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In this paper we provide the first solution to the challenging problem of designing a globally convergent estimator for the parameters of the standard model of a continuous stirred tank reactor. Because of the presence of non-separable exponential nonlinearities in the system dynamics that appear in Arrhenius law, none of the existing parameter estimators is able to deal with them in an efficient way and, in spite of many attempts, the problem was open for many years. To establish our result we propose a novel procedure to obtain a suitable nonlinearly parameterized regression equation and introduce a radically new estimation algorithm—derived applying the Immersion and Invariance methodology—that is applicable to these regression equations. A further contribution of the paper is that parameter convergence is exponential and is guaranteed with weak excitation requirements. To achieve this remarkable property we rely on the utilization of a recently introduced parameter estimator that seamlessly combines a classical least-squares search with the dynamic regressor extension and mixing estimation procedure. • A globally convergent estimator for the parameters of a CSTR. • A novel procedure to obtain a suitable nonlinearly parameterized regression equation of the CSTR. • Parameter convergence is guaranteed with extremely weak excitation requirements. [ABSTRACT FROM AUTHOR]

• The highly nonlinear and multi-modal response function for the day-to-day dynamics calibration is analyzed. • A surrogate-based approach is proposed to calibrate the day-to-day dynamics model. • The day-to-day dynamics model is validated with the license plate recognition data. This paper investigates the day-to-day dynamics model from the perspective of travelers' actual route choice behaviors, and calibrates and validates the route-based day-to-day dynamics model with the real-world license plate recognition (LPR) data. Due to the highly nonlinear and multi-modal response function in the calibration of the optimization problem, traditional gradient-based nonlinear regression algorithms or other analytical optimization approaches are inapplicable to deal with the calibration work. In this paper, a surrogate-based simulation optimization approach is proposed to deal with the expensive-to-evaluate response function in the day-to-day dynamics calibration work. More specifically, the kriging metamodel is adopted to surrogate the optimization function of the calibration process. With this meta-modeling approach, a sound solution can be achieved with only a few sampling points in a comfortably afforded computation burden, thus giving a valid estimation of the parameters in the day-to-day dynamics model. Finally, a case study based on the real-world LPR data is conducted to validate the proposed model and calibration method. [ABSTRACT FROM AUTHOR]

Highlights • The paper contributes set-membership regression (SMR), a new approach to nonlinear parameter estimation under measurement uncertainty. • Links between SMR and both guaranteed parameter estimation and classical statistical inference are investigated. • Several approaches to describing tight enclosures of the SMR regions using complete- search methods are developed. • Case studies are presented to illustrate various theoretical and computational aspects of SMR. Abstract This paper introduces set-membership nonlinear regression (SMR), a new approach to nonlinear regression under uncertainty. The problem is to determine the subregion in parameter space enclosing all (global) solutions to a nonlinear regression problem in the presence of bounded uncertainty on the observed variables. Our focus is on nonlinear algebraic models. We investigate the connections of SMR with (i) the classical statistical inference methods, and (ii) the usual set-membership estimation approach where the model predictions are constrained within bounded measurement errors. We also develop a computational framework to describe tight enclosures of the SMR regions using semi-infinite programming and complete-search methods, in the form of likelihood contour and polyhedral enclosures. The case study of a parameter estimation problem in microbial growth is presented to illustrate various theoretical and computational aspects of the SMR approach. [ABSTRACT FROM AUTHOR]

In this paper, a rapidly varying parameter estimation method for nonlinear systems is proposed. The parameters are supposed to be unknown functions of known causes, here referred to as associative memory variables. The estimation proposal consists of two stages; in the first one, an a priori estimation is calculated as the average of a dynamic subset of past estimates, defined by similarities between the current and past cause values. In this paper, this subset is referred to as associated memory. Each parameter of the model corresponds to an associated memory set, which is updated over time. In the second stage, the a priori estimation is updated using the innovation brought by the new incoming data and the recursive least squares algorithm. A nonlinear in the parameters moving average, a multi-parameter model, and a model with multi-dependent parameters are analyzed under this perspective. Two examples are shown to validate this proposal and alternative methods from the literature are used for performance comparison. [ABSTRACT FROM AUTHOR]

