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13 pages, 675 KiB

Open AccessArticle

SVD-Based Parameter Identification of Discrete-Time Stochastic Systems with Unknown Exogenous Inputs

by Andrey Tsyganov and Yulia Tsyganova

Mathematics 2024, 12(7), 1006; https://doi.org/10.3390/math12071006 - 28 Mar 2024

Viewed by 674

Abstract

This paper addresses the problem of parameter identification for discrete-time stochastic systems with unknown exogenous inputs. These systems form an important class of dynamic stochastic system models used to describe objects and processes under a high level of a priori uncertainty, when it [...] Read more.

This paper addresses the problem of parameter identification for discrete-time stochastic systems with unknown exogenous inputs. These systems form an important class of dynamic stochastic system models used to describe objects and processes under a high level of a priori uncertainty, when it is not possible to make any assumptions about the evolution of the unknown input signal or its statistical properties. The main purpose of this paper is to construct a new SVD-based modification of the existing Gillijns and De Moor filtering algorithm for linear discrete-time stochastic systems with unknown exogenous inputs. Using the theoretical results obtained, we demonstrate how this modified algorithm can be applied to solve the problem of parameter identification. The results of our numerical experiments conducted in MATLAB confirm the effectiveness of the SVD-based parameter identification method that was developed, under conditions of unknown exogenous inputs, compared to maximum likelihood parameter identification when exogenous inputs are known. Full article

(This article belongs to the Special Issue New Trends on Identification of Dynamic Systems)

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15 pages, 2080 KiB

Open AccessArticle

Spotting Suspicious Academic Citations Using Self-Learning Graph Transformers

by Renata Avros, Mor Ben Haim, Almog Madar, Elena Ravve and Zeev Volkovich

Mathematics 2024, 12(6), 814; https://doi.org/10.3390/math12060814 - 10 Mar 2024

Viewed by 502

Abstract

The study introduces a novel approach to identify potential citation manipulation within academic papers. This method utilizes perturbations of a deep embedding model, integrating Graph-Masked Autoencoders to merge textual information with evidence of graph connectivity. Consequently, it yields a more intricate model of [...] Read more.

The study introduces a novel approach to identify potential citation manipulation within academic papers. This method utilizes perturbations of a deep embedding model, integrating Graph-Masked Autoencoders to merge textual information with evidence of graph connectivity. Consequently, it yields a more intricate model of citation distribution. By training a deep network with partial data and reconstructing masked connections, the approach capitalizes on the inherent characteristics of central connections amidst network perturbations. It demonstrates its ability to pinpoint trustworthy citations within the analyzed dataset through comprehensive quantitative evaluations. Additionally, it raises concerns regarding the reliability of specific references, which may be subject to manipulation. Full article

(This article belongs to the Special Issue New Trends on Identification of Dynamic Systems)

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11 pages, 700 KiB

Open AccessArticle

Identification of Parameters of Conservative Multispecies Lotka-Volterra System Based on Sampled Data

by Aleksandr Semenov and Alexander Fradkov

Mathematics 2024, 12(2), 248; https://doi.org/10.3390/math12020248 - 12 Jan 2024

Viewed by 519

Abstract

In this paper, we propose a method for identifying the parameters of the multispecies Lotka-Volterra model based on sampled data. The conditions (nonhyperplanarity, recurrence) under which the “Stripe” algorithm achieves the identification goals are found. The relation between nonhyperplanar recurrent trajectories and the [...] Read more.

