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.

On data-driven nonlinear uncertainty modeling: Methods and application for control-oriented surface condition prediction in hard turning

2020 ◽  
Vol 87 (11) ◽  
pp. 732-741
Author(s):  
Felix Wittich ◽  
Lars Kistner ◽  
Andreas Kroll ◽  
Christopher Schott ◽  
Thomas Niendorf
Keyword(s):  
Hard Turning ◽  
Surface Condition ◽  
Gaussian Process Regression ◽  
Uncertainty Modeling ◽  
Data Driven ◽  
Machining Parameters ◽  
Robust Model ◽  
Bounded Error ◽  
Data Driven Modeling ◽  
Takagi Sugeno

AbstractIn this article, two data-driven modeling approaches are investigated, which allow an explicit modeling of uncertainty. For this purpose, parametric Takagi-Sugeno multi-models with bounded-error parameter estimation and nonparametric Gaussian process regression are applied and compared. These models can for instance be used for robust model-based control design. As an application, the prediction of residual stresses during hard turning depending on the machining parameters and the initial hardness is considered.

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 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 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.

Constructing and model-fitting receiver operator characteristics using continuous data.

2018 ◽  
Author(s):  
Josephine Ann Urquhart ◽  
Akira O'Connor
Keyword(s):  
Signal Detection ◽  
Least Squares Method ◽  
Model Fitting ◽  
Simulated Data ◽  
Continuous Variable ◽  
Continuous Data ◽  
Model Parameters ◽  
Operating Characteristics ◽  
Unequal Variance ◽  
Discrete Discrimination

Receiver operating characteristics (ROCs) are plots which provide a visual summary of a classifier’s decision response accuracy at varying discrimination thresholds. Typical practice, particularly within psychological studies, involves plotting an ROC from a limited number of discrete thresholds before fitting signal detection parameters to the plot. We propose that additional insight into decision-making could be gained through increasing ROC resolution, using trial-by-trial measurements derived from a continuous variable, in place of discrete discrimination thresholds. Such continuous ROCs are not yet routinely used in behavioural research, which we attribute to issues of practicality (i.e. the difficulty of applying standard ROC model-fitting methodologies to continuous data). Consequently, the purpose of the current article is to provide a documented method of fitting signal detection parameters to continuous ROCs. This method reliably produces model fits equivalent to the unequal variance least squares method of model-fitting (Yonelinas et al., 1998), irrespective of the number of data points used in ROC construction. We present the suggested method in three main stages: I) building continuous ROCs, II) model-fitting to continuous ROCs and III) extracting model parameters from continuous ROCs. Throughout the article, procedures are demonstrated in Microsoft Excel, using an example continuous variable: reaction time, taken from a single-item recognition memory. Supplementary MATLAB code used for automating our procedures is also presented in Appendix B, with a validation of the procedure using simulated data shown in Appendix C.

scholarly journals Experimental Verification of Real-Time Flow-Rate Estimations in a Tilting-Ladle-Type Automatic Pouring Machine

2021 ◽  
Vol 11 (15) ◽  
pp. 6701
Author(s):  
Yuta Sueki ◽  
Yoshiyuki Noda
Keyword(s):  
Real Time ◽  
Molten Metal ◽  
Flow Rate ◽  
Kalman Filters ◽  
Estimation Method ◽  
Estimation Methods ◽  
Liquid Volume ◽  
Model Parameters ◽  
Rate Estimation ◽  
Time Flow

This paper discusses a real-time flow-rate estimation method for a tilting-ladle-type automatic pouring machine used in the casting industry. In most pouring machines, molten metal is poured into a mold by tilting the ladle. Precise pouring is required to improve productivity and ensure a safe pouring process. To achieve precise pouring, it is important to control the flow rate of the liquid outflow from the ladle. However, due to the high temperature of molten metal, directly measuring the flow rate to devise flow-rate feedback control is difficult. To solve this problem, specific flow-rate estimation methods have been developed. In the previous study by present authors, a simplified flow-rate estimation method was proposed, in which Kalman filters were decentralized to motor systems and the pouring process for implementing into the industrial controller of an automatic pouring machine used a complicatedly shaped ladle. The effectiveness of this flow rate estimation was verified in the experiment with the ideal condition. In the present study, the appropriateness of the real-time flow-rate estimation by decentralization of Kalman filters is verified by comparing it with two other types of existing real-time flow-rate estimations, i.e., time derivatives of the weight of the outflow liquid measured by the load cell and the liquid volume in the ladle measured by a visible camera. We especially confirmed the estimation errors of the candidate real-time flow-rate estimations in the experiments with the uncertainty of the model parameters. These flow-rate estimation methods were applied to a laboratory-type automatic pouring machine to verify their performance.

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