scholarly journals Method and Algorithm for Estimating the Maximum Total Error of an Automotive LiDAR

2021 ◽  
Vol 2096 (1) ◽  
pp. 012179
Author(s):  
M A Romanova ◽  
M V Mamchenko
Keyword(s):  
Mathematical Model ◽  
Measurement Accuracy ◽  
Total Error ◽  
Weighted Average ◽  
Systematic Errors ◽  
Average Error ◽  
Generic Model ◽  
Technical Device ◽  
Technical Measurement ◽  
The Given

Abstract The article proposes a method and an appropriate algorithm for estimating the error of the measurements of the LiDAR as a technical measurement system to “include” this evaluation in the given accuracy. A generic model for the LiDAR’s measurements is described, a mathematical model of the measurements with the total values of random and systematic errors is given. Based on this method the algorithm for estimating the maximum total error (not exceeding the accuracy of the measurement) is formed. The algorithm complies both with the mathematical description presented in the article, and the methodology described in Russian standard GOST R 8.736-2011. On the basis of the calculated estimate of the weighted average error, it is possible to construct a technical device, that provides a three-fold reserve in terms of measurement accuracy.

scholarly journals A Chi-Squared Analysis of the Measurements of Two Cosmological Parameters over Time

Universe ◽  
2020 ◽  
Vol 6 (8) ◽  
pp. 114
Author(s):  
Timothy Faerber ◽  
Martín López-Corredoira
Keyword(s):  
Cosmological Parameters ◽  
Weighted Average ◽  
Statistical Error ◽  
Systematic Errors ◽  
Chi Squared ◽  
Data Points ◽  
Standard Cosmological Model ◽  
Linear Fit ◽  
Error Bars ◽  
The Given

The aim of this analysis was to determine whether or not the given error bars truly represented the dispersion of values in a historical compilation of two cosmological parameters: the amplitude of mass fluctuations (σ8) and Hubble’s constant (H0) parameters in the standard cosmological model. For this analysis, a chi-squared test was executed on a compiled list of past measurements. It was found through analysis of the chi-squared (χ2) values of the data that for σ8 (60 data points measured between 1993 and 2019 and χ2 between 182.4 and 189.0) the associated probability Q is extremely low, with Q=1.6×10−15 for the weighted average and Q=8.8×10−15 for the best linear fit of the data. This was also the case for the χ2 values of H0 (163 data points measured between 1976 and 2019 and χ2 between 480.1 and 575.7), where Q=1.8×10−33 for the linear fit of the data and Q=1.0×10−47 for the weighted average of the data. The general conclusion was that the statistical error bars associated with the observed parameter measurements have been underestimated or the systematic errors were not properly taken into account in at least 20% of the measurements. The fact that the underestimation of error bars for H0 is so common might explain the apparent 4.4σ discrepancy formally known today as the Hubble tension.

scholarly journals Computer Modeling of Aerosol Emissions Spread in the Atmosphere

2019 ◽  
Vol 97 ◽  
pp. 05023 ◽  
Author(s):  
Daler Sharipov ◽  
Sharofiddin Aynakulov ◽  
Otabek Khafizov
Keyword(s):  
Boundary Layer ◽  
Mathematical Model ◽  
Atmospheric Boundary Layer ◽  
Computer Modeling ◽  
Numerical Experiments ◽  
Climatic Factors ◽  
Numerical Algorithms ◽  
Aerosol Emissions ◽  
The Given ◽  
And Diffusion

The paper deals with the development of mathematical model and numerical algorithms for solving the problem of transfer and diffusion of aerosol emissions in the atmospheric boundary layer. The model takes into account several significant parameters such as terrain relief, characteristics of underlying surface and weather-climatic factors. A series of numerical experiments were conducted based on the given model. The obtained results presented here show how these factors affect aerosol emissions spread in the atmosphere.

scholarly journals On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
S. M. Al-Mekhlafi ◽  
A. O. Albalawi ◽  
D. Baleanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Weighted Average ◽  
Necessary Optimality Conditions ◽  
Numerical Approach ◽  
Population Number ◽  
Infected People ◽  
The Stability ◽  
Novel Coronavirus ◽  
Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

