Sensitivity analysis of respiratory parameter uncertainties: impact of criterion function form and constraints

1990 ◽  
Vol 69 (2) ◽  
pp. 766-775 ◽  
Author(s):  
K. R. Lutchen
Keyword(s):  
Sensitivity Analysis ◽  
Input Impedance ◽  
Element Model ◽  
Confidence Regions ◽  
Alternative Methods ◽  
Function Form ◽  
Parameter Uncertainties ◽  
Criterion Function ◽  
Transfer Impedance ◽  
Impedance Data

A sensitivity analysis based on weighted least-squares regression is presented to evaluate alternative methods for fitting lumped-parameter models to respiratory impedance data. The goal is to maintain parameter accuracy simultaneously with practical experiment design. The analysis focuses on predicting parameter uncertainties using a linearized approximation for joint confidence regions. Applications are with four-element parallel and viscoelastic models for 0.125- to 4-Hz data and a six-element model with separate tissue and airway properties for input and transfer impedance data from 2-64 Hz. The criterion function form was evaluated by comparing parameter uncertainties when data are fit as magnitude and phase, dynamic resistance and compliance, or real and imaginary parts of input impedance. The proper choice of weighting can make all three criterion variables comparable. For the six-element model, parameter uncertainties were predicted when both input impedance and transfer impedance are acquired and fit simultaneously. A fit to both data sets from 4 to 64 Hz could reduce parameter estimate uncertainties considerably from those achievable by fitting either alone. For the four-element models, use of an independent, but noisy, measure of static compliance was assessed as a constraint on model parameters. This may allow acceptable parameter uncertainties for a minimum frequency of 0.275-0.375 Hz rather than 0.125 Hz. This reduces data acquisition requirements from a 16- to a 5.33- to 8-s breath holding period. These results are approximations, and the impact of using the linearized approximation for the confidence regions is discussed.

Impact of frequency range and input impedance on airway-tissue separation implied from transfer impedance

1993 ◽  
Vol 74 (3) ◽  
pp. 1089-1099 ◽  
Author(s):  
K. R. Lutchen ◽  
J. R. Everett ◽  
A. C. Jackson
Keyword(s):  
Prior Knowledge ◽  
Input Impedance ◽  
Upper Airway ◽  
Element Model ◽  
Frequency Range ◽  
Tissue Properties ◽  
Transfer Impedance ◽  
Tissue Separation ◽  
Enhanced Sensitivity ◽  
Tissue Resistance

In humans, application of the DuBois (DuBois et al. J. Appl. Physiol. 8: 587–594, 1956) six-element model to respiratory transfer impedance (Ztr) data has been proposed as a means to noninvasively estimate airway and tissue properties. This approach requires prior knowledge of alveolar gas compressibility (Cg). With input impedance (Zin), prior knowledge of Cg is not required, but the data do not support a reliable separation of airway from tissue properties. In this study, we investigated the separation of airway and tissue properties when Ztr and Zin data are measured and analyzed simultaneously over a larger frequency range than usual. In 10 healthy adults, we measured Ztr and Zin from 2 to 64 Hz. Zin was measured using both the standard approach with oscillations directly into the airway opening (Zst) and the head generator approach (Zhg) with oscillations applied around the head. With Ztr data alone, we found that the airway resistance and inertance estimates were reliable with only 2- to 32-Hz data and were unaffected by including the additional 32- to 64-Hz data. Conversely, the estimates of tissue resistance and inertance were highly unreliable unless the 32- to 64-Hz data are included. Because of enhanced sensitivity of Ztr to Cg from 32 to 64 Hz, inaccuracies in the assigned Cg will distort the estimated tissue but not airway properties. The Ztr-based parameters predicted Zhg data far better than Zst data, which is consistent with Zhg data being less influenced by upper airway shunting over this frequency range. There was no apparent advantage to combining Ztr and Zhg data during parameter estimation. With Cg unfixed, the estimated Cg was 50–100% higher than expected from an independent measurement of functional residual capacity. These results confirm that Ztr alone can provide a reliable distinction of lumped respiratory airway and tissue properties that are little influenced by upper airway wall shunting but only if 2- to 64-Hz data are analyzed. This distinction, however, requires an accurate prior measurement of Cg, and this requirement cannot be removed by combining Ztr and Zin data.

