Parameter Estimation for Highly Nonlinear Models With Noisy Data

2003 ◽  
Author(s):  
A. F. Emery ◽  
D. Bardot
Keyword(s):  
Nonlinear Models ◽  
Distributed Parameter ◽  
Parameter Estimates ◽  
Confidence Limits ◽  
Nonlinear Functions ◽  
Thermal Systems ◽  
Nonnormal Distributions ◽  
Estimated Parameters ◽  
Highly Nonlinear ◽  
Normally Distributed

Thermal properties are generally determined through solving inverse problems. Because the temperature is a non-linear function of the properties, the solutions are usually effected by linearizing the equations. The statistics of these linearized estimates are based upon the assumptions that the measurement noise has zero mean and is normally distributed, yielding unbiased and normally distributed parameter estimates. In fact, even for this type of noise, nonlinear functions can lead to bias and nonnormal distributions of estimated properties. We examine these effects and show that for typical thermal systems that while the estimates are unbiased and normal, the confidence limits may be inaccurately defined and the residuals of the fits may not be zero mean and uncorrelated. Characterizing the estimated parameters is critical when nonlinear models are to be used for extrapolation.

scholarly journals A Monograph on Nonlinear Regression Models

2018 ◽  
Vol 7 (4.10) ◽  
pp. 543
Author(s):  
B. Mahaboob ◽  
B. Venkateswarlu ◽  
C. Narayana ◽  
J. Ravi sankar ◽  
P. Balasiddamuni
Keyword(s):  
Regression Model ◽  
Least Squares ◽  
Nonlinear Regression ◽  
Nonlinear Models ◽  
Nonlinear Least Squares ◽  
Error Variance ◽  
Ordinary Least Squares ◽  
Parameter Estimates ◽  
Nonlinear Regression Model ◽  
Nonlinear Regression Models

This research article uses Matrix Calculus techniques to study least squares application of nonlinear regression model, sampling distributions of nonlinear least squares estimators of regression parametric vector and error variance and testing of general nonlinear hypothesis on parameters of nonlinear regression model. Arthipova Irina et.al [1], in this paper, discussed some examples of different nonlinear models and the application of OLS (Ordinary Least Squares). MA Tabati et.al (2), proposed a robust alternative technique to OLS nonlinear regression method which provide accurate parameter estimates when outliers and/or influential observations are present. Xu Zheng et.al [3] presented new parametric tests for heteroscedasticity in nonlinear and nonparametric models.  

scholarly journals Using Weighted Entropy to Rank Chemicals in Quantitative High-Throughput Screening Experiments

2013 ◽  
Vol 19 (3) ◽  
pp. 344-353 ◽  
Author(s):  
Keith R. Shockley
Keyword(s):  
High Throughput ◽  
High Throughput Screening ◽  
Nonlinear Models ◽  
Hill Equation ◽  
Parameter Estimates ◽  
Chemical Library ◽  
Data Set ◽  
Screening Experiments ◽  
The Hill ◽  
Weighted Entropy

Quantitative high-throughput screening (qHTS) experiments can simultaneously produce concentration-response profiles for thousands of chemicals. In a typical qHTS study, a large chemical library is subjected to a primary screen to identify candidate hits for secondary screening, validation studies, or prediction modeling. Different algorithms, usually based on the Hill equation logistic model, have been used to classify compounds as active or inactive (or inconclusive). However, observed concentration-response activity relationships may not adequately fit a sigmoidal curve. Furthermore, it is unclear how to prioritize chemicals for follow-up studies given the large uncertainties that often accompany parameter estimates from nonlinear models. Weighted Shannon entropy can address these concerns by ranking compounds according to profile-specific statistics derived from estimates of the probability mass distribution of response at the tested concentration levels. This strategy can be used to rank all tested chemicals in the absence of a prespecified model structure, or the approach can complement existing activity call algorithms by ranking the returned candidate hits. The weighted entropy approach was evaluated here using data simulated from the Hill equation model. The procedure was then applied to a chemical genomics profiling data set interrogating compounds for androgen receptor agonist activity.

Robust Control of the Elastodynamic Vibrations of a Flexible Rotor System With Discontinuous Friction

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Mansour Karkoub
Keyword(s):  
Dynamic Model ◽  
Design Process ◽  
Nonlinear Models ◽  
Control Design ◽  
Rotor System ◽  
Control Technique ◽  
Flexible Rotor ◽  
Highly Nonlinear ◽  
Modeling Errors ◽  
The Difference

The work presented here deals with the control of a flexible rotor system using the μ-synthesis control technique. This technique allows for the inclusion of modeling errors in the control design process in terms of uncertainty weights. The dynamic model of the rotor system, which includes discontinuous friction, is highly nonlinear and has to be linearized around an operating point in order to use μ-synthesis. The difference between the linear and nonlinear models is characterized in terms of uncertainty weights and included in the control design process. The designed controller is robust to uncertainty in the dynamic model, spillover, actuator uncertainty, and noise. The theoretical findings of the μ-synthesis control design are validated through simulations and the results are presented and discussed here.

