Uncertainty In Reconstruction Research Articles

Reduced-Space Relevance Vector Machine for Adaptive Electrical Capacitance Volume Tomography

We introduce an efficient synthetic electrode selection strategy for use in Adaptive Electrical Capacitance Volume Tomography (AECVT). The proposed strategy is based on the Adaptive Relevance Vector Machine (ARVM) method and allows to successively obtain synthetic electrode configurations that yield the most decrease in the image reconstruction uncertainty for the spatial distribution of the permittivity in the region of interest. The problem is first formulated as an instance of the Quadratic Unconstrained Binary Optimization (QUBO). By noting that the QUBO formulation is an NP-hard problem and thus prohibitive in practice, we then introduce the Reduced ARVM method, corresponding to the application of the ARVM method to a reduced search space. By using the Reduced ARVM method, good image reconstruction and low uncertainty levels can be achieved in AECVT with considerably fewer measurements. To corroborate our analysis, we present simulation results for three representative AECVT scenarios.

The impact of inverted density gradients on density profiles measured by reflectometry: an experimental and numerical investigation at ASDEX Upgrade

The high-field side high-density (HFSHD) region at ASDEX Upgrade (AUG) is a well-documented phenomenon leading to a dense plasma in the inner divertor region that expands upwards to the midplane, resulting in poloidally asymmetric scrape-off layer density profiles. This work investigates, via simulation and experiment, whether the HFSHD at the midplane leads to hollow density profiles at the high-field side. Using the frequency-modulated continuous-wave O-mode reflectometer at AUG, experimental evidence has been found of reflection patterns compatible with a hollow density profile that are reproduced by 1D full-wave simulations. Furthermore, this work assesses the uncertainties in the density profile reconstruction as a consequence of the inverted gradient, showing that the presence of an HFSHD may lead to an overestimation of the density in the confined region.

Neural Process Enhanced Machining Error Evaluation for Coordinate Measuring Machines

Coordinate Measuring Machines that provide ultraprecise results are widely used in precision manufacturing. However, the traditional point-by-point measuring approaches are time-consuming, limiting their applications in modern manufacturing, especially for large-scale surface measurements and online measurements. In this paper, we propose an efficient machining error evaluation approach for complex surfaces based on the neural process. Without sacrificing accuracy, the proposed method improves the efficiency of measurement by sparse sampling and reconstruction. Using the neural process, the reconstruction algorithm models the machining error accurately and robustly. Besides, by estimating the reconstruction uncertainty, we further improve the sampling efficiency by introducing adaptive sampling. Intensive experiments show that the proposed method can achieve accurate reconstruction with high efficiency compared to existing approaches.

Sound speed uncertainty in acousto-electric tomography

The goal in acousto-electric tomography is to reconstruct an image of the unknown electric conductivity inside an object from boundary measurements of electrostatic currents and voltages collected while the object is penetrated by propagating ultrasound waves. This problem is a coupled-physics inverse problem. Accurate knowledge of the propagating ultrasound wave is usually assumed and required, but in practice tracking the propagating wave is hard due to inexact knowledge of the interior acoustic properties of the object. In this work, we model uncertainty in the sound speed of the acoustic wave, and formulate a suitable reconstruction method for the interior power density and conductivity. We also establish theoretical error bounds, and show that the suggested approach can be understood as a regularization strategy for the inverse problem. Finally, we numerically simulate the sound speed variations from a numerical breast tissue model, and computationally explore the effect of using an inaccurate sound speed on the error in reconstructions. Our results show that with reasonable uncertainty in the sound speed reliable reconstruction is still possible.