In this paper, we propose a method for identifying the parameters of the multispecies Lotka-Volterra model based on sampled data. The conditions (nonhyperplanarity, recurrence) under which the “Stripe” algorithm achieves the identification goals are found. The relation between nonhyperplanar recurrent trajectories and the persistent excitation condition for systems of general form is studied. Full article

(This article belongs to the Special Issue New Trends on Identification of Dynamic Systems)

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14 pages, 1152 KiB

Open AccessArticle

A Novel Approach to Modeling Incommensurate Fractional Order Systems Using Fractional Neural Networks

by Meshach Kumar, Utkal Mehta and Giansalvo Cirrincione

Mathematics 2024, 12(1), 83; https://doi.org/10.3390/math12010083 - 26 Dec 2023

Viewed by 732

Abstract

This research explores the application of the Riemann–Liouville fractional sigmoid, briefly

^{R L} F σ

, activation function in modeling the chaotic dynamics of Chua’s circuit through Multilayer Perceptron (MLP) architecture. Grounded in the context of chaotic systems, the study aims to address [...] Read more.

This research explores the application of the Riemann–Liouville fractional sigmoid, briefly

^{R L} F σ

, activation function in modeling the chaotic dynamics of Chua’s circuit through Multilayer Perceptron (MLP) architecture. Grounded in the context of chaotic systems, the study aims to address the limitations of conventional activation functions in capturing complex relationships within datasets. Employing a structured approach, the methods involve training MLP models with various activation functions, including

^{R L} F σ

, sigmoid, swish, and proportional Caputo derivative

^{P C} σ

, and subjecting them to rigorous comparative analyses. The main findings reveal that the proposed

^{R L} F σ

consistently outperforms traditional counterparts, exhibiting superior accuracy, reduced Mean Squared Error, and faster convergence. Notably, the study extends its investigation to scenarios with reduced dataset sizes and network parameter reductions, demonstrating the robustness and adaptability of

^{R L} F σ

. The results, supported by convergence curves and CPU training times, underscore the efficiency and practical applicability of the proposed activation function. This research contributes a new perspective on enhancing neural network architectures for system modeling, showcasing the potential of

^{R L} F σ

in real-world applications. Full article

(This article belongs to the Special Issue New Trends on Identification of Dynamic Systems)

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11 pages, 374 KiB

Open AccessArticle

Parameter Identification of the Discrete-Time Stochastic Systems with Multiplicative and Additive Noises Using the UD-Based State Sensitivity Evaluation

by Andrey Tsyganov and Yulia Tsyganova

Mathematics 2023, 11(24), 4964; https://doi.org/10.3390/math11244964 - 15 Dec 2023

Viewed by 544

Abstract

The paper proposes a new method for solving the parameter identification problem for a class of discrete-time linear stochastic systems with multiplicative and additive noises using a numerical gradient-based optimization. The constructed method is based on the application of a covariance UD filter [...] Read more.

The paper proposes a new method for solving the parameter identification problem for a class of discrete-time linear stochastic systems with multiplicative and additive noises using a numerical gradient-based optimization. The constructed method is based on the application of a covariance UD filter for the above systems and an original method for evaluating state sensitivities within the numerically stable, matrix-orthogonal MWGS transformation. In addition to the numerical stability of the proposed algorithm to machine roundoff errors due to the application of the MWGS-UD orthogonalization procedure at each step, the main advantage of the obtained results is the possibility of analytical calculation of derivatives at a given value of the identified parameter without the need to use finite-difference methods. Numerical experiments demonstrate how the obtained results can be applied to solve the parameter identification problem for the considered stochastic system model. Full article

(This article belongs to the Special Issue New Trends on Identification of Dynamic Systems)

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17 pages, 427 KiB

Open AccessArticle

Continuous-Time Subspace Identification with Prior Information Using Generalized Orthonormal Basis Functions

by Miao Yu, Youyi Wang, Wanli Wang and Yongtao Wei

Mathematics 2023, 11(23), 4765; https://doi.org/10.3390/math11234765 - 25 Nov 2023

Viewed by 499

Abstract

This paper presents a continuous-time subspace identification method utilizing prior information and generalized orthonormal basis functions. A generalized orthonormal basis is constructed by a rational inner function, and the transformed noises have ergodic properties. The lifting approach and the Hambo system transform are [...] Read more.