Flow of a fourth grade fluid between rotating disks

2020 ◽  
Vol 34 (10) ◽  
pp. 2050091
Author(s):  
A. M. Siddiqui ◽  
Ayesha Sohail ◽  
Khush Bakhat Akram ◽  
Qurat-ul-Ain Azim
Keyword(s):  
Nonlinear Models ◽  
Fluid Model ◽  
Three Dimensional ◽  
Fourth Grade ◽  
Perturbation Approach ◽  
Rotating Disks ◽  
Highly Nonlinear ◽  
Rotating Surface ◽  
Grade Fluid ◽  
Fourth Grade Fluid

Flow of fluids between rotating surface is encountered in many industrial, manufacturing, mixing and biological processes. These fluids are complex, exhibit various rheological characteristics, and thus follow highly nonlinear models. In this paper, we have used fourth grade fluid model to represent fluids involved in such processes. The steady flow between two coaxial rotating disks is modeled. The resulting highly nonlinear equations are solved using perturbation approach. The velocity field in three-dimensional cylindrical coordinate system is reported. The results are then simulated to present a visual understanding of the flow.

scholarly journals Improved non-parametric statistical methods for the estimation of Michaelis-Menten kinetic parameters by the direct linear plot

1977 ◽  
Vol 161 (2) ◽  
pp. 293-302 ◽  
Author(s):  
W R Porter ◽  
W F Trager
Keyword(s):  
Statistical Methods ◽  
Data Fitting ◽  
Confidence Limits ◽  
Estimated Parameters ◽  
Lower Confidence ◽  
Proper Design ◽  
Linear Plot ◽  
Replicate Measurements ◽  
Menten Kinetic ◽  
Non Parametric

The theoretical basis for the direct linear plot [Eisenthal & Cornish-Bowden (1974) Biochem. J. 139, 715-720], a non-parametric statistical method for the analysis of data-fitting the Michaelis-Menten equation, was reinvestigated in order to accommodate additional experimental designs and to provide estimates of precision more directly comparable with those obtained by parametric statistical methods. Methods are given for calculating upper and lower confidence limits for the estimated parameters, for accommodating replicate measurements and for comparing the results of two separate experiments. Factors that influence the proper design of experiments are discussed.

A Methodology for Optimal Sensor Locations for Identification of Dynamic Systems

1978 ◽  
Vol 45 (1) ◽  
pp. 188-196 ◽  
Author(s):  
P. C. Shah ◽  
F. E. Udwadia
Keyword(s):  
Dynamic Systems ◽  
Distributed Parameter ◽  
Parameter Estimates ◽  
Finite Sample ◽  
Finite Dimensional Representation ◽  
Ground Shaking ◽  
Finite Dimensional ◽  
Suitable Norm ◽  
Shear Beam ◽  
Single Sensor

The problem of optimally positioning sensors in lumped and distributed parameter dynamic systems for the purpose of system identification from time-domain input-output data is formulated and a methodology for its solution is presented. A linear relation between small perturbations in a finite-dimensional representation of the system parameters and a finite sample of observations of the system time response is used to determine approximately the covariance of the parameter estimates. The locations of a given number of sensors are then determined such that a suitable norm of the covariance matrix is minimized. The methodology is applied to the problem of optimally locating a single sensor in a building structure modeled by a shear beam, such that the estimates of the stiffness distributions, obtained from the records of strong ground shaking and the building response at the sensor location, are least uncertain.

Neural Network Predictive Controller Based Nonlinearity Identification Case Study: Nonlinear Process Reactor - CSTR

2014 ◽  
Vol 984-985 ◽  
pp. 1326-1334 ◽  
Author(s):  
M. Shyamalagowri ◽  
R. Rajeswari
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Nonlinear Models ◽  
Chemical Reactor ◽  
Nonlinear Process ◽  
Continuous Stirred Tank Reactor ◽  
Highly Nonlinear ◽  
Sophisticated Model ◽  
Predictive Controller ◽  
Complex Nonlinear Systems

In the last decades, a substantial amount of research has been carried out on identification of nonlinear processes. Dynamical systems can be better represented by nonlinear models, which illustrate the global behavior of the nonlinear process reactor over the entire range. CSTR is highly nonlinear chemical reactor. A compact and resourceful model which approximates both linear and nonlinear component of the process is of highly demand. Process modeling is an essential constituent in the growth of sophisticated model-based process control systems. Driven by the contemporary economical needs, developments in process design point out that deliberate operation requires better models. The neural network predictive controller is very efficient to identify complex nonlinear systems with no complete model information. Closed loop method is preferred because it is sensitive to disturbances, no need identify the transfer function model of an unstable system. In this paper identification nonlinearities for a nonlinear process reactor CSTR is approached using neural network predictive controller. KEYWORDS Continuous Stirred Tank Reactor, Multi Input Multi Output, Neural Networks, Chebyshev Neural Networks, Predictive Controller.

State-space likelihoods for nonlinear fisheries time-series

2005 ◽  
Vol 62 (9) ◽  
pp. 1937-1952 ◽  
Author(s):  
Perry de Valpine ◽  
Ray Hilborn
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Bayesian Analysis ◽  
State Space ◽  
Nonlinear Models ◽  
Confidence Regions ◽  
State Space Models ◽  
Model Complexity ◽  
Parameter Estimates ◽  
Nonlinear State Space Models

State-space models are commonly used to incorporate process and observation errors in analysis of fisheries time series. A gap in analysis methods has been the lack of classical likelihood methods for nonlinear state-space models. We evaluate a method that uses weighted kernel density estimates of Bayesian posterior samples to estimate likelihoods (Monte Carlo Kernel Likelihoods, MCKL). Classical likelihoods require integration over the state-space, and we compare MCKL to the widely used errors-in-variables (EV) method, which estimates states jointly with parameters by maximizing a nonintegrated likelihood. For a simulated, linear, autoregressive model and a Schaefer model fit to cape hake (Merluccius capensis × M. paradoxus) data, classical likelihoods outperform EV likelihoods, which give asymptotically biased parameter estimates and inaccurate confidence regions. Our results on the importance of integrated state-space likelihoods also support the value of Bayesian analysis with Monte Carlo posterior integration. Both approaches provide valuable insights and can be used complementarily. Previously, Bayesian analysis was the only option for incorporating process and observation errors with complex nonlinear models. The MCKL method provides a classical approach for such models, so that choice of analysis approach need not depend on model complexity.

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