Parameter Estimation and Sensitivity Analysis of a Nonlinearly Elastic Static Lung Model

1985 ◽  
Vol 107 (4) ◽  
pp. 315-320 ◽  
Author(s):  
J. R. Ligas ◽  
G. M. Saidel ◽  
F. P. Primiano
Keyword(s):  
Sensitivity Analysis ◽  
Parameter Estimation ◽  
Least Squares ◽  
Static Pressure ◽  
Optimal Parameter ◽  
Elastic Strain Energy ◽  
Lung Model ◽  
Model Parameters ◽  
Least Squares Fit ◽  
Parameter Values

A model for the static pressure-volume behavior of the lung parenchyma based on a pseudo-elastic strain energy function was tested. Values of the model parameters and their variances were estimated by an optimal least-squares fit of the model-predicted pressures to the corresponding data from excised, saline-filled dog lungs. Although the model fit data from twelve lungs very well, the coefficients of variation for parameter values differed greatly. To analyze the sensitivity of the model output to its parameters, we examined an approximate Hessian, H, of the least-squares objective function. Based on the determinant and condition number of H, we were able to set formal criteria for choosing the most reliable estimates of parameter values and their variances. This in turn allowed us to specify a normal range of parameter values for these dog lungs. Thus the model not only describes static pressure-volume data, but also uses the data to estimate parameters from a fundamental constitutive equation. The optimal parameter estimation and sensitivity analysis developed here can be widely applied to other physiologic systems.

scholarly journals Direct inversion of the apparent complex‐resistivity spectrum

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1399-1404 ◽  
Author(s):  
J. Xiang ◽  
N. B. Jones ◽  
D. Cheng ◽  
F. S. Schlindwein
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Optimal Parameter ◽  
Geophysical Methods ◽  
Inversion Method ◽  
Model Parameters ◽  
Complex Resistivity ◽  
Direct Inversion ◽  
Optimal Parameter Estimation ◽  
Cole Model

Cole‐Cole model parameters are widely used to interpret electrical geophysical methods and are obtained by inverting the induced polarization (IP) spectrum. This paper presents a direct inversion method for parameter estimation based on multifold least‐squares estimation. Two algorithms are described that provide optimal parameter estimation in the least‐squares sense. Simulations demonstrate that both algorithms can provide direct apparent spectral parameter inversion for complex resistivity data. Moreover, the second algorithm is robust under reasonably high noise.

scholarly journals A Stochastic Harmonic Oscillator Temperature Model for the Valuation of Weather Derivatives

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2890
Author(s):  
Alessio Giorgini ◽  
Rogemar S. Mamon ◽  
Marianito R. Rodrigo
Keyword(s):  
Sensitivity Analysis ◽  
Parameter Estimation ◽  
Harmonic Oscillator ◽  
Numerical Simulations ◽  
Model Parameters ◽  
Call Option ◽  
Temperature Model ◽  
Option Prices ◽  
Harmonic Oscillator Model ◽  
Temperature Dynamics

Stochastic processes are employed in this paper to capture the evolution of daily mean temperatures, with the goal of pricing temperature-based weather options. A stochastic harmonic oscillator model is proposed for the temperature dynamics and results of numerical simulations and parameter estimation are presented. The temperature model is used to price a one-month call option and a sensitivity analysis is undertaken to examine how call option prices are affected when the model parameters are varied.

