to search for an extremum do not guarantee finding a result – a global extremum, but allow you to get a solution of good enough quality for an acceptable time. The results of calculations by all the listed optimization methods are presented. Recommendations on the selection of method parameters are given. The obtained numerical results demonstrated the effectiveness of the proposed approach. The found approximate values of the estimated parameters slightly differ from the best known solutions obtained by other methods.

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Križmančić, Marko, and Stjepan Bogdan. "Adaptive connectivity control in networked multi-agent systems: A distributed approach." PLOS ONE 19, no. 12 (December 2, 2024): e0314642. https://doi.org/10.1371/journal.pone.0314642.

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Effective communication is crucial for the performance and collaboration within cooperative networked multi-agent systems. However, existing literature lacks comprehensive solutions for dynamically monitoring and adjusting communication topologies to balance connectivity and energy efficiency. This study addresses this gap by proposing a distributed approach for estimating and controlling system connectivity over time. We introduce a modified consensus protocol where agents exchange local assessments of communication link quality, enabling the estimation of a global weighted adjacency matrix without requiring centralized information. The system’s connectivity is measured using the second smallest eigenvalue of the communication graph Laplacian, commonly referred to as algebraic connectivity. Additionally, we enhance the consensus protocol with an adaptive mechanism to expedite convergence, irrespective of system size or structure. Furthermore, we present an analytical method for connectivity control based on the Fiedler vector approximation, facilitating the addition or removal of communication links. This method adjusts control parameters to accommodate minor variations in link quality while reconfiguring the network in response to significant changes. Notably, it identifies and eliminates energy-consuming yet non-contributory links, improving long-term connectivity efficiency. Simulation experiments across diverse scenarios and the number of agents validate the efficacy of our proposed algebraic connectivity estimation and tracking strategy. Results demonstrate robust connectivity maintenance against external disturbances and agent failures, underscoring the practical utility of our approach for real-world multi-agent systems.

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31

Yıldırım, Gamze, and Şuayip Yüzbaşı. "Clique Collocation Method to Solve the Third-Order Multisingular (MS) Functional Differential Equations." Fundamentals of Contemporary Mathematical Sciences 6, no. 1 (January 31, 2025): 59–74. https://doi.org/10.54974/fcmathsci.1470784.

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In this paper, a Clique collocation method is presented to numerically solve the third-order multisingular (MS) functional differential equation. This method convert this equation to a system of the algebraic equations via the collocation points and the matrix relations. Also, the error estimation technique is constituted for the third-order multisingular (MS) functional differential equation. Applications of the Clique collocation method and the error estimation technique are made for three examples. In addition, the comparison is made with another method in the literature. The obtained results are tabulated and visualized to demonstrate the effectiveness of the presented method. Applications of the method and graphics are made by using MATLAB. According to the applications, it is observed that the results have quite decent errors.

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32

Bapa kyzy, Ainura. "CONSTRUCTION OF A SOLUTION TO A SYSTEM OF QUASILINEAR EQUATIONS BY THE METHOD OF SIMPLE ITERATION." Alatoo Academic Studies 22, no. 3 (September 30, 2022): 402–6. http://dx.doi.org/10.17015/aas.2022.223.49.

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This article considers the problem of constructing a solution to a system of quasilinear algebraic equations by the method of simple iteration. The method of simple iteration refers to the type of successive approximations. This method is characterized by the fact that when finding the unknowns in the kth approximation, the values of the unknowns found in the (k-1)-approximation are substituted into the right parts of the initial equations. Attention is paid to the analysis of the iterative process from the point of view of convergence, the region of existence of solutions, as well as the estimation of the error between approximations and the exact solution. As an example, the problem of reducing a system of quasi-linear differential equations with a small parameter to a system of quasi-linear algebraic equations is considered.

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33

Kostiukov, Ivan. "Particular properties of estimation of partial capacitances of insulation of three core power cables by applying aggregate measurements." Ukrainian Metrological Journal, no. 1 (March 31, 2021): 15–20. http://dx.doi.org/10.24027/2306-7039.1.2021.228201.

