scholarly journals LEVENBERG-MARQUARDT METHOD APPLIED TO THE DETERMINATION OF VAPOR-LIQUID EQUILIBRIUM MODEL PARAMETERS

2014 ◽  
Vol 44 (4) ◽  
pp. 319-324
Author(s):  
J.A. F. OLIVEIRA ◽  
M.M. L. DUARTE ◽  
E. L. FOLETTO ◽  
O. CHIAVONE-FILHO
Keyword(s):  
Structural Parameters ◽  
Pure Component ◽  
Estimation Methods ◽  
Model Parameters ◽  
Arbitrary Matrix ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt ◽  
Equilibrium Data ◽  
Parameter Estimation Methods ◽  
Vaporliquid Equilibrium

 In order to correlate and optimize experimental data either from the laboratory or industry, one needs a robust method of data regression. Among the non-linear parameter estimation methods it may be pointed out of Levenberg, which applies the conversion of an arbitrary matrix into a positive definite one. Later, Marquardt applied the same procedure, calculating  parameter in an iterative form. The Levenberg-Marquardt algorithm is described and two routine for correlating vaporliquid equilibrium data for pure component and mixtures, based on this efficient method, have been applied. The routines have been written with an interface very accessible for both users and programmers, using Python language. The flexibility of the developed programs for introducing the desired details is quite interesting for both process simulators and modeling properties. Furthermore, for mixtures with electrolytes, it was obtained a coherent and compatible relation for the structural parameters of the salt species, with the aid of the method and the graphical interface designed.

scholarly journals Neuro-fuzzy-based Electronic Brake System Modeling using Real Time Vehicle Data

10.29007/q7pr ◽  
2019 ◽  
Author(s):  
Ana Farhat ◽  
Kyle Hagen ◽  
Ka C Cheok ◽  
Balaji Boominathan
Keyword(s):  
System Modeling ◽  
Least Square ◽  
Brake System ◽  
Model Parameters ◽  
Vehicle Data ◽  
Neuro Fuzzy ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt ◽  
Network Method ◽  
Fuzzy Network

Electronic Brake System (EBS) is considered as one of the most complicated systems whose performance depends on the subsystems parameters. Usually these parameters are difficult to predict. Based on the task to improve the EBS performance, this article presents a mathematical modeling approach based on neuro-fuzzy network method to model a subsystem of EBS. For the model parameters identification, a neuro-fuzzy network has been implemented based on Least Square Error (LSE) and Levenberg- Marquardt Algorithm (LMA) as the optimization algorithms. Finally, the performance of identified model has been evaluated.

scholarly journals An application of the ensemble Kalman filter in epidemiological modelling

PLoS ONE ◽  
2021 ◽  
Vol 16 (8) ◽  
pp. e0256227
Author(s):  
Rajnesh Lal ◽  
Weidong Huang ◽  
Zhenquan Li
Keyword(s):  
Parameter Estimation ◽  
Model Simulation ◽  
Synthetic Data ◽  
Estimation Methods ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Model Parameter ◽  
Reliable Model ◽  
Reported Data ◽  
Parameter Estimation Methods

Since the novel coronavirus (COVID-19) outbreak in China, and due to the open accessibility of COVID-19 data, several researchers and modellers revisited the classical epidemiological models to evaluate their practical applicability. While mathematical compartmental models can predict various contagious viruses’ dynamics, their efficiency depends on the model parameters. Recently, several parameter estimation methods have been proposed for different models. In this study, we evaluated the Ensemble Kalman filter’s performance (EnKF) in the estimation of time-varying model parameters with synthetic data and the real COVID-19 data of Hubei province, China. Contrary to the previous works, in the current study, the effect of damping factors on an augmented EnKF is studied. An augmented EnKF algorithm is provided, and we present how the filter performs in estimating models using uncertain observational (reported) data. Results obtained confirm that the augumented-EnKF approach can provide reliable model parameter estimates. Additionally, there was a good fit of profiles between model simulation and the reported COVID-19 data confirming the possibility of using the augmented-EnKF approach for reliable model parameter estimation.