Model misspecification and bias in the least-squares algorithm: Implications for linearized isotropic AVO

2021 ◽  
Vol 40 (9) ◽  
pp. 646-654
Author(s):  
Henning Hoeber
Keyword(s):  
Least Squares ◽  
Model Misspecification ◽  
Forward Model ◽  
Model Parameters ◽  
Omitted Variables ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Omitted Variable Bias ◽  
Least Squares Fit ◽  
Variable Bias

When inversions use incorrectly specified models, the estimated least-squares model parameters are biased. Their expected values are not the true underlying quantitative parameters being estimated. This means the least-squares model parameters cannot be compared to the equivalent values from forward modeling. In addition, the bias propagates into other quantities, such as elastic reflectivities in amplitude variation with offset (AVO) analysis. I give an outline of the framework to analyze bias, provided by the theory of omitted variable bias (OVB). I use OVB to calculate exactly the bias due to model misspecification in linearized isotropic two-term AVO. The resulting equations can be used to forward model unbiased AVO quantities, using the least-squares fit results, the weights given by OVB analysis, and the omitted variables. I show how uncertainty due to bias propagates into derived quantities, such as the χ-angle and elastic reflectivity expressions. The result can be used to build tables of unique relative rock property relationships for any AVO model, which replace the unbiased, forward-model results.

Integrating Parameter Estimation Solutions From the Time and Time-Scale Domains

2009 ◽  
Author(s):  
James R. McCusker ◽  
Kourosh Danai
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Time Scale ◽  
Prediction Error ◽  
Nonlinear Least Squares ◽  
Integrated Approach ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Single Model ◽  
Iterative Estimation

A method of parameter estimation was recently introduced that separately estimates each parameter of the dynamic model [1]. In this method, regions coined as parameter signatures, are identified in the time-scale domain wherein the prediction error can be attributed to the error of a single model parameter. Based on these single-parameter associations, individual model parameters can then be estimated for iterative estimation. Relative to nonlinear least squares, the proposed Parameter Signature Isolation Method (PARSIM) has two distinct attributes. One attribute of PARSIM is to leave the estimation of a parameter dormant when a parameter signature cannot be extracted for it. Another attribute is independence from the contour of the prediction error. The first attribute could cause erroneous parameter estimates, when the parameters are not adapted continually. The second attribute, on the other hand, can provide a safeguard against local minima entrapments. These attributes motivate integrating PARSIM with a method, like nonlinear least-squares, that is less prone to dormancy of parameter estimates. The paper demonstrates the merit of the proposed integrated approach in application to a difficult estimation problem.

scholarly journals Parameter estimation for functional–structural plant models when data are scarce: using multiple patterns for rejecting unsuitable parameter sets

2020 ◽  
Vol 126 (4) ◽  
pp. 559-570 ◽  
Author(s):  
Ming Wang ◽  
Neil White ◽  
Jim Hanan ◽  
Di He ◽  
Enli Wang ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Predictive Power ◽  
Model Performance ◽  
Persea Americana ◽  
Strong Interactions ◽  
Model Parameters ◽  
Timely Manner ◽  
Complex Interactions ◽  
Output Uncertainty ◽  
Parameter Values

Abstract Background and Aims Functional–structural plant (FSP) models provide insights into the complex interactions between plant architecture and underlying developmental mechanisms. However, parameter estimation of FSP models remains challenging. We therefore used pattern-oriented modelling (POM) to test whether parameterization of FSP models can be made more efficient, systematic and powerful. With POM, a set of weak patterns is used to determine uncertain parameter values, instead of measuring them in experiments or observations, which often is infeasible. Methods We used an existing FSP model of avocado (Persea americana ‘Hass’) and tested whether POM parameterization would converge to an existing manual parameterization. The model was run for 10 000 parameter sets and model outputs were compared with verification patterns. Each verification pattern served as a filter for rejecting unrealistic parameter sets. The model was then validated by running it with the surviving parameter sets that passed all filters and then comparing their pooled model outputs with additional validation patterns that were not used for parameterization. Key Results POM calibration led to 22 surviving parameter sets. Within these sets, most individual parameters varied over a large range. One of the resulting sets was similar to the manually parameterized set. Using the entire suite of surviving parameter sets, the model successfully predicted all validation patterns. However, two of the surviving parameter sets could not make the model predict all validation patterns. Conclusions Our findings suggest strong interactions among model parameters and their corresponding processes, respectively. Using all surviving parameter sets takes these interactions into account fully, thereby improving model performance regarding validation and model output uncertainty. We conclude that POM calibration allows FSP models to be developed in a timely manner without having to rely on field or laboratory experiments, or on cumbersome manual parameterization. POM also increases the predictive power of FSP models.