On Uncertainty Quantification in the Parametrization of Newman-Type Models of Lithium-Ion Batteries

We consider the problem of parameterizing Newman-type models of Li-ion batteries focusing on quantifying the inherent uncertainty of this process and its dependence on the discharge rate. In order to rule out genuine experimental error and instead isolate the intrinsic uncertainty of model fitting, we concentrate on an idealized setting where “synthetic” measurements in the form of voltage curves are manufactured using the full, and most accurate, Newman model with parameter values considered “true”, whereas parameterization is performed using simplified versions of the model, namely, the single-particle model and its recently proposed corrected version. By framing the problem in this way, we are able to eliminate aspects which affect uncertainty, but are hard to quantify such as, e.g., experimental errors. The parameterization is performed by formulating an inverse problem which is solved using a state-of-the-art Bayesian approach in which the parameters to be inferred are represented in terms of suitable probability distributions; this allows us to assess the uncertainty of their reconstruction. The key finding is that while at slow discharge rates the voltage curves can be reconstructed quite accurately, this can be achieved with some parameters varying by 300% or more, thus providing evidence for very high uncertainty of the parameter inference process. As the discharge rate increases, the reconstruction uncertainty is reduced. However, the fits to the voltage curves become less accurate and the reconstructed parameter values begin to deviate from the “true” ones. The decrease in the accuracy of fits is concomitant with the simplified models losing validity; at C-rates of 2C and above the single-particle model does not accurately capture the physics of (dis)charge. This reveals a pitfall that one needs to be mindful of, namely, that an accurate fit does not necessarily mean that the fitted model accurately describes the physics. We conclude that inverse modelling using simplified models appears to be a viable and useful strategy for parameterizing Newman-type models because they allow fitting to be carried out in a reduced parameter space, however, we should be careful to verify that the reduced models are valid before trusting the results.

Constraints on equivalence principle violation from gamma ray bursts

Theories of gravity that obey the Weak Equivalence Principle have the same Parametrised Post-Newtonian parameter $\gamma$ for all particles at all energies. The large Shapiro time delays of extragalactic sources allow us to put tight constraints on differences in $\gamma$ between photons of different frequencies from spectral lag data, since a non-zero $\Delta \gamma$ would result in a frequency-dependent arrival time. The majority of previous constraints have assumed that the Shapiro time delay is dominated by a few local massive objects, although this is a poor approximation for distant sources. In this work we consider the cosmological context of these sources by developing a source-by-source, Monte Carlo-based forward model for the Shapiro time delays by combining constrained realisations of the local density field using the Bayesian origin reconstruction from galaxies algorithm with unconstrained large-scale modes. Propagating uncertainties in the density field reconstruction and marginalising over an empirical model describing other contributions to the time delay, we use spectral lag data of Gamma Ray Bursts from the BATSE satellite to constrain $\Delta \gamma < 2.1 \times 10^{-15}$ at $1 \sigma$ confidence between photon energies of $25 {\rm \, keV}$ and $325 {\rm \, keV}$.

Southern Ocean sea surface temperature synthesis: Part 2. Penultimate glacial and last interglacial

The last interglacial (LIG: ∼130 to 115 thousand years before present) is often used as an analogue for near-future climate warming. Antarctic Ice Sheet response to LIG warming is of particular interest, because of its implications for sea level rise. Comparison between LIG climate simulations and proxy-based reconstructions of Southern Ocean sea surface temperature (SST) remains challenging, due to high uncertainties in both reconstructions and simulations. In this two-part study, the accompanying paper (Part 1) addressed uncertainties in the SST reconstructions by evaluating proxies relevant to Southern Ocean SST, and made recommendations for which proxies and respective calibrations are most reliable on glacial-interglacial time scales in this region. In the second part (this paper), we now apply these recommendations to a synthesis of Southern Ocean SST over the penultimate glacial and LIG. Similar to previous studies, we find that LIG warming at 40°S to 60°S reached 1.6 ± 1.1 °C (annual mean) or 1.9 ± 1.3 °C (austral summer: JFM) relative to present. Annual/summer cooling in the penultimate glacial maximum reached −3.6 ± 1.0 °C/−4.0 ± 1.2 °C, similar to the last glacial maximum. Compared with the previous LIG SST syntheses, our reported uncertainties more strongly reflect geographic variability and dating errors, as we have reduced errors in the individual temperature reconstructions and do not date records by aligning peaks in their SST. However, the reconstruction errors are still important, and we do not recommend detailed interpretation of temperature records from small numbers of sites. Instead, comparisons of our new synthesis with model simulations should focus only on the regional average.

