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Journal articles on the topic 'Stochastic algorithms parameters identification'
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1
Zhang, Ce, Xiangxiang Meng, and Yan Ji. "Parameter Estimation of Fractional Wiener Systems with the Application of Photovoltaic Cell Models." Mathematics 11, no. 13 (June 30, 2023): 2945. http://dx.doi.org/10.3390/math11132945.
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Fractional differential equations are used to construct mathematical models and can describe the characteristics of real systems. In this paper, the parameter estimation problem of a fractional Wiener system is studied by designing linear filters which can obtain smaller tunable parameters and maintain the stability of the parameters in any case. To improve the identification performance of the stochastic gradient algorithm, this paper derives two modified stochastic gradient algorithms for the fractional nonlinear Wiener systems with colored noise. By introducing the forgetting factor, a forgetting factor stochastic gradient algorithm is deduced to improve the convergence rate. To achieve more efficient and accurate algorithms, we propose a multi-innovation forgetting factor stochastic gradient algorithm by means of the multi-innovation theory, which expands the scalar innovation into the innovation vector. To test the developed algorithms, a fractional-order dynamic photovoltaic model is employed in the simulation, and the dynamic elements of this photovoltaic model are estimated using the modified algorithms. Concurrently, a numerical example is given, and the simulation results verify the feasibility and effectiveness of the proposed procedures.
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Ji, Yuejiang, and Lixin Lv. "Two Identification Methods for a Nonlinear Membership Function." Complexity 2021 (April 30, 2021): 1–7. http://dx.doi.org/10.1155/2021/5515888.
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This paper proposes two parameter identification methods for a nonlinear membership function. An equation converted method is introduced to turn the nonlinear function into a concise model. Then a stochastic gradient algorithm and a gradient-based iterative algorithm are provided to estimate the unknown parameters of the nonlinear function. The numerical example shows that the proposed algorithms are effective.
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Hu, Huiyi, Xiao Yongsong, and Rui Ding. "Multi-Innovation Stochastic Gradient Identification Algorithm for Hammerstein Controlled Autoregressive Autoregressive Systems Based on the Key Term Separation Principle and on the Model Decomposition." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/596141.
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An input nonlinear system is decomposed into two subsystems, one including the parameters of the system model and the other including the parameters of the noise model, and a multi-innovation stochastic gradient algorithm is presented for Hammerstein controlled autoregressive autoregressive (H-CARAR) systems based on the key term separation principle and on the model decomposition, in order to improve the convergence speed of the stochastic gradient algorithm. The key term separation principle can simplify the identification model of the input nonlinear system, and the decomposition technique can enhance computational efficiencies of identification algorithms. The simulation results show that the proposed algorithm is effective for estimating the parameters of IN-CARAR systems.
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Olama, Mohammed M., Kiran K. Jaladhi, Seddik M. Djouadi, and Charalambos D. Charalambous. "Recursive Estimation and Identification of Time-Varying Long-Term Fading Channels." Research Letters in Signal Processing 2007 (2007): 1–5. http://dx.doi.org/10.1155/2007/17206.
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This paper is concerned with modeling of time-varying wireless long-term fading channels, parameter estimation, and identification from received signal strength data. Wireless channels are represented by stochastic differential equations, whose parameters and state variables are estimated using the expectation maximization algorithm and Kalman filtering, respectively. The latter are carried out solely from received signal strength data. These algorithms estimate the channel path loss and identify the channel parameters recursively. Numerical results showing the viability of the proposed channel estimation and identification algorithms are presented.
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Ma, Ping, and Lei Wang. "Partially Coupled Stochastic Gradient Estimation for Multivariate Equation-Error Systems." Mathematics 10, no. 16 (August 16, 2022): 2955. http://dx.doi.org/10.3390/math10162955.
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This paper researches the identification problem for the unknown parameters of the multivariate equation-error autoregressive systems. Firstly, the original identification model is decomposed into several sub-identification models according to the number of system outputs. Then, based on the characteristic that the information vector and the parameter vector are common among the sub-identification models, the coupling identification concept is used to propose a partially coupled generalized stochastic gradient algorithm. Furthermore, by expanding the scalar innovation of each subsystem model to the innovation vector, a partially coupled multi-innovation generalized stochastic gradient algorithm is proposed. Finally, the numerical simulations indicate that the proposed algorithms are effective and have good parameter estimation performances.
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Tsyganov, Andrey, and Yulia Tsyganova. "SVD-Based Identification of Parameters of the Discrete-Time Stochastic Systems Models with Multiplicative and Additive Noises Using Metaheuristic Optimization." Mathematics 11, no. 20 (October 15, 2023): 4292. http://dx.doi.org/10.3390/math11204292.
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The paper addresses a parameter identification problem for discrete-time stochastic systems models with multiplicative and additive noises. Stochastic systems with additive and multiplicative noises are considered when solving many practical problems related to the processing of measurements information. The purpose of this work is to develop a numerically stable gradient-free instrumental method for solving the parameter identification problems for a class of mathematical models described by discrete-time linear stochastic systems with multiplicative and additive noises on the basis of metaheuristic optimization and singular value decomposition. We construct an identification criterion in the form of the negative log-likelihood function based on the values calculated by the newly proposed SVD-based Kalman-type filtering algorithm, taking into account the multiplicative noises in the equations of the state and measurements. Metaheuristic optimization algorithms such as the GA (genetic algorithm) and SA (simulated annealing) are used to minimize the identification criterion. Numerical experiments confirm the validity of the proposed method and its numerical stability compared with the usage of the conventional Kalman-type filtering algorithm.
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Kovacevic, Ivana, Branko Kovacevic, and Zeljko Djurovic. "On strong consistency of a class of recursive stochastic Newton-Raphson type algorithms with application to robust linear dynamic system identification." Facta universitatis - series: Electronics and Energetics 21, no. 1 (2008): 1–21. http://dx.doi.org/10.2298/fuee0801001k.
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The recursive stochastic algorithms for estimating the parameters of linear discrete-time dynamic systems in the presence of disturbance uncertainty has been considered in the paper. Problems related to the construction of min-max optimal recursive algorithms are demonstrated. In addition, the robustness of the proposed algorithms has been addressed. Since the min-max optimal solution cannot be achieved in practice, an approximate optimal solution based on a recursive stochastic Newton-Raphson type procedure is suggested. The convergence of the proposed practically applicable robustified recursive algorithm is established theoretically using the martingale theory. Both theoretical and experimental analysis related to the practical robustness of the proposed algorithm are also included. .
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Maitre, Julien, Sébastien Gaboury, Bruno Bouchard, and Abdenour Bouzouane. "A Black-Box Model for Estimation of the Induction Machine Parameters Based on Stochastic Algorithms." International Journal of Monitoring and Surveillance Technologies Research 3, no. 3 (July 2015): 44–67. http://dx.doi.org/10.4018/ijmstr.2015070103.