Transit Network Frequency Setting With Multi-Agent Simulation to Capture Activity-Based Mode Substitution

2021 ◽  
pp. 036119812110569
Author(s):  
Ziyi Ma ◽  
Joseph Y. J. Chow
Keyword(s):  
Large Scale ◽  
Operating Cost ◽  
Weighted Average ◽  
Average Error ◽  
Substitution Effects ◽  
Transit Network ◽  
Agent Simulation ◽  
Bus Network ◽  
Upper Level ◽  
Route Cost

We propose a bilevel transit network frequency setting problem in which the upper level consists of analytical route cost functions and the lower level is an activity-based market equilibrium derived using MATSim-NYC. The use of MATSim in the lower-level problem incorporates sensitivity of the design process to competition from other modes, including ride-hail, and can support large-scale optimization. The proposed method is applied to the existing Brooklyn bus network, which includes 78 bus routes, 650,000 passengers per day, 550 route-km, and 4,696 bus stops. MATSim-NYC modeling of the existing bus network has a ridership-weighted average error per route of 21%. The proposed algorithm is applied to a benchmark network and confirms their predicted 20% growth in ridership using their benchmark design. Applying our proposed algorithm to their network with 78 routes and 24 periods, we have a problem with 3,744 decision variables. The algorithm converged within 10 iterations to a delta of 0.064%. Compared with the existing scenario, we increased ridership by 20% and reduced operating cost by 25%. We improved the farebox recovery ratio from the existing 0.22 to 0.35, 0.06 more than the benchmark design. Analysis of mode substitution effects suggest that 2.5% of trips would be drawn from ride-hail while 74% would come from driving.

scholarly journals Mathematical Model to Optimize Production of Loading-Unloading Operations on the Vessel

2020 ◽  
pp. 29-30
Author(s):  
Ibraim Didmanidze ◽  
Givi Tsitskishvili
Keyword(s):  
Mathematical Model ◽  
Decision Making ◽  
Coming Out ◽  
Scientific Work ◽  
Equal Strength ◽  
Optimal Classification ◽  
A Priority ◽  
The Given

In scientific work it is shown, that our goal is to choose the desired option from variety of alternatives (in our case different options of loading-unloading operations on the vessel) or to take decision which is the best (optimal). Classification in this case is the grounds, as taking the choice is based on choosing certain class, which can be assigned to an alternative. Stratification and rating gives us wide option to make reasonable selection, or to take a kind of decision which will be optimal for the certain moment and occasion. These methods can be used with equal strength at all stages of the processes taking place in the area of current decision making management. This refers to the object of our study of course – solution of selecting optimal option to optimize loading-unloading operation on the vessel. It goes without saying that variety of alternatives doesn’t have any structure, thus abundance of each element was never structured randomly retrieved or no consideration has been proposed, and they are not a priority and in any order. Coming out of this it’s impossible to mention which alternative is better and which is less desirable. In order to solve the task of selecting a set of alternatives successfully, it is necessary, to make structure of the given abundance of alternatives in any form.

scholarly journals Time Coordination of Periodic Passenger Train Connections in Conditions of Single-Track Lines

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Filip Lorenz ◽  
Vit Janos ◽  
Dusan Teichmann ◽  
Michal Dorda
Keyword(s):  
Mathematical Model ◽  
Mathematical Programming ◽  
Real Data ◽  
Real Problem ◽  
Single Track ◽  
Railway Stations ◽  
Optimization Software ◽  
Proposed Model ◽  
The Individual ◽  
The Given

The article addresses creation of a mathematical model for a real problem regarding time coordination of periodic train connections operated on single-track lines. The individual train connections are dispatched with a predefined tact, and their arrivals at and departures to predefined railway stations (transfer nodes) need to be coordinated one another. In addition, because the train connections are operated on single-track lines, trains that pass each other in a predefined railway stations must be also coordinated. To optimize the process, mathematical programming methods are used. The presented article includes a mathematical model of the given task, and the proposed model is tested with real data. The calculation experiments were implemented using optimization software Xpress-IVE.