This paper presents a continuous-time subspace identification method utilizing prior information and generalized orthonormal basis functions. A generalized orthonormal basis is constructed by a rational inner function, and the transformed noises have ergodic properties. The lifting approach and the Hambo system transform are used to establish the equivalent nature of continuous and transformed discrete-time stochastic systems. The constrained least squares method is adopted to investigate the incorporation of prior knowledge in order to further increase the subspace identification algorithm’s accuracy. The input–output algebraic equation derives an optimal multistep forward predictor, and prior knowledge is expressed as equality constraints. In order to solve an optimization problem with equality constraints characterizing the prior knowledge, the proposed method reduces the computational burden. The effectiveness of the proposed method is provided by numerical simulations. Full article

(This article belongs to the Special Issue New Trends on Identification of Dynamic Systems)

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23 pages, 5571 KiB

Open AccessArticle

Identification of Linear Time-Invariant Systems: A Least Squares of Orthogonal Distances Approach

by Luis Alberto Cantera-Cantera, Rubén Garrido, Luis Luna, Cristóbal Vargas-Jarillo and Erick Asiain

Mathematics 2023, 11(5), 1238; https://doi.org/10.3390/math11051238 - 03 Mar 2023

Cited by 2 | Viewed by 1289

Abstract

This work describes the parameter identification of servo systems using the least squares of orthogonal distances method. The parameter identification problem was reconsidered as data fitting to a plane, which in turn corresponds to a nonlinear minimization problem. Three models of a servo [...] Read more.

This work describes the parameter identification of servo systems using the least squares of orthogonal distances method. The parameter identification problem was reconsidered as data fitting to a plane, which in turn corresponds to a nonlinear minimization problem. Three models of a servo system, having one, two, and three parameters, were experimentally identified using both the classic least squares and the least squares of orthogonal distances. The models with two and three parameters were identified through numerical routines. The servo system model with a single parameter only considered the input gain. In this particular case, the analytical conditions for finding the critical points and for determining the existence of a minimum were presented, and the estimate of the input gain was obtained by solving a simple quadratic equation whose coefficients depended on measured data. The results showed that as opposed to the least squares method, the least squares of orthogonal distances method experimentally produced consistent estimates without regard for the classic persistency-of-excitation condition. Moreover, the parameter estimates of the least squares of orthogonal distances method produced the best tracking performance when they were used to compute a trajectory-tracking controller. Full article

(This article belongs to the Special Issue New Trends on Identification of Dynamic Systems)

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19 pages, 661 KiB

Open AccessArticle

Unbiased Identification of Fractional Order System with Unknown Time-Delay Using Bias Compensation Method

by Zaineb Yakoub , Omar Naifar and Dmitriy Ivanov

Mathematics 2022, 10(16), 3028; https://doi.org/10.3390/math10163028 - 22 Aug 2022

Cited by 4 | Viewed by 2263

Abstract

In the field of engineering, time-delay is a typical occurrence. In reality, the inner dynamics of many industrial processes are impacted by delay or after-effect events. This paper discusses the identification of continuous-time fractional order system with unknown time-delay using the bias compensated [...] Read more.

In the field of engineering, time-delay is a typical occurrence. In reality, the inner dynamics of many industrial processes are impacted by delay or after-effect events. This paper discusses the identification of continuous-time fractional order system with unknown time-delay using the bias compensated least squares algorithm. The basic concept is to remove the imposed bias by including a correction term into the least squares estimations. The suggested approach makes a significant contribution by the estimation, iteratively, of fractional order system coefficients as well as the orders and the time-delay using a nonlinear optimization algorithm. The main advantage of this method is to provide a simple and powerful algorithm with good accuracy. The suggest method performances are assessed through two numerical examples. Full article

(This article belongs to the Special Issue New Trends on Identification of Dynamic Systems)

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16 pages, 482 KiB

Open AccessArticle

Algorithmic Differentiation of the MWGS-Based Arrays for Computing the Information Matrix Sensitivity Equations within the Problem of Parameter Identification

by Andrey Tsyganov and Julia Tsyganova

Mathematics 2022, 10(1), 126; https://doi.org/10.3390/math10010126 - 02 Jan 2022

Viewed by 1240

Abstract

The paper considers the problem of algorithmic differentiation of information matrix difference equations for calculating the information matrix derivatives in the information Kalman filter. The equations are presented in the form of a matrix MWGS (modified weighted Gram–Schmidt) transformation. The solution is based [...] Read more.

