Practical identifiability of model parameters by combined respirometric-titrimetric measurements

2001 ◽  
Vol 43 (7) ◽  
pp. 347-355 ◽  
Author(s):  
B. Petersen ◽  
K. Gernaey ◽  
P. A. Vanrolleghem
Keyword(s):  
Fisher Information Matrix ◽  
Information Matrix ◽  
Accurate Estimation ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Concentration Data ◽  
Sensitivity Functions ◽  
Practical Identifiability ◽  
Lower Accuracy ◽  
Accuracy Parameter

An earlier study on theoretical identifiability of parameters for a two-step nitrification model showed that a unique estimation of the yield YA1 is possible with combined respirometric-titrimetric data, contrary to the case where only one type of measurement is available. Here, the practical identifiability of model parameters was investigated via evaluation of the output sensitivity functions and the corresponding Fisher Information Matrix (FIM). It appeared that the FIM was not sufficiently powerful to predict the practical identifiability of this case with combined measurements as parameters could indeed be identified despite the fact that the FIM became singular. The accuracy of parameter estimates based on respirometric and titrimetric data and combination thereof was also investigated. Estimation on titrimetric data (Hp) was very accurate and a fast convergence of the objective function towards a minimum was obtained. The latter also holds for estimation on oxygen uptake rate data (rO), however with a lower accuracy. Parameter estimation based on oxygen concentration data (SO) was more complex but resulted in a higher accuracy. Thus, when the highest accuracy is needed it is recommended to estimate parameters initially on Hp and/or rO data, and to subsequently use these parameters as initial values for final, and more accurate estimation on SO data.

Derivation and Validation of a Prediction Tool for Venous Thromboembolism: A VERITY Registry Study.

Blood ◽  
2007 ◽  
Vol 110 (11) ◽  
pp. 697-697 ◽  
Author(s):  
Roopen Arya ◽  
Shankaranarayana Paneesha ◽  
Aidan McManus ◽  
Nick Parsons ◽  
Nicholas Scriven ◽  
...  
Keyword(s):  
Risk Factors ◽  
Venous Thromboembolism ◽  
Risk Score ◽  
Validation Cohort ◽  
Accurate Estimation ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Derivation Cohort ◽  
Hormonal Factor ◽  
Electronic Alerts

Abstract Accurate estimation of risk for venous thromboembolism (VTE) may help clinicians assess prophylaxis needs. Only empirical algorithms and risk scores have been described; an empirical risk score (‘Kucher’) based on 8 VTE risk factors (cancer, prior VTE, hypercoagulability, surgery, age>75 yrs, BMI>29, bed rest, hormonal factor) using electronic alerts improved hospitalized patient outcome (NEJM2005;352:969–77). We wished to develop a multivariate regression model for VTE risk, based on Kucher, and validate its performance. The initial derivation cohort consisted of patients enrolled in ‘VERITY’, a multicentre VTE treatment registry for whom the endpoint of VTE and all 8 risk factors were known. Initial univariate analysis (n=5928; 32.4% with diagnosis of VTE) suggested VTE risk was not accounted for by the 8 factors; an additional 3 were added (leg paralysis, smoking, IV drug use [IVD]). The final derivation cohort was 5241 patients (32.0% with VTE) with complete risk data. The validation cohort (n=915) was derived from a database of 928 consecutively enrolled patients at a single DVT clinic. Model parameters were estimated using the statistical package ‘R’ using a stepwise selection procedure to choose the optimal number of main effects and pair-wise interactions. This showed that advanced age (estimated odds ratio [OR]=2.8, p<0.001); inpatient (OR=3.0, p<0.001); surgery (OR=3.1, p<0.001); prior VTE (OR=2.9, p<0.001); leg paralysis (OR=3.8, p<0.001); cancer (OR=5.3, p<0.001); IVD (OR=14.3, p<0.001); smoking (OR=1.2, p=0.009); and thrombophilia (OR=2.8; p<0.001) increased the risk of VTE. Obesity (OR=0.7; p<0.001) increased the VTE risk only in patients with a hormonal factor (OR=2.0, p=0.007). Backward stepwise regression showed prior VTE as the most important factor followed by cancer, IVD, surgery, inpatient, age, leg paralysis, hormonal factor, obesity, thrombophilia and smoking. Expressing the parameter estimates in terms of probabilities defines a risk score model for VTE. Using the model, the receiver operating characteristic (ROC) curve (see figure) area under the curve (AUC) was estimated as 0.720 (95% CI, 0.705–0.735) for the model (dashed line), indicating a good diagnostic test significantly better (p<0.001) than Kucher (AUC=0.617, 95% CI, 0.599–0.634)(solid line). For the validation cohort, AUC was estimated as 0.678 (95% CI, 0.635–0.721) for the model, which was not significantly different from AUC for the full dataset used for model development, and was 0.587 (95% CI, 0.542–0.632) for Kucher. This model to predict individual patient risk of VTE may contribute to decision making regarding prophylaxis in clinical practice. Figure Figure

scholarly journals Practical Identifiability of the Manipulator Link Stiffness Parameters

