Estimation of Cumene Cracking Reaction-Diffusion Model Parameters: Uniqueness and Parametric Sensitivity Analysis

2003 ◽  
Vol 1 (1) ◽  
Author(s):  
Peter Schwan ◽  
Klaus P Möller
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Parameter Estimates ◽  
Physical Parameters ◽  
Model Parameters ◽  
Response Curves ◽  
Cumene Cracking ◽  
Irreversible Reaction ◽  
Reaction Diffusion Model ◽  
Order Of Magnitude

The pulse response of cumene cracking over ZSM5 extrudates has been measured using a Jetloop recycle reactor. A model assuming first order irreversible reaction with constant macro-pore diffusivity and linear adsorption was used to describe the response curves of the reactants and products. The model parameters adsorption, diffusion and reaction rate are in general highly correlated. Relationships for regions of parameter insensitivity and correlation functions between dependent parameters are given. With the aid of independent measurement of adsorption, a sensitivity analysis and a similarity analysis between equations, it was possible to reduce the 7 parameter model into a 2 parameter model for conditions of strong diffusion limitation observed in these experiments. Although good model fits could be achieved, a high degree of uncertainty in the parameter estimates remained, which reflects the high correlation of the physical parameters. Comparison with steady state results shows that the transient diffusivity for cumene is approximately equal to the Knudsen diffusivity, but an order of magnitude lower than the steady state diffusivity. The transient Thiele modulus for cumene was an order of magnitude higher than the steady state value.

scholarly journals Global sensitivity analysis, probabilistic calibration, and predictive assessment for the Data Assimilation Linked Ecosystem Carbon model

2014 ◽  
Vol 7 (5) ◽  
pp. 6893-6948
Author(s):  
C. Safta ◽  
D. Ricciuto ◽  
K. Sargsyan ◽  
B. Debusschere ◽  
H. N. Najm ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Data Assimilation ◽  
Global Sensitivity Analysis ◽  
Model Parameters ◽  
Forest Site ◽  
Carbon Cycle Model ◽  
Global Sensitivity ◽  
Predictive Skill ◽  
Ecosystem Carbon

Abstract. In this paper we propose a probabilistic framework for an uncertainty quantification study of a carbon cycle model. A Global Sensitivity Analysis (GSA) study indicates the parameters and parameter couplings that are important at different times of the year for Quantities of Interest obtained with the Data Assimilation Linked Ecosystem Carbon (DALEC) model. We then employ a Bayesian approach to calibrate the parameters of DALEC using net ecosystem exchange observations at the Harvard Forest site. The calibration exercise is guided by GSA and by Fisher information matrix results that quantify the amount of information carried by the experimental data about specific model parameters. The calibration results are employed in the second part of the paper to assess the predictive skill of the model via posterior predictive checks. These checks show a better performance for the non-steady state model during the growing season compared to the one employing steady state assumptions. Overall, this study leads to a 40% improvement in the predictive skill of DALEC and highlights the importance of considering correlations in the model parameters as informed by the data.

scholarly journals Global Stability of Pneumococcal Pneumonia with Awareness and Saturated Treatment

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Fulgensia Kamugisha Mbabazi ◽  
J. Y. T. Mugisha ◽  
Mark Kimathi
Keyword(s):  
Sensitivity Analysis ◽  
Antibiotic Resistance ◽  
Steady State ◽  
Global Stability ◽  
Influenza A ◽  
Pneumococcal Pneumonia ◽  
Effective Rate ◽  
Model Parameters ◽  
Saturated Treatment ◽  
Disease Free