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Knowledge on asynchronous machine parameters (resistances, inductances…) has become necessary for the manufacturing industry in the interest of optimizing performances in a production system (roll-to-roll processing, wind generator…). Indeed, accurate values of this machine allow improving control of the torque, speed and position, managing power consumption in the best way possible, and predicting induction machine failures with great effectiveness. In these regards, the authors of this paper propose a black-box modeling for a powerful identification of asynchronous machine parameters relying on stochastic research algorithms. The algorithms used for the estimation process are a single objective genetic algorithm, the well-known NSGA II and the new ?-NSGA III (multi-objective genetic algorithms). Results provided by those show that the best estimation of asynchronous machines parameters is given by ?-NSGA III. In addition, this outcome is confirmed by performing the identification process on three different induction machines.
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Hsu, Geesern, Andrew E. Yagle, Kenneth C. Ludema, and Joel A. Levitt. "Modeling and Identification of Lubricated Polymer Friction Dynamics." Journal of Dynamic Systems, Measurement, and Control 122, no. 1 (October 11, 1996): 78–88. http://dx.doi.org/10.1115/1.482431.
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A systematic approach is proposed to model the dynamics of lubricated polymer friction. It starts with the development of a physical model to describe the fundamental mechanisms of the friction. The physical model then serves as the basic structure for the development of a complex model able to capture a wider spectrum of the deterministic and stochastic dynamics of friction. To assess the accuracy of the complex model, two estimation algorithms are formulated to estimate the unknown parameters in the model and to test the model against experimental data. One algorithm is based on the maximum likelihood principle to estimate the constant parameters for stationary friction dynamics, and the other based on the extended Kalman filter to estimate the time-varying parameters for nonstationary friction dynamics. The model and the algorithms are all validated through experiments. [S0022-0434(00)00601-8]
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Krasheninnikov, Viktor R., Yuliya E. Kuvayskova, Olga E. Malenova, and Aleksey Y. Subbotin. "PSEUDOGRADIENT ALGORITHM FOR IDENTIFICATION OF DOUBLY STOCHASTIC CYLINDRICAL IMAGE." Автоматизация процессов управления 2, no. 64 (2021): 56–65. http://dx.doi.org/10.35752/1991-2927-2021-2-64-56-65.
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Nowadays image processing problems are becoming increasingly important due to development of the aerospace Earth monitoring systems, radio and sonar systems, medical devices for early diagnosis, etc. However, the most of the image processing works deals with images defined on rectangular two-dimensional grids or grids of higher dimension. In some practical situations images are set on a cylinder, for example images of pipeline sections, blood vessels, rotary parts, etc. The peculiarity of the domain for specifying such images requires its consideration in their models and processing algorithms. The article deals with autoregressive models of cylindrical images and gives some expressions of the correlation function depending on the autoregression parameters are given. To represent heterogeneous images with random heterogeneities, ‘doubly stochastic’ models are used in which one or more images control the parameters of resulted image. The spiral scan of a cylindrical image can be considered as a quasiperiodic process due to the correlation of image rows. The article proposes the pseudogradient algorithms for the modal identification. The statistical modeling proves these algorithms give good model identification.
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Angelova, Maria, and Tania Pencheva. "Tuning Genetic Algorithm Parameters to Improve Convergence Time." International Journal of Chemical Engineering 2011 (2011): 1–7. http://dx.doi.org/10.1155/2011/646917.
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Fermentation processes by nature are complex, time-varying, and highly nonlinear. As dynamic systems their modeling and further high-quality control are a serious challenge. The conventional optimization methods cannot overcome the fermentation processes peculiarities and do not lead to a satisfying solution. As an alternative, genetic algorithms as a stochastic global optimization method can be applied. For the purpose of parameter identification of a fed-batch cultivation ofS. cerevisiaealtogether four kinds of simple and four kinds of multipopulation genetic algorithms have been considered. Each of them is characterized with a different sequence of implementation of main genetic operators, namely, selection, crossover, and mutation. The influence of the most important genetic algorithm parameters—generation gap, crossover, and mutation rates has—been investigated too. Among the considered genetic algorithm parameters, generation gap influences most significantly the algorithm convergence time, saving up to 40% of time without affecting the model accuracy.
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BHATT, RAJEN B., and M. GOPAL. "ON THE STRUCTURE AND INITIAL PARAMETER IDENTIFICATION OF GAUSSIAN RBF NETWORKS." International Journal of Neural Systems 14, no. 06 (December 2004): 373–80. http://dx.doi.org/10.1142/s012906570400211x.
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We consider the efficient initialization of structure and parameters of generalized Gaussian radial basis function (RBF) networks using fuzzy decision trees generated by fuzzy ID3 like induction algorithms. The initialization scheme is based on the proposed functional equivalence property of fuzzy decision trees and generalized Gaussian RBF networks. The resulting RBF network is compact, easy to induce, comprehensible, and has acceptable classification accuracy with stochastic gradient descent learning algorithm.
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Ломов, Андрей Александрович. "Parameter identification of discrete stochastic systems by the inverse iteration method." Вычислительные технологии, no. 3 (July 15, 2020): 66–76. http://dx.doi.org/10.25743/ict.2020.25.3.008.
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Получены условия глобальной сходимости алгоритмов, основанных на обратных итерациях в переменной метрике, в задаче идентификации параметров дискретной стохастической системы с возмущениями в невязке уравнения и наблюдениях процессов. Доказана сходимость оценок параметров к истинному значению при увеличении объема выборки наблюдений истинного процесса. Приведены примеры расчетов The article addresses the problem of identifying parameters of discrete stochastic systems with perturbations in the residual of the equation and observation of variables. The identification functional in the problem has a complex nature of isosurfaces, which is why universal minimization algorithms based on estimates of the first and second derivatives have a small radius of convergence. It is proposed to employ efficient computational identification algorithms with inverse iterations in a variable metric for solving the convergence problem for two classes of systems with simple correspondence between matrix elements and parameters of equivalent systems without state variables. These algorithms are used for systems without state variables due to the large radius and high convergence rate since the 1970s. At first, a theorem on the conditions for convergence of inverse iterations from almost any initial approximation to a small neighborhood of the global minimum of the identification functional was proved. Secondly, a theorem on the convergence of the points of the global minimum of the identification functional to the desired true value with an increase in the sample size of observations is taken into account. Assumption of a zero first and restricted second moments of stochastic disturbances in the residual of the equation and observation of variables was made. The convergence of inverse iterations is shown numerically in a model example with significant values of disturbances. The result of the article is new theorems on the conditions of global convergence of computational algorithms with inverse iterations in the problem with mixed disturbances and the justification of possibility of using these algorithms to identify the parameters for discrete stochastic systems of two classes with a simple correspondence between matrix elements and parameters of equivalent systems without state variables
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Wang and Sun. "Self-Tuning Distributed Fusion Filter for Multi-Sensor Networked Systems with Unknown Packet Receiving Rates, Noise Variances, and Model Parameters." Sensors 19, no. 20 (October 13, 2019): 4436. http://dx.doi.org/10.3390/s19204436.
