Uncertainty In Shape Research Articles

Deriving and Analyzing Analytical Structures of a Class of Typical Interval Type-2 TS Fuzzy Controllers.

A conventional controller's explicit input-output mathematical relationship, also known as its analytical structure, is always available for analysis and design of a control system. In contrast, virtually all type-2 (T2) fuzzy controllers are treated as black-box controllers in the literature in that their analytical structures are unknown, which inhibits precise and comprehensive understanding and analysis. In this regard, a long-standing fundamental issue remains unresolved: how a T2 fuzzy set's footprint of uncertainty, a key element differentiating a T2 controller from a type-1 (T1) controller, affects a controller's analytical structure. In this paper, we describe an innovative technique for deriving analytical structures of a class of typical interval T2 (IT2) TS fuzzy controllers. This technique makes it possible to analyze the analytical structures of the controllers to reveal the role of footprints of uncertainty in shaping the structures. Specifically, we have mathematically proven that under certain conditions, the larger the footprints, the more the IT2 controllers resemble linear or piecewise linear controllers. When the footprints are at their maximum, the IT2 controllers actually become linear or piecewise linear controllers. That is to say the smaller the footprints, the more nonlinear the controllers. The most nonlinear IT2 controllers are attained at zero footprints, at which point they become T1 controllers. This finding implies that sometimes if strong nonlinearity is most important and desired, one should consider using a smaller footprint or even just a T1 fuzzy controller. This paper exemplifies the importance and value of the analytical structure approach for comprehensive analysis of T2 fuzzy controllers.

Camera-based speckle noise reduction for 3-D absolute shape measurements.

Simultaneous position and velocity measurements enable absolute 3-D shape measurements of fast rotating objects for instance for monitoring the cutting process in a lathe. Laser Doppler distance sensors enable simultaneous position and velocity measurements with a single sensor head by evaluating the scattered light signals. The superposition of several speckles with equal Doppler frequency but random phase on the photo detector results in an increased velocity and shape uncertainty, however. In this paper, we present a novel image evaluation method that overcomes the uncertainty limitations due to the speckle effect. For this purpose, the scattered light is detected with a camera instead of single photo detectors. Thus, the Doppler frequency from each speckle can be evaluated separately and the velocity uncertainty decreases with the square root of the number of camera lines. A reduction of the velocity uncertainty by the order of one magnitude is verified by the numerical simulations and experimental results, respectively. As a result, the measurement uncertainty of the absolute shape is not limited by the speckle effect anymore.

Integration of perception capabilities in gripper design using graspability maps

Agricultural environments impose high demands on robotic grippers since the objects to be grasped (e.g., fruit) suffer from inherent uncertainties in size, shape, weight, and texture, are typically highly sensitive to excessive force, and tend to be partly or fully occluded. This paper presents a methodology for evaluating the influence of perception capabilities on grasping and on gripper design using graspability maps. Graspability maps are spatial representations of grasp quality grades from wrist poses (position and orientation) about an object and are generated using simulation. A new module was developed to enable the insertion of object pose errors for testing the effects of perception inaccuracies on grasping. The methodology was implemented for comparing two grippers (Fin-Ray and Lip-type) for harvesting two sweet-pepper cultivars. A 3D model of each gripper was constructed and suitable grasp quality measures were developed and validated in a physical environment. Task and gripper-specific grasp quality measures were developed for each implementation. Sensitivity analyses included varying pepper dimensions and perception inaccuracies. These were followed by analyses of the influence of gripper design parameters on grasp capabilities. Results indicate that the Lip-type gripper is less sensitive to inaccuracies in object orientation, while both grippers are similarly sensitive to inaccuracies in object position. Specific perception system demands and design recommendations are given for each gripper, and cultivar. The results illustrate the importance of integrating perception analysis in the gripper design phase and the utility of the graspability simulation tool for design analysis.

