scholarly journals Optimal Experimental Design for Inverse Identification of Conductive and Radiative Properties of Participating Medium

Energies ◽  
2021 ◽  
Vol 14 (20) ◽  
pp. 6593
Author(s):  
Hua Liu ◽  
Xue Chen ◽  
Zhongcan Chen ◽  
Caobing Wei ◽  
Zuo Chen ◽  
...  
Keyword(s):  
A Priori ◽  
Radiative Properties ◽  
Transient Temperature ◽  
Model Parameters ◽  
Inverse Identification ◽  
Error Sources ◽  
Temperature Probe ◽  
Sensor Position ◽  
Uncertain Model ◽  
Cramer Rao Bound

The conductive and radiative properties of participating medium can be estimated by solving an inverse problem that combines transient temperature measurements and a forward model to predict the coupled conductive and radiative heat transfer. The procedure, as well as the estimates of parameters, are not only affected by the measurement noise that intrinsically exists in the experiment, but are also influenced by the known model parameters that are used as necessary inputs to solve the forward problem. In the present study, a stochastic Cramér–Rao bound (sCRB)-based error analysis method was employed for estimation of the errors of the retrieved conductive and radiative properties in an inverse identification process. The method took into account both the uncertainties of the experimental noise and the uncertain model parameter errors. Moreover, we applied the method to design the optimal location of the temperature probe, and to predict the relative error contribution of different error sources for combined conductive and radiative inverse problems. The results show that the proposed methodology is able to determine, a priori, the errors of the retrieved parameters, and that the accuracy of the retrieved parameters can be improved by setting the temperature probe at an optimal sensor position.

Generalised DOPs with Consideration of the Influence Function of Signal-in-Space Errors

2011 ◽  
Vol 64 (S1) ◽  
pp. S3-S18 ◽  
Author(s):  
Yuanxi Yang ◽  
Jinlong Li ◽  
Junyi Xu ◽  
Jing Tang
Keyword(s):  
Least Squares ◽  
Stochastic Models ◽  
Influence Function ◽  
A Priori ◽  
Functional Model ◽  
Global Navigation Satellite Systems ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Integrated Navigation ◽  
Satellite Systems

Integrated navigation using multiple Global Navigation Satellite Systems (GNSS) is beneficial to increase the number of observable satellites, alleviate the effects of systematic errors and improve the accuracy of positioning, navigation and timing (PNT). When multiple constellations and multiple frequency measurements are employed, the functional and stochastic models as well as the estimation principle for PNT may be different. Therefore, the commonly used definition of “dilution of precision (DOP)” based on the least squares (LS) estimation and unified functional and stochastic models will be not applicable anymore. In this paper, three types of generalised DOPs are defined. The first type of generalised DOP is based on the error influence function (IF) of pseudo-ranges that reflects the geometry strength of the measurements, error magnitude and the estimation risk criteria. When the least squares estimation is used, the first type of generalised DOP is identical to the one commonly used. In order to define the first type of generalised DOP, an IF of signal–in-space (SIS) errors on the parameter estimates of PNT is derived. The second type of generalised DOP is defined based on the functional model with additional systematic parameters induced by the compatibility and interoperability problems among different GNSS systems. The third type of generalised DOP is defined based on Bayesian estimation in which the a priori information of the model parameters is taken into account. This is suitable for evaluating the precision of kinematic positioning or navigation. Different types of generalised DOPs are suitable for different PNT scenarios and an example for the calculation of these DOPs for multi-GNSS systems including GPS, GLONASS, Compass and Galileo is given. New observation equations of Compass and GLONASS that may contain additional parameters for interoperability are specifically investigated. It shows that if the interoperability of multi-GNSS is not fulfilled, the increased number of satellites will not significantly reduce the generalised DOP value. Furthermore, the outlying measurements will not change the original DOP, but will change the first type of generalised DOP which includes a robust error IF. A priori information of the model parameters will also reduce the DOP.

Ductile fracture of solder-Cu interface and inverse identification of its interfacial model parameters

2017 ◽  
Vol 114 ◽  
pp. 279-292 ◽  
Author(s):  
Yangjian Xu ◽  
Shuai Zhao ◽  
Guohui Jin ◽  
Xiaogui Wang ◽  
Lihua Liang
Keyword(s):  
Ductile Fracture ◽  
Model Parameters ◽  
Inverse Identification

scholarly journals A Hail Growth Trajectory Model for Exploring the Environmental Controls on Hail Size: Model Physics and Idealized Tests