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In this study, we researched the problem of self-tuning (ST) distributed fusion state estimation for multi-sensor networked stochastic linear discrete-time systems with unknown packet receiving rates, noise variances (NVs), and model parameters (MPs). Packet dropouts may occur when sensor data are sent to a local processor. A Bernoulli distributed stochastic variable is adopted to depict phenomena of packet dropouts. By model transformation, the identification problem of packet receiving rates is transformed into that of unknown MPs for a new augmented system. The recursive extended least squares (RELS) algorithm is used to simultaneously identify packet receiving rates and MPs in the original system. Then, a correlation function method is used to identify unknown NVs. Further, a ST distributed fusion state filter is achieved by applying identified packet receiving rates, NVs, and MPs to the corresponding optimal estimation algorithms. It is strictly proven that ST algorithms converge to optimal algorithms under the condition that the identifiers for parameters are consistent. Two examples verify the effectiveness of the proposed algorithms.
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Li, Huan, Siqi Bu, Jiong-Ran Wen, and Cheng-Wei Fei. "Synthetical Modal Parameters Identification Method of Damped Oscillation Signals in Power System." Applied Sciences 12, no. 9 (May 6, 2022): 4668. http://dx.doi.org/10.3390/app12094668.
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It is vital to improve the stability of the power system by accurately identifying the modal parameters of damped low-frequency oscillations (DLFO) and controlling the oscillation in time. A new method based on empirical mode decomposition (EMD), stochastic subspace identification (SSI), and Prony algorithms, called synthetical modal parameters identification (SMPI) method, is developed by efficiently matching the modal parameters of DLFO which are acquired from the SSI and Prony algorithm. In this approach, EMD is used for denoising the raw oscillation signals thereby enhancing the noise resistance, and then using the SSI and Prony algorithms to identify the precise modal parameters assisted by parameter matching. It is demonstrated that the proposed SMPI method holds great accuracy in identifying full modal parameters including natural frequencies, damping ratios, amplitudes, and phase angles with simulated signals with known modal parameters and real-time signals from some power system case studies. The strategy of SMPI has effectively overcome the weakness of a single approach, and the identification results are promising to heighten the stabilization of power systems. Besides, SMPI shows the potential to troubleshoot in different fields, such as construction, aeronautics, and marine, for its satisfactory robustness and generalization ability.
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Zhou, Yulin, Xulei Jiang, Mingjin Zhang, Jinxiang Zhang, Hao Sun, and Xin Li. "Modal parameters identification of bridge by improved stochastic subspace identification method with Grubbs criterion." Measurement and Control 54, no. 3-4 (February 18, 2021): 457–64. http://dx.doi.org/10.1177/0020294021993831.
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In the wind tunnel test of a long-span bridge model, to ensure that the dynamic characteristics of the model can satisfy the test design requirements, it is particularly important to accurately identify the modal parameters of the model. First, the stochastic subspace identification algorithm was used to analyze the modal parameters of the model in the wind tunnel test; then, Grubbs criterion was introduced to effectively eliminate outliers in the damping ratio matrix. Stochastic subspace identification algorithm with Grubbs criterion improved the accuracy of the modal parameter identification and the ability to determine system matrix order and prevented the modal omissions caused by determining the stable condition of the damping ratio in the stability diagram. Finally, Oujiang Bridge was used as an example to verify the stochastic subspace identification algorithm with Grubbs criterion and compare with the results of the finite element method. The example shows that the improved method can be effectively applied to the modal parameter identification of bridges.
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Legowo, Ari, Zahratu H. Mohamad, and Hoon Cheol Park. "Mixed Unscented Kalman Filter and Differential Evolution for Parameter Identification." Applied Mechanics and Materials 256-259 (December 2012): 2347–53. http://dx.doi.org/10.4028/www.scientific.net/amm.256-259.2347.
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This paper presents parameters estimation techniques for coupled industrial tanks using the mixed Unscented Kalman Filter (UKF) and Differential Evolution (DE) method. UKF have known to be a typical estimation technique used to estimate the state vectors and parameters of nonlinear dynamical systems and DE is one of the most powerful stochastic real-parameter optimization algorithms. Meanwhile, liquid tank systems play important role in industrial application such as in food processing, beverage, dairy, filtration, effluent treatment, pharmaceutical industry, water purification system, industrial chemical processing and spray coating. The aim is to model the coupled tank system using mixed UKF and DE method to estimate the parameters of the tank. First, a non-linear mathematical model is developed. Next, its parameters are identified using mixed Unscented Kalman Filter (UKF) and Differential Evolution (DE) based on the experimental data. DE algorithm is integrated into the UKF algorithm to optimize the Kalman gain obtained. The obtained results demonstrate good performances.
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Bouzbida, Mohamed, Lassad Hassine, and Abdelkader Chaari. "Robust Kernel Clustering Algorithm for Nonlinear System Identification." Mathematical Problems in Engineering 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/2427309.
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In engineering field, it is necessary to know the model of the real nonlinear systems to ensure its control and supervision; in this context, fuzzy modeling and especially the Takagi-Sugeno fuzzy model has drawn the attention of several researchers in recent decades owing to their potential to approximate nonlinear behavior. To identify the parameters of Takagi-Sugeno fuzzy model several clustering algorithms are developed such as the Fuzzy C-Means (FCM) algorithm, Possibilistic C-Means (PCM) algorithm, and Possibilistic Fuzzy C-Means (PFCM) algorithm. This paper presents a new clustering algorithm for Takagi-Sugeno fuzzy model identification. Our proposed algorithm called Robust Kernel Possibilistic Fuzzy C-Means (RKPFCM) algorithm is an extension of the PFCM algorithm based on kernel method, where the Euclidean distance used the robust hyper tangent kernel function. The proposed algorithm can solve the nonlinear separable problems found by FCM, PCM, and PFCM algorithms. Then an optimization method using the Particle Swarm Optimization (PSO) method combined with the RKPFCM algorithm is presented to overcome the convergence to a local minimum of the objective function. Finally, validation results of examples are given to demonstrate the effectiveness, practicality, and robustness of our proposed algorithm in stochastic environment.
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Abu Hasan, Muhammad Danial Bin, Zair Asrar Bin Ahmad, Mohd Salman Leong, and Lim Meng Hee. "Automated Harmonic Signal Removal Technique Using Stochastic Subspace-Based Image Feature Extraction." Journal of Imaging 6, no. 3 (March 5, 2020): 10. http://dx.doi.org/10.3390/jimaging6030010.
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This paper presents automated harmonic removal as a desirable solution to effectively identify and discard the harmonic influence over the output signal by neglecting any user-defined parameter at start-up and automatically reconstruct back to become a useful output signal prior to system identification. Stochastic subspace-based algorithms (SSI) methods are the most practical tool due to the consistency in modal parameters estimation. However, it will be problematic when applied to structures with rotating machines and the presence of harmonic excitations. Difficulties arise when automating this procedure without any human interaction and the problem is still unresolved because stochastic subspace-based algorithms (SSI) methods still require parameters (the maximum within-cluster distance) that are compulsory to be defined at start-up for each analysis of the dataset. Thus, the use of image-based feature extraction for clustering and classification of harmonic components and structural poles directly from a stabilization diagram and for modal system identification is the focus of the present paper. As a fundamental necessary condition, the algorithm has been assessed first from computed numerical responses and then applied to the experimental dataset with the presence of harmonic excitation. Results of the proposed approach for estimating modal parameters demonstrated very high accuracy and exhibited consistent results before and after removing harmonic components from the response signal.