Signal Sampling and Accuracy Analysis of Large Gear’s Angular Displacement Measuring its Deviation On-Machine

2011 ◽  
Vol 189-193 ◽  
pp. 4201-4204
Author(s):  
Jia Qi Jin ◽  
Hui Li
Keyword(s):  
Measurement Accuracy ◽  
Angular Displacement ◽  
Total Error ◽  
Measuring Method ◽  
Displacement Measurement ◽  
Signal Acquisition ◽  
Accuracy Analysis ◽  
Friction Disc ◽  
Large Gear ◽  
Circular Grating

To solve the critical problem of large gear deviation on-machine: angle displacement measurement that is how to get signal acquisition and accuracy analysis of angle displacement. A new measuring method is proposed, which applies the dividing mechanism (it is composed of friction disc and circular grating) to ensure index and pick up signal of gear corner correctly and strictly according to the principle of angular displacement measurement. Furthermore, the main error which affects measurement accuracy is analyzed, and accuracy is analyzed with geometrical theory such as Fourier series and error synthesis principle etc. The experimental results indicate that angel dividing and signal samplings are easier and more efficient by the dividing mechanism, furthermore, the accuracy is in the range of total error that is permitted by verification, and the mechanism can also meet the requirement of high accuracy, so the method is significance that assessing transmission accuracy of involutes gear.

Determination of a Loading Pressure in the Metal Forming by the Given Movements

2013 ◽  
Vol 842 ◽  
pp. 494-499 ◽  
Author(s):  
Evgenii V. Murashkin ◽  
Marina V. Polonik
Keyword(s):  
Mathematical Model ◽  
Metal Forming ◽  
External Pressure ◽  
Stress Changes ◽  
The Given

We propose a mathematical model of large elastocreep deformations. As part of the constructed mathematical model the problem of deformation of the material in the vicinity of microdefect was solved. Integro-differential dependence of external pressure from irreversible deformations and displacements was obtained. The laws of loading material from vector displacements were calculated. We have shown that the monotonous laws of deformation can lead to non-monotonous stress changes.

scholarly journals The Differential Astrometric Reference Frame on short timescales in the Gaia Era

2017 ◽  
Vol 12 (S330) ◽  
pp. 79-80
Author(s):  
Ummi Abbas ◽  
Beatrice Bucciarelli ◽  
Mario G. Lattanzi ◽  
Mariateresa Crosta ◽  
Mario Gai ◽  
...  
Keyword(s):  
Reference Frame ◽  
Large Scale ◽  
Total Error ◽  
Systematic Errors ◽  
Field Of View ◽  
Small Field ◽  
Inertial Reference Frame ◽  
Error Budget ◽  
G 14 ◽  
High Cadence

AbstractWe use methods of differential astrometry to construct a small field inertial reference frame stable at the micro-arcsecond level. Using Gaia measurements of field angles we look at the influence of the number of reference stars and the stars magnitude as well as astrometric systematics on the total error budget with the help of Gaia-like simulations around the Ecliptic Pole in a differential astrometric scenario. We find that the systematic errors are modeled and reliably estimated to the μas level even in fields with a modest number of 37 stars with G <13 mag over a 0.24 sq. degrees field of view for short timescales of the order of a day for a perfect instrument and with high-cadence observations. Accounting for large-scale calibrations by including the geometric instrument model over such short timescales requires fainter stars down to G=14 mag without diminishing the accuracy of the reference frame.

Error sources and models of the laser tracker without a beam steering mirror

2021 ◽  
Author(s):  
Radoslav Choleva ◽  
Alojz Kopáčik
Keyword(s):  
Measurement Accuracy ◽  
Beam Steering ◽  
Systematic Errors ◽  
Error Modeling ◽  
Laser Tracker ◽  
High Demand ◽  
Error Sources ◽  
Error Models ◽  
Measurement Results

AbstractThe laser tracker is a widely used instrument in many industrial and metrological applications with high demand measurement accuracy. Imperfections in construction and misalignment of individual parts deliver systematic errors in the measurement results. All error sources need to be identified and reduced to the minimum to achieve the best possible accuracy. The paper summarizes error sources of the laser tracker without beam steering mirror with emphasis on error modeling. Descriptions of error models are provided for the static and kinematic type of measurement.

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