Estimation Of Physical Parameters Research Articles

Modeling and Estimation of Adaptive Optics-Corrected long-exposure Point Spread Function Using Gaussian Sum Approximation

Abstract Adaptive optics (AO) enhances astronomical images by correcting perturbations in the optical system, resulting in complex point spread function (PSF) shapes, which provide critical information for optical design, calibration, and diagnostics. This paper presents a parametric model for an AO-corrected long-exposure PSF that adapts to complex shapes and various seeing conditions. A complementary estimation method is also introduced, addressing the inverse problem of estimating the atmospheric PSF or power spectral density (PSD) from observed PSF data. The model, based on Gaussian sum approximation (GSA), was tested using simulated PSF data from the OOMAO toolbox for Fried parameter (r0) values ranging from 0.10 to 0.20 m and on-sky data from the Very Large Telescope’s MUSE instrument. Two approaches were analyzed: (i) direct PSF estimation using GSA, and (ii) PSF estimation derived from atmospheric PSD estimation. Both methods were evaluated using root mean square error (RMSE). While approach (i) provided the best performance, approach (ii) produced more accurate atmospheric PSF estimates compared to the Moffat approximation and the Fetick method. Additionally, approach (ii) enabled the estimation of key physical parameters, such as the Fried parameter (r0) and residual AO variance ($\sigma _{AO}^2$). The proposed methods effectively estimate atmospheric PSF and PSD, even for complex PSF shapes influenced by spiders, central obstructions, or static aberrations.

Development of the algorithm for determining the thickness of the structural layers of the non-rigid pavement and searching for local inclusions using sub-surface georadiolocation methods

Problem. The article is part of the authors' research in the field of road construction using GPR technologies. Ensuring a certain level of pavement reliability on highways requires the development of methods and means for continuous information acquisition and processing in real time, taking into account the parameters of structural heterogeneity, heterogeneity of physical and mechanical parameters of structures, as well as their changes over time. The solution of this problem is limited by the complexity of tasks of obtaining and interpreting the data of subsurface sensing and the associated errors in determining the parameters of structures, imperfection of methods of flaw detection of structures with subsurface inhomogeneities, multifactorial tasks of estimation of physical and mechanical parameters of multicomponent materials. Goal. Improving the accuracy and reliability of determining the boundaries of layers of non-rigid pavement structure, which have a low level of electrodynamic contrast due to interpenetration of layer materials or changes in their physical and mechanical properties. The solution of this problem is connected with the development of a method of obtaining reflected GPR signals and the improvement of algorithms for their processing. Methodology. The development of methods for the analysis of the electromagnetic field with a variable state of polarization makes it possible to assess the localization of violations of the integrity of the pavement structure at a qualitatively new level and allows the positioning of small inclusions even with a slight contrast in the dielectric constant. The proposed method of recording the reflection of an ultra-wideband GPR pulse signal at different polarizations is implemented by measuring the reflected signal from a metal sheet at oblique incidence and parallel polarization, recording the reflected pulse at perpendicular polarization, followed by measuring the reflection coefficient from the structure of the nonrigid pavement under study at parallel and perpendicular polarization. The electrophysical parameter recovery procedure is based on the solution of inverse scattering problems and ensures the accuracy of determining the low-contrast boundaries of the pavement structure and increases the accuracy of positioning subsurface heterogeneities. GPR signal processing algorithms are based on procedures for analyzing their polarization state, which allows determining the geometric parameters of subsurface heterogeneities. Practical value. The combination of the obtained results increases the accuracy and reliability of the results of GPR diagnosis and assessment of the condition of non-rigid pavement based on the most complete and reliable information about the subsu

Tailored accelerometer calibration by POD for thermospheric density retrieval with GRACE and GRACE-FO