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Wang, Peng, Ge Li, Yong Peng, and Rusheng Ju. "Random Finite Set Based Parameter Estimation Algorithm for Identifying Stochastic Systems." Entropy 20, no. 8 (July 31, 2018): 569. http://dx.doi.org/10.3390/e20080569.
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Parameter estimation is one of the key technologies for system identification. The Bayesian parameter estimation algorithms are very important for identifying stochastic systems. In this paper, a random finite set based algorithm is proposed to overcome the disadvantages of the existing Bayesian parameter estimation algorithms. It can estimate the unknown parameters of the stochastic system which consists of a varying number of constituent elements by using the measurements disturbed by false detections, missed detections and noises. The models used for parameter estimation are constructed by using random finite set. Based on the proposed system model and measurement model, the key principles and formula derivation of the proposed algorithm are detailed. Then, the implementation of the algorithm is presented by using sequential Monte Carlo based Probability Hypothesis Density (PHD) filter and simulated tempering based importance sampling. Finally, the experiments of systematic errors estimation of multiple sensors are provided to prove the main advantages of the proposed algorithm. The sensitivity analysis is carried out to further study the mechanism of the algorithm. The experimental results verify the superiority of the proposed algorithm.
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Fadhil Shazmir, M., N. Ayuni Safari, M. Azhan Anuar, A. A.Mat Isa, and Zamri A.R. "Operational Modal Analysis on a 3D Scaled Model of a 3-Storey Aluminium Structure." International Journal of Engineering & Technology 7, no. 4.27 (November 30, 2018): 78. http://dx.doi.org/10.14419/ijet.v7i4.27.22485.
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Obtaining a good experimental modal data is essential in modal analysis in order to ensure accurate extraction of modal parameters. The parameters are compared with other extraction methods to ascertain its consistency and validity. This paper demonstrates the extraction of modal parameters using various identification algorithms in Operational Modal Analysis (OMA) on a 3D scaled model of a 3-storey aluminium structure. Algorithms such as Frequency Domain Decomposition (FDD), Enhanced Frequency Domain Decomposition (EFDD) and Stochastic Subspace Identification (SSI) are applied in this study to obtain modal parameters. The model test structure is fabricated of aluminium and assembled using bolts and nuts. Accelerometers were used to collect the responses and the commercial post processing software was used to obtain the modal parameters. The resulting natural frequencies and mode shapes using FDD method are then compared with other OMA parametric technique such as EFDD and SSI algorithm by comparing the natural frequencies and Modal Assurance Criterion (MAC). Comparison of these techniques will be shown to justify the validity of each technique used and hence confirming the accuracy of the measurement taken.
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Goryainov, V. B., and W. M. Khing. "Comparison of Classical and Robust Estimates of Threshold Auto-regression Parameters." Mathematics and Mathematical Modeling, no. 5 (February 6, 2021): 33–44. http://dx.doi.org/10.24108/mathm.0520.0000224.
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The exponential auto-regression model is a discrete analog of the second-order nonlinear differential equations of the type of Duffing and van der Pol oscillators. It is used to describe nonlinear stochastic processes with discrete time, such as vehicle vibrations, ship roll, electrical signals in the cerebral cortex. When applying the model in practice, one of the important tasks is its identification, in particular, an estimate of the model parameters from observations of the stochastic process it described. A traditional technique to estimate autoregressive parameters is the nonlinear least squares method. Its disadvantage is high sensitivity to the measurement errors of the process observed. The M-estimate method largely has no such a drawback. The M-estimates are based on the minimization procedure of a non-convex function of several variables. The paper studies the effectiveness of several well-known minimization methods to find the M-estimates of the parameters of an exponential autoregressive model. The paper demonstrates that the sequential quadratic programming algorithm, the active set algorithm, and the interior-point algorithm have shown the best and approximately the same accuracy. The quasi-Newton algorithm is inferior to them in accuracy a little bit, but is not inferior in time. These algorithms had approximately the same speed and were one and a half times faster than the Nelder-Mead algorithm and 14 times faster than the genetic algorithm. The Nelder-Mead algorithm and the genetic algorithm have shown the worst accuracy. It was found that all the algorithms are sensitive to initial conditions. The estimate of parameters, on which the autoregressive equation linearly depends, is by an order of magnitude more accurate than that of the parameter on which the auto-regression equation depends in a nonlinear way.
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Zhao, Baigang, and Xianku Zhang. "An improved nonlinear innovation-based parameter identification algorithm for ship models." Journal of Navigation 74, no. 3 (March 5, 2021): 549–57. http://dx.doi.org/10.1017/s0373463321000102.
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AbstractTo solve the problem of identifying ship model parameters quickly and accurately with the least test data, this paper proposes a nonlinear innovation parameter identification algorithm for ship models. This is based on a nonlinear arc tangent function that can process innovations on the basis of an original stochastic gradient algorithm. A simulation was carried out on the ship Yu Peng using 26 sets of test data to compare the parameter identification capability of a least square algorithm, the original stochastic gradient algorithm and the improved stochastic gradient algorithm. The results indicate that the improved algorithm enhances the accuracy of the parameter identification by about 12% when compared with the least squares algorithm. The effectiveness of the algorithm was further verified by a simulation of the ship Yu Kun. The results confirm the algorithm's capacity to rapidly produce highly accurate parameter identification on the basis of relatively small datasets. The approach can be extended to other parameter identification systems where only a small amount of test data is available.
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Wen, Peng, Inamullah Khan, Jie He, and Qiaofeng Chen. "Application of Improved Combined Deterministic-Stochastic Subspace Algorithm in Bridge Modal Parameter Identification." Shock and Vibration 2021 (March 10, 2021): 1–11. http://dx.doi.org/10.1155/2021/8855162.
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Modal parameter identification is considered to be one of the most important tasks in structural health monitoring because it provides a reliable reference for structural vibration control, damage severity, and operational state. Moreover, at present, the combined deterministic-stochastic subspace algorithm is cogitated as one of the key algorithms in the modal parameter identification, which is why it is widely used in the modal parameter identification of bridge structures. In this paper, a novel method is proposed, which is a time-domain identification algorithm, based on sliding window-fuzzy C-means clustering algorithm-combined with deterministic-stochastic subspace identification (SC-CDSI), to achieve online intelligent tracking and identification of modal parameters for nonlinear time-varying structures. First of all, to realize the online tracking and identification process, it is necessary to divide the input and output signal of the nonlinear time-varying structure by windowing; for that, to determine the window function, window size and window step length according to the characteristics of the signal are analyzed. Secondly, in order to satisfy the intelligent identification of effective modals in stability diagram, the fuzzy C-means clustering algorithm is kept as a base, whereas frequency, damping ratio, and modal shapes serve as clustering elements, applied to fuzzy C-means clustering algorithm, and then the intelligent selection of effective modals is achieved. Finally, a shaking table test bridge is used as a modal parameter identification in lab, and its results are compared with the MIDAS finite element results. The compared results show that the proposed SC-CDSI identification algorithm can accurately achieve the intelligent identification of online tracking of the structural frequency, and the identification results are reliable to be used in real-life bridge structures.
