Uncertainty In Shape Research Articles

Prior-shape-guided photometric stereo model for 3D damage measurement of worn surfaces

Three-dimensional (3D) damage measurement often encounters limited accuracy due to the non-Lambertian effects on worn surfaces. To address this issue, a prior-shape-guided surface reconstruction model is introduced with photometric stereo vision. Initially, an illumination calibration method is constructed to mitigate the uneven brightness on worn surface images. Subsequently, a prior-shape-guided network is developed that employs the feature aggregation strategy and prior shape uncertainty to guide worn surface reconstruction. Experimental results reveal that the proposed model can effectively recover the typical morphologies of worn surfaces, and the root mean square error is reduced from 7.39 to 1.59 when compared to existing methods. Most importantly, this model has been applied to detect aero-engine bearings and achieve 3D quantitative characterization for worn damages.

Locating clustered seismicity using Distance Geometry Solvers: applications for sparse and single-borehole DAS networks

Summary The determination of seismic event locations with sparse networks or single-borehole systems remains a significant challenge in observational seismology. Leveraging the advantages of the location approach HADES (eartHquake locAtion via Distance gEometry Solvers), which was initially developed for locating clustered seismicity recorded at two stations, through the solution of a Distance Geometry Problem, we present here an improved version of the methodology: HADES-R (HADES-Relative). Where HADES previously needed a minimum of 4 absolutely located master events, HADES-R solves a least-squares problem to find the relative inter-event distances in the cluster, and uses only a single master event to find the locations of all events, and subsequently applies rotational optimizer to find the cluster orientation. It can leverage iterative station combinations if multiple receivers are available, to describe the cluster shape and orientation uncertainty with a bootstrap approach. The improved method requires P- and S-phase arrival picks, a homogeneous velocity model, a single master event with a known location, and an estimate of the cluster width. The approach is benchmarked on the 2019 Ridgecrest sequence recorded at two stations, and applied to two seismic clusters at the FORGE geothermal test site in Utah, USA, with a microseismic monitoring scenario with a DAS in a vertical borehole. Traditional procedures struggle in these settings due to the ill-posed network configuration. The azimuthal ambiguity in such a scenario is partially overcome by the assumption that all events belong to the same cluster around the master event and a cluster width estimate. We are able to find the cluster shape in both cases, although the orientation remains uncertain. HADES-R contributes to an efficient way to locate multiple events simultaneously with minimal prior information. The method’s ability to constrain the cluster shape and location with only one well-located event offers promising implications, especially for environments where limited or specialised instrumentation is in use.

Io's Long‐Wavelength Topography as a Probe for a Subsurface Magma Ocean

AbstractWe investigated how spatial variations in tidal heating affect Io's isostatic topography at long wavelengths. The long‐wavelength relief is less than the 0.3 km uncertainty in Io's global shape. Assuming Airy isostasy, degree‐2 topography <0.3 km amplitude is only possible if surface heat flux varies spatially by <19% of the mean value. This is consistent with Io's volcano distribution and is possible if tidal heat is generated within and redistributed by a convecting layer underneath the lithosphere. However, that layer would require a viscosity <1010 Pa s. A magma ocean would have low enough viscosity but would not generate enough tidal heat internally. Conversely, assuming Pratt isostasy, we found ∼0.15 km degree‐2 topography is easily achievable. If a magma ocean was present, Airy isostasy would dominate; we therefore conclude that Io is unlikely to possess a magma ocean.

Firm input choice under trade policy uncertainty

We examine the role of trade policy uncertainty (TPU) in shaping the import decisions of firms. In a model where firms must incur sunk costs to adopt new imported varieties of an input, a reduction in TPU for a given input increases imports of that input (a substitution effect) and possibly other inputs (a scale effect). We explore this in the context of China’s accession to the WTO, which bound China’s tariffs. We find that, controlling for current tariffs, the threat of reversion to past high tariffs reduces imports, but much less so after WTO accession, consistent with lower TPU. The current-tariff trade elasticity also increases after WTO entry, reflecting a greater perceived permanence of current tariffs. We find evidence of both substitution and scale effects for imports, and post accession, firms were more likely to adopt products previously subject to higher tariff risk.

