Study of the grey Verhulst model based on the weighted least square method

2020 ◽  
Vol 545 ◽  
pp. 123615 ◽  
Author(s):  
Liwei Tang ◽  
Yayun Lu
Keyword(s):  
Least Square Method ◽  
Least Square ◽  
Model Based ◽  
Weighted Least Square ◽  
Grey Verhulst Model ◽  
Verhulst Model

scholarly journals Grey power models based on optimization of initial condition and model parameters

2014 ◽  
Vol 4 (2) ◽  
pp. 370-382 ◽  
Author(s):  
Yunchol Jong ◽  
Sifeng Liu
Keyword(s):  
Least Square Method ◽  
Least Square ◽  
Model Parameters ◽  
Initial Condition ◽  
Content Type ◽  
Novel Approach ◽  
New Information ◽  
Power Models ◽  
Grey Verhulst Model ◽  
Verhulst Model

Purpose – The purpose of this paper is to propose a novel approach to improve prediction accuracy of grey power models including GM(1, 1) and grey Verhulst model. Design/methodology/approach – The modified new models are proposed by optimizing the initial condition and model parameters. The new initial condition consists of the first item and the last item of a sequence generated by applying the first-order accumulative generation operator on the sequence of raw data. Findings – It is shown that the newly modified grey power model is an extension of the previous optimized GM(1, 1) and grey Verhulst model. And the optimized initial condition reflected the principle of new information priority. Practical implications – The result of a numerical example indicates that the modified grey model presented in this paper with better prediction performance. Originality/value – The new initial condition are derived by weighted combination of the first item and the last item. The coefficients of weight obtained by the least square method.

Model-based control of the substrate concentration in an aeration basin using the wastewater level

1998 ◽  
Vol 37 (12) ◽  
pp. 335-342 ◽  
Author(s):  
Jacek Czeczot
Keyword(s):  
Substrate Concentration ◽  
Consumption Rate ◽  
Least Square Method ◽  
Estimation Procedure ◽  
Adaptive Controller ◽  
Open Loop ◽  
Least Square ◽  
Substrate Consumption ◽  
Model Based ◽  
Effluent Flow Rate

This paper deals with the minimal-cost control of the modified activated sludge process with varying level of wastewater in the aerator tank. The model-based adaptive controller of the effluent substrate concentration, basing on the substrate consumption rate and manipulating the effluent flow rate outcoming from the aerator tank, is proposed and its performance is compared with conventional PI controller and open loop behavior. Since the substrate consumption rate is not measurable on-line, the estimation procedure on the basis of the least-square method is suggested. Finally, it is proved that cooperation of the DO concentration controller with the adaptive controller of the effluent substrate concentration allows the process to be operated at minimum costs (low consumption of aeration energy).

scholarly journals Research on the Grey Verhulst Model Based on Particle Swarm Optimization and Markov Chain to Predict the Settlement of High Fill Subgrade in Xiangli Expressway

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Haiming Liu ◽  
Wei Guo ◽  
Chao Zhang ◽  
Huaihao Yang
Keyword(s):  
Particle Swarm Optimization ◽  
Markov Chain ◽  
Particle Swarm ◽  
Time Interval ◽  
Grey Theory ◽  
Swarm Optimization ◽  
Model Based ◽  
Grey Verhulst Model ◽  
Competing Models ◽  
Verhulst Model

It is of vital significance to accurately forecast the settlement of high fill subgrade, which is the foundation for disaster prevention and treatment of subgrade. According to the monitoring data of high fill subgrade, a novel model, called PSOMGVM model, based on particle swarm optimization (PSO) and Markov chain is proposed. Firstly, the typical characteristics of settlement curve are analyzed from the aspect of geomechanics theory and based on the grey theory, the grey Verhulst model (GVM) with unequal time-interval is proposed. Then, according to the theory of Markov chain, the grey Verhulst model is built to revise the relative residuals of the GVM, in which the effects of volatility characteristics can be considered. Finally, the PSOMGVM model based on PSO algorithm and Markov chain is set up, which whitens the parameters of the grey interval. In order to demonstrate the fitness and the ability of the proposed model, five competing models are introduced to predict the settlement of the high fill subgrade of Xiangli Expressway in Yunnan Province. Through the analysis of APE, MAPE, and RMSE, it states that the accuracy and performance of the PSOMGVM model outperform the other five competing models for simulative and predictive periods.

Numerical Analysis of Electromagnetic Levitation Employing Meshless Method Based on Weighted Least Square Method

2015 ◽  
Vol 15 (1) ◽  
pp. 29-34 ◽  
Author(s):  
Shuhei Matsuzawa ◽  
Kenta Mitsufuji ◽  
Yurika Miyake ◽  
Katsuhiro Hirata ◽  
Fumikazu Miyasaka
Keyword(s):  
Magnetic Field ◽  
Meshless Method ◽  
Fluid Motion ◽  
Electromagnetic Levitation ◽  
Least Square Method ◽  
Least Square ◽  
Weighted Least Square ◽  
Frequency Magnetic Field ◽  
Thermo Physical Properties ◽  
The Magnetic Field

AbstractElectromagnetic levitation is a kind of magnetohydrodynamic phenomena which is useful to measure the thermo-physical properties of pure metals under high temperature. However, this phenomenon is complicated and detailed mechanisms of this phenomenon have not been clarified yet. This study proposes the meshless method based on weighted least square method for the analysis of electromagnetic levitation. In this study, the fluid motion equation and the magnetic field equation are coupled by this method. The behavior of a molten metal under high-frequency magnetic field is calculated by this method.

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