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Khemani, Varun, Michael H. Azarian, and Michael G. Pecht. "Efficient Identification of Jiles–Atherton Model Parameters Using Space-Filling Designs and Genetic Algorithms." Eng 3, no. 3 (August 18, 2022): 364–72. http://dx.doi.org/10.3390/eng3030026.
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The Jiles–Atherton model is widespread in the hysteresis description of ferromagnetic, ferroelectric, magneto strictive, and piezoelectric materials. However, the determination of model parameters is not straightforward because the model involves numerical integration and the solving of ordinary differential equations, both of which are error prone. As a result, stochastic optimization techniques have been used to explore the vast ranges of these parameters in an effort to identify the parameter values that minimize the error differential between experimental and modelled hysteresis curves. Because of the time-consuming nature of these optimization techniques, this paper explores the design space of the parameters using a space-filling design. This design provides a narrower range of parameters to look at with optimization algorithms, thereby reducing the time required to identify the optimal Jiles–Atherton model parameters. This procedure can also be carried out without using expensive hysteresis measurement devices, provided the desired transformer’s secondary voltage is known.
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Lv, Li Xing, and Jing Chen. "Modified Stochastic Gradient Algorithm for Hammerstein Systems." Applied Mechanics and Materials 336-338 (July 2013): 2320–23. http://dx.doi.org/10.4028/www.scientific.net/amm.336-338.2320.
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This paper proposes a modified stochastic gradient algorithm for Hammerstein systems. By the Weierstrass approximation theorem, the model of the nonlinear Hammerstein systems be changed to an identification model, then based on the derived model, a modified stochastic gradient identification algorithm is used to estimate all the unknown parameters of the systems. An example is provided to show the effectiveness of the proposed algorithm.
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Pramod, B. R., and S. C. Bose. "System Identification Using ARMA Modeling and Neural Networks." Journal of Engineering for Industry 115, no. 4 (November 1, 1993): 487–91. http://dx.doi.org/10.1115/1.2901794.
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Stochastic system identification is an important tool for control of discrete dynamic systems. Among the modeling strategies developed for this purpose, Auto Regressive Moving Average (ARMA for discrete systems) models offer an accurate identification technique. The disadvantage with these models are that they are extremely complicated to implement on-line, especially for nonlinear time-variant systems. This paper utilizes a Neural Network structure for identification of stochastic processes and tracks system dynamics by on-line adjustments of network parameters. Neural dynamics is based on impulse responses and an iterative learning algorithm is derived using conventional principles of gradient descent and backpropagation. The learning algorithm is analyzed and shown to be fast and accurate in the identification of parameters for stochastic processes in both time-invariant and time-variant cases.
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Liu, Bingwen, Zhiyong Ji, Tie Wang, Zhenghao Tang, and Guoxing Li. "Failure Identification of Dump Truck Suspension Based on an Average Correlation Stochastic Subspace Identification Algorithm." Applied Sciences 8, no. 10 (October 1, 2018): 1795. http://dx.doi.org/10.3390/app8101795.
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This paper proposes a fault identification method based on an improved stochastic subspace modal identification algorithm to achieve high-performance fault identification of dump truck suspension. The sensitivity of modal parameters to suspension faults is evaluated, and a fault diagnosis method based on modal energy difference is established. The feasibility of the proposed method is validated by numerical simulation and full-scale vehicle tests. The result shows that the proposed average correlation signal based stochastic subspace identification (ACS-SSI) method can identify the fluctuation of vehicle modal parameters effectively with respect to different spring stiffness and damping ratio conditions, and then fault identification of the suspension system can be realized by the variation of the modal energy difference (MED).
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Moufida, Moussaoui, Rehab Bekkouche Souhila, Kamouche Houda, Benayoun Fadila, and Goudjil Kamel. "Identification of Soil Mechanical Parameters by Inverse Analysis Using Stochastic Methods." Selected Scientific Papers - Journal of Civil Engineering 17, no. 1 (December 1, 2022): 1–12. http://dx.doi.org/10.2478/sspjce-2022-0018.
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Abstract The mechanical parameters of the soil that must be introduced into geotechnical calculations, in particular those carried out by the Finite Element Method, are often poorly understood. The search for the numerical values of these parameters so that the models best reflect the observed reality constitutes the inverse analysis approach. In this article, we are interested in the identification of the mechanical parameters of the soil based on the principle of inverse analysis using the two methods of stochastic optimization, the genetic algorithm and the hybrid genetic algorithm with Tabu search. Soil behavior is represented by the constitutive soil Mohr-Coulomb model. The identification relates to the following two parameters: The shear modulus (G) and the friction angle (φ). The validation of these two stochastic optimization methods is done on the experimental sheet pile wall of Hochstetten in Germany. The results obtained by applying the genetic algorithm method and the hybrid genetic algorithm method for the identification of the two Mohr-Coulomb parameters (G, φ) show that the hybridization process of the genetic algorithm combined with the Tabu search method accelerated the convergence of the algorithm to the exact solution of the problem whereas the genetic algorithm alone takes a much longer computation time to reach the exact solution of the problem.
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Zhang, Yanhui, and Wenyu Yang. "A comparative study of the stochastic simulation methods applied in structural health monitoring." Engineering Computations 31, no. 7 (September 30, 2014): 1484–513. http://dx.doi.org/10.1108/ec-07-2013-0185.
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Purpose – The purpose of this paper is to discuss the characteristics of several stochastic simulation methods applied in computation issue of structure health monitoring (SHM). Design/methodology/approach – On the basis of the previous studies, this research focusses on four promising methods: transitional Markov chain Monte Carlo (TMCMC), slice sampling, slice-Metropolis-Hasting (M-H), and TMCMC-slice algorithm. The slice-M-H is the improved slice sampling algorithm, and the TMCMC-slice is the improved TMCMC algorithm. The performances of the parameters samples generated by these four algorithms are evaluated using two examples: one is the numerical example of a cantilever plate; another is the plate experiment simulating one part of the mechanical structure. Findings – Both the numerical example and experiment show that, identification accuracy of slice-M-H is higher than that of slice sampling; and the identification accuracy of TMCMC-slice is higher than that of TMCMC. In general, the identification accuracy of the methods based on slice (slice sampling and slice-M-H) is higher than that of the methods based on TMCMC (TMCMC and TMCMC-slice). Originality/value – The stochastic simulation methods evaluated in this paper are mainly two categories of representative methods: one introduces the intermediate probability density functions, and another one is the auxiliary variable approach. This paper provides important references about the stochastic simulation methods to solve the ill-conditioned computation issue, which is commonly encountered in SHM.
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Grigoriev, Vasiliy V., and Petr N. Vabishchevich. "Bayesian Estimation of Adsorption and Desorption Parameters for Pore Scale Transport." Mathematics 9, no. 16 (August 18, 2021): 1974. http://dx.doi.org/10.3390/math9161974.