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This paper presents a description of specific properties of determining the values of partial capacitances of insulation gaps in power cables with paper insulation for various ways of forming and solving the system of linear algebraic equations. Possible ways of inspection the insulation of three core power cables for the estimation of values of partial capacitances by applying aggregate measurements which are based on various ways of connection of emittance meter to tested sample of power cable are given. Estimation of partial capacitances by the direct solution of a system of linear algebraic equations, by minimizing the root mean square error of solving an overdetermined system of equations by the least squares method, as well as by finding a normal solution of an indefinite system of equations by the pseudo-inverse matrix, is also considered. It is shown that minimization of the root mean square error by the least squares method and the direct solution of system of equations show quite similar results for the case of estimation of partial capacitances by means of aggregate measurements, at the same time the solution of an indefinite system of equations by the method of a pseudo-inverted matrix allows to reproduce rather accurately only 3 out of 6 values of partial capacitances. The uneven effect of frequency on the electrical capacitance of the insulation gaps between the cores of the power cable and between its cores and the sheath is shown. It was proposed to use the frequency dependence of the electrical capacitance of insulation gaps as an informative parameter about the technical state of insulating gaps between the cores of the power cable and between its cores and its sheath. Keywords: root mean square error; least squares method; system of linear algebraic equations; dielectric losses; dielectric permittivity.

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34

Pan, Jie, and Fu Jiang. "Low Complexity Beamspace Super Resolution for DOA Estimation of Linear Array." Sensors 20, no. 8 (April 15, 2020): 2222. http://dx.doi.org/10.3390/s20082222.

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Beamspace processing has become much attractive in recent radar and wireless communication applications, since the advantages of complexity reduction and of performance improvements in array signal processing. In this paper, we concentrate on the beamspace DOA estimation of linear array via atomic norm minimization (ANM). The existed generalized linear spectrum estimation based ANM approaches suffer from the high computational complexity for large scale array, since their complexity depends upon the number of sensors. To deal with this problem, we develop a low dimensional semidefinite programming (SDP) implementation of beamspace atomic norm minimization (BS-ANM) approach for DFT beamspace based on the super resolution theory on the semi-algebraic set. Then, a computational efficient iteration algorithm is proposed based on alternating direction method of multipliers (ADMM) approach. We develop the covariance based DOA estimation methods via BS-ANM and apply the BS-ANM based DOA estimation method to the channel estimation problem for massive MIMO systems. Simulation results demonstrate that the proposed methods exhibit the superior performance compared to the state-of-the-art counterparts.

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35

Chen, Dandan, Ting-Zhu Huang, and Liang Li. "Comparison of Algebraic Multigrid Preconditioners for Solving Helmholtz Equations." Journal of Applied Mathematics 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/367909.

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An algebraic multigrid (AMG) with aggregation technique to coarsen is applied to construct a better preconditioner for solving Helmholtz equations in this paper. The solution process consists of constructing the preconditioner by AMG and solving the preconditioned Helmholtz problems by Krylov subspace methods. In the setup process of AMG, we employ the double pairwise aggregation (DPA) scheme firstly proposed by Y. Notay (2006) as the coarsening method. We compare it with the smoothed aggregation algebraic multigrid and meanwhile show shifted Laplacian preconditioners. According to numerical results, we find that DPA algorithm is a good choice in AMG for Helmholtz equations in reducing time and memory. Spectral estimation of system preconditioned by the three methods and the influence of second-order and fourth-order accurate discretizations on the three techniques are also considered.

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36

Marcos-Andrade, David, Francisco Beltran-Carbajal, Alexis Castelan-Perez, Ivan Rivas-Cambero, and Jesús C. Hernández. "Online Algebraic Estimation of Parameters and Disturbances in Brushless DC Motors." Machines 13, no. 1 (December 30, 2024): 16. https://doi.org/10.3390/machines13010016.

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Parameter identification in dynamical systems is a well-known problem with many applications in control design, system monitoring, and fault detection. As these systems are increasingly integrated into complex and demanding environments, challenges such as rapid response, uncertainty handling, and disturbance rejection must be addressed. This paper presents a real-time estimation technique for parameters and load torque in brushless DC (BLDC) motors. These electrical machines are extensively used in engineering applications and often operate under hard conditions. The proposed method is based on algebraic identification, known for its robust performance in both linear and nonlinear systems. In utilizing the mathematical model of a BLDC motor, a set of equations is derived to enable parameter estimation, assuming the availability of input and output measurements in open loop. Moreover, unknown load torque is estimated by approximating the disturbance over a short time window using Taylor series expansion polynomials. The theoretical contribution is analytically validated and is also verified through numerical evaluations revealing the effectiveness of the proposed technique for real-time parameter and disturbance estimation in BLDC motors over other important techniques. Additionally, to address potential peaks in the estimation process, a modification involving an exponent is introduced to mitigate these issues.

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37

Ali, A. N., E. Che Mid, N. B. Ahamad, E. Ruslan, and D. A. Hadi. "Parameter Estimation of DC Motor using Multiparametric Programming." Journal of Physics: Conference Series 2312, no. 1 (August 1, 2022): 012035. http://dx.doi.org/10.1088/1742-6596/2312/1/012035.