Pneumocccal pneumonia, a secondary bacterial infection that follows influenza A infection, is responsible for morbidity and mortality in children, elderly, and immunocomprised groups. A mathematical model to study the global stability of pneumococcal pneumonia with awareness and saturated treatment is presented. The basic reproduction number, R0, is computed using the next generation matrix method. The results show that if R0<1, the disease-free steady state is locally asymptotically stable; thus, pneumococcal pneumonia would be eradicated in the population. On the other hand, if R0>1 the endemic steady state is globally attractive; thus, the disease would persist in the population. The quadratic-linear and Goh–Voltera Lyapunov functionals approach are used to prove the global stabilities of the disease-free and endemic steady states, respectively. The sensitivity analysis of R0 on model parameters shows that, it is positively sensitive to the maximal effective rate before antibiotic resistance awareness, rate of relapse encountered in administering treatment, and loss of information by aware susceptible individuals. Contrarily, the sensitivity analysis of R0 on model parameters is negatively sensitive to recovery rate due to treatment and the rate at which unaware susceptible individuals become aware. The numerical analysis of the model shows that awareness about antibiotic resistance and treatment plays a significant role in the control of pneumococcal pneumonia.

scholarly journals Racing against stomatal attenuation: rapid CO2 response curves more reliably estimate photosynthetic capacity than steady state curves in a low conductance species

2020 ◽  
Author(s):  
C Vincent ◽  
MO Pierre ◽  
JR Stinziano
Keyword(s):  
Steady State ◽  
Stomatal Conductance ◽  
Gas Exchange ◽  
Signal To Noise Ratio ◽  
Stomatal Closure ◽  
Parameter Estimates ◽  
Response Curves ◽  
Co2 Response ◽  
Attenuation Effect ◽  
Internal Concentration

AbstractA/Ci curves are an important gas-exchange-based approach to understanding the regulation of photosynthesis, describing the response of net CO2 assimilation (A) to leaf internal concentration of CO2 (Ci). Low stomatal conductance species pose a challenge to the measurement of A/Ci curves by reducing the signal-to-noise ratio of gas exchange measures. Additionally, the stomatal attenuation effect of elevated ambient CO2 leads to further reduction of conductance and may lead to erroneous interpretation of high Ci responses of A. Rapid A/Ci response (RACiR) curves offer a potential practice to develop A/Ci curves faster than the stomatal closure response to elevated CO2. We used the moderately low conductance Citrus to compare traditional steady state (SS) A/Ci curves with RACiR curves. SS curves failed more often than RACiR curves. Overall parameter estimates were the same between SS and RACiR curves. When low stomatal conductance values were removed, triose-phosphate utilization (TPU) limitation estimates increased. Overall RACiR stomatal conductance values began and remained higher than SS values. Based on the comparable resulting parameter estimates, higher likelihood of success and reduced measurement time, we propose RACiR as a valuable tool to measure A/Ci responses in low conductance species.

Relative sensitivity analysis of the predictive properties of sloppy models

2018 ◽  
Vol 16 (02) ◽  
pp. 1840008 ◽  
Author(s):  
Ekaterina Myasnikova ◽  
Alexander Spirov
Keyword(s):  
Sensitivity Analysis ◽  
Predictive Power ◽  
Regulatory Gene ◽  
Relative Sensitivity ◽  
Drosophila Embryo ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Sigmoid Function ◽  
Essential Difference ◽  
System Behavior

Commonly among the model parameters characterizing complex biological systems are those that do not significantly influence the quality of the fit to experimental data, so-called “sloppy” parameters. The sloppiness can be mathematically expressed through saturating response functions (Hill’s, sigmoid) thereby embodying biological mechanisms responsible for the system robustness to external perturbations. However, if a sloppy model is used for the prediction of the system behavior at the altered input (e.g. knock out mutations, natural expression variability), it may demonstrate the poor predictive power due to the ambiguity in the parameter estimates. We introduce a method of the predictive power evaluation under the parameter estimation uncertainty, Relative Sensitivity Analysis. The prediction problem is addressed in the context of gene circuit models describing the dynamics of segmentation gene expression in Drosophila embryo. Gene regulation in these models is introduced by a saturating sigmoid function of the concentrations of the regulatory gene products. We show how our approach can be applied to characterize the essential difference between the sensitivity properties of robust and non-robust solutions and select among the existing solutions those providing the correct system behavior at any reasonable input. In general, the method allows to uncover the sources of incorrect predictions and proposes the way to overcome the estimation uncertainties.