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Stochastic parameter estimation and inversion have become increasingly popular in recent years. Nowadays, it is computationally reasonable and regular to solve complex inverse problems within the Bayesian framework. Applications of Bayesian inferences for inverse problems require investigation of the posterior distribution, which usually has a complex landscape and is highly dimensional. In these cases, Markov chain Monte Carlo methods (MCMC) are often used. This paper discusses a Bayesian approach for identifying adsorption and desorption rates in combination with a pore-scale reactive flow. Markov chain Monte Carlo sampling is used to estimate adsorption and desorption rates. The reactive transport in porous media is governed by incompressible Stokes equations, coupled with convection–diffusion equation for species’ transport. Adsorption and desorption are accounted via Robin boundary conditions. The Henry isotherm is considered for describing the reaction terms. The measured concentration at the outlet boundary is provided as additional information for the identification procedure. Metropolis–Hastings and Adaptive Metropolis algorithms are implemented. Credible intervals have been plotted from sampled posterior distributions for both algorithms. The impact of the noise in the measurements and influence of several measurements for Bayesian identification procedure is studied. Sample analysis using the autocorrelation function and acceptance rate is performed to estimate mixing of the Markov chain. As result, we conclude that MCMC sampling algorithm within the Bayesian framework is good enough to determine an admissible set of parameters via credible intervals.
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Angelova, Maria, Stoyan Tzonkov, and Tania Pencheva. "Parameter Identification of a Fed-Batch Cultivation of S. Cerevisiae using Genetic Algorithms." Serdica Journal of Computing 4, no. 1 (March 31, 2010): 11–18. http://dx.doi.org/10.55630/sjc.2010.4.11-18.
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Fermentation processes as objects of modelling and high-quality control are characterized with interdependence and time-varying of process variables that lead to non-linear models with a very complex structure. This is why the conventional optimization methods cannot lead to a satisfied solution. As an alternative, genetic algorithms, like the stochastic global optimization method, can be applied to overcome these limitations. The application of genetic algorithms is a precondition for robustness and reaching of a global minimum that makes them eligible and more workable for parameter identification of fermentation models. Different types of genetic algorithms, namely simple, modified and multi-population ones, have been applied and compared for estimation of nonlinear dynamic model parameters of fed-batch cultivation of S. cerevisiae.
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Черникова, Оксана Сергеевна, Александр Сергеевич Толстиков, and Юлия Сергеевна Четвертакова. "Application of adaptive identification methods for refining parameters of radiation pressure models." Вычислительные технологии, no. 3 (July 15, 2020): 35–45. http://dx.doi.org/10.25743/ict.2020.25.3.005.
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Представлены две адаптивные модификации сигма-точечного фильтра Калмана с рекуррентным оцениванием ковариационных матриц шумов системы и измерений, на основе которых выполняется процедура параметрической идентификации нелинейных непрерывно-дискретных систем. Применение процедуры адаптивной параметрической идентификации позволило вычислить с достаточной точностью оценки параметров нескольких моделей радиационного давления солнечного излучения. Полученные результаты повысили качество прогнозирования траектории движения навигационного спутника Purpose. The paper considers the problem of estimation of unknown parameters for various models of solar radiation based on adaptive modifications of the unscented Kalman filter. The estimations of the obtained parameters are used both in solar radiation models and in construction of trajectory of a navigation satellite. Methodology. To solve the problem of parametric identification of stochastic nonlinear continuous-discrete systems, several adaptive modifications of the unscented Kalman filter are considered. The algorithms assume recurrent estimation of covariance matrices of system noise and measurements. The maximum likelihood method is used for parametric identification of stochastic nonlinear continuous-discrete systems. Adaptive modifications of the unscented Kalman filter are used in the construction of the identification criterion. Estimates of unknown parameters of various solar radiation models are found for the movement for the navigation satellite model as an example. The satellite orbital movement forecast is made. Finding and value. The application of the adaptive parametric identification procedure allows calculating the estimates for the parameters of several models of the solar radiation with sufficient accuracy. The obtained results lead to significant improvement of quality of the prediction for satellite trajectory
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Chen, Jing, and Ruifeng Ding. "Two Identification Methods for Dual-Rate Sampled-Data Nonlinear Output-Error Systems." Mathematical Problems in Engineering 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/329437.
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This paper presents two methods for dual-rate sampled-data nonlinear output-error systems. One method is the missing output estimation based stochastic gradient identification algorithm and the other method is the auxiliary model based stochastic gradient identification algorithm. Different from the polynomial transformation based identification methods, the two methods in this paper can estimate the unknown parameters directly. A numerical example is provided to confirm the effectiveness of the proposed methods.
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Xia, Huafeng, and Feiyan Chen. "Filtering-Based Parameter Identification Methods for Multivariable Stochastic Systems." Mathematics 8, no. 12 (December 21, 2020): 2254. http://dx.doi.org/10.3390/math8122254.
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This paper presents an adaptive filtering-based maximum likelihood multi-innovation extended stochastic gradient algorithm to identify multivariable equation-error systems with colored noises. The data filtering and model decomposition techniques are used to simplify the structure of the considered system, in which a predefined filter is utilized to filter the observed data, and the multivariable system is turned into several subsystems whose parameters appear in the vectors. By introducing the multi-innovation identification theory to the stochastic gradient method, this study produces improved performances. The simulation numerical results indicate that the proposed algorithm can generate more accurate parameter estimates than the filtering-based maximum likelihood recursive extended stochastic gradient algorithm.
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Lobaty, A. A., and V. Y. Stepanov. "PARAMETRIC IDENTIFICATION OF STOCHASTIC SYSTEM BY NON-GRADIENT RANDOM SEARCHING." Science & Technique 16, no. 3 (May 26, 2017): 256–61. http://dx.doi.org/10.21122/2227-1031-2017-16-3-256-261.
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At this moment we know a great variety of identification objects, tasks and methods and its significance is constantly increasing in various fields of science and technology. The identification problem is dependent on a priori information about identification object, besides that the existing approaches and methods of identification are determined by the form of mathematical models (deterministic, stochastic, frequency, temporal, spectral etc.). The paper considers a problem for determination of system parameters (identification object) which is assigned by the stochastic mathematical model including random functions of time. It has been shown that while making optimization of the stochastic systems subject to random actions deterministic methods can be applied only for a limited approximate optimization of the system by taking into account average random effects and fixed structure of the system. The paper proposes an algorithm for identification of parameters in a mathematical model of the stochastic system by non-gradient random searching. A specific feature of the algorithm is its applicability practically to mathematic models of any type because the applied algorithm does not depend on linearization and differentiability of functions included in the mathematical model of the system. The proposed algorithm ensures searching of an extremum for the specified quality criteria in terms of external uncertainties and limitations while using random searching of parameters for a mathematical model of the system. The paper presents results of the investigations on operational capability of the considered identification method while using mathematical simulation of hypothetical control system with a priori unknown parameter values of the mathematical model. The presented results of the mathematical simulation obviously demonstrate the operational capability of the proposed identification method.