The paper considers the problem of algorithmic differentiation of information matrix difference equations for calculating the information matrix derivatives in the information Kalman filter. The equations are presented in the form of a matrix MWGS (modified weighted Gram–Schmidt) transformation. The solution is based on the usage of special methods for the algorithmic differentiation of matrix MWGS transformation of two types: forward (MWGS-LD) and backward (MWGS-UD). The main result of the work is a new MWGS-based array algorithm for computing the information matrix sensitivity equations. The algorithm is robust to machine round-off errors due to the application of the MWGS orthogonalization procedure at each step. The obtained results are applied to solve the problem of parameter identification for state-space models of discrete-time linear stochastic systems. Numerical experiments confirm the efficiency of the proposed solution. Full article

(This article belongs to the Special Issue New Trends on Identification of Dynamic Systems)

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29 pages, 16690 KiB

Open AccessArticle

A Simple Analytical Method for Estimation of the Five-Parameter Model: Second-Order with Zero Plus Time Delay

by Tomaž Kos and Damir Vrančić

Mathematics 2021, 9(14), 1707; https://doi.org/10.3390/math9141707 - 20 Jul 2021

Cited by 2 | Viewed by 2046

Abstract

Process models play an important role in the process industry. They are used for simulation purposes, quality control, fault detection, and control design. Many researchers have been engaged in model identification. However, it is difficult to find an analytical identification method that provides [...] Read more.

Process models play an important role in the process industry. They are used for simulation purposes, quality control, fault detection, and control design. Many researchers have been engaged in model identification. However, it is difficult to find an analytical identification method that provides a good model and requires a relatively simple experiment. This is the advantage of the method of moments. In this paper, an analytical method based on the measurement of the process moments (characteristic areas) is proposed, to identify the five-parameter model (second-order process with zero plus time delay) from either the closed-loop or open-loop time responses of the process (in the time-domain), or the general-order transfer function with time delay (in the frequency-domain). The only parameter required by the user is the type of process (minimum phase or non-minimum phase process), which in practice can be easily determined from the time response of the process. The method can also be used to reduce the higher-order process model. The proposed identification method was tested on several illustrative examples, and compared to other identification methods. The comparison with existing methods showed the superiority of the proposed method. Moreover, the tests confirmed that the algorithm of the proposed method works properly for a wide family of process models, even in the presence of moderate process noise. Full article

(This article belongs to the Special Issue New Trends on Identification of Dynamic Systems)

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Review

Jump to: Research

21 pages, 2299 KiB

Open AccessReview

Overview of Identification Methods of Autoregressive Model in Presence of Additive Noise

by Dmitriy Ivanov and Zaineb Yakoub

Mathematics 2023, 11(3), 607; https://doi.org/10.3390/math11030607 - 26 Jan 2023

Cited by 1 | Viewed by 1868

Abstract

This paper presents an overview of the main methods used to identify autoregressive models with additive noises. The classification of identification methods is given. For each group of methods, advantages and disadvantages are indicated. The article presents the simulation results of a large [...] Read more.

This paper presents an overview of the main methods used to identify autoregressive models with additive noises. The classification of identification methods is given. For each group of methods, advantages and disadvantages are indicated. The article presents the simulation results of a large number of the described methods and gives recommendations on choosing the best methods. Full article

(This article belongs to the Special Issue New Trends on Identification of Dynamic Systems)

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