scholarly journals Improving Levenberg-Marquardt Algorithm Inversion Result Using Singular Value Decomposition

2016 ◽  
Vol 5 (2) ◽  
pp. 20
Author(s):  
Widodo Widodo ◽  
Durra Handri Saputera
Keyword(s):  
Singular Value Decomposition ◽  
Singular Value ◽  
Parameter Analysis ◽  
Model Parameters ◽  
Inversion Result ◽  
One Dimensional ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt ◽  
Value Decomposition ◽  
Lm Algorithm

Inversion is a process to determine model parameters from data. In geophysics this process is very important because subsurface image is obtained from this process. There are many inversion algorithms that have been introduced and applied in geophysics problems; one of them is Levenberg-Marquardt (LM) algorithm. In this paper we will present one of LM algorithm application in one-dimensional magnetotelluric (MT) case. The LM algorithm used in this study is improved version of LM algorithm using singular value decomposition (SVD). The result from this algorithm is then compared with the algorithm without SVD in order to understand how much it has been improved. To simplify the comparison, simple synthetic model is used in this study. From this study, the new algorithm can improve the result of the original LM algorithm. In addition, SVD is allowing more parameter analysis to be done in its process. The algorithm created from this study is then used in our modeling program, called MAT1DMT.

scholarly journals Kinetic Parameter Estimation Using Modified Differential Evolution

2011 ◽  
pp. 113-116
Author(s):  
Rakesh Angira
Keyword(s):  
Parameter Estimation ◽  
Kinetic Parameter ◽  
Differential Evolution ◽  
Chemical Engineering ◽  
Estimation Methods ◽  
Model Parameters ◽  
De Algorithm ◽  
Kinetic Parameter Estimation ◽  
Advanced Control ◽  
Parameter Estimation Methods

For the development of mathematical models in chemical engineering, the parameter estimation methods are very important as design, optimization and advanced control of chemical processes depend on values of model parameters obtained from experimental data. Nonlinearity in models makes the estimation of parameter more difficult and more challenging. This paper presents an evolutionary computation approach for solving such problems. In this work, a modified version of Differential Evolution (DE) algorithm [named Modified Differential evolution (MDE)] is used to solve a kinetic parameter estimation problem from chemical engineering field. The computational efficiency of MDE is compared with that of original DE and Trigonometric Differential Evolution (TDE). Results indicate that performance of MDE algorithm is better than that of DE and TDE.

Evaluation of methods for feasible parameter set estimation of Takagi-Sugeno models for nonlinear regression with bounded errors

2021 ◽  
Vol 69 (10) ◽  
pp. 836-847
Author(s):  
Felix Wittich ◽  
Andreas Kroll
Keyword(s):  
Simulated Data ◽  
Estimation Methods ◽  
Point Estimate ◽  
Model Parameters ◽  
Set Estimation ◽  
Bounded Error ◽  
Parameter Estimation Methods ◽  
Data Driven Modeling ◽  
Takagi Sugeno ◽  
Error Parameter

Abstract In data-driven modeling besides the point estimate of the model parameters, an estimation of the parameter uncertainty is of great interest. For this, bounded error parameter estimation methods can be used. These are particularly interesting for problems where the stochastical properties of the random effects are unknown and cannot be determined. In this paper, different methods for obtaining a feasible parameter set are evaluated for the use with Takagi-Sugeno models. Case studies with simulated data and with measured data from a manufacturing process are presented.

scholarly journals Tikhonov Regularized Variable Projection Algorithms for Separable Nonlinear Least Squares Problems

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Zhengqing Fu ◽  
Lanlan Guo
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Nonlinear Least Squares ◽  
Real Data ◽  
Estimation Methods ◽  
Linear Parameter ◽  
Nonlinear Parameters ◽  
Marquardt Algorithm ◽  
Tikhonov Regularisation ◽  
Parameter Estimation Methods