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Hartel, Udo, Alexander Ilin, Steffen Sonntag, and Vesselin Michailov. "Nonlinear Optimization Methods for the Determination of Heat Source Model Parameters." Materials Science Forum 879 (November 2016): 2008–13. http://dx.doi.org/10.4028/www.scientific.net/msf.879.2008.
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In this paper the technique of parameter identification is investigated to reconstruct the 3D transient temperature field for the simulation of laser beam welding. The reconstruction bases on volume heat source models and makes use of experimental data. The parameter identification leads to an inverse heat conduction problem which cannot be solved exactly but in terms of an optimal alignment of the simulation and experimental data. To solve the inverse problem, methods of nonlinear optimization are applied to minimize a problem dependent objective function.In particular the objective function is generated based on the Response Surface Model (RSM) technique. Sampling points on the RSM are determined by means of Finite-Element-Analysis (FEA). The scope of this research paper is the evaluation and comparison of gradient based and stochastic optimization algorithms. The proposed parameter identification makes it possible to determine the heat source model parameters in an automated way. The methodology is applied on welds of dissimilar material joints.
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Liu, Yang, Qiang Zhang, Longjin Wang, Shun An, Yan He, Zhimin Fan, and Fang Deng. "Identification of Multi-Innovation Stochastic Gradients with Maximum Likelihood Algorithm Based on Ship Maneuverability and Wave Peak Models." Journal of Marine Science and Engineering 12, no. 1 (January 11, 2024): 142. http://dx.doi.org/10.3390/jmse12010142.
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This paper investigates the problem of real-time parameter identification for ship maneuvering parameters and wave peak frequency in an ocean environment. Based on the idea of Euler discretion, a combined model of ship maneuvering and wave peak frequency (ship–wave) is made a discretion, and a discrete-time auto-regressive moving-average model with exogenous input (ARMAX) is derived for parameter identification. Based on the ideas of stochastic gradient identification and multi-innovation theory, a multi-innovation stochastic gradient (MI-SG) algorithm is derived for parameter identification of the ship–wave discretion model. Maximum likelihood theory is introduced to propose a maximum likelihood-based multi-innovation stochastic gradient (ML-MI-SG) algorithm. Compared to the MI-SG algorithm, the ML-MI-SG algorithm shows improvements in both parameter identification accuracy and identification convergence speed. Simulation results verify the effectiveness of the proposed algorithm.
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Xu, Bao-chang, Zhong-hua Lin, Ying-Dan Zhang, and Yu-yue Xiao. "Extended Stochastic Gradient Identification Method for Hammerstein Model Based on Approximate Least Absolute Deviation." Mathematical Problems in Engineering 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/9548428.
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In order to identify the parameters of nonlinear Hammerstein model which are contaminated by colored noise and peak noise, the least absolute deviation (LAD) is selected as the objective function to solve the problem of large residual square when the identification data is disturbed by the impulse noise which obeys symmetrical alpha stable (SαS) distribution. However, LAD cannot meet the need of differentiability required by most algorithms. To improve robustness and to solve the nondifferentiable problem, an approximate least absolute deviation (ALAD) objective function is established by introducing a deterministic function to replace absolute value under certain situations. The proposed method is derived from ALAD criterion and extended stochastic gradient method. Due to the differentiability of the objective function, we can get a recursive identification algorithm which is simple and easy to calculate compared with LAD. The convergence of the proposed identification method is also proved by Lyapunov stability theory, and the simulation experiments show that the proposed method has higher accuracy and stronger robustness than the least square (LS) method in the identification of Hammerstein model with colored noise and impulse noise. The impact of impulse noise can be restrained effectively.
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Wu, Haishan, and Yifeng Huang. "Modal Parameter Identification of Recursive Stochastic Subspace Method." Symmetry 15, no. 6 (June 11, 2023): 1243. http://dx.doi.org/10.3390/sym15061243.
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In bridge health monitoring, in order to closely monitor the structural state changes of the bridge under heavy traffic load and other harsh environments, the monitoring system is required to give the change process of structural modal parameters. Due to the symmetric variables of bridge monitoring during operation, the evaluation needs to be completed by the recursive identification of modal parameters based on environmental excitation, especially the recursive recognition of the random subspace method with high recognition accuracy. We have studied the recursive identification methods of covariance-driven and data-driven random subspace categories respectively, established the corresponding recursive format, and used the model structure of the ASCE structural health monitoring benchmark problem as a numerical example to verify the reliability of the proposed method. First, based on the similar interference environment of the observation data at the same time, a reference point covariance-driven random subspace recursive algorithm (IV-RSSI/Cov) based on the auxiliary variable projection approximation tracking (IV-PAST) algorithm is established. The recursive format of the system matrix and modal parameters is obtained. Based on Givens rotation, the rank-2 update form of the row space projection matrix is established, and the recursive format of the data-driven recursive random subspace method (RSSI/Data) under the PAST algorithm is obtained. Then, based on the benchmark problem of ASCE-SHM, the response of the model structure under environmental excitation is numerically simulated, the frequency, damping ratio and vibration mode of the structure are recursively tracked, and their reliability and shortcomings are studied. After improving the recursive method, the frequency tracking accuracy has been improved, with a maximum accuracy of 99.8%.
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Roeva, Olympia, and Dafina Zoteva. "Model Identification of E. coli Cultivation Process Applying Hybrid Crow Search Algorithm." Fermentation 10, no. 1 (December 22, 2023): 12. http://dx.doi.org/10.3390/fermentation10010012.
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Cultivation process (CP) modeling and optimization are ambitious tasks due to the nonlinear nature of the models and interdependent parameters. The identification procedures for such models are challenging. Metaheuristic algorithms exhibit promising performance for such complex problems since a near-optimal solution can be found in an acceptable time. The present research explores a new hybrid metaheuristic algorithm built upon the good exploration of the genetic algorithm (GA) and the exploitation of the crow search algorithm (CSA). The efficiency of the proposed GA-CSA hybrid is studied with the model parameter identification procedure of the E. coli BL21(DE3)pPhyt109 fed-batch cultivation process. The results are compared with those of the pure GA and pure CSA applied to the same problem. A comparison with two deterministic algorithms, i.e., sequential quadratic programming (SQP) and the Quasi-Newton (Q-N) method, is also provided. A more accurate model is obtained by the GA-CSA hybrid with fewer computational resources. Although SQP and Q-N find a solution for a smaller number of function evaluations, the resulting models are not as accurate as the models generated by the three metaheuristic algorithms. The InterCriteria analysis, a mathematical approach to revealing certain relations between given criteria, and a series of statistical tests are employed to prove that there is a statistically significant difference between the results of the three stochastic algorithms. The obtained mathematical models are then successfully verified with a different set of experimental data, in which, again, the closest one is the GA-CSA model. The GA-CSA hybrid proposed in this paper is proven to be successful in the collaborative hybridization of GA and CSA with outstanding performance.
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Chub, E. G., and V. A. Pogorelov. "Identification algorithm for telecommunication systems with uncertain parameters of their vector of state stochastic model." Journal of Physics: Conference Series 2131, no. 2 (December 1, 2021): 022090. http://dx.doi.org/10.1088/1742-6596/2131/2/022090.