The density of the upper atmosphere can be determined by orbit and accelerometer data from low Earth orbit satellites as insitu measurements along the orbit. One main challenge therein is the estimation of physical accelerometer calibration parameters, meaning that these parameters should not absorb other effects and model deficiencies in the Precise Orbit Determination (POD) process. The accelerometers of all geodetic satellites like GRACE and GRACE-FO are affected by time dependent bias and scale factors. Therefore a calibration of the data is indispensable.A dynamic POD based physical accelerometer calibration is developed for the complete GRACE and GRACE-FO missions. We investigate different parametrization strategies and utilize different observation data, as the accurate inter-satellite ranging additionally to GPS orbit data. For the estimation parameters we distinguish between offset and scale, furthermore, cross-track and radial directions are significantly less sensitive than along-track and require a different evaluation. For the offset, constant and time dependent parameters are investigated. Furthermore, a continuous offset calibration over arc boundaries is implemented and tested. The sensitivity of the scale factor is lower, although, in contrast to the offset, it increases with higher total accelerations. This means that it needs to be estimated over longer time periods. We investigate periods between three hours and one month as well as results from Gravity Field Recovery (GFR). Monthly scale factors give valuable results, at least for x-axis and when the Solar activity is not very low. Nevertheless, we also estimate weighted constant scale factors from the monthly results and use these in a subsequent POD, giving more realistic offset results for most periods and cross-track and radial directions.From the used background models in the POD, Earth’s gravitational model has a noticeable influence on the estimated calibration parameters, especially the scale factors. We utilized several different models. Results with monthly ITSG solutions are distinctly better than the ones with the time dependent GOCO06s model.We show that the validation with usual metrics, like post-fit POD residuals, is not able to reflect the quality of the different estimated calibration parameters. For a quantitative validation we introduce an approach based on the modeled non-gravitational accelerations. Therefore, the uncertainty of the models is evaluated first. The influence of main error sources in the models is assessed and propagated to the results.We compare our scale parameters to available references and the complete calibration to TU Delft’s latest results. Finally we show the effect of different calibration options on the retrieved density.The estimated calibration parameters and non-gravitational accelerations for the whole GRACE and GRACE-FO missions are available on our data server www.zarm.uni-bremen.de/zarm_daten.

The effects of non-local observations on the adjoint estimation of local model parameters: An example of Manning’s n coefficient in a tidal model over the Bohai, Yellow, and East China Seas

Accurate parameter estimation is a key issue for enhancing the performance of hydrological models. With the rapid development of satellite technology, integrating satellite data and numerical modelling for parameter estimation has gained more prominence. The limited spatial coverage of altimeters necessitates areas without direct local observations to rely only on information from nearby non-local observations. However, the relation is far from clear between non-local observations and the estimation of local model parameters. In this study, a two-dimensional adjoint tidal model over the Bohai, Yellow, and East China Seas (BYECS) is developed, assimilating observations from TOPEX/Poseidon, Jason-1, and Jason-2 altimeters in conjunction with tide-gauge stations. In twin experiments, the feasibility and reliability of utilizing non-local observations are emphasized by varying synthetic observations. The experiments also reveal how the number and distance of non-local observations affect the ill-posedness of local parameter estimation. The estimation errors can be reduced by increasing observations within a ‘critical distance’, beyond which the accuracy does not improve further. Subsequently, the robustness of ‘critical distance’ is discussed under different prescribed parameter distributions, sizes of predefined optimized area, and random observational errors, indicating that the ‘critical distance’ is approximately 1.0°-2.0°. These results provide a positive reference for practical experiment. In BYECS, the order of Manning’s n coefficient ranges from 10-4 to 10-1, with an average value of 0.0246 in shallow waters. The spatial distribution reveals 9 high-value areas, primarily modulated by a concurrence of sandy sediment and weak tidal currents. This study offers valuable insights into refining the adjoint model for physical parameter estimation, particularly in anticipation of the expanded spatial coverage of SWOT. Compared to only assimilating T/P series altimeters, incorporating SWOT reduces discrepancies by over 38%. Additionally, the spatial Manning’s n coefficient provides guidance for enhancing tidal simulation in other models.

Truncated Gauss-Newton full-waveform inversion of pure quasi-P waves in vertical transverse isotropic media

Full-waveform inversion (FWI) uses the full information of seismic data to obtain a quantitative estimation of subsurface physical parameters. Anisotropic FWI has the potential to recover high-resolution velocity and anisotropy parameter models, which are critical for imaging the long-offset and wide-azimuth data. We develop an acoustic anisotropic FWI method based on a simplified pure quasi P-wave (qP-wave) equation, which can be solved efficiently and is beneficial for the subsequent inversion. Using the inverse Hessian operator to precondition the functional gradients helps to reduce the parameter tradeoff in the multi-parameter inversion. To balance the accuracy and efficiency, we extend the truncated Gauss-Newton (TGN) method into FWI of pure qP-waves in vertical transverse isotropic (VTI) media. The inversion is performed in a nested way: a linear inner loop and a nonlinear outer loop. We derive the formulation of Hessian-vector products for pure qP-waves in VTI media based on the Lagrange multiplier method and compute the model update by solving a Gauss-Newton linear system via a matrix-free conjugate gradient method. A suitable preconditioner and the Eisenstat and Walker stopping criterion for the inner iterations are used to accelerate the convergence and avoid prohibitive computational cost. We test the proposed FWI method on several synthetic data sets. Inversion results reveal that the pure acoustic VTI FWI exhibits greater accuracy than the conventional pseudoacoustic VTI FWI. Additionally, the TGN method proves effective in mitigating the parameter crosstalk and increasing the accuracy of anisotropy parameters.