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Abstract Parameter estimation is important in aspects for applied in many process models in control system design, chemistry, and other engineering application for expectation models of statistical observation. The focus of this work is on a nonlinear ordinary differential equation (ODEs) system which is a direct current (DC) motor model to estimate the model parameters using multiparametric programming. In this work, the ODE model is discretized by implementing Euler’s method to obtain the algebraic equation. The model parameters of the DC motor will be derived as an explicit function of measurements to estimate the parameter values. The applicability of the proposed method and accuracy of parameter estimation is demonstrated.

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38

Li, Jing, Hao Wu, Xianwen Zhan, and Deqiang Gan. "Estimation of the Region of Attraction of Polynomial Swing Equation Using Sum of Squares Theory." Energies 17, no. 5 (February 23, 2024): 1050. http://dx.doi.org/10.3390/en17051050.

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Estimation of the region of attraction of the power system using sum of squares (SOS) programming theory is investigated in this paper. Firstly, the Taylor expansion formula is applied to explore the inherent polynomial structure of the swing equation. The single machine projection equation for a multi-machine system is proposed based on the amplitude characteristic of the rotor angle response in decoupled space. Secondly, the theory of SOS programming originating from the polynomial system is derived, and the theory about estimation of the region of attraction for the differential algebraic system is summarized. Thirdly, the method for estimating the region of attraction for the polynomial swing equation based on a V-S two-stage iterative procedure is proposed. Finally, a single machine infinite bus power system, an IEEE 3-machine power system, and an IEEE 4-machine power system are employed to validate the effectiveness and accuracy of the proposed method and analysis.

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39

Petrut, Teodor, Thomas Geay, Cédric Gervaise, Philippe Belleudy, and Sebastien Zanker. "Passive acoustic measurement of bedload grain size distribution using self-generated noise." Hydrology and Earth System Sciences 22, no. 1 (January 26, 2018): 767–87. http://dx.doi.org/10.5194/hess-22-767-2018.

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Abstract. Monitoring sediment transport processes in rivers is of particular interest to engineers and scientists to assess the stability of rivers and hydraulic structures. Various methods for sediment transport process description were proposed using conventional or surrogate measurement techniques. This paper addresses the topic of the passive acoustic monitoring of bedload transport in rivers and especially the estimation of the bedload grain size distribution from self-generated noise. It discusses the feasibility of linking the acoustic signal spectrum shape to bedload grain sizes involved in elastic impacts with the river bed treated as a massive slab. Bedload grain size distribution is estimated by a regularized algebraic inversion scheme fed with the power spectrum density of river noise estimated from one hydrophone. The inversion methodology relies upon a physical model that predicts the acoustic field generated by the collision between rigid bodies. Here we proposed an analytic model of the acoustic energy spectrum generated by the impacts between a sphere and a slab. The proposed model computes the power spectral density of bedload noise using a linear system of analytic energy spectra weighted by the grain size distribution. The algebraic system of equations is then solved by least square optimization and solution regularization methods. The result of inversion leads directly to the estimation of the bedload grain size distribution. The inversion method was applied to real acoustic data from passive acoustics experiments realized on the Isère River, in France. The inversion of in situ measured spectra reveals good estimations of grain size distribution, fairly close to what was estimated by physical sampling instruments. These results illustrate the potential of the hydrophone technique to be used as a standalone method that could ensure high spatial and temporal resolution measurements for sediment transport in rivers.

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40

Yüzbaşı, Şuayip. "A Numerical Method for Solving Second-Order Linear Partial Differential Equations Under Dirichlet, Neumann and Robin Boundary Conditions." International Journal of Computational Methods 14, no. 02 (February 22, 2017): 1750015. http://dx.doi.org/10.1142/s0219876217500153.

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The aim of this paper is to give a collocation method to solve second-order partial differential equations with variable coefficients under Dirichlet, Neumann and Robin boundary conditions. By using the Bessel functions of the first kind, the matrix operations and the collocation points, the method is constructed and it transforms the partial differential equation problem into a system of algebraic equations. The unknown coefficients of the assuming solution are determined by solving this system. The algorithm of the proposed method is presented. Also, error estimation technique is introduced and the approximate solutions are improved by means of it. To show the validity and applicability of the presented method, we solve numerical examples and give the comparison of solutions and comparisons of the errors (actual and estimation).

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41

Yüzbaşı, Şuayip, and Gamze Yıldırım. "Legendre Collocation Method to Solve the Riccati Equations with Functional Arguments." International Journal of Computational Methods 17, no. 10 (May 21, 2020): 2050011. http://dx.doi.org/10.1142/s0219876220500115.

