scholarly journals Kinetics of Impurity Removal in Zinc Hydrometallurgy Based on Parameter Estimation

2021 ◽  
Vol 267 ◽  
pp. 02051
Author(s):  
Qianqian Wang ◽  
Minan Tang ◽  
Aimin An ◽  
Jiawei Lu ◽  
Yingying Zhao
Keyword(s):  
Parameter Estimation ◽  
Objective Function ◽  
Hessian Matrix ◽  
Zinc Powder ◽  
Ion Concentration ◽  
Practical Implementation ◽  
Model Parameters ◽  
Impurity Removal ◽  
Lead Zinc ◽  
Zinc Hydrometallurgy

Impurity removal is a momentous part of zinc hydrometallurgy process. In this paper, a hybrid modeling method of mechanism modeling and parameter estimation modeling was proposed on the basis of not changing the actual production process of lead-zinc smeltery. Firstly, the overall nonlinear dynamic mechanism model was established, and then the deviation between the theoretical value and the actual detected outlet ion concentration was taken as the objective function to establish the parameter estimation optimization model. The gradient vector and Hessian matrix of the objective function with respect to the parameter vector were derived, and the algorithm based on the steepest descent and Newton method was given. Finally, using the production data of a lead-zinc smeltery in China, the model parameters were inversed. An intensive simulation validation and analysis of the dynamic characteristics shows the accuracy and the potential of the model, also in the perspective of practical implementation, which provides the basis for the optimal control of system output and the guidance for zinc powder addition.

scholarly journals Parameter optimal identification and dynamic behavior analysis of nonlinear model for the solution purification process of zinc hydrometallurgy

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Qianqian Wang ◽  
Minan Tang ◽  
Aimin An ◽  
Jiawei Lu ◽  
Yingying Zhao
Keyword(s):  
Optimal Control ◽  
Parameter Identification ◽  
Objective Function ◽  
Ion Concentration ◽  
Steepest Descent Method ◽  
Practical Implementation ◽  
Model Parameters ◽  
Purification Process ◽  
Lead Zinc ◽  
Zinc Hydrometallurgy

<p style='text-indent:20px;'>Impurity removal is a momentous part of zinc hydrometallurgy process, and the quality of products and the stability of the whole process are affected directly by its control effect. The application of dynamic model is of great significance to the prediction of key indexes and the optimization of process control. In this paper, considering the complex coupling relationship of stage II purification process, a hybrid modeling method of mechanism modeling and parameter identification modeling was proposed on the basis of not changing the actual production process of lead-zinc smeltery. Firstly, the overall nonlinear dynamic mechanism model was established, and then the deviation between the theoretical value and the actual detected outlet ion concentration was taken as the objective function to establish the parameter identification optimization model. Since the built model is nonlinear, it may pose implementation problems. On the premise of deriving the gradient vector and Hessian matrix of the objective function with respect to the parameter vector, an optimization algorithm based on the steepest descent method and Newton method is proposed. Finally, using the historical production data of a lead-zinc smeltery in China, the model parameters were accurately inversed. An intensive simulation validation and analysis of the dynamic characteristics about the whole model shows the accuracy and the potential of the model, also in the perspective of practical implementation, which provides the basis for the optimal control of system output and the guidance for the optimal control of zinc powder addition.</p>

scholarly journals Constrained Parameter Estimation for a Mechanistic Kinetic Model of Cobalt–Hydrogen Electrochemical Competition during a Cobalt Removal Process

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 387
Author(s):  
Yiting Liang ◽  
Yuanhua Zhang ◽  
Yonggang Li
Keyword(s):  
Parameter Estimation ◽  
Kinetic Model ◽  
Model Parameters ◽  
Hydrogen Ions ◽  
Removal Process ◽  
Cobalt Removal ◽  
Estimation Scheme ◽  
Zinc Hydrometallurgy ◽  
The Impact ◽  
Parameter Estimation Scheme

A mechanistic kinetic model of cobalt–hydrogen electrochemical competition for the cobalt removal process in zinc hydrometallurgical was proposed. In addition, to overcome the parameter estimation difficulties arising from the model nonlinearities and the lack of information on the possible value ranges of parameters to be estimated, a constrained guided parameter estimation scheme was derived based on model equations and experimental data. The proposed model and the parameter estimation scheme have two advantages: (i) The model reflected for the first time the mechanism of the electrochemical competition between cobalt and hydrogen ions in the process of cobalt removal in zinc hydrometallurgy; (ii) The proposed constrained parameter estimation scheme did not depend on the information of the possible value ranges of parameters to be estimated; (iii) the constraint conditions provided in that scheme directly linked the experimental phenomenon metrics to the model parameters thereby providing deeper insights into the model parameters for model users. Numerical experiments showed that the proposed constrained parameter estimation algorithm significantly improved the estimation efficiency. Meanwhile, the proposed cobalt–hydrogen electrochemical competition model allowed for accurate simulation of the impact of hydrogen ions on cobalt removal rate as well as simulation of the trend of hydrogen ion concentration, which would be helpful for the actual cobalt removal process in zinc hydrometallurgy.

