Uncertainty Analysis of Planar Robots With Joint Clearance

1998 ◽  
Author(s):  
Jianmin Zhu ◽  
Kwun-Lon Ting
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Distribution Functions ◽  
Joint Clearance ◽  
Performance Quality ◽  
The Impact ◽  
Random Nature ◽  
Deviation Zone ◽  
Planar Robots

Abstract Joint clearance in mechanisms and robots leads to uncertainty in function deviation. Unlike the impact of the link tolerance on the performance quality, the uncertain effect of the joint clearance to the performance can not be eliminated by calibration because of the random nature. In this paper, based on the probability theory, a general probability density function for the output of planar robots is established for any probability density function of joint clearance. The result is demonstrated by a uniform distribution in the joint clearance and a table of the resulting functions is presented. These distribution functions and the table provide a convenient way to obtain the probability value for a planar robot to position its end point within a desired deviation zone and to determine the joint clearance value based on the concerned shape of tolerance zone and the specified probability value of repeatability.

scholarly journals Noise Propagation in Multiple-Input ADC-Based Measurement Systems

2014 ◽  
Vol 14 (6) ◽  
pp. 302-307 ◽  
Author(s):  
Diego Bellan
Keyword(s):  
Vector Field ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Amplitude Spectrum ◽  
Field Amplitude ◽  
Noise Levels ◽  
Statistical Characterization ◽  
Multiple Input ◽  
The Impact

Abstract In this paper, the complete statistical characterization of the amplitude spectrum at the output of a multiple-input ADC-based measurement system is derived under the assumption of input channels with different noise levels. In practical applications the input channels correspond to the spatial components of a vector field (e.g., magnetic/electric field). Each output spectral line represents the amplitude of the vector field at a specific frequency. Such amplitude is a random variable depending on the noise levels (internal and external noise) of the input channels. Closed form analytical solution for the probability density function of the vector field amplitude is not available in the mathematical literature under the hypothesis of different noise levels. Therefore, an analytical expression for the probability density function is derived on the basis of a Laguerre series expansion. The impact of the kind of time window, the sampling frequency, and the number of samples is clearly derived and put into evidence. Approximate analytical expressions for the mean value and the variance of the vector field amplitude are also provided. Analytical results are validated by means of numerical simulations.

scholarly journals The Impact of Land–Atmosphere Interactions on the Temporal Variability of Soil Moisture at the Regional Scale

2005 ◽  
Vol 6 (1) ◽  
pp. 53-67 ◽  
Author(s):  
John P. Kochendorfer ◽  
Jorge A. Ramírez
Keyword(s):  
Differential Equation ◽  
Soil Moisture ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Temporal Variability ◽  
Regional Scale ◽  
Precipitation Efficiency ◽  
Precipitation Recycling ◽  
The Impact

Abstract This study examines the impact of the nonlinear dynamics of soil-moisture feedbacks to precipitation on the temporal variability of soil moisture at the regional scale. It is a modeling study in which the large-scale soil-water balance is first formulated as an ordinary differential equation and then recast as a stochastic differential equation by incorporating colored noise representing the high-frequency temporal variability and correlation of precipitation. The underlying model couples the atmospheric and surface-water balances and accounts for both precipitation recycling and precipitation-efficiency feedbacks, which arise from the surface energy balance. Based on the governing Fokker–Planck equation, three different analytical solutions (corresponding to differing forms and combinations of feedbacks) are derived for the steady-state probability density function of soil moisture. Using NCEP–NCAR reanalysis data, estimates of potential evapotranspiration, and long-term observations of precipitation, streamflow, and soil moisture, the model is parameterized for a 5° × 5° region encompassing the state of Illinois. It is shown that precipitation-efficiency feedbacks can be significant contributors to the variability of soil moisture at the regional scale. Precipitation recycling, on the other hand, increases the variability by a negligible amount. For all feedback cases, the probability density function is unimodal and nearly symmetric. The analysis concludes with an examination of the dependence of the shape of the probability density functions on spatial scale. It is shown that the associated increases in either the correlation time scale or the variance of the noise will produce a bimodal distribution when precipitation-efficiency feedbacks are included. However, the magnitudes of the necessary increases are of an unrealistic magnitude.