Dynamic modelling and a dual vector modulated improved model predictive control with auto tuning feature of active front‐end converters for distributed energy resources

AbstractThe operational performance of grid‐connected active front‐end converters (AFEs) faces challenges arising from the intricate interplay among phase‐locked loop (PLL) non‐linearities, grid impedance, and conventional control strategies, resulting in compromised stability. This study introduces a refined approach to dynamic model predictive control (MPC) by integrating recursive least squares (RLS) for the precise estimation of physical model parameters, thereby addressing stability concerns. Unlike conventional methodologies, the proposed enhanced RLS‐based MPC approach, equipped with an auto‐tuning feature, allows for the design of controllers without a prerequisite understanding of exact external dynamics. Notably, this technique exhibits exceptional disturbance rejection capabilities. The evaluation of the cost function at each sampling interval facilitates the determination of optimal switching states based on predicted variables. Gate pulses for the switches of the AFEs are generated accordingly. Employing a simulation platform, the proposed control structure's performance across varied conditions is comprehensively assessed, encompassing alterations in grid impedance and system non‐linearities. The method adeptly integrates inherent non‐linearities within the system, showcasing exceptional robustness in diverse dynamic scenarios. To further substantiate the efficacy of the proposed control system over conventional approaches, simulation results are validated using a laboratory hardware platform equipped with Typhoon HIL and dSPACE real‐time emulators, providing tangible evidence of the proposed control system's effectiveness in real‐world hardware setups. The multifaceted approach, encompassing precise parameter estimation, predictive control, auto‐tuning, disturbance rejection, robust design, and real‐time evaluation, collectively establishes a resilient foundation for enhancing and maintaining the overall stability of the system across diverse operating scenarios.

Accurate reconstruction of 4D spectral–spatial images from sparse-view data in continuous-wave EPRI

In continuous-wave electron paramagnetic resonance imaging (CW EPRI), data are collected generally at densely sampled views sufficient for achieving accurate reconstruction of a four dimensional spectral–spatial (4DSS) image by use of the conventional filtered-backprojection (FBP) algorithm. It is desirable to minimize the scan time by collection of data only at sparsely sampled views, referred to as sparse-view data. Interest thus remains in investigation of algorithms for accurate reconstruction of 4DSS images from sparse-view data collected for potentially enabling fast data acquisition in CW EPRI. In this study, we investigate and demonstrate optimization-based algorithms for accurate reconstruction of 4DSS images from sparse-view data. Numerical studies using simulated and real sparse-view data acquired in CW EPRI are conducted that reveal, in terms of image visualization and physical-parameter estimation, the potential of the algorithms developed for yielding accurate 4DSS images from sparse-view data in CW EPRI. The algorithms developed may be exploited for enabling sparse-view scans with minimized scan time in CW EPRI for yielding 4DSS images of quality comparable to, or better than, that of the FBP reconstruction from data collected at densely sampled views.

How many random observations are needed for good phase coverage of a periodic source?

The specific problem considered is the number of radial velocity measurements required to obtain good estimates of physical parameters of binary star. It is assumed that observations are made at random binary phases. The loss of information due to poor phase coverage is explored, and a suggested limit on the largest acceptable gap introduced. The statistical distribution of maximum gap lengths can then be used to specify the minimum number of velocity measurements to obtain good phase coverage with a specified confidence limit. The effects of non-zero orbital eccentricity are discussed, as are the ramifications of having multiple binary targets. The theory is also applicable to the characterisation of the radial velocity curves induced by exoplanets on their host stars, provided that the periods and eccentricities are known (from e.g. transit observations).