Abstract: Nonlinear models play an important role in various scientific disciplines and engineering. The parameter estimation of these models should be efficient to make better decisions. Ordinary least squares (OLS) method is used for estimating the parameters of nonlinear regression models when all regression assumptions are satisfied. If there is a problem with these assumptions, OLS fails to give efficient results. This paper examines the efficiency of parameter estimation under the problem of autocorrelated errors. Some methods have been proposed in order to overcome the problem and obtain efficient parameter estimates especially for autoregressive (AR) processes. One of the most commonly used method is two-stage least squares (2SLS). This method is based on generalized least squares. In this paper, a novel approach is proposed for 2SLS method by evaluating a polynomial tapering procedure on autocorrelated errors. This new method is called tapered two-stage least squares (T2SLS). The finite sample properties and improvements of T2SLS are explored by means of some real life examples and a Monte Carlo simulation study. Both numerical and experimental results reveal that T2SLS can give more efficient parameter estimates especially in small samples under the autocorrelation problem when compared to OLS and 2SLS. [Copyright &y& Elsevier]

• Improved method in a class of ill-conditioned parameter estimation problems. • A subset selection criterion based on MSE for the estimates. • Statistical analysis to compare the proposed and conventional methods. • Performance comparison through two case studies: linear and nonlinear regressions. • The proposed method gives better estimates with smaller variances. In cases of ill-conditioned estimation problems, not all parameters can be estimated accurately and a selection of parameter subset composed of more influential and less correlated parameters may be needed to increase parameter estimability. This paper proposes to choose a subset for estimation from transformed parameters along the directions of the principal components of the parameter covariance matrix while retaining the initial guesses for the unselected transformed parameters. Since estimating a subset of the transformed parameters can adjust all the original parameter values and any constraint on the original parameter values can still be applied to the transformed parameters, the proposed regularization method can overcome the limitation of the existing methods, i.e., parameter subset selection and truncated singular value decomposition (also known as 'principal component regression'). It is demonstrated that the proposed method can provide better parameter estimates with smaller variances than the existing parameter subset selection methods, first through statistical analysis, and then through case studies of linear and nonlinear regressions. In addition, based on the derived statistical properties, a criterion is suggested for selecting an optimal subset, which gives the smallest mean squared error of the estimates. Furthermore, with the advantage of a lower variance of the estimates, the proposed regularization method gives a more consistent choice of the number of parameters to estimate with the smallest mean squared error of the estimates even when significant errors in the initial guesses and high levels of measurement noise exist. [ABSTRACT FROM AUTHOR]

Abstract: Predicting the performance of chemical reactions with a mechanistic model is desired during the development of pharmaceutical and other high value chemical syntheses. Model parameters usually must be regressed to experimental observations. However, experimental error may not follow conventional distributions and the validity of common statistical assumptions used for regression should be examined when fitting mechanistic models. This paper compares different techniques to estimate parameter confidence for reaction models encountered in pharmaceutical manufacturing, simulated with either normally distributed or experimentally measured noise. Confidence intervals were calculated following standard linear approaches and two Markov Chain Monte Carlo algorithms utilizing a Bayesian approach to parameter estimation: one assuming a normal error distribution, and a new non-parametric likelihood function. While standard frequentist approaches work well for simpler nonlinear models and normal distributions, only MCMC accurately estimates uncertainty when the system is highly nonlinear, and can account for any measurement bias via customized likelihood functions. [Copyright &y& Elsevier]