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In this study, a method for numerically solving Riccatti type differential equations with functional arguments under the mixed condition is presented. For the method, Legendre polynomials, the solution forms and the required expressions are written in the matrix form and the collocation points are defined. Then, by using the obtained matrix relations and the collocation points, the Riccati problem is reduced to a system of nonlinear algebraic equations. The condition in the problem is written in the matrix form and a new system of the nonlinear algebraic equations is found with the aid of the obtained matrix relation. This system is solved and thus the coefficient matrix is detected. This coefficient matrix is written in the solution form and hence approximate solution is obtained. In addition, by defining the residual function, an error problem is established and approximate solutions which give better numerical results are obtained. To demonstrate that the method is trustworthy and convenient, the presented method and error estimation technique are explicated by numerical examples. Consequently, the numerical results are shown more clearly with the aid of the tables and graphs and also the results are compared with the results of other methods.

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42

Henningsson, Axel, and Johannes Hendriks. "Intragranular strain estimation in far-field scanning X-ray diffraction using a Gaussian process." Journal of Applied Crystallography 54, no. 4 (June 14, 2021): 1057–70. http://dx.doi.org/10.1107/s1600576721005112.

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A new method for estimation of intragranular strain fields in polycrystalline materials based on scanning three-dimensional X-ray diffraction (scanning 3DXRD) data is presented and evaluated. Given an a priori known anisotropic compliance, the regression method enforces the balance of linear and angular momentum in the linear elastic strain field reconstruction. By using a Gaussian process (GP), the presented method can yield a spatial estimate of the uncertainty of the reconstructed strain field. Furthermore, constraints on spatial smoothness can be optimized with respect to measurements through hyperparameter estimation. These three features address weaknesses discussed for previously existing scanning 3DXRD reconstruction methods and, thus, offer a more robust strain field estimation. The method is twofold validated: firstly by reconstruction from synthetic diffraction data, and secondly by reconstruction of a previously studied tin (Sn) grain embedded in a polycrystalline specimen. Comparison against reconstructions achieved by a recently proposed algebraic inversion technique is also presented. It is found that the GP regression consistently produces reconstructions with lower root-mean-square errors, mean absolute errors and maximum absolute errors across all six components of strain.

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43

Ogungbenle, Gbenga Michael. "A confirmation of the expected interval: Ab initio estimation technique of parsimonious Gompertz mortality parameters." Nepalese Journal of Insurance and Social Security 4, no. 1 (December 31, 2021): 34–50. http://dx.doi.org/10.3126/njiss.v4i1.42353.

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The Gompertz law states a functional relationship on exponential scale between instantaneous intensity and age. The objective is to first estimate the model parameters by using mortality data and then confirm the interval of validity for the estimated parameters. The parsimonious model is implicitly expressed in terms of age and level of mortality while the force of mortality is the dependent variable. Current contributions in actuarial literature have made it tractable to obtain life span from the actuarial point of view, making the life table invaluable analytical tool for insurers. Mortality functions which have been developed recently possess sophisticated actuarial techniques with many parameters hence they are very complex to estimate numerically making it difficult to fit to mortality data. In order to overcome this problem, we need to employ numerical algebraic method to estimate the appropriate values of model parameters and which may enable us fit the function to mortality data. In this paper, the direct algebraic method offers simpler perspective of approximating mortality parameter and was decomposed into systems of algebraic equations. We observed that mortality over all ages for males is lower than that of females while the initial mortality for male is higher than that of female. The R-language software was employed in the computation. In view of actuarial benchmarks, our results confirm that the values of and for both males and females lie within the expected interval. (see PDF for further information).

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44

Huang, Xiang Yang, Ming Shun Ai, and Peng Peng Yu. "An Efficient DOA Estimation Algorithm for Spatial-Temporal Correlated Sources." Advanced Materials Research 716 (July 2013): 554–58. http://dx.doi.org/10.4028/www.scientific.net/amr.716.554.

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This paper presents a signal direction-of-arrival (DOA) estimation approach that possesses excellent performance in spatial and temporal correlated signals environments. Firstly, an algebraic solution of the null subspace is derived based on the Vandermonde structured steering vectors of uniform linear array when all the sources possess identical nonzero mean value, and then, the DOA estimation is obtained with a polynomial rooting method. The novel algorithm performs much better than the conventional algorithms in the situation that the sources are closely spaced or correlated, and simulations have verified the validity of the algorithm.

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45

Zhu, Fanglai, and Chengmin Tan. "Consensus Control of Linear Parameter-Varying Multi-Agent Systems with Unknown Inputs." Sensors 23, no. 11 (May 27, 2023): 5125. http://dx.doi.org/10.3390/s23115125.