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Abstract The described method of structure identification of the state vector of a telecommunication system stochastic model is based on a posteriori probability density approximation (APDA) by a system of a posteriori moments. An assumption of possible APDA approximation by a class of Pearson distributions resulted in a closed system of moment equations. Implementation of optimal non-linear stochastic object control techniques helped to solve the problem of structural identification. Introduction of the proposed approach into contemporary telecommunication systems will not impose additional requirements on the calculating equipment, thus making this method well-suited for a wide range of applications.
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Zou, Hong Fen. "Identification of Hammerstein Systems with Two-Segment Preload Nonlinearity Based on the Gradient Search." Applied Mechanics and Materials 651-653 (September 2014): 2314–17. http://dx.doi.org/10.4028/www.scientific.net/amm.651-653.2314.
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This paper deals with the parameter identication problem for Hammerstein systems with two-segment preload nonlinearity. Taking into account the complexity of Hammerstein systems, we use theWeierstrass approximation theorem to convert a Hammerstein system into a special form that has linear-in-parameters, and propose a stochastic gradient algorithm to estimate all unknown parameters of Hammerstein systems. Furthermore, a modified stochastic gradient algorithm is given to improve the convergence rate. The applicability of the approach is illustrated by a simulation example.
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Ahmed, N. U., and S. M. Radaideh. "Identification of linear stochastic systems based on partial information." Journal of Applied Mathematics and Stochastic Analysis 8, no. 3 (January 1, 1995): 249–60. http://dx.doi.org/10.1155/s1048953395000220.
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In this paper, we consider an identification problem for a system of partially observed linear stochastic differential equations. We present a result whereby one can determine all the system parameters including the covariance matrices of the noise processes. We formulate the original identification problem as a deterministic control problem and prove the equivalence of the two problems. The method of simulated annealing is used to develop a computational algorithm for identifying the unknown parameters from the available observation. The procedure is then illustrated by some examples.
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Gel, Yulia R., and Vladimir N. Fomin. "Identification of an unstable ARMA equation." Mathematical Problems in Engineering 7, no. 1 (2001): 97–112. http://dx.doi.org/10.1155/s1024123x01001557.
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Usually the coefficients in a stochastic time series model are partially or entirely unknown when the realization of the time series is observed. Sometimes the unknown coefficients can be estimated from the realization with the required accuracy. That will eventually allow optimizing the data handling of the stochastic time series.Here it is shown that the recurrent least-squares (LS) procedure provides strongly consistent estimates for a linear autoregressive (AR) equation of infinite order obtained from a minimal phase regressive (ARMA) equation. The LS identification algorithm is accomplished by the Padé approximation used for the estimation of the unknown ARMA parameters.
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Raffy, M., and C. Gontier. "Statistical asymptotic error on modal parameters in combined deterministic–stochastic identification algorithm." Mechanical Systems and Signal Processing 19, no. 4 (July 2005): 714–35. http://dx.doi.org/10.1016/j.ymssp.2004.11.001.
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Zhang, Qingsong, Yibo He, Meng Shu, Weizheng Zhang, Daojian Yang, Jinhua Song, Guanhua Li, et al. "A Level-Based Learning Swarm Optimizer with Stochastic Fractal Search for Parameters Identification of Solar Photovoltaic Models." Mathematical Problems in Engineering 2023 (February 22, 2023): 1–16. http://dx.doi.org/10.1155/2023/3397430.
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As the most popular renewable energy, solar energy could be converted into electricity by photovoltaic (PV) systems directly. To maximize the effectiveness of the conversion, it is critical to find the precise and accurate parameters of the PV model. In this paper, we propose a level-based learning swarm optimizer with stochastic fractal search (LLSOF) to tackle the parameter estimation of several kinds of solar PV models. The population is separated into multiple levels according to their fitness at first. The individuals at the lower levels evolve through learning from the individuals at the higher levels. Benefiting from the interactive learning among levels, the population could approach the multiple optimal regions rapidly. To enhance the local search ability, stochastic fractal search is introduced to locate the optima accurately. Combination of both, the proposed LLSOF could achieve a good balance on both exploration and exploitation. To evaluate the performance of LLSOF, it is used to obtain the parameters of three PV models and compared with nine well-established algorithms. Comparative results validate the excellent performance of LLSOF. Moreover, the application manufactory’s data sheets report the superior efficiency and effectiveness of LLSOF for the parameter estimation of PV systems.
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Zhang, Jinfang, Guodou Huang, and Li Zhang. "Generalized Correntropy Criterion-Based Performance Assessment for Non-Gaussian Stochastic Systems." Entropy 23, no. 6 (June 17, 2021): 764. http://dx.doi.org/10.3390/e23060764.
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Control loop performance assessment (CPA) is essential in the operation of industrial systems. In this paper, the shortcomings of existing performance assessment methods and indicators are summarized firstly, and a novel evaluation method based on generalized correntropy criterion (GCC) is proposed to evaluate the performance of non-Gaussian stochastic systems. This criterion could characterize the statistical properties of non-Gaussian random variables more fully, so it can be directly used as the assessment index. When the expected output of the given system is unknown, generalized correntropy is used to describe the similarity of two random variables in the joint space neighborhood controlled and take it as the criterion function of the identification algorithms. To estimate the performance benchmark more quickly and accurately, a hybrid-EDA (H-EDA) combined with the idea of “wading across the stream algorithm” is proposed to obtain the system parameters and disturbance noise PDF. Through the simulation of a single loop feedback control system under different noise disturbances, the effectiveness of the improved algorithm and new indexes are verified.
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Bianconi, Francesca, Georgios Panagiotis Salachoris, Francesco Clementi, and Stefano Lenci. "A Genetic Algorithm Procedure for the Automatic Updating of FEM Based on Ambient Vibration Tests." Sensors 20, no. 11 (June 10, 2020): 3315. http://dx.doi.org/10.3390/s20113315.
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The dynamic identification of the modal parameters of a structure, in order to gain control of its functionality under operating conditions, is currently under discussion from a scientific and technical point of views. The experimental observations obtained through structural health monitoring (SHM) are a useful calibration reference of numerical models (NMs). In this paper, the procedures for the identification of modal parameters in historical bell towers using a stochastic subspace identification (SSI) algorithm are presented. Then, NMs are manually calibrated on the identification’s results. Finally, the applicability of a genetic algorithm for the automatic calibration of the elastic parameters is considered with the aim of searching for the properties of the autochthonous material, in order to reduce modelling error following the model assurance criterion (MAC). In this regard, several material values on the same model are examined to see how to approach the evolution and the distribution of these features, comparing the characterization proposed by the genetic algorithm with the results considered by the manual iterative procedure.
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Zhigang, Wu, Wang Benli, and Ma Xingrui. "Theory and algorithm of optimal control solution to dynamic system parameters identification (II) — Stochastic system parameters identification and application example." Applied Mathematics and Mechanics 20, no. 3 (March 1999): 241–46. http://dx.doi.org/10.1007/bf02463848.
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