2013 ◽  
Author(s):  
Alexandr Klimchik ◽  
Stéphane Caro ◽  
Anatol Pashkevich
Keyword(s):  
Industrial Robot ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Stiffness Modeling ◽  
Practical Identifiability ◽  
Machining Force ◽  
Observation Matrix ◽  
Reduction Methods ◽  
Manipulator Link ◽  
Selection Of

The paper addresses a problem of the manipulator stiffness modeling, which is extremely important for the precise manufacturing of contemporary aeronautic materials where the machining force causes significant compliance errors in the robot end-effector position. The main contributions are in the area of the elastostatic parameters identification. Particular attention is paid to the practical identifiability of the model parameters, which completely differs from the theoretical one that relies on the rank of the observation matrix only, without taking into account essential differences in the model parameter magnitudes and the measurement noise impact. This problem is relatively new in robotics and essentially differs from that arising in geometrical calibration. To solve the problem, several physical and statistical model reduction methods are proposed. They are based on the stiffness matrix sparseness taking into account the physical properties of the manipulator elements and also on the heuristic selection of the practically non-identifiable parameters that employs numerical analyses of the parameter estimates. The advantages of the developed approach are illustrated by an application example that deals with the stiffness modeling of an industrial robot used in aerospace industry.

scholarly journals On Optimal Test Signal Design and Parameter Identification Schemes for Dynamic Takagi-Sugeno Fuzzy Models Using the Fisher Information Matrix

2021 ◽  
Author(s):  
Matthias Himmelsbach ◽  
Andreas Kroll
Keyword(s):  
Fisher Information ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Parameter Estimate ◽  
Model Parameters ◽  
Signal Design ◽  
Optimal Test ◽  
Identification Schemes ◽  
Fuzzy Models ◽  
Takagi Sugeno

AbstractThis paper is concerned with the analysis of optimization procedures for optimal experiment design for locally affine Takagi-Sugeno (TS) fuzzy models based on the Fisher Information Matrix (FIM). The FIM is used to estimate the covariance matrix of a parameter estimate. It depends on the model parameters as well as the regression variables. Due to the dependency on the model parameters good initial models are required. Since the FIM is a matrix, a scalar measure of the FIM is optimized. Different measures and optimization goals are investigated in three case studies.

Optimal experiment design for nonlinear models subject to large prior uncertainties

1987 ◽  
Vol 253 (3) ◽  
pp. R530-R534 ◽  
Author(s):  
E. Walter ◽  
L. Pronzato
Keyword(s):  
Optimal Design ◽  
Parameter Uncertainty ◽  
Fisher Information Matrix ◽  
Nonlinear Models ◽  
A Priori ◽  
Information Matrix ◽  
Experiment Design ◽  
Model Parameters ◽  
Optimal Experiment ◽  
Classical Experiment

Classical experiment design generally yields an experiment that depends on the value of the parameters to be estimated, which are, of course, unknown. Assuming that the model parameters belong to a population with known statistics, we propose to take the a priori parameter uncertainty into account by optimizing the mathematical expectation of a functional of the Fisher information matrix. This optimization is performed with a stochastic approximation algorithm that makes robust experiment design almost as simple as classical D-optimal design. The resulting methodology is applied to the choice of measurement times for multiexponential models.

scholarly journals Reliability estimation for the randomly censored pareto distribution

2019 ◽  
Vol 9 (4) ◽  
pp. 3272
Author(s):  
Mahmoud M. Smadi ◽  
Saiful Islam Ansari ◽  
Ahmed A. Jaradat
Keyword(s):  
Fisher Information Matrix ◽  
Pareto Distribution ◽  
Survival Function ◽  
Information Matrix ◽  
Reliability Estimation ◽  
Model Parameters ◽  
Random Censoring ◽  
Asymptotic Confidence Intervals ◽  
Estimate Reliability ◽  
Censoring Scheme