Abstract: We observe a surface roughness in end milling machining process which is influenced by machine parameters, namely radial rake angle, speed and feed rate cutting condition. In this machining, we need to minimize and to obtain as low as possible the surface roughness by determining the optimum values of the three parameters. In previous works, some researchers used a response surface methodology (RSM) and a soft-computing approach, which was based on ordinary linear regression and genetic algorithms (GAs), to estimate the minimum surface roughness and its corresponding values of the parameters. However, the construction of the ordinary regression models was conducted without considering the existence of multicollinearity which can lead to inappropriate prediction. Beside that it is known the relation between the surface roughness and the three parameters is nonlinear, which implies that a linear regression model can be inappropriate model to approximate it. In this paper, we present a technique developed using hybridization of kernel principal component analysis (KPCA) based nonlinear regression and GAs to estimate the optimum values of the three parameters such that the estimated surface roughness is as low as possible. We use KPCA based regression to construct a nonlinear regression and to avoid the effect of multicollinearity in its prediction model. We show that the proposed technique gives more accurate prediction model than the ordinary linear regression’s approach. Comparing with the experiment data and RSM, our technique reduces the minimum surface roughness by about 45.3% and 54.2%, respectively. [Copyright &y& Elsevier]

Abstract: We consider in this paper the fault diagnosis problem of a three tank system DTS-200 pilot plant. The presented approach is based on the analysis of the variogram, which is a graphical variance representation that characterizes the distribution of a measured dataset, and is used to extract the sensor fault parameters. These parameters are obtained by determining the best mathematical model that fits the empirical data. Nonlinear regression techniques are used to estimate the model coefficients. Experimental study is provided to illustrate the potential applicability of this method in process monitoring. [Copyright &y& Elsevier]

Abstract: This paper presents a Matlab™ toolbox to assess the accuracy of the estimated parameters of environmental models, based on their approximate confidence regions. Before describing the application, the underlying theory is briefly recalled to familiarize the reader with the numerical methods involved. The software, named PEAS as an acronym for Parameter Estimation Accuracy Software, performs both the estimation and the accuracy analysis, using a user-friendly graphical interface to minimize the required programming. The user is required to specify the model structure according to the Matlab/Simulink™ syntax, supply the experimental data, provide an initial parameter guess and select an estimation method. PEAS provides several model assessment tools, in addition to parameter estimation, such as error function plotting, trajectory sensitivity, Monte Carlo analysis, all useful to assess the adequacy of the experimental data to the estimation problem. After the parameters have been estimated, the reliability assessment is performed: approximate and exact confidence regions are computed and a confidence test is produced. The Monte Carlo analysis is available for approximate accuracy assessment whenever the model structure prevents the application of the confidence regions method. The software, which is freely available for research purposes, is demonstrated here with two examples: a dynamical and an algebraic model. In both cases, software usage and outputs are presented and commented. The examples show how the user is guided through the application of the methods and how warning messages are returned if the estimation does not satisfy the accuracy criteria. [Copyright &y& Elsevier]

Abstract: The CFSE dye dilution assay is widely used to determine the number of divisions a given CFSE labelled cell has undergone in vitro and in vivo. In this paper, we consider how the data obtained with the use of CFSE (CFSE data) can be used to estimate the parameters determining cell division and death. For a homogeneous cell population (i.e., a population with the parameters for cell division and death being independent of time and the number of divisions cells have undergone), we consider a specific biologically based “Smith–Martin” model of cell turnover and analyze three different techniques for estimation of its parameters: direct fitting, indirect fitting and rescaling method. We find that using only CFSE data, the duration of the division phase (i.e., approximately the S+G2 +M phase of the cell cycle) can be estimated with the use of either technique. In some cases, the average division or cell cycle time can be estimated using the direct fitting of the model solution to the data or by using the Gett–Hodgkin method [Gett A. and Hodgkin, P. 2000. A cellular calculus for signal integration by T cells. Nat. Immunol. 1:239-244]. Estimation of the death rates during commitment to division (i.e., approximately the G1 phase of the cell cycle) and during the division phase may not be feasible with the use of only CFSE data. We propose that measuring an additional parameter, the fraction of cells in division, may allow estimation of all model parameters including the death rates during different stages of the cell cycle. [Copyright &y& Elsevier]