This paper considers the classical separable nonlinear least squares problem. Such problems can be expressed as a linear combination of nonlinear functions, and both linear and nonlinear parameters are to be estimated. Among the existing results, ill-conditioned problems are less often considered. Hence, this paper focuses on an algorithm for ill-conditioned problems. In the proposed linear parameter estimation process, the sensitivity of the model to disturbance is reduced using Tikhonov regularisation. The Levenberg–Marquardt algorithm is used to estimate the nonlinear parameters. The Jacobian matrix required by LM is calculated by the Golub and Pereyra, Kaufman, and Ruano methods. Combining the nonlinear and linear parameter estimation methods, three estimation models are obtained and the feasibility and stability of the model estimation are demonstrated. The model is validated by simulation data and real data. The experimental results also illustrate the feasibility and stability of the model.

Factual data banks and their application to the synthesis and design of chemical processes and the development and testing of thermophysical property estimation methods

2009 ◽  
Vol 81 (10) ◽  
pp. 1745-1768 ◽  
Author(s):  
Jürgen Rarey ◽  
Jürgen Gmehling
Keyword(s):  
Thermophysical Property ◽  
Process Simulation ◽  
Data Bank ◽  
Pure Component ◽  
Estimation Methods ◽  
Model Parameters ◽  
Environmental Models ◽  
Property Estimation ◽  
Factual Data ◽  
Data Banks

Factual data banks nowadays play an important role as a source for thermophysical property data for use in chemical process simulation, environmental models, and many other computer-based applications. In this work, the historical developments leading to modern factual data banks, the differences compared to other more bibliographically oriented data banks, and their most important applications and future potential will be discussed by using the example of the Dortmund Data Bank (DDB). As the development of the different predictive models for mixtures is covered in a separate publication, this paper focuses on pure-component property estimation, regression of model parameters, test and verification of model parameters prior to process simulation, and advanced topics in process synthesis such as selection of entrainers and data-mining applications.

Comparison of an Artificial Neural Network and a Multiple Linear Regression in Predicting the Heat of Combustion of Diesel Fuel Based on Hydrocarbon Groups

2020 ◽  
Vol 71 (6) ◽  
pp. 66-74
Author(s):  
Younis M. Younis ◽  
Salman H. Abbas ◽  
Farqad T. Najim ◽  
Firas Hashim Kamar ◽  
Gheorghe Nechifor
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Diesel Fuel ◽  
Back Propagation ◽  
Second Step ◽  
Heating Value ◽  
Network Training ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt ◽  
Propagation Network

A comparison between artificial neural network (ANN) and multiple linear regression (MLR) models was employed to predict the heat of combustion, and the gross and net heat values, of a diesel fuel engine, based on the chemical composition of the diesel fuel. One hundred and fifty samples of Iraqi diesel provided data from chromatographic analysis. Eight parameters were applied as inputs in order to predict the gross and net heat combustion of the diesel fuel. A trial-and-error method was used to determine the shape of the individual ANN. The results showed that the prediction accuracy of the ANN model was greater than that of the MLR model in predicting the gross heat value. The best neural network for predicting the gross heating value was a back-propagation network (8-8-1), using the Levenberg�Marquardt algorithm for the second step of network training. R = 0.98502 for the test data. In the same way, the best neural network for predicting the net heating value was a back-propagation network (8-5-1), using the Levenberg�Marquardt algorithm for the second step of network training. R = 0.95112 for the test data.

Prediction of the McAllister model parameters from pure component properties for liquid binary n-alkane systems

1991 ◽  
Vol 30 (7) ◽  
pp. 1666-1669 ◽  
Author(s):  
Abdul Fattah A. Asfour ◽  
Elizabeth F. Copper ◽  
Jiangning Wu ◽  
Rouchdy R. Zahran
Keyword(s):  
Pure Component ◽  
Model Parameters
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