Downscaling CESM2 in CLM5 to Hindcast Preindustrial Equilibrium Line Altitudes for Tropical Mountain Glaciers

AbstractTropical mountain glaciers are an important water resource and highly impacted by recent climate change. Tropical mountain glaciation also occurred in the recent and deep past, which presents opportunities for better validating paleoclimate simulations in continental interiors and mountainous regions but requires bridging global model scales (hundreds of kilometers) with the 1–10 km scale of glaciers when paleotopography is poorly known. Here, we hindcast tropical mountain glaciation in preindustrial time by using global climate model meteorology to force standalone simulations in its land component that use high‐resolution topography to resolve selected tropical mountain glaciers. These simulations underestimate observed equilibrium line altitudes (ELAs) by 249 330 m, but the simulated ELA and snow lines capture observed intermountain ELA variability. Errors in large‐scale model precipitation and ELA reconstruction uncertainty are the main contributors to this bias.

Reconstructing a point source from diffusion fluxes to narrow windows in three dimensions

We develop a computational approach to locate the source of a steady-state gradient of diffusing particles from the fluxes through narrow windows distributed either on the boundary of a three-dimensional half-space or on a sphere. This approach is based on solving the mixed boundary stationary diffusion equation with Neumann–Green’s function. The method of matched asymptotic expansions enables the computation of the probability fluxes. To explore the range of validity of this expansion, we develop a fast analytical-Brownian numerical scheme. This scheme accelerates the simulation time by avoiding the explicit computation of Brownian trajectories in the infinite domain. The results obtained from our derived analytical formulae and the fast numerical simulation scheme agree on a large range of parameters. Using the analytical representation of the particle fluxes, we show how to reconstruct the location of the point source. Furthermore, we investigate the uncertainty in the source reconstruction due to additive fluctuations present in the fluxes. We also study the influence of various window configurations: clustered versus uniform distributions on recovering the source position. Finally, we discuss possible applications for cell navigation in biology.

Structural dynamic response reconstruction and virtual sensing using a sequence to sequence modeling with attention mechanism

Structural condition perception is a crucial step in contemporary structural health monitoring. Sensor malfunction and under-sensing seriously hamper the performance of the structural health monitoring system. This paper proposes a novel structural dynamic response reconstruction and virtual sensing approach for structural health monitoring using a sequence-to-sequence modeling framework with a soft attention mechanism from the perspective of sequence data generation. This framework explicitly utilizes the potential spatiotemporal correlation in sequence data and promotes the efficient flow of information in the network, thereby significantly improving the reconstruction performance. In addition, a reconstruction error estimation and uncertainty quantification method based on signal complexity characterized by entropy is also developed. The effectiveness and robustness of the proposed method are verified based on the vibration signals of a footbridge measured on-site under low-amplitude ambient excitation. Finally, the applicability of this method in the scenarios of modal identification and sensor validation is demonstrated.

Kalman filtering approach to particle track filtering and track uncertainty quantification for 3D PTV measurement

Three-dimensional Particle Tracking Velocimetry (3D-PTV) is a non-invasive flow measurement technique that computes the velocity field by reconstructing 3D particle positions of individual tracer particles and by subsequently tracking those positions. The particle velocity measurement accuracy depends on the faithful reconstruction of 3D particle positions. The complex measurement chain in 3D-PTV involves several steps, from calibration to 3D position reconstruction and particle position tracking, each having its own source of error. Additionally, higher seeding density increases the uncertainty in particle reconstruction and tracking, which in turn, increases the noise in the estimated tracks. A noisy track decreases the measurement accuracy and amplifies any noise in the PTV-derived quantities of interest, which includes acceleration, pressure and vorticity. Thus, track filtering techniques are critical in a 3D-PTV measurement. Track fitting using polynomial functions, filtering methods adopted from signal processing and object tracking are among the well-established techniques used to achieve smooth position, velocity estimates from reconstructed particle trajectories. The Kalman filter is one such filtering technique that is widely used in various applications. The strength of the Kalman filter lies in its ability to perform noise reduction that is informed by existing physical models and the uncertainty estimates of recorded measurements. However, the measurement uncertainty input to the Kalman filter needs to be known at priori, which in many cases may not be available or could be difficult to estimate. In the literature on Kalman filters and their variants applied to 2D-PIV/PTV, the position uncertainty data fed to the filter is either user-defined or estimated based on global noise levels in the PTV measurements. But instantaneous position and velocity uncertainty quantification for individual particle positions/tracks has been challenging in the 3D PTV community. Recent work by Bhattacharya and Vlachos (2020) provides an estimate of the uncertainty in the reconstructed particle positions for a 3D PTV measurement. This position uncertainty estimate dynamically updates the filter gain for each track and enables the evaluation of the performance of the Kalman filter in 3D PTV track filtering.