Evaluation of the effect of data quality on the profile uncertainty of critical dimension small angle x-ray scattering

A line grating prepared via a self-aligned quadruple patterning method was measured using critical dimension small angle x-ray scattering. A Monte Carlo Markov chain algorithm was used to analyze the uncertainty of the model fit over subsets of the full angular range and for a time series with decreasing signal-to-noise in order to determine the effect of the data quality on the final profile shape uncertainty. These results show how the total measurement time can be reduced while maintaining satisfactory profile shape uncertainty. We found that the typical measurement conditions are highly oversampled and can be reduced considerably with only marginal effect on the shape uncertainty. A comparison is made between the synchrotron measurements and a laboratory system, demonstrating that both measurements result in similar structures.

The effectiveness of contractual and trust-based governance in strategic alliances under behavioral and environmental uncertainty

We examine the interplay of behavioral and environmental uncertainty in shaping the effectiveness of two key governance mechanisms used by strategic alliances: contractual and trust-based governance. We develop and test hypotheses, using a meta-analytic dataset encompassing over 15,000 strategic alliances across 82 independent samples. We find that contractual governance works best under low to moderate levels of behavioral uncertainty and moderate to high levels of environmental uncertainty, while it is detrimental to alliance performance when both types of uncertainty are low or high. Trust-based governance is most effective at high levels of behavioral uncertainty and low levels of environmental uncertainty. It suffers a large loss of usefulness at high behavioral uncertainty as environmental uncertainty increases.

Development of Structural Analysis Method with Uncertainty in Shape to Follow Non-normal Distribution by Stochastic Finite Element Method

Development of Structural Analysis Method with Uncertainty in Shape to Follow Non-normal Distribution by Stochastic Finite Element Method

Global 3νoscillation analysis: Status of unknown parameters and future systematic challenges for ORCA and PINGU

Within the standard 3ν oscillation framework, we illustrate the status of currently unknown oscillation parameters: the θ23 octant, the mass hierarchy (normal or inverted), and the possible CP-violating phase δ, as derived by a (preliminary) global analysis of oscillation data available in 2015. We then discuss some challenges that will be faced by future, high-statistics analyses of spectral data, starting with one-dimensional energy spectra in reactor experiments, and concluding with two-dimensional energy-angle spectra in large-volume atmospheric experiments. It is shown that systematic uncertainties in the spectral shapes can noticeably affect the prospective sensitivities to unknown oscillation parameters, in particular to the mass hierarchy.

A strain measurement model using a limited number of sensors for steel beam structures subjected to uncertain loadings

The maximum stress of a structural member has been extensively adopted as a safety assessment indicator in structural health monitoring. Due to construction errors in the field and changes in the loading conditions during or after construction, it is impractical to accurately predict the location and magnitude of the maximum strain of a member a priori. To avoid the dependency of strain sensing methods on information of the structural and loading conditions, this paper proposes a strain distribution measurement model for steel beam structures subjected to uncertain loadings with uncertainties in magnitudes and shapes. With strains measured from a limited number of sensors, a general form equation of the strain distribution is determined for the estimation of the strain distribution. The performance of the strain distribution measurement model is verified by comparing estimated strain values from the proposed method and measured strains directly from fiber Bragg grating sensors or electrical strain gauges during static loading tests on single- and multi-span beam structures.

Development and characterisation of a state-of-the-art GOME-2 formaldehyde air-mass factor algorithm