Sensitivity of Polarization to Grain Shape. I. Convex Shapes

Aligned interstellar grains produce polarized extinction (observed at wavelengths from the far-ultraviolet to the mid-infrared) and polarized thermal emission (observed at far-infrared and submm wavelengths). The grains must be quite nonspherical, but the actual shapes are unknown. The relative efficacy for aligned grains to produce polarization at optical versus infrared wavelengths depends on particle shape. The discrete dipole approximation is used to calculate polarization cross sections for 20 different convex shapes, for wavelengths from 0.1 to 100 μm, and grain sizes a eff from 0.05 to 0.3 μm. Spheroids, cylinders, square prisms, and triaxial ellipsoids are considered. Minimum aspect ratios required by the observed starlight polarization are determined. Some shapes can also be ruled out because they provide too little or too much polarization at far-infrared and submm wavelengths. The ratio of 10 μm polarization to integrated optical polarization is almost independent of grain shape, varying by only ±8% among the viable convex shapes; thus, at least for convex grains, uncertainties in grain shape cannot account for the discrepancy between predicted and observed 10 μm polarization toward Cyg OB2-12.

Microhabitat conditions drive uncertainty of risk and shape neophobic responses in Trinidadian guppies, Poecilia reticulata.

In response to uncertain risks, prey may rely on neophobic phenotypes to reduce the costs associated with the lack of information regarding local conditions. Neophobia has been shown to be driven by information reliability, ambient risk and predator diversity, all of which shape uncertainty of risk. We similarly expect environmental conditions to shape uncertainty by interfering with information availability. In order to test how environmental variables might shape neophobic responses in Trinidadian guppies (Poecilia reticulata), we conducted an in situ field experiment of two high-predation risk guppy populations designed to determine how the 'average' and 'variance' of several environmental factors might influence the neophobic response to novel predator models and/or novel foraging patches. Our results suggest neophobia is shaped by water velocity, microhabitat complexity, pool width and depth, as well as substrate diversity and heterogeneity. Moreover, we found differential effects of the 'average' and 'variance' environmental variables on food- and predator-related neophobia. Our study highlights that assessment of neophobic drivers should consider predation risk, various microhabitat conditions and neophobia being tested. Neophobic phenotypes are expected to increase the probability of prey survival and reproductive success (i.e. fitness), and are therefore likely linked to population health and species survival. Understanding the drivers and consequences of uncertainty of risk is an increasingly pressing issue, as ecological uncertainty increases with the combined effects of climate change, anthropogenic disturbances and invasive species.

Novel bootstrap-based ellipsoidal convex model for non-probabilistic reliability-based design optimization with insufficient input data

Performing reliability-based design optimization with insufficient input data is a significant and challenging issue as accurately quantifying epistemic uncertainty can be difficult in such scenarios. Non-probabilistic models can marginally alleviate the need for a large sample size by constructing the boundaries of uncertainty parameters. However, most of the existing non-probabilistic models account for only the available or known samples. For cases with insufficient data, the compact uncertainty domain may result in considerably hazardous results, particularly for the problems that require high reliability. Therefore, a novel bootstrap-based ellipsoidal convex model (BECM) is proposed herein to account for both known and unknown data. Herein, the bootstrap method is introduced to non-probabilistic convex models for the first time to quantify the ellipsoidal shape uncertainty caused by insufficient input data. Further, the proposed BECM is also integrated into non-probabilistic reliability-based design optimization. The entire framework of uncertainty quantification and reliability optimization design for insufficient input data is established. Marginally conservative results can finally be achieved in a rational and objective manner by partially sacrificing the ellipsoid volume. Comprehensive comparisons and detailed discussions on aspects, including the problem complexity, initial sample size, and distribution type, are also conducted. The numerical results show that the BECM displays the best performance in terms of accuracy and robustness. It can achieve an approximate balance between being conservative and taking risks. The significant advantages are also illustrated by an engineering example of linear buckling analysis of stiffened cylindrical shells.

Characterizing process window for microscale selective laser sintering

This paper outlines the experimental approach to create a sintering window for a microscale metal additive manufacturing (AM) process. The experimental framework discussed in the paper involves fabricating sintered features by varying pattern area and laser irradiance. The sintered features are then imaged under a microscope and the processed images are compared against an ideal image to quantify the uncertainty in near-net shape of the feature. Evaluating this data defines the process window within which good sintering and near-net shaped features can be expected in the microscale AM process.