Nonlinear Adaptive Observer for a Lithium-Ion Battery Cell Based on Coupled Electrochemical–Thermal Model

2015 ◽  
Vol 137 (11) ◽  
Author(s):  
S. Dey ◽  
B. Ayalew ◽  
P. Pisu
Keyword(s):  
Thermal Model ◽  
Adaptive Observer ◽  
Parameter Estimates ◽  
Physical Parameters ◽  
Model Parameters ◽  
Battery Cell ◽  
Thermal Dynamics ◽  
Adaptive Scheme ◽  
Li Ion ◽  
Battery Cells

Real-time estimation of battery internal states and physical parameters is of the utmost importance for intelligent battery management systems (BMS). Electrochemical models, derived from the principles of electrochemistry, are arguably more accurate in capturing the physical mechanism of the battery cells than their counterpart data-driven or equivalent circuit models (ECM). Moreover, the electrochemical phenomena inside the battery cells are coupled with the thermal dynamics of the cells. Therefore, consideration of the coupling between electrochemical and thermal dynamics inside the battery cell can be potentially advantageous for improving the accuracy of the estimation. In this paper, a nonlinear adaptive observer scheme is developed based on a coupled electrochemical–thermal model of a Li-ion battery cell. The proposed adaptive observer scheme estimates the distributed Li-ion concentration and temperature states inside the electrode, and some of the electrochemical model parameters, simultaneously. These states and parameters determine the state of charge (SOC) and state of health (SOH) of the battery cell. The adaptive scheme is split into two separate but coupled observers, which simplifies the design and gain tuning procedures. The design relies on a Lyapunov's stability analysis of the observers, which guarantees the convergence of the combined state-parameter estimates. To validate the effectiveness of the scheme, both simulation and experimental studies are performed. The results show that the adaptive scheme is able to estimate the desired variables with reasonable accuracy. Finally, some scenarios are described where the performance of the scheme degrades.

scholarly journals Near-resonant dynamics, period doubling and chaos of a 3-DOF vibro-impact system

2021 ◽  
Author(s):  
Pawel Fritzkowski ◽  
Jan Awrejcewicz
Keyword(s):  
Steady State ◽  
Multiple Scales ◽  
Period Doubling ◽  
Harmonic Excitation ◽  
Linear Oscillator ◽  
Model Parameters ◽  
Response Curves ◽  
Approximate Analytical Solutions ◽  
Resonant Dynamics ◽  
Periodic Steady State

Abstract A mechanical system composed of two weakly coupled oscillators under harmonic excitation is considered. Its main part is a vibro-impact unit composed of a linear oscillator with an internally colliding small block. This block is coupled with the secondary part being a damped linear oscillator. The mathematical model of the system has been presented in a non-dimensional form. The analytical studies are restricted to the case of a periodic steady-state motion with two symmetric impacts per cycle near 1:1 resonance. The multiple scales method combined with the sawtooth-function-based modelling of the non-smooth dynamics is employed. The approximate analytical solutions allow for stability analysis of the periodic motions. Moreover, the frequency-response curves and force-response curves with stable and unstable branches are determined, and the interplay between various model parameters is investigated. The theoretical predictions related to the motion amplitude and the range of stability of the periodic steady-state response is verified via a series of numerical experiments and computation of Lyapunov exponents.

scholarly journals Near-resonant dynamics, period doubling and chaos of a 3-DOF vibro-impact system