Abstract. Space-borne observations of formaldehyde (HCHO) are frequently used to derive surface emissions of isoprene, an important biogenic volatile organic compound. The conversion of retrieved HCHO slant column concentrations from satellite line-of-sight measurements to vertical columns is determined through application of an air mass factor (AMF), accounting for instrument viewing geometry, radiative transfer, and vertical profile of the absorber in the atmosphere. This step in the trace gas retrieval is subject to large errors. This work presents the AMF algorithm in use at the University of Leicester (UoL), which introduces scene-specific variables into a per-observation full radiative transfer AMF calculation, including increasing spatial resolution of key environmental parameter databases, input variable area weighting, instrument-specific scattering weight calculation, and inclusion of an ozone vertical profile climatology. Application of these updates to HCHO slant columns from the GOME-2 instrument is shown to typically adjust the AMF by ±20 %, compared to a reference algorithm without these advanced parameterisations. On average the GOME-2 AMFs increase by 4 %, with over 70 % of locations having an AMF of 0–20 % larger than originally, largely resulting from the use of the latest GOME-2 reflectance product. Furthermore, the new UoL algorithm also incorporates a full radiative transfer error calculation for each scene to help characterise AMF uncertainties. Global median AMF errors are typically 50–60 %, and are driven by uncertainties in the HCHO profile shape and its vertical distribution relative to clouds and aerosols. If uncertainty on the a priori HCHO profile is relatively small (< 10 %) then the median AMF total error decreases to about 30–40 %.

Dexterous grasping under shape uncertainty

An important challenge in robotics is to achieve robust performance in object grasping and manipulation, dealing with noise and uncertainty. This paper presents an approach for addressing the performance of dexterous grasping under shape uncertainty. In our approach, the uncertainty in object shape is parametrized and incorporated as a constraint into grasp planning. The proposed approach is used to plan feasible hand configurations for realizing planned contacts using different robotic hands. A compliant finger closing scheme is devised by exploiting both the object shape uncertainty and tactile sensing at fingertips. Experimental evaluation demonstrates that our method improves the performance of dexterous grasping under shape uncertainty.

Crucial problems in the design of a terahertz tripler

A frequency-multiplied source at the terahertz band using discrete planar Schottky diodes, which is a critical element in heterodyne instruments, has been studied by some domestic research institutions in recent years. Besides the design method, there are still many crucial problems that must be taken into consideration in the design. This article mainly discuss three aspects based on the measured data of a 225 GHz tripler that we designed. Firstly, the accuracy of the diode model concerns the reliability of the simulation results. According to the Spice parameters and the measured results, the physical size and the DC parameter of the Schottky diode can be corrected until there is a good consistency between the simulated and measured results. Secondly, the heat accumulation happens to the Schottky junction when the high input power is added. A steady-state thermal simulation is done and the results show that the hottest temperature is about 140 °C with 250 mW input power, which is safe to the diode. Lastly, some non-ideal factors are brought during the assembly process such as the uncertainty in the conductive adhesive shape and location deviation of the circuit. Furthermore, the effect on the performance of the frequency multiplier is calculated in this work.

PINGU and the neutrino mass hierarchy: Statistical and systematic aspects

The proposed PINGU project (Precision IceCube Next Generation Upgrade) is expected to collect $O({10}^{5})$ atmospheric muon and electron neutrino events in a few years of exposure, and to probe the neutrino mass hierarchy through its imprint on the event spectra in energy and direction. In the presence of non-negligible and partly unknown shape systematics, the analysis of high-statistics spectral variations will face subtle challenges that are largely unprecedented in neutrino physics. We discuss these issues both on general grounds and in the currently envisaged PINGU configuration, where we find that possible shape uncertainties at the (few) percent level can noticeably affect the sensitivity to the hierarchy. We also discuss the interplay between the mixing angle ${\ensuremath{\theta}}_{23}$ and the PINGU sensitivity to the hierarchy. Our results suggest that more refined estimates of spectral uncertainties are needed in next-generation, large-volume atmospheric neutrino experiments.

Category-based task specific grasping

The problem of finding stable grasps has been widely studied in robotics. However, in many applications the resulting grasps should not only be stable but also applicable for a particular task. Task-specific grasps are closely linked to object categories so that objects in a same category can be often used to perform the same task. This paper presents a probabilistic approach for task-specific stable grasping of objects with shape variations inside the category. An optimal grasp is found as a grasp that is maximally likely to be task compatible and stable taking into account shape uncertainty in a probabilistic context. The method requires only partial models of new objects for grasp generation and only few models and example grasps are used during the training stage. The experiments show that the approach can use multiple models to generalize to new objects in that it outperforms grasping based on the closest model. The method is shown to generate stable grasps for new objects belonging to the same class as well as for similar in shape objects of different categories.