Effects of flood wave shape on probabilistic slope stability of dikes under transient groundwater conditions

ABSTRACT The time-dependent response of pore water pressures during floods largely determines the safety against geotechnical failure of dikes, which is deemed to be highly dependent on the uncertain shape (duration, maximum height, etc.) of the flood discharge wave. This paper derives the uncertainty of flood wave shape from a database of precalculated hydrographs (GRADE) and evaluates the effect of shape variability on probabilistic safety estimates of slope stability, using a modelling chain consisting of a transient hydrological model (MODFLOW) and a probabilistic dike slope safety assessment (FORM). Accounting for flood wave uncertainty with transient groundwater flow generally leads to higher reliability estimates for slope stability, compared to the steady-state groundwater condition and other conservative assumptions, but to lower reliability estimates compared to a single design flood wave. Furthermore, the uncertainty of the flood wave shape can be as important as the uncertainty in geotechnical properties. For landside dike slope stability, the volume of the flood wave is the most important factor, while riverside slope stability depends mainly on the total water level drop after the peak. These two waveform characteristics are thus essential uncertainties to consider in probabilistic assessments of dike safety with transient groundwater conditions.

The managerial perception of uncertainty and cost elasticity

Theoretical research demonstrates the important role of uncertainty in shaping a firm's cost elasticity. We contribute to this literature by analyzing the inherent tension between the effects of uncertainty about unit contribution margin (CM) and sales volume on cost elasticity. We identify the occurrence of words implying uncertainty in managerial forward-looking statements and employ a novel methodology to construct distinct measures of the managerial perceptions of overall, unit CM, and volume uncertainty. We find a significantly positive (negative) association between the uncertainty about unit CM (volume) and cost elasticity. These associations vary predictably with firm and industry characteristics. Our empirical evidence supports the theoretical argument that managerial perceptions of uncertainty and its components differentially influence their resource allocation decisions and suggests that any analysis of the relation between uncertainty and a firm's cost elasticity should specify the type of uncertainty as well as the firm and industry characteristics.

Aerosol optical properties calculated from size distribution measurements: An uncertainty study

We use Monte Carlo uncertainty propagation to estimate the uncertainty of aerosol scattering coefficients, σs, that have been derived from measured particle size distributions. We consider the particular case where the size distributions are measured using a combination of a scanning mobility particle sizer (SMPS) and an aerodynamic particle sizer (APS). Uncertainties that are propagated include those intrinsic to the instruments and those that arise from variabilities in aerosol microphysical properties, including particle shape, density, and complex refractive index. Particular emphasis is put on the size dependent counting efficiency of both instruments which have weaknesses in a particle size range that dominates aerosol optical properties. The T-matrix method is utilized to simulate the effect of particle shapes on σs. To narrow the probability distribution of aerosol properties we discuss uncertainties for a single geographic location, which is the Southern Great Plains site (SGP) of the Department of Energy’s Atmospheric Radiation Measurement (ARM) User Facility. We estimate a 95% confidence interval for σs between −40% and +68%. A partial dependence analysis, for which we use generalized additive models, identifies uncertainties in counting efficiency and particle shapes as the dominant contributors to the size of the confidence interval.

Towards a sub-percent precision measurement of sin2θ13 with reactor antineutrinos

Measuring the neutrino mixing parameter sin2θ13 to the sub-percent precision level could be necessary in the next ten years for the precision unitary test of the PMNS matrix. In this work, we discuss the possibility of such a measurement with reactor antineutrinos. We find that a single liquid scintillator detector on a reasonable scale could achieve the goal. We propose to install a detector of ∼ 10% energy resolution at about 2.0 km from the reactors with a JUNO-like overburden. The integrated luminosity requirement is about 150 kton · GW · year, corresponding to 4 years’ operation of a 4 kton detector near a reactor complex of 9.2 GW thermal power like Taishan reactor. Unlike the previous θ13 experiments with identical near and far detectors, which can suppress the systematics especially the rate uncertainty by the near-far relative measurement and the optimal baseline is at the first oscillation maximum of about 1.8 km, a single-detector measurement prefers to offset the baseline from the oscillation maximum. At low statistics ≲ 10 kton · GW · year, the rate uncertainty dominates the systematics, and the optimal baseline is about 1.3 km. At higher statistics, the spectral shape uncertainty becomes dominant, and the optimal baseline shifts to about 2.0 km. The optimal baseline keeps being ∼ 2.0 km for an integrated luminosity up to 106 kton · GW · year. Impacts of other factors on the precision sin2θ13 measurement are also discussed. We have assumed that the TAO experiment will improve our understanding of the spectral shape uncertainty, which gives the highest precision measurement of reactor antineutrino spectrum for neutrino energy in the range of 3–6 MeV. We find that the optimal baseline is ∼ 2.9 km with a flat input spectral shape uncertainty provided by the future summation or conversion methods’ prediction. The shape uncertainty would be the bottleneck of the sin2θ13 precision measurement. The sin2θ13 precision is not sensitive to the detector energy resolution and the precision of other oscillation parameters.