A Hierarchical Method for Locating the Interferometric Fringes of Celestial Sources in the Visibility Data

In source detection in the Tianlai project, locating the interferometric fringe in visibility data accurately will influence downstream tasks drastically, such as physical parameter estimation and weak source exploration. Considering that traditional locating methods are time-consuming and supervised methods require a great quantity of expensive labeled data, in this paper, we first investigate characteristics of interferometric fringes in the simulation and real scenario separately, and integrate an almost parameter-free unsupervised clustering method and seeding filling or eraser algorithm to propose a hierarchical plug and play method to improve location accuracy. Then, we apply our method to locate single and multiple sources’ interferometric fringes in simulation data. Next, we apply our method to real data taken from the Tianlai radio telescope array. Finally, we compare with unsupervised methods that are state of the art. These results show that our method has robustness in different scenarios and can improve location measurement accuracy effectively.

A Novel Image Formation Model for Descattering.

In the field of image descattering, the image formation models employed for restoration approaches are often simplified. In these models, scattering distribution is uniform in homogeneous media when transmission is fixed. Through specifically designed experiments, we discover that scattering exhibits non-uniform characteristics even in homogeneous media. Neglecting non-uniform scattering in these models limits their accuracy in representing scattering distribution, resulting in existing image descattering approaches inadequate. To tackle these issues, this paper proposes a novel image formation model for image descattering, considering more physical parameters, such as zenith angle, azimuth angle, scattering phase function, and camera focal length. Our model describes the light transfer process in scattering media more accurately. For image descattering, we introduce corresponding algorithms for parameter estimation in our model and simultaneous restoration from degraded images. Experimental evaluations demonstrate the effectiveness of our proposed model in various tasks, including physical parameter estimation, pure-scattering removal, image dehazing, and underwater image restoration. In terms of calculating parameters, our results are close to the real values; in terms of underwater image restoration, our work outperforms the state-of-art methods; in terms of image dehazing, our work promotes the performance of existing methods by replacing previous models with our model.

The Advantages of Global Photometric Models in Fitting Transit Variations

Estimation of planetary orbital and physical parameters from light-curve data relies heavily on the accurate interpretation of Transit Timing Variation (TTV) measurements. In this letter, we review the process of TTV measurement and compare two fitting paradigms—one that relies on making transit-by-transit timing estimates and then fitting a TTV model to the observed timings, and one that relies on fitting a global flux model to the entire light-curve data set simultaneously. The latter method is achieved either by solving for the underlying planetary motion (often referred to as “photodynamics”), or by using an approximate or empirical shape of the TTV signal. We show that, across a large range of the transit S/N regime, the probability distribution function of the mid-transit time significantly deviates from a Gaussian, even if the flux errors do distribute normally. Treating the timing uncertainties as if they are distributed normally leads, in such a case, to a wrong interpretation of the TTV measurements. We illustrate these points using numerical experiments and conclude that a fitting process that relies on a global flux fitting, rather than the derived TTVs, should be preferred.

Beagle-agn I: simultaneous constraints on the properties of gas in star-forming and AGN narrow-line regions in galaxies

ABSTRACT We present the addition of nebular emission from the narrow-line regions (NLR) surrounding active galactic nuclei (AGNs) to beagle (BayEsian Analysis of GaLaxy sEds). Using a set of idealized spectra, we fit to a set of observables (emission-line ratios and fluxes) and test the retrieval of different physical parameters. We find that fitting to standard diagnostic-line ratios plus [O ii] λ3726, λ3729/[O iii] λ5007, H β/H α, [O i] λ6300/[O ii] λ3726, λ3729, and H α flux, degeneracies remain between dust-to-metal mass ratio ($\xi _\rm {d}^{\small NLR}$) and ionization parameter ($U_\rm {s}^{\small NLR}$) in the NLR gas, and between slope of the ionizing radiation ($\alpha _{\small PL}$, characterizing the emission from the accretion disc around the central black hole) and total accretion-disc luminosity ($L_\rm {acc}$). Since these degeneracies bias the retrieval of other parameters even at maximal signal-to-noise ratio (S/N), without additional observables, we suggest fixing $\alpha _{\small PL}$ and dust-to-metal mass ratios in both NLR and H ii regions. We explore the S/N in H β required for un-biased estimates of physical parameters, finding that S/N(H β) ∼ 10 is sufficient to identify an NLR contribution, but that higher S/N is required for un-biased parameter retrieval (∼20 for NLR-dominated systems, ∼30 for objects with approximately equal H β contributions from NLR and H ii regions). We also compare the predictions of our models for different line ratios to previously published models and data. By adding [He ii] λ4686-line measurements to a set of published line fluxes for a sample of 463 AGN NLR, we show that our models with $-4\lt \hbox{$\log U_{\small S}^{\small NLR}$}\lt -1.5$ can account for the full range of observed AGN properties in the local Universe.