Widespread applications of random censoring in life testing experiments to estimate reliability of engineering products or systems are avialable. Different parametric statistical models such as exponential, Rayleigh, Weibull and Maxwell distributions are used under random censoring scheme. In this paper, random censoring under Pareto distribution is considered. The maximum likelihood estimators (MLE’s) of the model parameters and survival function were derived along with Fisher information matrix and asymptotic confidence intervals. A simulation study was performed to observe the behavior of the MLE’s. The simulation results showed that the bias and MSE were reasonably small in all cases.

scholarly journals Multi-Objective Optimization of Experiments Using Curvature and Fisher Information Matrix

2017 ◽  
Author(s):  
Erica Manesso ◽  
Sridharan Srinath ◽  
Rudiyanto Gunawan
Keyword(s):  
Fisher Information ◽  
Fisher Information Matrix ◽  
Dynamic Models ◽  
Information Matrix ◽  
Model Parameters ◽  
Multi Objective Optimization ◽  
Experimental Conditions ◽  
Maximum Information ◽  
Multi Objective ◽  
Highly Nonlinear

The bottleneck in creating dynamic models of biological networks and processes often lies in estimating unknown kinetic model parameters from experimental data. In this regard, experimental conditions have a strong influence on parameter identifiability and should therefore be optimized to give the maximum information for parameter estimation. Existing model-based design of experiment (MBDOE) methods commonly rely on the Fisher Information Matrix (FIM) for defining a metric of data informativeness. When the model behavior is highly nonlinear, FIM-based criteria may lead to suboptimal designs since the FIM only accounts for the linear variation of the model outputs with respect to the parameters. In this work, we developed a multi-objective optimization (MOO) MBDOE, where model nonlinearity was taken into consideration through the use of curvature. The proposed MOO MBDOE involved maximizing data informativeness using a FIM-based metric and at the same time minimizing the model curvature. We demonstrated the advantages of the MOO MBDOE over existing FIM-based and other curvature-based MBDOEs in an application to the kinetic modeling of fed-batch fermentation of Baker's yeast.

Simultaneous structure and parameter identification of multivariate systems by matrix decomposition

2016 ◽  
Vol 38 (12) ◽  
pp. 1411-1420 ◽  
Author(s):  
Benben Jiang ◽  
Fan Yang ◽  
Dexian Huang
Keyword(s):  
Parameter Identification ◽  
Structure Determination ◽  
Information Matrix ◽  
Matrix Decomposition ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Model Structure ◽  
Multiple Model ◽  
Process Data ◽  
Multivariate Systems

Structure determination and parameter identification of multivariate systems are crucial but rather difficult issues in system identification. Due to the explosive growth of process data along with the scale increase of industrial processes, directional links between variables of such complex processes are often undistinguishable, which is indispensable to model structure determination but is often assumed to be known beforehand in most identification methods. In this article, a new modelling approach is developed to simultaneously estimate the model parameters and structures (including model orders as well as the directional links between different process variables) of multivariate systems. A vector auto-regressive (VAR) form is utilized as the model formulation in this algorithm. The key technique lies in constructing an interleaved information matrix with respect to a multiple model structure formulated for the VAR representation. Then by utilizing the upper diagonal factorization, all the parameter estimates of all path models with orders from zero to m, as well as the corresponding cost function values, can be obtained simultaneously. The effectiveness of the proposed method is demonstrated via a numerical example and a distillation column system.

Multiple-objective criteria for optimal experimental design: application to ferrokinetics

1985 ◽  
Vol 248 (3) ◽  
pp. R378-R386 ◽  
Author(s):  
M. H. Nathanson ◽  
G. M. Saidel
Keyword(s):  
Experimental Design ◽  
Optimal Design ◽  
Objective Function ◽  
Information Matrix ◽  
Optimal Experimental Design ◽  
Multiple Objective ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Experimental Conditions ◽  
New Criterion

Optimal experimental design is used to predict the experimental conditions that will allow the "best" estimates of model parameters. A variety of criteria must be considered before an optimal design is chosen. Maximizing the determinant of the information matrix (D optimality), which tends to produce the most precise simultaneous estimates of all parameters, is commonly considered as the primary criterion. To complement this criterion, we present another whose effect is to reduce the interaction among the parameter estimates so that changes in any one parameter can be more distinct. This new criterion consists of maximizing the determinant of an appropriately scaled information matrix (M optimality). These criteria are applied jointly in a multiple-objective function. To illustrate the use of these concepts, we develop an optimal experimental design of blood sampling schedules using a detailed ferrokinetic model.

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