NUMERICAL VALIDATION OF PROBABILISTIC LAWS TO EVALUATE FINITE ELEMENT ERROR ESTIMATES

We propose a numerical validation of a probabilistic approach applied to estimate the relative accuracy between two Lagrange finite elements Pk and Pm,(k < m). In particular, we show practical cases where finite element Pk gives more accurate results than finite element Pm. This illustrates the theoretical probabilistic framework we recently derived in order to evaluate the actual accuracy. This also highlights the importance of the extra caution required when comparing two numerical methods, since the classical results of error estimates concerns only the asymptotic convergence rate.

Determination of error of sector location of subterrene stabilizing section based on coordinate control data

Results of the study of actual accuracy of the stabilizing section shell of the prototype subterrene are presented. The problem of experimental verification of the assumptions made in modeling is formulated. The research described in the article was carried out on the basis of experimental data obtained by coordinate control of the shell of the prototype subterrene. Data analysis was carried out by mathematical modeling of the surface of the shell of the stabilizing section as a whole and the surfaces of each individual sector. The obtained mathematical models are based on the approximation of sets of points obtained in the process of coordinate control by cylindrical surfaces. The article shows that at least a significant part of the deviations of the geometric shape of the section shell (from 30.3 to 52.3%) is explained by errors in the location of the sectors and errors in their radii. On the basis of the performed modeling, absolute values of the corresponding errors and actual values of the dimensions and deviations were determined. Studies confirmed the possibility of ensuring the specified accuracy of the shell surface when implementing the assembly technology used in a pilot production. At the same time, the proximity of actual deviations to maximum permissible values can lead to problems in ensuring the stable quality of subterrene case products in mass production. Correlation analysis of coordinate control data and statistical analysis of the series of residuals of developed models were carried out. Correlation analysis confirmed the dependence of deviations of experimental points on their cylindrical coordinates, which confirms the significance of the error in the location of the sectors in deviations from the geometric accuracy of the shell.

Shifted Sobol points and multigrid Monte Carlo simulation

Multidimensional integrals arise in many problems of physics. For example, moments of the distribution function in the problems of transport of various particles (photons, neutrons, etc.) are 6-dimensional integrals. When calculating the coefficients of electrical conductivity and thermal conductivity, scattering integrals arise, the dimension of which is equal to 12. There are also problems with a significantly large number of variables. The Monte Carlo method is the most effective method for calculating integrals of such a high multiplicity. However, the efficiency of this method strongly depends on the choice of a sequence that simulates a set of random numbers. A large number of pseudo-random number generators are described in the literature. Their quality is checked using a battery of formal tests. However, the simplest visual analysis shows that passing such tests does not guarantee good uniformity of these sequences. The magic Sobol points are the most effective for calculating multidimensional integrals. In this paper, an improvement of these sequences is proposed: the shifted magic Sobol points that provide better uniformity of points distribution in a multidimensional cube. This significantly increases the cubature accuracy. A significant difficulty of the Monte Carlo method is a posteriori confirmation of the actual accuracy. In this paper, we propose a multigrid algorithm that allows one to find the grid value of the integral simultaneously with a statistically reliable accuracy estimate. Previously, such estimates were unknown. Calculations of representative test integrals with a high actual dimension up to 16 are carried out. The multidimensional Weierstrass function, which has no derivative at any point, is chosen as the integrand function. These calculations convincingly show the advantages of the proposed methods.

STUDY OF MEASUREMENT SYSTEM ACCURACY OF OPEN PIT SIDES DISPLACEMENT ON THE EXAMPLE OF 3DRADARGROUNDPROBESSR-XT

The article considers the modern technology of interferometric measurementsfor the purposes of open pit sides geotechnical monitoring, based on the use of 3D radar Ground Probe SSR-XT. Experimental research of measurement accuracy of the given equipment was performed. The results of the mentioned research state the actual accuracy of interferometric measurement method.The optimal application of this method for studying the sides of quarries is described. With the interferometric measurement method for geotechnical monitoring of the sides of quarries under development, there is no need to install deformation marks, which simplifies the work process. With traditional methods, it is necessary to install such marks, which increases security risks for the performers of geotechnical monitoring.

Analysis of Situational Awareness for Online Taxibike Driver in Yogyakarta Using QUASA Analysis

Online taxibike servicehas its own charm because it is a new breakthrough for current conditions that make it easy for consumers to order a vehicle. Riding a motorcycle is an activity that requires awareness against road conditions that are dynamic and can change in seconds. This study aims to determine the level of awareness of online taxibikedriver when using a GPS and non GPS. The method used in this research is the QUASA method which combines the probing method in the situational awareness process with the self rating method. The results of data processing obtained that the value of actual accuracy and perceived accuracy when online taxibikedriver uses a GPS is greater than non GPS. In addition, other results stated that the level of awareness of online taxibikedriver when using a GPS was 4.7% greater than when without non GPS.