scholarly journals Determination of synchronous generator nonlinear model parameters based on power rejection tests using a gradient optimization algorithm

2017 ◽  
Vol 65 (4) ◽  
pp. 479-488 ◽  
Author(s):  
A. Boboń ◽  
A. Nocoń ◽  
S. Paszek ◽  
P. Pruski
Keyword(s):  
Parameter Estimation ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Least Squares Method ◽  
Synchronous Generator ◽  
Operating Conditions ◽  
Model Parameters ◽  
State Variables ◽  
Starting Point ◽  
Gradient Optimization

AbstractThe paper presents a method for determining electromagnetic parameters of different synchronous generator models based on dynamic waveforms measured at power rejection. Such a test can be performed safely under normal operating conditions of a generator working in a power plant. A generator model was investigated, expressed by reactances and time constants of steady, transient, and subtransient state in the d and q axes, as well as the circuit models (type (3,3) and (2,2)) expressed by resistances and inductances of stator, excitation, and equivalent rotor damping circuits windings. All these models approximately take into account the influence of magnetic core saturation. The least squares method was used for parameter estimation. There was minimized the objective function defined as the mean square error between the measured waveforms and the waveforms calculated based on the mathematical models. A method of determining the initial values of those state variables which also depend on the searched parameters is presented. To minimize the objective function, a gradient optimization algorithm finding local minima for a selected starting point was used. To get closer to the global minimum, calculations were repeated many times, taking into account the inequality constraints for the searched parameters. The paper presents the parameter estimation results and a comparison of the waveforms measured and calculated based on the final parameters for 200 MW and 50 MW turbogenerators.

scholarly journals Mathematical model parameter estimation of a generating unit operating in the Polish National Power System

2016 ◽  
Vol 64 (2) ◽  
pp. 409-416
Author(s):  
Ł. Majka ◽  
S. Paszek
Keyword(s):  
Mathematical Model ◽  
Parameter Estimation ◽  
Power System ◽  
Objective Function ◽  
Model Parameters ◽  
Gradient Algorithms ◽  
Hybrid Optimization Algorithm ◽  
National Power ◽  
The Mathematical Model ◽  
Paper Method

Abstract In the paper, a method and results of parameter estimation of the mathematical model of a generating unit operating in the Polish National Power System are presented. Computations of the parameters were carried out based on measurement and simulation of dynamic waveforms of selected quantities of the generating unit. The problem of parameter identification was brought to minimization of the objective function determined by the vector of deviations between the approximated and approximating waveforms computed on the basis of the models expressed by the searched parameters. A hybrid optimization algorithm, being a serial combination of genetic and gradient algorithms, was used for minimization of the objective function. A methodology for filtering the recorded measurement signals is proposed in the paper. Method and results calculation of the sensitivity to changes of the model parameters of selected dynamic waveforms are also presented.

scholarly journals CH<sub>4</sub> parameter estimation in CLM4.5bgc using surrogate global optimization

2015 ◽  
Vol 8 (10) ◽  
pp. 3285-3310 ◽  
Author(s):  
J. Müller ◽  
R. Paudel ◽  
C. A. Shoemaker ◽  
J. Woodbury ◽  
Y. Wang ◽  
...  
Keyword(s):  
Global Optimization ◽  
Parameter Estimation ◽  
Objective Function ◽  
Methane Emission ◽  
Optimization Algorithm ◽  
Model Parameters ◽  
Ch4 Emission ◽  
Community Land Model ◽  
Model Predictions ◽  
Pseudo Data

Abstract. Over the anthropocene methane has increased dramatically. Wetlands are one of the major sources of methane to the atmosphere, but the role of changes in wetland emissions is not well understood. The Community Land Model (CLM) of the Community Earth System Models contains a module to estimate methane emissions from natural wetlands and rice paddies. Our comparison of CH4 emission observations at 16 sites around the planet reveals, however, that there are large discrepancies between the CLM predictions and the observations. The goal of our study is to adjust the model parameters in order to minimize the root mean squared error (RMSE) between model predictions and observations. These parameters have been selected based on a sensitivity analysis. Because of the cost associated with running the CLM simulation (15 to 30 min on the Yellowstone Supercomputing Facility), only relatively few simulations can be allowed in order to find a near-optimal solution within an acceptable time. Our results indicate that the parameter estimation problem has multiple local minima. Hence, we use a computationally efficient global optimization algorithm that uses a radial basis function (RBF) surrogate model to approximate the objective function. We use the information from the RBF to select parameter values that are most promising with respect to improving the objective function value. We show with pseudo data that our optimization algorithm is able to make excellent progress with respect to decreasing the RMSE. Using the true CH4 emission observations for optimizing the parameters, we are able to significantly reduce the overall RMSE between observations and model predictions by about 50 %. The methane emission predictions of the CLM using the optimized parameters agree better with the observed methane emission data in northern and tropical latitudes. With the optimized parameters, the methane emission predictions are higher in northern latitudes than when the default parameters are used. For the tropics, the optimized parameters lead to lower emission predictions than the default parameters.