Li-Ion Cell Aging Model Online Parameter Estimation for Improved Prognosis

2016 ◽  
Author(s):  
Punit Tulpule ◽  
Chin-Yao Chang ◽  
Giorgio Rizzoni
Keyword(s):  
Sensitivity Analysis ◽  
Parameter Estimation ◽  
Lithium Ion ◽  
Remaining Useful Life ◽  
Estimation Methods ◽  
Cell Aging ◽  
Model Parameters ◽  
Positive Electrodes ◽  
Aging Model ◽  
Estimation Algorithms

In this paper, a semi-empirical aging model of lithium-ion pouch cells containing blended spinel and layered-oxide positive electrodes is calibrated using aging campaigns. Sensitivity analysis is done on this model to identify the effect of parameter variations on the State of Health (SOH) prediction. The sensitivity analysis shows that the aging model alone is not robust enough to perform long term predictions, hence we propose to use online parameter estimation algorithms to adapt the model parameters. Four different estimation methods are compared using aging campaign. It is demonstrated that the estimation algorithms improve aging model leading to significant improvement in Remaining Useful Life (RUL) prediction.

scholarly journals Data assimilation in integrated hydrological modelling in the presence of observation bias

2015 ◽  
Vol 12 (8) ◽  
pp. 8131-8173 ◽  
Author(s):  
J. Rasmussen ◽  
H. Madsen ◽  
K. H. Jensen ◽  
J. C. Refsgaard
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Stream Flow ◽  
Groundwater Modeling ◽  
Optimal Parameter ◽  
Estimation Methods ◽  
Model Parameters ◽  
Stream Discharge ◽  
Groundwater Head ◽  
Observation Bias

Abstract. The use of bias-aware Kalman filters for estimating and correcting observation bias in groundwater head observations is evaluated using both synthetic and real observations. In the synthetic test, groundwater head observations with a constant bias and unbiased stream discharge observations are assimilated in a catchment scale integrated hydrological model with the aim of updating stream discharge and groundwater head, as well as several model parameters relating to both stream flow and groundwater modeling. The Colored Noise Kalman filter (ColKF) and the Separate bias Kalman filter (SepKF) are tested and evaluated for correcting the observation biases. The study found that both methods were able to estimate most of the biases and that using any of the two bias estimation methods resulted in significant improvements over using a bias-unaware Kalman Filter. While the convergence of the ColKF was significantly faster than the convergence of the SepKF, a much larger ensemble size was required as the estimation of biases would otherwise fail. Real observations of groundwater head and stream discharge were also assimilated, resulting in improved stream flow modeling in terms of an increased Nash-Sutcliffe coefficient while no clear improvement in groundwater head modeling was observed. Both the ColKF and the SepKF tended to underestimate the biases, which resulted in drifting model behavior and sub-optimal parameter estimation, but both methods provided better state updating and parameter estimation than using a bias-unaware filter.

scholarly journals Improving SWAT Model Calibration Using Soil MERGE (SMERGE)

Water ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 2039 ◽  
Author(s):  
Kenneth J. Tobin ◽  
Marvin E. Bennett
Keyword(s):  
Great Plains ◽  
Assessment Tool ◽  
Root Zone ◽  
Optimal Parameter ◽  
Swat Model ◽  
Model Parameters ◽  
Highly Sensitive ◽  
Improved Performance ◽  
Parameter Values ◽  
Sensitive Parameters