Statistical Uncertainty in Paleoclimate Proxy Reconstructions.

A quantitative analysis of any environment older than the instrumental record relies on proxies. Uncertainties associated with proxy reconstructions are often underestimated, which can lead to artificial conflict between different proxies, and between data and models. In this paper, using ordinary least squares linear regression as a common example, we describe a simple, robust and generalizable method for quantifying uncertainty in proxy reconstructions. We highlight the primary controls on the magnitude of uncertainty, and compare this simple estimate to equivalent estimates from Bayesian, nonparametric and fiducial statistical frameworks. We discuss when it may be possible to reduce uncertainties, and conclude that the unexplained variance in the calibration must always feature in the uncertainty in the reconstruction. This directs future research toward explaining as much of the variance in the calibration data as possible. We also advocate for a “data‐forward” approach, that clearly decouples the presentation of proxy data from plausible environmental inferences.

A muon-track reconstruction exploiting stochastic losses for large-scale Cherenkov detectors

IceCube is a cubic-kilometer Cherenkov telescope operating at the South Pole. The main goal of IceCube is the detection of astrophysical neutrinos and the identification of their sources. High-energy muon neutrinos are observed via the secondary muons produced in charge current interactions with nuclei in the ice. Currently, the best performing muon track directional reconstruction is based on a maximum likelihood method using the arrival time distribution of Cherenkov photons registered by the experiment's photomultipliers. A known systematic shortcoming of the prevailing method is to assume a continuous energy loss along the muon track. However at energies >1 TeV the light yield from muons is dominated by stochastic showers. This paper discusses a generalized ansatz where the expected arrival time distribution is parametrized by a stochastic muon energy loss pattern. This more realistic parametrization of the loss profile leads to an improvement of the muon angular resolution of up to 20% for through-going tracks and up to a factor 2 for starting tracks over existing algorithms. Additionally, the procedure to estimate the directional reconstruction uncertainty has been improved to be more robust against numerical errors.

Twentieth century global glacier mass change: an ensemble-based model reconstruction

Abstract. Negative glacier mass balances in most of Earth's glacierized regions contribute roughly one-quarter to currently observed rates of sea-level rise and have likely contributed an even larger fraction during the 20th century. The distant past and future of glaciers' mass balances, and hence their contribution to sea-level rise, can only be estimated using numerical models. Since, independent of complexity, models always rely on some form of parameterizations and a choice of boundary conditions, a need for optimization arises. In this work, a model for computing monthly mass balances of glaciers on the global scale was forced with nine different data sets of near-surface air temperature and precipitation anomalies, as well as with their mean and median, leading to a total of 11 different forcing data sets. The goal is to better constrain the glaciers' 20th century sea-level budget contribution and its uncertainty. Therefore, five global parameters of the model's mass balance equations were varied systematically, within physically plausible ranges, for each forcing data set. We then identified optimal parameter combinations by cross-validating the model results against in situ annual specific mass balance observations, using three criteria: model bias, temporal correlation, and the ratio between the observed and modeled temporal standard deviation of specific mass balances. These criteria were chosen in order not to trade lower error estimates by means of the root mean squared error (RMSE) for an unrealistic interannual variability. We find that the disagreement between the different optimized model setups (i.e., ensemble members) is often larger than the uncertainties obtained via the leave-one-glacier-out cross-validation, particularly in times and places where few or no validation data are available, such as the first half of the 20th century. We show that the reason for this is that in regions where mass balance observations are abundant, the meteorological data are also better constrained, such that the cross-validation procedure only partly captures the uncertainty of the glacier model. For this reason, ensemble spread is introduced as an additional estimate of reconstruction uncertainty, increasing the total uncertainty compared to the model uncertainty merely obtained by the cross-validation. Our ensemble mean estimate indicates a sea-level contribution by global glaciers (outside of the ice sheets; including the Greenland periphery but excluding the Antarctic periphery) for 1901–2018 of 69.2 ± 24.3 mm sea-level equivalent (SLE), or 0.59 ± 0.21 mm SLE yr−1. While our estimates lie within the uncertainty range of most of the previously published global estimates, they agree less with those derived from GRACE data, which only cover the years 2002–2018.