A deep learning-based stripe self-correction method for stitched microscopic images

Stitched fluorescence microscope images inevitably exist in various types of stripes or artifacts caused by uncertain factors such as optical devices or specimens, which severely affects the image quality and downstream quantitative analysis. Here, we present a deep learning-based Stripe Self-Correction method, so-called SSCOR. Specifically, we propose a proximity sampling scheme and adversarial reciprocal self-training paradigm that enable SSCOR to utilize stripe-free patches sampled from the stitched microscope image itself to correct their adjacent stripe patches. Comparing to off-the-shelf approaches, SSCOR can not only adaptively correct non-uniform, oblique, and grid stripes, but also remove scanning, bubble, and out-of-focus artifacts, achieving the state-of-the-art performance across different imaging conditions and modalities. Moreover, SSCOR does not require any physical parameter estimation, patch-wise manual annotation, or raw stitched information in the correction process. This provides an intelligent prior-free image restoration solution for microscopists or even microscope companies, thus ensuring more precise biomedical applications for researchers.

Using deep learning to accelerate magnetic resonance measurements of molecular exchange.

Real-time monitoring and quantitative measurement of molecular exchange between different microdomains are useful to characterize the local dynamics in porous media and biomedical applications of magnetic resonance. Diffusion exchange spectroscopy (DEXSY) is a noninvasive technique for such measurements. However, its application is largely limited by the involved long acquisition time and complex parameter estimation. In this study, we introduce a physics-guided deep neural network that accelerates DEXSY acquisition in a data-driven manner. The proposed method combines sampling pattern optimization and physical parameter estimation into a unified framework. Comprehensive simulations and experiments based on a two-site exchange system are conducted to demonstrate this new sampling optimization method in terms of accuracy, repeatability, and efficiency. This general framework can be adapted for other molecular exchange magnetic resonance measurements.

An Evaluation of Non-Gaussian Data Assimilation Methods in Moist Convective Regimes

Abstract Obtaining a faithful probabilistic depiction of moist convection is complicated by unknown errors in subgrid-scale physical parameterization schemes, invalid assumptions made by data assimilation (DA) techniques, and high system dimensionality. As an initial step toward untangling sources of uncertainty in convective weather regimes, we evaluate a novel Bayesian data assimilation methodology based on particle filtering within a WRF ensemble analysis and forecasting system. Unlike most geophysical DA methods, the particle filter (PF) represents prior and posterior error distributions nonparametrically rather than assuming a Gaussian distribution and can accept any type of likelihood function. This approach is known to reduce bias introduced by Gaussian approximations in low-dimensional and idealized contexts. The form of PF used in this research adopts a dimension-reduction strategy, making it affordable for typical weather applications. The present study examines posterior ensemble members and forecasts for select severe weather events between 2019 and 2020, comparing results from the PF with those from an ensemble Kalman filter (EnKF). We find that assimilating with a PF produces posterior quantities for microphysical variables that are more consistent with model climatology than comparable quantities from an EnKF, which we attribute to a reduction in DA bias. These differences are significant enough to impact the dynamic evolution of convective systems via cold pool strength and propagation, with impacts to forecast verification scores depending on the particular microphysics scheme. Our findings have broad implications for future approaches to the selection of physical parameterization schemes and parameter estimation within preexisting data assimilation frameworks. Significance Statement The accurate prediction of severe storms using numerical weather models depends on effective parameterization schemes for small-scale processes and the assimilation of incomplete observational data in a manner that faithfully represents the probabilistic state of the atmosphere. Current generation methods for data assimilation typically assume a standard form for the error distributions of relevant quantities, which can introduce bias that not only hinders numerical prediction, but that can also confound the characterization of errors from the model itself. The current study performs data assimilation using a novel method that does not make such assumptions and explores characteristics of resulting model fields and forecasts that might make such a method useful for improving model parameterization schemes.