2021 ◽  
Vol 106 (1) ◽  
pp. 81-103
Author(s):  
Pawel Fritzkowski ◽  
Jan Awrejcewicz
Keyword(s):  
Steady State ◽  
Multiple Scales ◽  
Period Doubling ◽  
Harmonic Excitation ◽  
Linear Oscillator ◽  
Model Parameters ◽  
Response Curves ◽  
Resonant Dynamics ◽  
Periodic Steady State ◽  
The Stability

AbstractA mechanical system composed of two weakly coupled oscillators under harmonic excitation is considered. Its main part is a vibro-impact unit composed of a linear oscillator with an internally colliding small block. This block is coupled with the secondary part being a damped linear oscillator. The mathematical model of the system has been presented in a non-dimensional form. The analytical studies are restricted to the case of a periodic steady-state motion with two symmetric impacts per cycle near 1:1 resonance. The multiple scales method combined with the sawtooth-function-based modelling of the non-smooth dynamics is employed. A conception of the stability analysis of the periodic motions suited for this theoretical approach is presented. The frequency–response curves and force–response curves with stable and unstable branches are determined, and the interplay between various model parameters is investigated. The theoretical predictions related to the motion amplitude and the range of stability of the periodic steady-state response are verified via a series of numerical experiments and computation of Lyapunov exponents. Finally, the limitations and extensibility of the approach are discussed.

scholarly journals Uncertainty quantification, propagation and characterization by Bayesian analysis combined with global sensitivity analysis applied to dynamical intracellular pathway models

2018 ◽  
Author(s):  
Olivia Eriksson ◽  
Alexandra Jauhiainen ◽  
Sara Maad Sasane ◽  
Andrei Kramer ◽  
Anu G Nair ◽  
...  
Keyword(s):  
Experimental Data ◽  
Sensitivity Analysis ◽  
Bayesian Analysis ◽  
Uncertainty Quantification ◽  
Posterior Distribution ◽  
Global Sensitivity Analysis ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Individual Parameter ◽  
Global Sensitivity

AbstractMotivationDynamical models describing intracellular phenomena are increasing in size and complexity as more information is obtained from experiments. These models are often over-parameterized with respect to the quantitative data used for parameter estimation, resulting in uncertainty in the individual parameter estimates as well as in the predictions made from the model. Here we combine Bayesian analysis with global sensitivity analysis in order to give better informed predictions; to point out weaker parts of the model that are important targets for further experiments, as well as give guidance on parameters that are essential in distinguishing different qualitative output behaviours.ResultsWe used approximate Bayesian computation (ABC) to estimate the model parameters from experimental data, as well as to quantify the uncertainty in this estimation (inverse uncertainty quantification), resulting in a posterior distribution for the parameters. This parameter uncertainty was next propagated to a corresponding uncertainty in the predictions (forward uncertainty propagation), and a global sensitivity analysis was performed on the prediction using the posterior distribution as the possible values for the parameters. This methodology was applied on a relatively large and complex model relevant for synaptic plasticity, using experimental data from several sources. We could hereby point out those parameters that by themselves have the largest contribution to the uncertainty of the prediction as well as identify parameters important to separate between qualitatively different predictions.This approach is useful both for experimental design as well as model building.

Holdup and holdup profiles in the reciprocating plate extractor VPE

1990 ◽  
Vol 55 (11) ◽  
pp. 2648-2661 ◽  
Author(s):  
Helena Sovová ◽  
Vladislav Bízek ◽  
Jaroslav Procházka
Keyword(s):  
Steady State ◽  
Experimental Results ◽  
Model Parameters ◽  
Dispersed Phase ◽  
Pulse Form ◽  
Sieve Plates

In this work measurements of mean holdup of dispersed phase, of axial holdup profiles and of flooding points in a reciprocating plate contactor with both the VPE-type plates and the sieve plates were carried out. The experimental results were compared with a monodisperse model of steady-state column hydrodynamics and the model parameters were evaluated. Important differences in the behaviour of the two plate types could be identified. Comparison was also made between two reciprocating drives of different pulse form.

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