scholarly journals Sensitivity Analysis of the Influence of Structural Parameters on Dynamic Behaviour of Highly Redundant Cable-Stayed Bridges

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
B. Asgari ◽  
S. A. Osman ◽  
A. Adnan
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Finite Element Model ◽  
Model Updating ◽  
Structural Parameters ◽  
Element Model ◽  
Structural Behavior ◽  
Model Tuning ◽  
The Finite Element Model ◽  
Cable Stayed Bridges

The model tuning through sensitivity analysis is a prominent procedure to assess the structural behavior and dynamic characteristics of cable-stayed bridges. Most of the previous sensitivity-based model tuning methods are automatic iterative processes; however, the results of recent studies show that the most reasonable results are achievable by applying the manual methods to update the analytical model of cable-stayed bridges. This paper presents a model updating algorithm for highly redundant cable-stayed bridges that can be used as an iterative manual procedure. The updating parameters are selected through the sensitivity analysis which helps to better understand the structural behavior of the bridge. The finite element model of Tatara Bridge is considered for the numerical studies. The results of the simulations indicate the efficiency and applicability of the presented manual tuning method for updating the finite element model of cable-stayed bridges. The new aspects regarding effective material and structural parameters and model tuning procedure presented in this paper will be useful for analyzing and model updating of cable-stayed bridges.

Human respiratory input impedance from 4 to 200 Hz: physiological and modeling considerations

1988 ◽  
Vol 64 (2) ◽  
pp. 823-831 ◽  
Author(s):  
H. L. Dorkin ◽  
K. R. Lutchen ◽  
A. C. Jackson
Keyword(s):  
Input Impedance ◽  
Element Model ◽  
Forced Oscillations ◽  
Parameter Estimates ◽  
Tissue Resistance ◽  
Thoracic Gas Volume ◽  
Reliable Parameter ◽  
Quarter Wave ◽  
Lumped Element Model ◽  
Gas Volume

Recent studies on respiratory impedance (Zrs) have predicted that at frequencies greater than 64 Hz a second resonance will occur. Furthermore, if one intends to fit a model more complicated than the simple series combination of a resistance, inertance, and compliance to Zrs data, the only way to ensure statistically reliable parameter estimates is to include data surrounding this second resonance. An additional question, however, is whether the resulting parameters are physiologically meaningful. We obtained input impedance data from eight healthy adult humans using discrete frequency forced oscillations from 4 to 200 Hz. Three resonant frequencies were seen: 8 +/- 2, 151 +/- 10, and 182 +/- 16 Hz. A seven-parameter lumped element model provided an excellent fit to the data in all subjects. This model consists of an airway resistance (Raw), which is linearly dependent on frequency, and airway inertance separated from a tissue resistance, inertance, and compliance by a shunt compliance (Cg) thought to represent gas compressibility. Model estimates of Raw and Cg were compared with those suggested by measurement of Raw and thoracic gas volume using a plethysmograph. In all subjects the model Raw and Cg were significantly lower than and not correlated with the corresponding plethysmographic measurement. We hypothesize that the statistically reliable but physiologically inconsistent parameters are a consequence of the distorting influence of airway wall compliance and/or airway quarter-wave resonance. Such factors are not inherent to the seven-parameter model.

scholarly journals Additional High Input Low Output Impedance Analog Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Sudhanshu Maheshwari ◽  
Bhartendu Chaturvedi
Keyword(s):  
Sensitivity Analysis ◽  
Input Impedance ◽  
Second Order ◽  
Current Conveyor ◽  
Output Impedance ◽  
High Input ◽  
High Input Impedance ◽  
Pspice Simulations ◽  
Voltage Mode ◽  
Good Agreement

This paper presents some additional high input low output impedance analog networks realized using a recently introduced single Dual-X Current Conveyor with buffered output. The new circuits encompass several all-pass sections of first- and second-order. The voltage-mode proposals benefit from high input impedance and low output impedance. Nonideality and sensitivity analysis is also performed. The circuit performances are depicted through PSPICE simulations, which show good agreement with theory.

scholarly journals A Multi-Fidelity Model for Simulations and Sensitivity Analysis of Piezoelectric Inkjet Printheads