Zircon U‐Pb Geochronology Constrains Continental Expression of Great Meteor Hotspot Magmatism

AbstractThe New England‐Québec Igneous Province is considered to be a continental expression of Great Meteor Hotspot magmatism, though other geodynamic scenarios have been suggested. Existing geochronologic data lack the needed accuracy and precision to permit tests of potential causal mechanisms. We provide zircon U‐Pb ages for four igneous centers and a suite of plate reconstructions and show that the duration between magmatism in each branch of this province is ca. 3–6 Myr shorter and ca. 10 Myr older than predicted if the spatial‐temporal distribution of magmatism conformed to a well‐defined age progression. However, in addition to uncertainties in plate reconstructions, variable regional crustal thickness or lithospheric topography likely played a role in mediating the rates of melt transport to emplacement depth and we therefore cannot reject the hotspot hypothesis. Our results place the best‐available chronological constraints on continental magmatism associated with one of the oldest and longest‐lived hotspots.

Average annual total sunspot area in the last 410 yr: the most probable values and limits of their uncertainties

ABSTRACT The aim of this work is to create a long (410-yr) series of average annual total sunspot areas AR – a physically based index of sunspot activity. We use telescopic observations of the AR index in 1832–1868 and 1875–2020, as well as the relationship between AR and long series of sunspot indices SN (international sunspot numbers, version 2.0) and sunspot groups GN (Svalgaard and Schatten’s version of group sunspot numbers). The Royal Greenwich Observatory series after 1976 is extended by the Kislovodsk Mountain Astronomical Station data. When reconstructing AR from SN, it is taken into account that the function AR = f(SN) has a non-linear systematic character and uncertainty associated with the heterogeneity of these indices. Therefore, in addition to modelling the most probable AR values, predictive limits of reconstruction uncertainty are determined. In the interval 1610–1699 we carried out the reconstruction on the basis of the GN series using the previously proposed decomposition in pseudo-phase space (DPS) method. The resulting series NO21y is freely available online. We show that for this series the empirical Gnevyshev–Ohl rule and Waldmeier effect are fulfilled. Wavelet analysis reveals periodicities of 8.4–13.8 yr for the main cycle (with a sharp decrease of the period before the global Maunder and Dalton minima) and a two-component Gleissberg cycle with typical periods of 50–60 and 90–110 yr.

Calibration and uncertainty analysis of a combined tracking-based vision measurement system using Monte Carlo simulation

A global stereovision system combined with a local vision sensor is an effective approach to large-scale object measurement. However, obtaining the error distribution of such an approach remains a key research challenge in vision metrological applications. This paper investigates the calibration and the reconstruction uncertainty estimation method of the combined vision system. The measurement principle and the calibration method of the transformation matrix between the tracking-based measurement coordinate systems are presented. Furthermore, Monte Carlo simulation is utilized to determine the reconstruction uncertainty based on the theoretical measurement model and the experiment-based input uncertainty. The overall measurement uncertainty of the combined system is found to be 34.5% higher than that of the global vision system, which is more sensitive to the input pixel uncertainty than the local vision system. However, the combined vision system can achieve comparable measurement results within its larger working volume. This work contributes to a better understanding of the measurement uncertainty in combined tracking-based vision systems, as well as providing a few useful practice guidelines for using such a visual system.