The Elephant in the Machine: Proposing a New Metric of Data Reliability and its Application to a Medical Case to Assess Classification Reliability

In this paper, we present and discuss a novel reliability metric to quantify the extent a ground truth, generated in multi-rater settings, as a reliable basis for the training and validation of machine learning predictive models. To define this metric, three dimensions are taken into account: agreement (that is, how much a group of raters mutually agree on a single case); confidence (that is, how much a rater is certain of each rating expressed); and competence (that is, how accurate a rater is). Therefore, this metric produces a reliability score weighted for the raters’ confidence and competence, but it only requires the former information to be actually collected, as the latter can be obtained by the ratings themselves, if no further information is available. We found that our proposal was both more conservative and robust to known paradoxes than other existing agreement measures, by virtue of a more articulated notion of the agreement due to chance, which was based on an empirical estimation of the reliability of the single raters involved. We discuss the above metric within a realistic annotation task that involved 13 expert radiologists in labeling the MRNet dataset. We also provide a nomogram by which to assess the actual accuracy of a classification model, given the reliability of its ground truth. In this respect, we also make the point that theoretical estimates of model performance are consistently overestimated if ground truth reliability is not properly taken into account.

Collective communication and behaviour in response to uncertain ‘Danger’ in network experiments

In emergencies, social coordination is especially challenging. People connected with each other may respond better or worse to an uncertain danger than isolated individuals. We performed experiments involving a novel scenario simulating an unpredictable situation faced by a group in which 2480 subjects in 108 groups had to both communicate information and decide whether to ‘evacuate’. We manipulated the permissible sorts of interpersonal communication and varied group topology and size. Compared to groups of isolated individuals, we find that communication networks suppress necessary evacuations because of the spontaneous and diffuse emergence of false reassurance; yet, communication networks also restrain unnecessary evacuations in situations without disasters. At the individual level, subjects have thresholds for responding to social information that are sensitive to the negativity, but not the actual accuracy, of the signals being transmitted. Social networks can function poorly as pathways for inconvenient truths that people would rather ignore.

APPLYING SMARTPHONES FOR POSITIONING IN THE MIDDLE OF THE ROOM

The article deals with the problem of navigating indoors in conditions of satellite signal unavailability. In this case, alternative sources of positioning are used to determine the location of the objects. Use for navigation tasks inside the premises of the smartphone allows you to get comprehensive data on its operation. To solve the problem of navigation, the most important elements of the data sets is the unique identifier of the monitored device and the relative power level of the signal received from it. The data of the calculations and experiments show that the navigation measurements with the help of smartphones allow to qualitatively solve the problem of observation at given distances between sensors not exceeding 5-7 meters. The relative position of the sensors and the moving objects is important. At a distance of 5 m from the beacons and the object, the actual accuracy of the object coordinates is 1-2 m, which is sufficient for traditional navigation tasks in the middle of buildings.

Quantifying Actual and Perceived Inaccuracy When Estimating the Sugar, Energy Content and Portion Size of Foods

In order to adhere to dietary guidelines and manage health risks, consumers need to be able to estimate with some accuracy the sugar and energy content of foods. The present study compared how well participants could estimate the sugar and energy content of foods, the weight of foods, and approximate portion size (using a hand measure estimation aid). The study had three aims. First, it aimed to investigate differences in accuracy across the four measures. Second, it aimed to examine whether these differences in accuracy between estimation measures were accurately perceived by the participants. Third, it aimed to test if estimation accuracy was related to food journaling experience, body-mass index or gender. One hundred and ninety-seven participants took part in an estimation task and filled in a questionnaire. While the participants were inaccurate when using all four estimation measures, inaccuracy was most pronounced for sugar content (ds ≥ 0.39), which was consistently overestimated by between 62.1% and 98.5% of the sample. None of the other measures showed a consistent pattern of under- or overestimation. Participants’ perceived accuracy did not match their actual accuracy (rs ≤ |0.20|, ps ≥ 0.005). Actual accuracy showed only marginal covariation with food journaling experience (ts ≤ 2.01, ps ≥ 0.049, ds ≤ 0.14), body-mass index (rs ≤ |0.15|, ps ≥ 0.041) or gender (ts ≤ 3.17, ps ≥ 0.002, ds ≤ 0.46). It is particularly challenging for consumers to estimate the sugar content of food, which might have negative consequences for health and well-being. Thus, more education about sugar content and misperceptions is needed to support consumers so that they can make healthy food choices.