Planning Visual-Tactile Precision Grasps via Complementary Use of Vision and Touch

Reliably planning fingertip grasps for multi-fingered hands lies as a key challenge for many tasks including tool use, insertion, and dexterous in-hand manipulation. This task becomes even more difficult when the robot lacks an accurate model of the object to be grasped. Tactile sensing offers a promising approach to account for uncertainties in object shape. However, current robotic hands tend to lack full tactile coverage. As such, a problem arises of how to plan and execute grasps for multi-fingered hands such that contact is made with the area covered by the tactile sensors. To address this issue, we propose an approach to grasp planning that explicitly reasons about where the fingertips should contact the estimated object surface while maximizing the probability of grasp success. Key to our method's success is the use of visual surface estimation for initial planning to encode the contact constraint. The robot then executes this plan using a tactile-feedback controller that enables the robot to adapt to online estimates of the object's surface to correct for errors in the initial plan. Importantly, the robot never explicitly integrates object pose or surface estimates between visual and tactile sensing, instead it uses the two modalities in complementary ways. Vision guides the robots motion prior to contact; touch updates the plan when contact occurs differently than predicted from vision. We show that our method successfully synthesises and executes precision grasps for previously unseen objects using surface estimates from a single camera view. Further, our approach outperforms a state of the art multi-fingered grasp planner, while also beating several baselines we propose.

Individual tree segmentation and tree-counting using supervised clustering

Individual tree segmentation (ITS), or tree counting, is a fundamental work in precision forestry and agriculture processes. Rather than the time-consuming and labor-intensive manual inspection, computer vision has shown substantial prospects in unmanned aerial vehicle (UAV)-based applications; one such application includes the automatic tree-counting problem in the forest resource inventory. However, it is difficult to obtain individual trees owing to the particularity of tree canopy crowns, such as color graduality, shape uncertainty, and overlapping. In this study, we propose a learning framework based on supervised data clustering. Here, both ITS and tree counting can be obtained accurately and simultaneously from a two-dimensional (2D) top-view tree canopy crowns whether they are isolated, overlapped, or both. A pixel-precision classifier is used to recognize tree pixels or superpixels (a set of meaningful pixels), rather than using complex image preprocessing or feature construction techniques. The obtained tree superpixels are then grouped into individual trees by the proposed supervised clustering method. To obtain accurate ITS and tree counts, the similarity used for the clustering is “learned” from the user-supplied supervisions, rather than “pre-specified” or “grid-search” as in the existing state-of-the-art methods. This study also includes an extensive experimental comparison of homogenous and heterogeneous high-resolution images. The results demonstrate that our method is superior to the state-of-the-art methods in both visualized ITS and numeric tree-counting results, even comparable to human vision. It achieves a counting accuracy of 99.16 % in terms of the R2 value and 2.2923 in terms of the pixel mean absolute error (MAE). These are 22.04 % higher and 8.727 lower, respectively, than those of the second-best method.