Micromachines ◽  
2021 ◽  
Vol 12 (9) ◽  
pp. 1038
Author(s):  
Vinh-Tan Nguyen ◽  
Jason Yu Chuan Leong ◽  
Satoshi Watanabe ◽  
Toshimitsu Morooka ◽  
Takayuki Shimizu
Keyword(s):  
Sensitivity Analysis ◽  
Three Dimensional ◽  
Element Model ◽  
Geometrical Parameters ◽  
Generation Process ◽  
Mechanical Coupling ◽  
Design Variables ◽  
Computational Structural Mechanics ◽  
Lumped Element Model ◽  
Inkjet Printhead

The ink drop generation process in piezoelectric droplet-on-demand devices is a complex multiphysics process. A fully resolved simulation of such a system involves a coupled fluid–structure interaction approach employing both computational fluid dynamics (CFD) and computational structural mechanics (CSM) models; thus, it is computationally expensive for engineering design and analysis. In this work, a simplified lumped element model (LEM) is proposed for the simulation of piezoelectric inkjet printheads using the analogy of equivalent electrical circuits. The model’s parameters are computed from three-dimensional fluid and structural simulations, taking into account the detailed geometrical features of the inkjet printhead. Inherently, this multifidelity LEM approach is much faster in simulations of the whole inkjet printhead, while it ably captures fundamental electro-mechanical coupling effects. The approach is validated with experimental data for an existing commercial inkjet printhead with good agreement in droplet speed prediction and frequency responses. The sensitivity analysis of droplet generation conducted for the variation of ink channel geometrical parameters shows the importance of different design variables on the performance of inkjet printheads. It further illustrates the effectiveness of the proposed approach in practical engineering usage.

scholarly journals Linking biogeochemistry to hydro-geometrical variability in tidal estuaries: a generic modeling approach

2015 ◽  
Vol 12 (7) ◽  
pp. 6351-6435
Author(s):  
C. Volta ◽  
G. G. Laruelle ◽  
S. Arndt ◽  
P. Regnier
Keyword(s):  
Sensitivity Analysis ◽  
World Ocean ◽  
Reaction Network ◽  
Co2 Exchange ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Tidal Estuaries ◽  
Biogeochemical Indicators ◽  
C And N ◽  
Co2 Sink

Abstract. This study applies the Carbon-Generic Estuary Model (C-GEM) modeling platform to simulate the estuarine biogeochemical dynamics – in particular the air-water CO2 exchange – in three idealized end-member systems covering the main features of tidal alluvial estuaries. C-GEM uses a generic biogeochemical reaction network and a unique set of model parameters extracted from a comprehensive literature survey to perform steady-state simulations representing average conditions for temperate estuaries worldwide. Climate and boundary conditions are extracted from published global databases (e.g. World Ocean Atlas, GLORICH) and catchment model outputs (GlobalNEWS2). The whole-system biogeochemical indicators Net Ecosystem Metabolism (NEM), C and N filtering capacities (FCTC and FCTN, respectively) and CO2 gas exchanges (FCO2) are calculated across the three end-member systems and are related to their main hydrodynamic and transport characteristics. A sensitivity analysis, which propagates the parameter uncertainties, is also carried out, followed by projections of changes in the biogeochemical indicators for the year 2050. Results show that the average C filtering capacities for baseline conditions are 40, 30 and 22% for the marine, mixed and riverine estuary, respectively. This translates into a first-order, global CO2 outgassing flux for tidal estuaries between 0.04 and 0.07 Pg C yr−1. N filtering capacities, calculated in similar fashion, range from 22% for the marine estuary to 18 and 15% for the mixed and the riverine estuary, respectively. Sensitivity analysis performed by varying the rate constants for aerobic degradation, denitrification and nitrification over the range of values reported in the literature significantly widens these ranges for both C and N. Simulations for the year 2050 indicate that all end-member estuaries will remain net heterotrophic and while the riverine and mixed systems will only marginally be affected by river load changes and increase in atmospheric pCO2, the marine estuary is likely to become a significant CO2 sink in its downstream section. In the decades to come, such change of behavior might strengthen the overall CO2 sink of the estuary-coastal ocean continuum.