Search-Guided Sampling to Reduce Uncertainty of Minimum Deviation Zone Estimation

2007 ◽  
Vol 7 (4) ◽  
pp. 360-371 ◽  
Author(s):  
Ahmad Barari ◽  
Hoda A. ElMaraghy ◽  
George K. Knopf
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Search Method ◽  
Inspection System ◽  
Search Procedure ◽  
Sculptured Surfaces ◽  
Minimum Deviation ◽  
Geometric Deviations ◽  
Deviation Zone

Integrating computational tasks in coordinate metrology and its effect on the inspection’s uncertainty is studied. It is shown that implementation of an integrated inspection system is crucial to reduce the uncertainty in minimum deviation zone (MDZ) estimation. An integrated inspection system based on the iterative search procedure and online MDZ estimation is presented. The search procedure uses the Parzen Windows technique to estimate the probability density function of the geometric deviations between the actual and substitute surfaces. The computed probability density function is used to recognize the critical points in the MDZ estimation and to identify portions of the surface that require further iterative measurements until the desired level of convergence is achieved. Reduction of the uncertainty in the MDZ estimation using the developed search method compared to the MDZ estimations using the traditional sampling methods is demonstrated by presenting experiments including both actual and virtual inspection data. The proposed search method can be used for assessing any geometric deviations when no prior assumptions about the fundamental form and distribution of the underlying manufacturing errors are required. The search method can be used to inspect and evaluate both primitive geometric features and complicated sculptured surfaces. Implementation of this method reduces inspection cost as well as the cost of rejecting good parts or accepting bad parts.

scholarly journals Mixed-Stable Models: An Application to High-Frequency Financial Data

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 739
Author(s):  
Igoris Belovas ◽  
Leonidas Sakalauskas ◽  
Vadimas Starikovičius ◽  
Edward W. Sun
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
High Frequency ◽  
Financial Data ◽  
Stock Index ◽  
Parameter Estimates ◽  
Goodness Of Fit Test ◽  
The Impact ◽  
Stable Models

The paper extends the study of applying the mixed-stable models to the analysis of large sets of high-frequency financial data. The empirical data under review are the German DAX stock index yearly log-returns series. Mixed-stable models for 29 DAX companies are constructed employing efficient parallel algorithms for the processing of long-term data series. The adequacy of the modeling is verified with the empirical characteristic function goodness-of-fit test. We propose the smart-Δ method for the calculation of the α-stable probability density function. We study the impact of the accuracy of the computation of the probability density function and the accuracy of ML-optimization on the results of the modeling and processing time. The obtained mixed-stable parameter estimates can be used for the construction of the optimal asset portfolio.

scholarly journals GTS v1.0: a macrophysics scheme for climate models based on a probability density function

2021 ◽  
Vol 14 (1) ◽  
pp. 177-204
Author(s):  
Chein-Jung Shiu ◽  
Yi-Chi Wang ◽  
Huang-Hsiung Hsu ◽  
Wei-Ting Chen ◽  
Hua-Lu Pan ◽  
...  
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Thermodynamic Parameters ◽  
General Circulation ◽  
Large Scale ◽  
General Circulation Models ◽  
Tropospheric Temperature ◽  
Cloud Water Content ◽  
The Impact