Quantifying the impact of shape uncertainty on predicted arrhythmias

Background.Personalised computer models are increasingly used to diagnose cardiac arrhythmias and tailor treatment. Patient-specific models of the left atrium are often derived from pre-procedural imaging of anatomy and fibrosis. These images contain noise that can affect simulation predictions. There are few computationally tractable methods for propagating uncertainties from images to clinical predictions. Method.We describe the left atrium anatomy using our Bayesian shape model that captures anatomical uncertainty in medical images and has been validated on 63 independent clinical images. This algorithm describes the left atrium anatomy using Nmodes=15 principal components, capturing 95% of the shape variance and calculated from 70 clinical cardiac magnetic resonance (CMR) images. Latent variables encode shape uncertainty: we evaluate their posterior distribution for each new anatomy. We assume a normally distributed prior. We use the unscented transform to sample from the posterior shape distribution. For each sample, we assign the local material properties of the tissue using the projection of late gadolinium enhancement CMR (LGE-CMR) onto the anatomy to estimate local fibrosis. To test which activation patterns an atrium can sustain, we perform an arrhythmia simulation for each sample. We consider 34 possible outcomes (31 macro-re-entries, functional re-entry, atrial fibrillation, and non-sustained arrhythmia). For each sample, we determine the outcome by comparing pre- and post-ablation activation patterns following a cross-field stimulus. Results.We create patient-specific atrial electrophysiology models of ten patients. We validate the mean and standard deviation maps from the unscented transform with the same statistics obtained with 12,000 Monte Carlo (ground truth) samples. We found discrepancies <3% and <2% for the mean and standard deviation for fibrosis burden and activation time, respectively. For each patient case, we then compare the predicted outcome from a model built on the clinical data (deterministic approach) with the probability distribution obtained from the simulated samples. We found that the deterministic approach did not predict the most likely outcome in 80% of the cases. Finally, we estimate the influence of each source of uncertainty independently. Fixing the anatomy to the posterior mean and maintaining uncertainty in fibrosis reduced the prediction of self-terminating arrhythmias from ≃14% to ≃7%. Keeping the fibrosis fixed to the sample mean while retaining uncertainty in shape decreased the prediction of substrate-driven arrhythmias from ≃33% to ≃18% and increased the prediction of macro-re-entries from ≃54% to ≃68%. Conclusions.We presented a novel method for propagating shape uncertainty in atrial models through to uncertainty in numerical simulations. The algorithm takes advantage of the unscented transform to compute the output distribution of the outcomes. We validated the unscented transform as a viable sampling strategy to deal with anatomy uncertainty. We then showed that the prediction computed with a deterministic model does not always coincide with the most likely outcome. Finally, we found that shape uncertainty affects the predictions of macro-re-entries, while fibrosis uncertainty affects the predictions of functional re-entries.

Uncertainty EM Scattering Prediction for Inhomogeneous Dielectric Bodies of Revolution

A perturbed volumetric integral equation is fabricated to predict the uncertain scattering characteristics for the in-homogeneous dielectric bodies of revolution (BoRs) targets. The transverse surface of the body of revolution is discretized in terms of the rectangular and triangular basis functions. In this way, all the unknowns are assigned to the electric flux density and the governing equation can be solved mode by mode. Both the geometrical and dielectric uncertainties are taken into consideration for EM scattering characteristics. On one hand, the geometrical shape uncertainty is described with the nonuniform rational B-spline surface by using several independent random variables. On the other hand, the dielectric uncertainty is represented by the perturbed permittivity. Thus, the volume integral equation is reconstructed by the perturbed electric flux density. Both the mean value and variance of the radar cross Section can be derived to account for the geometrical and dielectric uncertainties. Numerical results are given to show that the calculation efficiency of the proposed method is higher than that of the traditional Monte Carlo method.

Numerical upscaling of parametric microstructures in a possibilistic uncertainty framework with tensor trains

A fuzzy arithmetic framework for the efficient possibilistic propagation of shape uncertainties based on a novel fuzzy edge detection method is introduced. The shape uncertainties stem from a blurred image that encodes the distribution of two phases in a composite material. The proposed framework employs computational homogenisation to upscale the shape uncertainty to a effective material with fuzzy material properties. For this, many samples of a linear elasticity problem have to be computed, which is significantly sped up by a highly accurate low-rank tensor surrogate. To ensure the continuity of the underlying mapping from shape parametrisation to the upscaled material behaviour, a diffeomorphism is constructed by generating an appropriate family of meshes via transformation of a reference mesh. The shape uncertainty is then propagated to measure the distance of the upscaled material to the isotropic and orthotropic material class. Finally, the fuzzy effective material is used to compute bounds for the average displacement of a non-homogenized material with uncertain star-shaped inclusion shapes.