scholarly journals CH<sub>4</sub> parameter estimation in CLM4.5bgc using surrogate global optimization

2015 ◽  
Vol 8 (1) ◽  
pp. 141-207 ◽  
Author(s):  
J. Müller ◽  
R. Paudel ◽  
C. A. Shoemaker ◽  
J. Woodbury ◽  
Y. Wang ◽  
...  
Keyword(s):  
Global Optimization ◽  
Parameter Estimation ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Efficient Global Optimization ◽  
Model Parameters ◽  
Ch4 Emission ◽  
Community Land Model ◽  
Model Predictions ◽  
Pseudo Data

Abstract. Over the anthropocene methane has increased dramatically. Wetlands are one of the major sources of methane to the atmosphere, but the role of changes in wetland emissions is not well understood. The Community Land Model (CLM) of the Community Earth System Models contains a module to estimate methane emissions from natural wetlands and rice paddies. Our comparison of CH4 emission observations at 16 sites around the planet reveals, however, that there are large discrepancies between the CLM predictions and the observations. The goal of our study is to adjust the model parameters in order to minimize the root mean squared error (RMSE) between model predictions and observations. These parameters have been selected based on a sensitivity analysis. Because of the cost associated with running the CLM simulation (15 to 30 min on the Yellowstone Supercomputing Facility), only relatively few simulations can be allowed in order to find a near optimal solution within an acceptable time. Our results indicate that the parameter estimation problem has multiple local minima. Hence, we use a computationally efficient global optimization algorithm that uses a radial basis function (RBF) surrogate model to approximate the objective function. We use the information from the RBF to select parameter values that are most promising with respect to improving the objective function value. We show with pseudo data that our optimization algorithm is able to make excellent progress with respect to decreasing the RMSE. Using the true CH4 emission observations for optimizing the parameters, we are able to significantly reduce the overall RMSE between observations and model predictions by about 50%. The CLM predictions with the optimized parameters agree for northern and tropical latitudes more with the observed data than when using the default parameters and the emission predictions are higher than with default settings in northern latitudes and lower than default settings in the tropics.

scholarly journals Commonalities between Copper Neurotoxicity and Alzheimer’s Disease

Toxics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 4
Author(s):  
Roshni Patel ◽  
Michael Aschner
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Structural Changes ◽  
Copper Ion ◽  
Plaque Formation ◽  
Ion Concentration ◽  
Medical Community ◽  
Disease Etiology ◽  
Parent Protein ◽  
Lead Zinc

Alzheimer’s disease, a highly prevalent form of dementia, targets neuron function beginning from the hippocampal region and expanding outwards. Alzheimer’s disease is caused by elevated levels of heavy metals, such as lead, zinc, and copper. Copper is found in many areas of daily life, raising a concern as to how this metal and Alzheimer’s disease are related. Previous studies have not identified the common pathways between excess copper and Alzheimer’s disease etiology. Our review corroborates that both copper and Alzheimer’s disease target the hippocampus, cerebral cortex, cerebellum, and brainstem, affecting motor skills and critical thinking. Additionally, Aβ plaque formation was analyzed beginning from synthesis at the APP parent protein site until Aβ plaque formation was completed. Structural changes were also noted. Further analysis revealed a relationship between amyloid-beta plaques and copper ion concentration. As copper ion levels increased, it bound to the Aβ monomer, expediting the plaque formation process, and furthering neurodegeneration. These conclusions can be utilized in the medical community to further research on the etiology of Alzheimer’s disease and its relationships to copper and other metal-induced neurotoxicity.