Abstract. Cloud macrophysics schemes are unique parameterizations for general circulation models. We propose an approach based on a probability density function (PDF) that utilizes cloud condensates and saturation ratios to replace the assumption of critical relative humidity (RH). We test this approach, called the Global Forecast System (GFS) – Taiwan Earth System Model (TaiESM) – Sundqvist (GTS) scheme, using the macrophysics scheme within the Community Atmosphere Model version 5.3 (CAM5.3) framework. Via single-column model results, the new approach simulates the cloud fraction (CF)–RH distributions closer to those of the observations when compared to those of the default CAM5.3 scheme. We also validate the impact of the GTS scheme on global climate simulations with satellite observations. The simulated CF is comparable to CloudSat/Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) data. Comparisons of the vertical distributions of CF and cloud water content (CWC), as functions of large-scale dynamic and thermodynamic parameters, with the CloudSat/CALIPSO data suggest that the GTS scheme can closely simulate observations. This is particularly noticeable for thermodynamic parameters, such as RH, upper-tropospheric temperature, and total precipitable water, implying that our scheme can simulate variation in CF associated with RH more reliably than the default scheme. Changes in CF and CWC would affect climatic fields and large-scale circulation via cloud–radiation interaction. Both climatological means and annual cycles of many of the GTS-simulated variables are improved compared with the default scheme, particularly with respect to water vapor and RH fields. Different PDF shapes in the GTS scheme also significantly affect global simulations.

scholarly journals Combustion Characteristics of a Non-Premixed Oxy-Flame Applying a Hybrid Filtered Eulerian Stochastic Field/Flamelet Progress Variable Approach

2019 ◽  
Vol 9 (7) ◽  
pp. 1320 ◽  
Author(s):  
Rihab Mahmoud ◽  
Mehdi Jangi ◽  
Florian Ries ◽  
Benoit Fiorina ◽  
Johannes Janicka ◽  
...  
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Combustion Characteristics ◽  
Combustion Model ◽  
Structure Stability ◽  
Stochastic Field ◽  
Jet Flame ◽  
Progress Variable ◽  
The Impact

The oxidation of methane under oxy-fuel combustion conditions with carbon capture is attractive and deserves huge interest towards reducing CO2 and NOx emissions. The current paper reports on the predictions and analysis of combustion characteristics of a turbulent oxy-methane non-premixed flame operating under highly diluted conditions of CO2 and H2 in oxidizer and fuel streams, respectively. These are achieved by applying a novel, well-designed numerical combustion model. The latter consists of a large eddy simulation (LES) extension of a recently suggested hybrid model in Reynolds averaging-based numerical simulation (RANS) context by the authors. It combines a transported joint scalar probability density function (T-PDF) following the Eulerian Stochastic Field methodology (ESF) on the one hand, and a flamelet progress variable (FPV) turbulent combustion model under consideration of detailed chemical reaction mechanism on the other hand. This novel hybrid ESF/FPV approach removes the weaknesses of the presumed-probability density function (P-PDF)-based FPV modeling, along with the solving of associated additional modeled transport equations while rendering the T-PDF computationally less affordable. First, the prediction capability of the LES hybrid ESF/FPV was appraised on the well-known air-piloted methane jet flame (Sandia Flame D). Then, it was assessed in analyzing the combustion properties of a non-premixed oxy-flame and in capturing the CO2 dilution effect on the oxy-fuel flame behavior. To this end, the so-called oxy-flame B3, already numerically investigated in a RANS context, was analyzed. Comparisons with experimental data in terms of temperature, scalar distributions, and scatter plots agree satisfactorily. Finally, the impact of generating the FPV chemistry table under condition of unity Lewis number, even with CO2 dilution, was investigated on the general prediction of the oxy-fuel flame structure, stability and emissions. In particular, it turns out that 68% molar percentage of CO2 leads to 0.39% of CO formation near the burner fuel nozzle and 0.62% at 10 dfuel above the nozzle.

scholarly journals Partial Histogram Bayes Learning Algorithm for Classification Applications

2018 ◽  
Vol 7 (4.11) ◽  
pp. 126
Author(s):  
Haider O. Lawend ◽  
Anuar M. Muad ◽  
Aini Hussain
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Learning Algorithm ◽  
Gaussian Function ◽  
Real Data ◽  
Distribution Functions ◽  
Factors Affecting ◽  
Probability Distribution Functions ◽  
Large Memory