Differential Flatness-Based Parameter Estimation for Suspended Load Drones

The transportation of goods by drones using cable towing has recently attracted considerable attention. When flying a suspended load drone, any discrepancy between the mathematical model and the actual drone deteriorates control performance. However, because some physical parameters are difficult to measure, creating an accurate mathematical model is extremely difficult. Therefore, we propose a parameter estimation method using differential flatness that can be extended for application to suspended load drones. This method overcomes the problem of dealing with higher-order derivatives of flat outputs and enables the estimation of physical parameters. In this study, we experimentally show that the proposed method improves trajectory tracking performance.

Forecasting of volumetric flow rate of Ergene river using machine learning

Today, the significance of the estimation of physical parameters has considerably increased; for example, the prediction of water flow rate (WFR) is one of the types that will gain a substantial importance among the others. The predictions of WFR of rivers play a prominent role in the plans and constructions of new water dams, or to operate the ones that were formerly constructed. In this study, a variety of machine learning algorithms have been suggested in the estimations of one-ahead instantaneous measurement of river WFR. In this regard, four different prediction algorithms including long short-term memory (LSTM) neural network, adaptive neuro-fuzzy inference system (ANFIS) with fuzzy c-means (FCM), ANFIS with subtractive clustering (SC), and the ANFIS with grid partition (GP) were initially trained and secondly tested. The study region was selected as Inanli measurement station, which is located on the Ergene River. A cumulative of 134 different models were formed using these algorithms. Instantaneous WFR predictions in terms of WFR data have shown that ANFIS-FCM and ANFIS-SC had given the best statistical error outcomes. Accordingly, the values of 0.34 m3/s, 0.72 m3/s, and 0.9728 have been found as a result of machine learning establishment corresponding to statistical accuracy results of MAE, RMSE, and R values, respectively. Namely, it has been concluded that error values of the ANFIS-FCM and ANFIS-SC computations have outcome to be sufficiently good. Also, it was concluded and shown in the current study that both tools of the ANFIS can be two efficacious methods to WFR forecasting.

Seismic pre-stack inversion for physical and anisotropic parameters in fractured shale reservoirs

AbstractThe estimation of physical and anisotropic parameters is of great importance for the characterization of fractured reservoirs. Vertical fractures developing in a laterally isotropic (VTI) setting are equivalent to orthotropic anisotropic (OA) media common in stratified fractured shale reservoirs. To obtain independent anisotropic and physical information, a novel reflection coefficient approximation containing physical and anisotropic parameters is derived to improve the stability of the inversion for orthotropic media. To simplify the equation for the reflection coefficient, an approximate rock physics model is constructed using the approximate theory of rock modulus. The estimated parameters are reduced from nine to six. The accuracy analysis reveals that the new reflection coefficient is appropriate and suitable for inversion. In addition, a stepwise Bayesian amplitude versus angle and azimuth (AVAZ) inversion method with smooth background constraints is developed to estimate the anisotropic and physical parameters from the azimuthal seismic data. The smooth background constraint improves the robustness of the inversion. And the stepwise inversion strategy solves the problem that the contribution of the fracture parameter to the reflection coefficient is smaller than the other parameters. Synthetic cases show that the proposed stepwise Bayesian AVAZ inversion method is feasible in estimating the anisotropic parameters for OA media even when the signal-to-noise ratio is 2. The field cases show that the proposed inversion method has good stability and robustness in predicting shale reservoirs with vertical or near-vertical fractures.

Thermal uncertainty analysis of a single particle model for a Lithium-Ion cell

In recent years, the sustained increase in the worldwide demand for lithium batteries goes side by side with the need for reliable methods to assess battery performance. Of particular importance is assessing Lithium-Ion cell’s thermal behavior given its role on hazard and aging of batteries. An essential task towards developing battery management systems is the estimation of physical parameters and their uncertainties in terms of both models and observations. Consequently, this paper analyzes the uncertainty in a thermal single particle model for a lithium-ion cell. In the first part of the manuscript, we explore the model adequacy by analyzing the forward and backward uncertainty propagation in the model in terms of diffusion coefficients, reaction rate constants, and observations of cell voltage. In the second part of the manuscript, we infer the cell’s reversible heat given the energy balance equation and the cell’s temperature observations. We argue that the methods proposed here may be extended to analyze other more general lithium-ion models.

Estimation of Depth, Physical Parameters, and Location Using Nonlinear Inverse Modeling of Magnetic Data by Bhattacharya Method in a Field of NW Iran

Estimation of Depth, Physical Parameters, and Location Using Nonlinear Inverse Modeling of Magnetic Data by Bhattacharya Method in a Field of NW Iran