Handling uncertainties in background shapes: the discrete profiling method

A common problem in data analysis is that the functional form, as well as the parameter values, of the underlying model which should describe a dataset is not known a priori. In these cases some extra uncertainty must be assigned to the extracted parameters of interest due to lack of exact knowledge of the functional form of the model. A method for assigning an appropriate error is presented. The method is based on considering the choice of functional form as a discrete nuisance parameter which is profiled in an analogous way to continuous nuisance parameters. The bias and coverage of this method are shown to be good when applied to a realistic example.

Cloud-Based Grasp Analysis and Planning for Toleranced Parts Using Parallelized Monte Carlo Sampling

This paper considers grasp planning in the presence of shape uncertainty and explores how cloud computing can facilitate parallel Monte Carlo sampling of combination actions and shape perturbations to estimate a lower bound on the probability of achieving force closure. We focus on parallel-jaw push grasping for the class of parts that can be modeled as extruded 2-D polygons with statistical tolerancing. We describe an extension to model part slip and experimental results with an adaptive sampling algorithm that can reduce sample size by 90%. We show how the algorithm can also bound part tolerance for a given grasp quality level and report a sensitivity analysis on algorithm parameters. We test a cloud-based implementation with varying numbers of nodes, obtaining a 515 × speedup with 500 nodes in one case, suggesting the algorithm can scale linearly when all nodes are reliable. Code and data are available at: http://automation.berkeley.edu/cloud-based-grasping.

A note on the uncertainty in tsunami shape for estimation of its run-up heights

In practice, when tsunami approaches the coast and the time for decision making and issuing warning alert is limited, design formulas for fast estimation of tsunami run-up characteristics are applied. The most famous and the most used among them assume that incoming wave has a solitonic shape. However, the exact shape of the incoming wave is usually unknown. This is why it is important to know the error caused by the wave shape uncertainty. In this paper, we discuss how the uncertainty of the incoming wave shape influences its run-up characteristics in different bays. Two typical beach geometries: plane beach and U-shaped bay are considered.

確率有限要素法による形状不確定性を考慮した構造解析手法について

A new method of structural analysis is proposed for the solution of problems of response uncertainty for the case that involves uncertainty in shape. The method makes use of a Hermite polynomial chaos expansion of the process. The proposed method involves a mathematical formulation which is a natural extension of the deterministic finite element concept to the space of random functions. In this paper, two example problems are investigated by the new method, i.e., a plate with a circular hole at the center and a cruciform weld joint. Then accuracy of the analysis will be discussed for different size of a plate with a circular hole. The validity of a new method of structural analysis is discussed using a result of uncertainty analysis through a Monte-Carlo simulation by solution of the deterministic problems.

Stochastic modal models of slender uncertain curved beams preloaded through clamping

This paper addresses the stochastic modeling of the stiffness matrix of slender uncertain curved beams that are forced fit into a clamped–clamped fixture designed for straight beams. Because of the misfit with the clamps, the final shape of the clamped–clamped beams is not straight and they are subjected to an axial preload. Both of these features are uncertain given the uncertainty on the initial, undeformed shape of the beams and affect significantly the stiffness matrix associated with small motions around the clamped–clamped configuration. A modal model using linear modes of the straight clamped–clamped beam with a randomized stiffness matrix is employed to characterize the linear dynamic behavior of the uncertain beams. This stiffness matrix is modeled using a mixed nonparametric–parametric stochastic model in which the nonparametric (maximum entropy) component is used to model the uncertainty in final shape while the preload is explicitly, parametrically included in the stiffness matrix representation. Finally, a maximum likelihood framework is proposed for the identification of the parameters associated with the uncertainty level and the mean model, or part thereof, using either natural frequencies only or natural frequencies and mode shape information of the beams around their final clamped–clamped state. To validate these concepts, three simulated, computational experiments were conducted within Nastran to produce populations of natural frequencies and mode shapes of uncertain slender curved beams after clamping. The three experiments differed from each other by the nature of the clamping condition in the in-plane direction. One experiment assumed a no-slip condition (zero in-plane displacement), another a perfect slip (no in-plane force), while the third one invoked friction. The first two experiments gave distributions of frequencies with similar features while the latter one yielded a strong deterministic dependence of the frequencies on each other, a situation observed and explained recently and thus not considered further here. Then, the application of the stochastic modeling concepts to the no-slip simulated data was carried out and led to a good matching of the probability density functions of the natural frequencies and the modal components, even though this information was not used in the identification process. These results strongly suggest the applicability of the proposed stochastic model.