History Matching in Two-Phase Petroleum Reservoirs

1980 ◽  
Vol 20 (06) ◽  
pp. 521-532 ◽  
Author(s):  
A.T. Watson ◽  
J.H. Seinfeld ◽  
G.R. Gavalas ◽  
P.T. Woo
Keyword(s):  
Optimal Control ◽  
Parameter Estimation ◽  
Objective Function ◽  
History Matching ◽  
Computing Time ◽  
Absolute Permeability ◽  
Two Phase ◽  
Automatic History Matching ◽  
Control Approach ◽  
First Order

Abstract An automatic history-matching algorithm based onan optimal control approach has been formulated forjoint estimation of spatially varying permeability andporosity and coefficients of relative permeabilityfunctions in two-phase reservoirs. The algorithm usespressure and production rate data simultaneously. The performance of the algorithm for thewaterflooding of one- and two-dimensional hypotheticalreservoirs is examined, and properties associatedwith the parameter estimation problem are discussed. Introduction There has been considerable interest in thedevelopment of automatic history-matchingalgorithms. Most of the published work to date onautomatic history matching has been devoted tosingle-phase reservoirs in which the unknownparameters to be estimated are often the reservoirporosity (or storage) and absolute permeability (ortransmissibility). In the single-phase problem, theobjective function usually consists of the deviationsbetween the predicted and measured reservoirpressures at the wells. Parameter estimation, orhistory matching, in multiphase reservoirs isfundamentally more difficult than in single-phasereservoirs. The multiphase equations are nonlinear, and in addition to the porosity and absolutepermeability, the relative permeabilities of each phasemay be unknown and subject to estimation. Measurements of the relative rates of flow of oil, water, and gas at the wells also may be available forthe objective function. The aspect of the reservoir history-matchingproblem that distinguishes it from other parameterestimation problems in science and engineering is thelarge dimensionality of both the system state and theunknown parameters. As a result of this largedimensionality, computational efficiency becomes aprime consideration in the implementation of anautomatic history-matching method. In all parameterestimation methods, a trade-off exists between theamount of computation performed per iteration andthe speed of convergence of the method. Animportant saving in computing time was realized insingle-phase automatic history matching through theintroduction of optimal control theory as a methodfor calculating the gradient of the objective functionwith respect to the unknown parameters. Thistechnique currently is limited to first-order gradientmethods. First-order gradient methods generallyconverge more slowly than those of higher order.Nevertheless, the amount of computation requiredper iteration is significantly less than that requiredfor higher-order optimization methods; thus, first-order methods are attractive for automatic historymatching. The optimal control algorithm forautomatic history matching has been shown toproduce excellent results when applied to field problems. Therefore, the first approach to thedevelopment of a general automatic history-matchingalgorithm for multiphase reservoirs wouldseem to proceed through the development of anoptimal control approach for calculating the gradientof the objective function with respect to theparameters for use in a first-order method. SPEJ P. 521＾

scholarly journals A Stochastic Harmonic Oscillator Temperature Model for the Valuation of Weather Derivatives

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2890
Author(s):  
Alessio Giorgini ◽  
Rogemar S. Mamon ◽  
Marianito R. Rodrigo
Keyword(s):  
Sensitivity Analysis ◽  
Parameter Estimation ◽  
Harmonic Oscillator ◽  
Numerical Simulations ◽  
Model Parameters ◽  
Call Option ◽  
Temperature Model ◽  
Option Prices ◽  
Harmonic Oscillator Model ◽  
Temperature Dynamics

Stochastic processes are employed in this paper to capture the evolution of daily mean temperatures, with the goal of pricing temperature-based weather options. A stochastic harmonic oscillator model is proposed for the temperature dynamics and results of numerical simulations and parameter estimation are presented. The temperature model is used to price a one-month call option and a sensitivity analysis is undertaken to examine how call option prices are affected when the model parameters are varied.

scholarly journals ESTIMASI PARAMETER PADA MODEL COX MULTIVARIAT DENGAN METODE MAXIMUM PARTIAL LIKELIHOOD ESTIMATION

2012 ◽  
Vol 4 (1) ◽  
pp. 185
Author(s):  
Irfan Wahyudi ◽  
Purhadi Purhadi ◽  
Sutikno Sutikno ◽  
Irhamah Irhamah
Keyword(s):  
Parameter Estimation ◽  
Likelihood Function ◽  
Cox Model ◽  
Hessian Matrix ◽  
Likelihood Estimation ◽  
Partial Likelihood ◽  
Estimation Methods ◽  
Hazard Functions ◽  
Score Vector ◽  
Parameter Estimation Methods

Multivariate Cox proportional hazard models have ratio property, that is the ratio of  hazard functions for two individuals with covariate vectors  z1 and  z2 are constant (time independent). In this study we talk about estimation of prameters on multivariate Cox model by using Maximum Partial Likelihood Estimation (MPLE) method. To determine the appropriate estimators  that maximize the ln-partial likelihood function, after a score vector and a Hessian matrix are found, numerical iteration methods are applied. In this case, we use a Newton Raphson method. This numerical method is used since the solutions of the equation system of the score vector after setting it equal to zero vector are not closed form. Considering the studies about multivariate Cox model are limited, including the parameter estimation methods, but the methods are urgently needed by some fields of study related such as economics, engineering and medical sciences. For this reasons, the goal of this study is designed to develop parameter estimation methods from univariate to multivariate cases.

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