2020 ◽  
Vol 77 (8) ◽  
pp. 2765-2791 ◽  
Author(s):  
Matthew R. Kumjian ◽  
Kelly Lombardo
Keyword(s):  
Residence Time ◽  
Vertical Wind Shear ◽  
Squall Line ◽  
Model Parameters ◽  
Convective Storms ◽  
Environmental Controls ◽  
Supercell Storm ◽  
Uncertain Model ◽  
Supercell Storms ◽  
Microphysical Processes

Abstract A detailed microphysical model of hail growth is developed and applied to idealized numerical simulations of deep convective storms. Hailstone embryos of various sizes and densities may be initialized in and around the simulated convective storm updraft, and then are tracked as they are advected and grow through various microphysical processes. Application to an idealized squall line and supercell storm results in a plausibly realistic distribution of maximum hailstone sizes for each. Simulated hail growth trajectories through idealized supercell storms exhibit many consistencies with previous hail trajectory work that used observed storms. Systematic tests of uncertain model parameters and parameterizations are performed, with results highlighting the sensitivity of hail size distributions to these changes. A set of idealized simulations is performed for supercells in environments with varying vertical wind shear to extend and clarify our prior work. The trajectory calculations reveal that, with increased zonal deep-layer shear, broader updrafts lead to increased residence time and thus larger maximum hail sizes. For cases with increased meridional low-level shear, updraft width is also increased, but hailstone sizes are smaller. This is a result of decreased residence time in the updraft, owing to faster northward flow within the updraft that advects hailstones through the growth region more rapidly. The results suggest that environments leading to weakened horizontal flow within supercell updrafts may lead to larger maximum hailstone sizes.

scholarly journals Technical Note: Improved sampling of behavioral subsurface flow model parameters using active subspaces

2020 ◽  
Vol 24 (9) ◽  
pp. 4567-4574
Author(s):  
Daniel Erdal ◽  
Olaf A. Cirpka
Keyword(s):  
A Priori ◽  
Behavioral Model ◽  
Technical Note ◽  
Sampling Scheme ◽  
Model Parameters ◽  
Test Case ◽  
Sampling Efficiency ◽  
Subspace Decomposition ◽  
Plausible Model ◽  
Active Subspaces

Abstract. In global sensitivity analysis and ensemble-based model calibration, it is essential to create a large enough sample of model simulations with different parameters that all yield plausible model results. This can be difficult if a priori plausible parameter combinations frequently yield non-behavioral model results. In a previous study (Erdal and Cirpka, 2019), we developed and tested a parameter-sampling scheme based on active-subspace decomposition. While in principle this scheme worked well, it still implied testing a substantial fraction of parameter combinations that ultimately had to be discarded because of implausible model results. This technical note presents an improved sampling scheme and illustrates its simplicity and efficiency by a small test case. The new sampling scheme can be tuned to either outperform the original implementation by improving the sampling efficiency while maintaining the accuracy of the result or by improving the accuracy of the result while maintaining the sampling efficiency.

Inversion and uncertainty estimation of gravity data using simulated annealing: An application over Lake Vostok, East Antarctica

Geophysics ◽  
2005 ◽  
Vol 70 (1) ◽  
pp. J1-J12 ◽  
Author(s):  
Lopamudra Roy ◽  
Mrinal K. Sen ◽  
Donald D. Blankenship ◽  
Paul L. Stoffa ◽  
Thomas G. Richter
Keyword(s):  
Simulated Annealing ◽  
Gravity Data ◽  
A Priori ◽  
Model Space ◽  
Uncertainty Estimation ◽  
East Antarctica ◽  
Airborne Gravity ◽  
Model Parameters ◽  
Data Set ◽  
Lake Vostok

Interpretation of gravity data warrants uncertainty estimation because of its inherent nonuniqueness. Although the uncertainties in model parameters cannot be completely reduced, they can aid in the meaningful interpretation of results. Here we have employed a simulated annealing (SA)–based technique in the inversion of gravity data to derive multilayered earth models consisting of two and three dimensional bodies. In our approach, we assume that the density contrast is known, and we solve for the coordinates or shapes of the causative bodies, resulting in a nonlinear inverse problem. We attempt to sample the model space extensively so as to estimate several equally likely models. We then use all the models sampled by SA to construct an approximate, marginal posterior probability density function (PPD) in model space and several orders of moments. The correlation matrix clearly shows the interdependence of different model parameters and the corresponding trade-offs. Such correlation plots are used to study the effect of a priori information in reducing the uncertainty in the solutions. We also investigate the use of derivative information to obtain better depth resolution and to reduce underlying uncertainties. We applied the technique on two synthetic data sets and an airborne-gravity data set collected over Lake Vostok, East Antarctica, for which a priori constraints were derived from available seismic and radar profiles. The inversion results produced depths of the lake in the survey area along with the thickness of sediments. The resulting uncertainties are interpreted in terms of the experimental geometry and data error.