This study examined eight Great Plains moderate-sized (832 to 4892 km2) watersheds. The Soil and Water Assessment Tool (SWAT) autocalibration routine SUFI-2 was executed using twenty-three model parameters, from 1995 to 2015 in each basin, to identify highly sensitive parameters (HSP). The model was then run on a year-by-year basis, generating optimal parameter values for each year (1995 to 2015). HSP were correlated against annual precipitation (Parameter-elevation Regressions on Independent Slopes Model—PRISM) and root zone soil moisture (Soil MERGE—SMERGE 2.0) anomaly data. HSP with robust correlation (r > 0.5) were used to calibrate the model on an annual basis (2016 to 2018). Results were compared against a baseline simulation, in which optimal parameters were obtained by running the model for the entire period (1992 to 2015). This approach improved performance for annual simulations generated from 2016 to 2018. SMERGE 2.0 produced more robust results compared with the PRISM product. The main virtue of this approach is that it constrains parameter space, minimizesing equifinality and promotesing modeling based on more physically realistic parameter values.

scholarly journals Sensitivity analysis and parameter estimation for the distributed modeling of infiltration excess overland flow

2007 ◽  
Vol 4 (1) ◽  
pp. 363-405 ◽  
Author(s):  
W. Castaings ◽  
D. Dartus ◽  
F.-X. Le Dimet ◽  
G.-M. Saulnier
Keyword(s):  
Sensitivity Analysis ◽  
Parameter Estimation ◽  
Overland Flow ◽  
Flash Flood ◽  
Parametric Uncertainty ◽  
Optimization Techniques ◽  
Model Parameters ◽  
Adjoint Sensitivity ◽  
Gradient Based ◽  
Infiltration Excess

Abstract. The variational methods widely used for other environmental systems are applied to a spatially distributed flash flood model coupling kinematic wave overland flow and Green Ampt infiltration. Using an idealized configuration where only parametric uncertainty is addressed, the potential of this approach is illustrated for sensitivity analysis and parameter estimation. Adjoint sensitivity analysis provides an extensive insight into the relation between model parameters and the hydrological response and enables the use of efficient gradient based optimization techniques.

scholarly journals Parameter variations in prediction skill optimization at ECMWF

2013 ◽  
Vol 20 (6) ◽  
pp. 1001-1010 ◽  
Author(s):  
P. Ollinaho ◽  
P. Bechtold ◽  
M. Leutbecher ◽  
M. Laine ◽  
A. Solonen ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Weather Prediction ◽  
Prediction Skill ◽  
Convective Precipitation ◽  
Ensemble Prediction ◽  
Model Parameters ◽  
Ongoing Research ◽  
Medium Range ◽  
Parameter Values ◽  
Very High

Abstract. Algorithmic numerical weather prediction (NWP) skill optimization has been tested using the Integrated Forecasting System (IFS) of the European Centre for Medium-Range Weather Forecasts (ECMWF). We report the results of initial experimentation using importance sampling based on model parameter estimation methodology targeted for ensemble prediction systems, called the ensemble prediction and parameter estimation system (EPPES). The same methodology was earlier proven to be a viable concept in low-order ordinary differential equation systems, and in large-scale atmospheric general circulation models (ECHAM5). Here we show that prediction skill optimization is possible even in the context of a system that is (i) of very high dimensionality, and (ii) carefully tuned to very high skill. We concentrate on four closure parameters related to the parameterizations of sub-grid scale physical processes of convection and formation of convective precipitation. We launch standard ensembles of medium-range predictions such that each member uses different values of the four parameters, and make sequential statistical inferences about the parameter values. Our target criterion is the squared forecast error of the 500 hPa geopotential height at day three and day ten. The EPPES methodology is able to converge towards closure parameter values that optimize the target criterion. Therefore, we conclude that estimation and cost function-based tuning of low-dimensional static model parameters is possible despite the very high dimensional state space, as well as the presence of stochastic noise due to initial state and physical tendency perturbations. The remaining question before EPPES can be considered as a generally applicable tool in model development is the correct formulation of the target criterion. The one used here is, in our view, very selective. Considering the multi-faceted question of improving forecast model performance, a more general target criterion should be developed. This is a topic of ongoing research.

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