The PMIP4 Last Glacial Maximum experiments: preliminary results and comparison with the PMIP3 simulations

Abstract. The Last Glacial Maximum (LGM, ∼ 21 000 years ago) has been a major focus for evaluating how well state-of-the-art climate models simulate climate changes as large as those expected in the future using paleoclimate reconstructions. A new generation of climate models has been used to generate LGM simulations as part of the Paleoclimate Modelling Intercomparison Project (PMIP) contribution to the Coupled Model Intercomparison Project (CMIP). Here, we provide a preliminary analysis and evaluation of the results of these LGM experiments (PMIP4, most of which are PMIP4-CMIP6) and compare them with the previous generation of simulations (PMIP3, most of which are PMIP3-CMIP5). We show that the global averages of the PMIP4 simulations span a larger range in terms of mean annual surface air temperature and mean annual precipitation compared to the PMIP3-CMIP5 simulations, with some PMIP4 simulations reaching a globally colder and drier state. However, the multi-model global cooling average is similar for the PMIP4 and PMIP3 ensembles, while the multi-model PMIP4 mean annual precipitation average is drier than the PMIP3 one. There are important differences in both atmospheric and oceanic circulations between the two sets of experiments, with the northern and southern jet streams being more poleward and the changes in the Atlantic Meridional Overturning Circulation being less pronounced in the PMIP4-CMIP6 simulations than in the PMIP3-CMIP5 simulations. Changes in simulated precipitation patterns are influenced by both temperature and circulation changes. Differences in simulated climate between individual models remain large. Therefore, although there are differences in the average behaviour across the two ensembles, the new simulation results are not fundamentally different from the PMIP3-CMIP5 results. Evaluation of large-scale climate features, such as land–sea contrast and polar amplification, confirms that the models capture these well and within the uncertainty of the paleoclimate reconstructions. Nevertheless, regional climate changes are less well simulated: the models underestimate extratropical cooling, particularly in winter, and precipitation changes. These results point to the utility of using paleoclimate simulations to understand the mechanisms of climate change and evaluate model performance.

On the treatment of lens optical center uncertainty in simultaneous reconstruction of flame temperature and soot volume fraction distributions by a CCD camera

In general, when charge-coupled device (CCD) cameras are used to reconstruct key flame parameters via inverse radiation analysis, the uncertainty of the camera lens optical center will introduce difficulties for practical applications and also reduce the reconstruction accuracy. This paper investigated the effect of the camera lens optical center location on the accuracy for concurrently reconstructing the distributions of temperature and soot volume fraction in an optically thin, axisymmetric flame with a single CCD camera via inverse radiation analysis. The impact of the ray number and measurement error on the precision of reconstruction was analyzed. Overall, the measurement error played a crucial role in reconstruction accuracy while the increase of the ray number could improve the reconstruction accuracy. When the lens optical center used for reconstruction was inconsistent with the actual one, the reconstructed errors can remain in an acceptable range. In summary, the effect of the lens optical center uncertainty on the reconstruction accuracy could be small. The conclusion obtained here can be useful for the practical reconstruction process.

Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal Solution Characterization for Computational Imaging

Computational image reconstruction algorithms generally produce a single image without any measure of uncertainty or confidence. Regularized Maximum Likelihood (RML) and feed-forward deep learning approaches for inverse problems typically focus on recovering a point estimate. This is a serious limitation when working with under-determined imaging systems, where it is conceivable that multiple image modes would be consistent with the measured data. Characterizing the space of probable images that explain the observational data is therefore crucial. In this paper, we propose a variational deep probabilistic imaging approach to quantify reconstruction uncertainty. Deep Probabilistic Imaging (DPI) employs an untrained deep generative model to estimate a posterior distribution of an unobserved image. This approach does not require any training data; instead, it optimizes the weights of a neural network to generate image samples that fit a particular measurement dataset. Once the network weights have been learned, the posterior distribution can be efficiently sampled. We demonstrate this approach in the context of interferometric radio imaging, which is used for black hole imaging with the Event Horizon Telescope, and compressed sensing Magnetic Resonance Imaging (MRI).