Error estimation and sensitivity analysis of the 3-UPU translational parallel robot due to design parameter uncertainties

2018 ◽  
Vol 233 (8) ◽  
pp. 2713-2727 ◽  
Author(s):  
S El Hraiech ◽  
AH Chebbi ◽  
Z Affi ◽  
L Romdhane
Keyword(s):  
Sensitivity Analysis ◽  
Vertical Axis ◽  
Parallel Robot ◽  
Design Parameters ◽  
Analysis Method ◽  
Parameter Uncertainties ◽  
End Effector ◽  
Interval Analysis Method ◽  
Influential Parameters ◽  
Kinematic Errors

This work deals with the estimation and the sensitivity analysis of the 3-UPU parallel robot error. Based on the Newton–Euler formalism, the robot dynamic model is given in a closed form. This model is validated by the software ADAMS. Using the interval analysis method, a new algorithm is proposed, which estimates the errors in the motion of the end-effector and the errors in the actuator forces as a function of the design parameters uncertainties. The obtained results show that the kinematic errors are minimal at the workspace center. Moreover, these errors increase as the platform moves along the vertical axis. It is also shown that kinematic errors in the actuator joints are the most influential parameters on the manipulator accuracy. Therefore, using actuators with a higher accuracy can highly reduce the errors in motion of the platform.

Nonintrusive Global Sensitivity Analysis for Linear Systems With Process Noise

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Souransu Nandi ◽  
Tarunraj Singh
Keyword(s):  
Sensitivity Analysis ◽  
Linear Systems ◽  
Global Sensitivity Analysis ◽  
Benchmark Problems ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Sobol Indices ◽  
Global Sensitivity ◽  
Time Invariant ◽  
The Impact

The focus of this paper is on the global sensitivity analysis (GSA) of linear systems with time-invariant model parameter uncertainties and driven by stochastic inputs. The Sobol' indices of the evolving mean and variance estimates of states are used to assess the impact of the time-invariant uncertain model parameters and the statistics of the stochastic input on the uncertainty of the output. Numerical results on two benchmark problems help illustrate that it is conceivable that parameters, which are not so significant in contributing to the uncertainty of the mean, can be extremely significant in contributing to the uncertainty of the variances. The paper uses a polynomial chaos (PC) approach to synthesize a surrogate probabilistic model of the stochastic system after using Lagrange interpolation polynomials (LIPs) as PC bases. The Sobol' indices are then directly evaluated from the PC coefficients. Although this concept is not new, a novel interpretation of stochastic collocation-based PC and intrusive PC is presented where they are shown to represent identical probabilistic models when the system under consideration is linear. This result now permits treating linear models as black boxes to develop intrusive PC surrogates.

Modeling of respiratory system impedances in dogs

1987 ◽  
Vol 62 (2) ◽  
pp. 414-420 ◽  
Author(s):  
A. C. Jackson ◽  
K. R. Lutchen
Keyword(s):  
Respiratory System ◽  
Element Model ◽  
Parameter Estimates ◽  
Frequency Range ◽  
Nonlinear Regression Analysis ◽  
Entire Frequency Range ◽  
Frequency Dependent ◽  
Impedance Data ◽  
Parameter Values ◽  
Gas Compressibility

Mechanical impedances between 4 and 64 Hz of the respiratory system in dogs have been reported (A.C. Jackson et al. J. Appl. Physiol. 57: 34–39, 1984) previously by this laboratory. It was observed that resistance (the real part of impedance) decreased slightly with frequency between 4 and 22 Hz then increased considerably with frequency above 22 Hz. In the current study, these impedance data were analyzed using nonlinear regression analysis incorporating several different lumped linear element models. The five-element model of Eyles and Pimmel (IEEE Trans. Biomed. Eng. 28: 313–317, 1981) could only fit data where resistance decreased with frequency. However, when the model was applied to these data the returned parameter estimates were not physiologically realistic. Over the entire frequency range, a significantly improved fit was obtained with the six-element model of DuBois et al. (J. Appl. Physiol. 8: 587–594, 1956), since it could follow the predominate frequency-dependent characteristic that was the increase in resistance. The resulting parameter estimates suggested that the shunt compliance represents alveolar gas compressibility, the central branch represents airways, and the peripheral branch represents lung and chest wall tissues. This six-element model could not fit, with the same set of parameter values, both the frequency-dependent decrease in Rrs and the frequency-dependent increase in resistance. A nine-element model recently proposed by Peslin et al. (J. Appl. Physiol. 39: 523–534, 1975) was capable of fitting both the frequency-dependent decrease and the frequency-dependent increase in resistance. However, the data only between 4 and 64 Hz was not sufficient to consistently determine unique values for all nine parameters.

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