A novel method for creation of complex microstructure cells through artificial molecular dynamics simulations

Composites have a spectrum of mechanical behavior resulting from uncertainty and variation in the microstructure shape and position. With microstructural simulation of fiber architectures, complex numerical algorithms are needed to enforce boundary constraints such as fiber-to-fiber overlap or periodic boundary conditions. Variations are not typically modeled because randomization of unique aggregate shapes can be challenging and current methods for doing so do not achieve high fiber volume fraction (FVF) when packing; however, this can cause inaccurate predictions in simulations. To address this challenge, a novel approach is developed using Molecular Dynamics (MD), achieving high FVFs up to 85% with rapid speed, easy user implementation, and a potential for capturing non-uniform fiber geometry. Two types of packing are presented to demonstrate the scope of possibilities with this approach: a post randomization molecular dynamics (PRMD) method for uniform fibers, and a mixed aggregate randomization using varying radii circles. Comparisons between periodic hexagonal, randomized, and variable radii packing fiber microstructures are performed to determine the significance of randomization and non-uniform aggregate shape for mechanical property homogenization and damage prediction in a unidirectional laminate. It was found that homogenization between the three microstructures do not vary from randomization; however, using the molecular dynamics approach randomizing fiber position and aggregate shape resulted in significant differences in predicting the transverse damage initiation, reducing the error by approximately 25% from the periodic method.

Quantifying uncertainty of salt body shapes recovered from gravity data using trans-dimensional Markov chain Monte Carlo sampling

SUMMARY Accurate delineation of salt body shapes is critical for hydrocarbon exploration. Various imaging methods based on seismic data have been developed. Due to the density contrast between salt and sedimentary rocks, gravity data have also been used as a de-risking tool to constrain the salt body shapes. However, quantifying uncertainties of the salt body shapes recovered from gravity data remains underexplored. Our goal is to understand and quantify how different constraints affect uncertainties of the salt body shapes reconstructed from gravity data. We adopt a trans-dimensional Markov chain Monte Carlo (MCMC) approach to explore the uncertainties. To address the computational challenges with MCMC sampling, we resort to two methods: sparse geometry parametrization and randomized parallel tempering. The first uses a set of simple geometries (e.g. ellipses) to approximate the complex shapes of salt bodies, greatly reducing the number of parameters to be sampled and making the MCMC approach computationally feasible. The second serves to further improve the acceptance ratio and computational efficiency. To quantify the uncertainties of the recovered salt body shapes, we design several scenarios to simulate different constraints on the top boundary of salt bodies from seismic imaging. We develop a new method to impose structural constraints on the top boundaries of salt bodies. This new method combines a set of fixed ellipses with randomly sampled ellipses through a concave hull. The results from different scenarios are compared to understand how uncertainties are reduced when stronger constraints are imposed. In addition, to make our uncertainty quantification results more relevant for practitioners, we propose to compute the salt probability models which show the spatial distribution of probabilities of salt materials at each cell. Finally, we investigate the effect of an uncertain salt density on the salt body reconstruction and the case of depth-varying densities in the sedimentary background. We apply our methods to the modified 2-D SEG-EAGE and Sigsbee salt models and quantify the uncertainties of the recovered salt body shapes in different scenarios. Our results highlight the importance of properly interpreting the uncertainty estimates in light of prior information and information content in the data.

The Effect of Segmentation Variability in Forward ECG Simulation.

Segmentation of patient-specific anatomical models is one of the first steps in Electrocardiographic imaging (ECGI). However, the effect of segmentation variability on ECGI remains unexplored. In this study, we assess the effect of heart segmentation variability on ECG simulation. We generated a statistical shape model from segmentations of the same patient and generated 262 cardiac geometries to run in an ECG forward computation of body surface potentials (BSPs) using an equivalent dipole layer cardiac source model and 5 ventricular stimulation protocols. Variability between simulated BSPs for all models and protocols was assessed using Pearson's correlation coefficient (CC). Compared to the BSPs of the mean cardiac shape model, the lowest variability (average CC = 0.98 ± 0.03) was found for apical pacing whereas the highest variability (average CC = 0.90 ± 0.23) was found for right ventricular free wall pacing. Furthermore, low amplitude BSPs show a larger variation in QRS morphology compared to high amplitude signals. The results indicate that the uncertainty in cardiac shape has a significant impact on ECGI.