This paper presents a proposed supervised classification technique namely partial histogram Bayes (PHBayes) learning algorithm. Conventional classifier based on Gaussian function has limitation when dealing with different probability distribution functions and requires large memory for large number of instance. Alternatively, histogram based classifiers are flexible for different probability density function. The aims of PHBayes are to handle large number of instances in datasets with lesser memory requirement, and fast in training and testing phases. The PHBayes depends on portion of the observed histogram that is similar to the probability density function. PHBayes was analyzed using synthetic and real data. Several factors affecting classification accuracy were considered. The PHBayes was compared with other established classifiers and demonstrated higher accurate classification, lesser memory even when dealing with large number of instance, and faster in training and testing phases.  

scholarly journals An investigation on the impact of small-scale models in gasoline direct injection sprays (ECN Spray G)

2019 ◽  
Vol 21 (1) ◽  
pp. 217-225 ◽  
Author(s):  
Salvador Navarro-Martinez ◽  
Giovanni Tretola ◽  
Mohammad Reza Yosri ◽  
Robert L Gordon ◽  
Konstantina Vogiatzaki
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Adaptive Mesh Refinement ◽  
Direct Injection ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Gasoline Direct Injection ◽  
Small Scales ◽  
The Impact

The work presents a numerical investigation of gasoline direct injection and the resulting early development of spray plumes from an eight-hole injector (Engine Combustion Network Spray G). The objective is to evaluate the impact on the droplet size distribution (DSD) statistics from the assumed model physics, particularly for the small scales. Two modelling approaches are compared: Eulerian–Lagrangian spray atomisation with adaptive mesh refinement and a stochastic fields transported probability density function method. The two models simulate the small scales and sub-grid droplet physics with different approaches, but based on the same concept of transport of liquid surface density. Both approaches predict similar liquid distributions in the near-field comparable to experimental measurements. The spray break-up patterns are very similar and both models reproduce quasi-log-normal droplet distributions, with same overall Sauter mean diameters. The Eulerian–Lagrangian spray atomisation with probability density function approach shows different break-up behaviour between droplets originating from the dilute region and those originating from the dense core region. The transition from Eulerian to Lagrangian can be observed in the Eulerian–Lagrangian spray atomisation with adaptive mesh refinement predicted distribution with an abrupt change in the DSD. Both methods are able to produce similar DSD below filter width/grid size resolution.

scholarly journals GTS v1.0: A Macrophysics Scheme for Climate Models Based on a Probability Density Function

2020 ◽  
Author(s):  
Chein-Jung Shiu ◽  
Yi-Chi Wang ◽  
Huang-Hsiung Hsu ◽  
Wei-Ting Chen ◽  
Hua-Lu Pan ◽  
...  
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Thermodynamic Parameters ◽  
General Circulation ◽  
Large Scale ◽  
General Circulation Models ◽  
Tropospheric Temperature ◽  
Cloud Water Content ◽  
The Impact

Abstract. Cloud macrophysics schemes are unique parameterizations for general circulation models. We propose an approach based on a probability density function (PDF) that utilizes cloud condensates and saturation ratios to replace the assumption of critical relative humidity (RH). We test this approach, called the GFS-TaiESM-Sundqvist (GTS) scheme, using the macrophysics scheme within the Community Atmospheric Model version 5.3 (CAM5.3) framework. Via single-column model results, the new approach reveals a stronger linear relationship between the cloud fraction (CF) and RH when compared to that of the default CAM5.3 scheme. We also validate the impact of the GTS scheme on global climate simulations with satellite observations. The simulated CF is comparable to CloudSat/CALIPSO data. Comparisons of the vertical distributions of CF and cloud water content (CWC), as functions of large-scale dynamic and thermodynamic parameters, with the CloudSat/CALIPSO data suggest that the GTS scheme can closely simulate observations. This is particularly noticeable for thermodynamic parameters, such as RH, upper-tropospheric temperature, and total precipitable water, implying that our scheme can simulate variation in CF associated with RH more reliably than the default scheme. Changes in CF and CWC would affect climatic fields and large-scale circulation via cloud–radiation interactions. Both climatological means and annual cycles of many of the GTS-simulated variables are improved compared with the default scheme, particularly with respect to water vapor and RH fields. Different PDF shapes in the GTS scheme also significantly affect global simulations.

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