PSO-Markov residual correction method based on Verhulst-Fourier prediction model

Niu, Tong; Zhang, Lin; Zhang, Bo; Li, Bo; Zhang, Baoshan; Wang, Wenfeng

doi:10.1080/21642583.2020.1863277

Cited by 4 publications

(6 citation statements)

References 9 publications

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“…Definition 4. (see [32]). Consider the X (0) sequence in Definition 1 and the predicted values given by the NGMs, and then, the error sequence of X (0) can be defined as…”

Section: Modification Of Ngvm Using Fourier Series Of Errormentioning

confidence: 96%

“…. GVM is a special kind of model within the grey system, which is first introduced by German biologist Pierre Franois Verhulst [31,32]. e main purpose of GVM is to limit the whole development for a real system, and it is effective in describing some increasing processes, such as an S-curve that has a saturation region [20].…”

Section: Nonequidistant Grey Verhulst Model (Ngvm)mentioning

confidence: 99%

“…At the same time, because of the internal of initial value x (1) (t 1 ) and adjustment coefficient λ of the background value sequence for NGMs, the prediction error of the model will also increase. erefore, in this study, Fourier series is introduced to reduce the periodic residual error in NGVM [31][32][33]. Definition 4.…”

Section: Modification Of Ngvm Using Fourier Series Of Errormentioning

confidence: 99%

“…In equation (19), T � n − 1 indicates the length of the residual series, and F � (n − 1/2) − 1 means the minimum deployment frequency of Fourier series. It is obvious that T will be an integer number, and F will be selected as an integer number [32]. Equation ( 22) can be rewritten as follows:…”

Section: Modification Of Ngvm Using Fourier Series Of Errormentioning

confidence: 99%

See 3 more Smart Citations

Prediction of Final Displacement of Tunnels in Time-Dependent Rock Mass Based on the Nonequidistant Grey Verhulst Model

Han¹,

Choe²,

Hong³

et al. 2022

Mathematical Problems in Engineering

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Time-dependent deformations of rock are important factors for the design and construction of tunnels in the rock masses with time-dependent strength and deformation properties. Therefore, determination displacement and stable time of tunnel are an indispensable task in geotechnical engineering, especially during the design and construction of underground structures. However, in some types of rock masses, the tunnel displacement may increase for months or years after the excavation owing to the rheological behavior of the surrounding rock masses, which greatly influences the selection of the initial tunnel support system, the excavation layout, and the determination of its load-carrying capacity. In this paper, we present a method to quickly predict the final displacement and stable time of tunnels in time-dependent rock mass using the improved nonequidistant grey Verhulst model (INGVM) with Fourier series, which is used to reduce the periodic residual error. The proposed method is validated fairly via a test for a newly excavated roadway of −600 m level in a coal mine, Democratic People’s Republic of Korea. These results are useful references for similar projects in the future.

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“…Definition 4. (see [32]). Consider the X (0) sequence in Definition 1 and the predicted values given by the NGMs, and then, the error sequence of X (0) can be defined as…”

Section: Modification Of Ngvm Using Fourier Series Of Errormentioning

confidence: 96%

Section: Nonequidistant Grey Verhulst Model (Ngvm)mentioning

confidence: 99%

Section: Modification Of Ngvm Using Fourier Series Of Errormentioning

confidence: 99%

Section: Modification Of Ngvm Using Fourier Series Of Errormentioning

confidence: 99%

See 2 more Smart Citations

Prediction of Final Displacement of Tunnels in Time-Dependent Rock Mass Based on the Nonequidistant Grey Verhulst Model

Han¹,

Choe²,

Hong³

et al. 2022

Mathematical Problems in Engineering

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“…The basic PSO approach has been widely adopted for image enhancement. A PSO-based automatic image enhancement technique has been proposed in [9], where PSO has been utilized to maximize an objective fitness criterion with the purpose of enhancing the contrast and details in the picture. Results show that the PSO-based automatic image enhancement technique obtains satisfactory performance in maximizing the number of pixels in the edges.…”

Section: Image Enhancementmentioning

confidence: 99%

A Survey of Algorithms, Applications and Trends for Particle Swarm Optimization

Fang

Liu

Chen

et al. 2023

IJNDI

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Survey/review study A Survey of Algorithms, Applications and Trends for Particle Swarm Optimization Jingzhong Fang 1, Weibo Liu 1,*, Linwei Chen 2, Stanislao Lauria 1, Alina Miron 1, and Xiaohui Liu 1 1 Department of Computer Science, Brunel University London, Uxbridge, Middlesex, UB8 3PH, United Kingdom 2 The School of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom * Correspondence: Weibo.Liu2@brunel.ac.uk Received: 18 October 2022 Accepted: 28 November 2022 Published: Abstract: Particle swarm optimization (PSO) is a popular heuristic method, which is capable of effectively dealing with various optimization problems. A detailed overview of the original PSO and some PSO variant algorithms is presented in this paper. An up-to-date review is provided on the development of PSO variants, which include four types i.e., the adjustment of control parameters, the newly-designed updating strategies, the topological structures, and the hybridization with other optimization algorithms. A general overview of some selected applications (e.g., robotics, energy systems, power systems, and data analytics) of the PSO algorithms is also given. In this paper, some possible future research topics of the PSO algorithms are also introduced.

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Multi-objective Optimization of Curtain Grouting Construction Scheme with Ensemble Residual Surrogate Model

Zhang,

Wang,

et al. 2024

Rock Mech Rock Eng

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PSO-Markov residual correction method based on Verhulst-Fourier prediction model

Cited by 4 publications

References 9 publications

Prediction of Final Displacement of Tunnels in Time-Dependent Rock Mass Based on the Nonequidistant Grey Verhulst Model

Prediction of Final Displacement of Tunnels in Time-Dependent Rock Mass Based on the Nonequidistant Grey Verhulst Model

A Survey of Algorithms, Applications and Trends for Particle Swarm Optimization

Multi-objective Optimization of Curtain Grouting Construction Scheme with Ensemble Residual Surrogate Model

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