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This paper investigates the observer-based consensus control problem for linear parameter-varying (LPV) multi-agent systems (MASs) with unknown inputs. Firstly, an interval observer (IO) is designed to generate the state interval estimation for each agent. Secondly, an algebraic relationship is established between the system state and unknown input (UI). Thirdly, an unknown input observer (UIO) capable of generating estimates of UI and the system state has been developed through the algebraic relations. Finally, a UIO-based distributed control protocol scheme is proposed to realize the consensus of the MASs. In the end, to verify the validity of the proposed method, an example of a numerical simulation is given.

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46

Лихачев, А. В. "A new tomography method in the presence of an opaque object." Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), no. 2 (May 23, 2017): 129–37. http://dx.doi.org/10.26089/nummet.v18r210.

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Разработан новый метод реконструкции изображения сечения объекта, содержащего непрозрачное включение. Для того чтобы оценить неизвестные данные в области тени, решается система линейных алгебраических уравнений, построенная на основе представления моментов проекций однородными полиномами. По результатам проведенного вычислительного эксперимента оказалось, что метод имеет преимущества перед альтернативными подходами. A new tomography method for a two-dimensional object containing an opaque inclusion is developed. For the estimation of unknown data in the opaque object's shadow, the system of linear algebraic equations derived from the representation of projections of moments by homogeneous polynomials is solved. The numerical results show that the method has a number of advantages over alternative approaches.

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47

Mirzaee, Farshid, and Nasrin Samadyar. "Parameters estimation of HIV infection model of CD4+T-cells by applying orthonormal Bernstein collocation method." International Journal of Biomathematics 11, no. 02 (February 2018): 1850020. http://dx.doi.org/10.1142/s1793524518500201.

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The HIV infection model of CD4[Formula: see text][Formula: see text]T-cells corresponds to a class of nonlinear ordinary differential equation systems. In this study, we provide the approximate solution of this model by using orthonormal Bernstein polynomials (OBPs). By applying the proposed method, the nonlinear system of ordinary differential equations reduces to a nonlinear system of algebraic equations which can be solved by using a suitable numerical method such as Newton’s method. We prove some useful theorems concerning the convergence and error estimate associated to the present method. Finally, we apply the proposed method to get the numerical solution of this model with the arbitrary initial conditions and values. Furthermore, the numerical results obtained by the suggested method are compared with the results achieved by other previous methods. These results indicate that this method agrees with other previous methods.

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48

Ling, Xufeng, Haichuan Xu, Weijie Weng, and Fanglai Zhu. "Distributed Consensus Control for Discrete-Time T–S Fuzzy Multiple-Agent Systems Based on an Unknown Input Observer." Sensors 24, no. 24 (December 20, 2024): 8149. https://doi.org/10.3390/s24248149.

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This paper investigates a consensus problem for a class of T–S fuzzy multiple-agent systems (MASs) with unknown input (UI). To begin with, an unknown input observer (UIO) is able to asymptotically estimate the system state and the UI is designed for each agent. In order to construct the UIO, the state interval estimation is obtained by first using zonotope theory. Next, using the interval estimation of the state, a correlation of the state and the UI is built. Subsequently, a UIO is constructed, which is proposed by building upon the algebraic relationship. Moreover, by using the estimations of the state and the UI, a distributed control protocol is developed based on the proposed UIO. And, with the proposed distributed control protocol, the T–S fuzzy MAS can achieve consensus, in that all the states of the agents can converge to the leader’s state asymptotically. Finally, the effectiveness of the proposed method is demonstrated through two simulation examples.

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49

Teschke, Gerd, and Volker Lehmann. "Mean wind vector estimation using the velocity–azimuth display (VAD) method: an explicit algebraic solution." Atmospheric Measurement Techniques 10, no. 9 (September 6, 2017): 3265–71. http://dx.doi.org/10.5194/amt-10-3265-2017.

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Abstract. This paper deals with the analysis of the sampling setup for Doppler profilers aiming at the determination of vertical profiles of the wind. An explicit solution for the retrieval of mean wind vectors under the assumption of local homogeneity is presented for the case of a symmetric velocity–azimuth display sampling, and a stability analysis is performed. Furthermore, the explicit solution allows a detailed investigation of the propagation of radial wind measurement errors on the retrieved wind vector.

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50

Lee, Meei-Yow Lin. "Estimation of the Error in the Reduced Basis Method Solution of Differential Algebraic Equation Systems." SIAM Journal on Numerical Analysis 28, no. 2 (April 1991): 512–28. http://dx.doi.org/10.1137/0728028.

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