scholarly journals Quantification of uncertainties in OCO-2 measurements of XCO<sub>2</sub>: simulations and linear error analysis

2016 ◽  
Vol 9 (10) ◽  
pp. 5227-5238 ◽  
Author(s):  
Brian Connor ◽  
Hartmut Bösch ◽  
James McDuffie ◽  
Tommy Taylor ◽  
Dejian Fu ◽  
...  
Keyword(s):  
Bias Correction ◽  
Total Error ◽  
Important Variable ◽  
Model Parameters ◽  
Error Sources ◽  
Variable Error ◽  
Operational Algorithm ◽  
The Difference ◽  
Variable Errors ◽  
Types Of Error

Abstract. We present an analysis of uncertainties in global measurements of the column averaged dry-air mole fraction of CO2 (XCO2) by the NASA Orbiting Carbon Observatory-2 (OCO-2). The analysis is based on our best estimates for uncertainties in the OCO-2 operational algorithm and its inputs, and uses simulated spectra calculated for the actual flight and sounding geometry, with measured atmospheric analyses. The simulations are calculated for land nadir and ocean glint observations. We include errors in measurement, smoothing, interference, and forward model parameters. All types of error are combined to estimate the uncertainty in XCO2 from single soundings, before any attempt at bias correction has been made. From these results we also estimate the "variable error" which differs between soundings, to infer the error in the difference of XCO2 between any two soundings. The most important error sources are aerosol interference, spectroscopy, and instrument calibration. Aerosol is the largest source of variable error. Spectroscopy and calibration, although they are themselves fixed error sources, also produce important variable errors in XCO2. Net variable errors are usually < 1 ppm over ocean and ∼ 0.5–2.0 ppm over land. The total error due to all sources is ∼ 1.5–3.5 ppm over land and ∼ 1.5–2.5 ppm over ocean.

scholarly journals Selection of catchment descriptors for the physical similarity approach. Part II: Application

2013 ◽  
Vol 8 (No. 4) ◽  
pp. 186-194
Author(s):  
M. Heřmanovský ◽  
P. Pech
Keyword(s):  
Land Cover ◽  
A Priori ◽  
Model Parameters ◽  
Physical Similarity ◽  
Model Parameter ◽  
Soil Moisture Accounting ◽  
Estimated Parameters ◽  
Selection Of

This paper demonstrates an application of the previously published method for selection of optimal catchment descriptors, according to which similar catchments can be identified for the purpose of estimation of the Sacramento &ndash; Soil Moisture Accounting (SAC-SMA) model parameters for a set of tested catchments, based on the physical similarity approach. For the purpose of the analysis, the following data from the Model Parameter Estimation Experiment (MOPEX) project were taken: a priori model parameter sets used as reference values for comparison with the newly estimated parameters, and catchment descriptors of four categories (climatic descriptors, soil properties, land cover and catchment morphology). The inverse clustering method, with Andrews&rsquo; curves for a homogeneity check, was used for the catchment grouping process. The optimal catchment descriptors were selected on the basis of two criteria, one comparing different subsets of catchment descriptors of the same size (MIN), the other one evaluating the improvement after addition of another catchment descriptor (MAX). The results suggest that the proposed method and the two criteria used may lead to the selection of a subset of conditionally optimal catchment descriptors from a broader set of them. As expected, the quality of the resulting subset of optimal catchment descriptors is mainly dependent on the number and type of the descriptors in the broader set. In the presented case study, six to seven catchment descriptors (two climatic, two soil and at least two land-cover descriptors) were identified as optimal for regionalisation of the SAC-SMA model parameters for a set of MOPEX catchments.

scholarly journals Modelling temperature variations in polar snow using DAISY

1997 ◽  
Vol 43 (143) ◽  
pp. 180-191 ◽  
Author(s):  
Ε. M. Morris ◽  
H. -P. Bader ◽  
P. Weilenmann
Keyword(s):  
Field Experiments ◽  
A Priori ◽  
Model Parameters ◽  
Data Set ◽  
International Geophysical Year ◽  
Snow Model ◽  
Using Data ◽  
Polar Snow ◽  
Parameter Values ◽  
The Antarctic

AbstractA physics-based snow model has been calibrated using data collected at Halley Bay, Antarctica, during the International Geophysical Year. Variations in snow temperature and density are well-simulated using values for the model parameters within the range reported from other polar field experiments. The effect of uncertainty in the parameter values on the accuracy of the predictions is no greater than the effect of instrumental error in the input data. Thus, this model can be used with parameters determined a priori rather than by optimization. The model has been validated using an independent data set from Halley Bay and then used to estimate 10 m temperatures on the Antarctic Peninsula plateau over the last half-century.

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