Granular robust mean-CVaR feedstock flow planning for waste-to-energy systems under integrated uncertainty.

In the context of robust optimization with information granules for distributional parameters, this paper investigates a two-stage waste-to-energy feedstock flow planning problem with uncertain capacity expansion costs. The objective is to minimize the worst-case overall loss in a mean-risk criterion where the risk is measured by a conditional value-at-risk operator. As a salient feature, an integrated uncertainty is considered which consists of not only the uncertainty in distribution shapes of the uncertain variables, but also the manifold uncertainties of the mean parameters. To tackle the robust optimization under such integrated uncertainty, we first discuss a distributional robust two-stage feedstock flow planning model with precise mean parameters that handles the uncertainty in distribution shape, and the model can be equivalently transformed into a linear program (LP). Furthermore, the precise-mean-based robust model is extended into the case of multifaceted uncertainty for mean-parameters that are allowed to assume intervals, historical-data-based probabilistic estimates, and/or human-knowledge-centric fuzzy set estimates, under different circumstances. These multifaceted uncertain mean-parameters are uniformly represented by using information granules, and a granular robust optimization model is then developed which maximizes the robustness of the solution within a shortfall tolerance, and realizes a tradeoff between the solution conservativeness and robustness. It is showed that the granular robust model is equivalent to solving a series of LPs and can be efficiently handled by a nested binary search algorithm. Finally, the computational study illustrates the model performance, solution analysis, and underlines a much higher scalability of the developed robust model compared to the stochastic programming approach.

Neutrino mass hierarchy and electron neutrino oscillation parameters with one hundred thousand reactor events

Proposed medium-baseline reactor neutrino experiments offer unprecedented opportunities to probe, at the same time, the mass-mixing parameters which govern $\nu_e$ oscillations both at short wavelength (delta m^2 and theta_{12}) and at long wavelength (Delta m^2 and theta_{13}), as well as their tiny interference effects related to the mass hierarchy (i.e., the relative sign of Delta m^2 and delta m^2). In order to take full advantage of these opportunities, precision calculations and refined statistical analyses of event spectra are required. In such a context, we revisit several input ingredients, including: nucleon recoil in inverse beta decay and its impact on energy reconstruction and resolution, hierarchy and matter effects in the oscillation probability, spread of reactor distances, irreducible backgrounds from geoneutrinos and from far reactors, and degeneracies between energy scale and spectrum shape uncertainties. We also introduce a continuous parameter alpha, which interpolates smoothly between normal hierarchy (alpha=+1) and inverted hierarchy (alpha=-1). The determination of the hierarchy is then transformed from a test of hypothesis to a parameter estimation, with a sensitivity given by the distance of the true case (either alpha=+1 or alpha=-1) from the undecidable case (alpha=0). Numerical experiments are performed for the specific set up envisaged for the JUNO project, assuming a realistic sample of O(10^5) reactor events. We find a typical sensitivity of ~2 sigma to the hierarchy in JUNO, which, however, can be challenged by energy scale and spectrum shape systematics, whose possible conspiracy effects are investigated. The prospective accuracy reachable for the other mass-mixing parameters is also discussed.