scholarly journals Uncertainty Analysis and Characterization of the SOFAST Mirror Facet Characterization System

2011 ◽  
Author(s):  
Nolan S. Finch ◽  
Charles E. Andraka
Keyword(s):  
Uncertainty Analysis ◽  
Focal Length ◽  
Input Parameter ◽  
Fringe Analysis ◽  
Development Partner ◽  
Input Parameters ◽  
Deviation Measurement ◽  
Facet Surface ◽  
Setup Variables

Sandia Optical Fringe Analysis Slope Tool (SOFAST) is a mirror facet characterization system based on fringe reflection technology that has been applied to dish and heliostat mirror facet development at Sandia National Laboratories and development partner sites. The tool provides a detailed map of mirror facet surface normals as compared to design and fitted surfaces. In addition, the surface fitting process provides insights into systematic facet slope characterization, such as focal lengths, tilts, and twist of the facet. In this paper, a preliminary analysis of the sensitivities of the facet characterization outputs to variations of SOFAST input parameters is presented. The results of the sensitivity analysis provided the basis for a linear uncertainty analysis which is also included here. Input parameters included hardware parameters and SOFAST setup variables. Output parameters included the fitted shape parameters (focal lengths and twist) and the residuals (typically called slope error). The study utilized empirical propagation of input parameter errors through facet characterization calculations to the output parameters, based on the measurement of an Advanced Dish Development System (ADDS) structural gore point-focus facet. Thus, this study is limited to the characterization of sensitivities of the SOFAST embodiment intended for dish facet characterization. With reasonably careful setup, SOFAST is demonstrated to provide facet focal length characterization within 0.5% of actual. Facet twist is accurate within ± 0.03 mrad/m. The local slope deviation measurement is accurate within ± 0.05 mrad, while the global slope residual is accurate within ± 0.005 mrad. All uncertainties are quoted with 95% confidence.

Effects of Parameter Distributions and Correlations on Uncertainty Analysis of Highway Capacity Manual Delay Model for Signalized Intersections

2005 ◽  
Vol 1920 (1) ◽  
pp. 118-124 ◽  
Author(s):  
Xiaojin Ji ◽  
Panos D. Prevedouros
Keyword(s):  
Uncertainty Analysis ◽  
Confidence Intervals ◽  
Probability Distributions ◽  
Input Parameter ◽  
Major Effect ◽  
Degree Of Saturation ◽  
Delay Model ◽  
Highway Capacity ◽  
Highway Capacity Manual ◽  
Input Parameters

The uncertainty analysis of the Highway Capacity Manual (HCM) delay model often assumes parameter variances and distributions. In light of the difficulty in specifying distributions and estimating correlations, the present study investigated (a) the possibility of assumed distributions’ major effect on the results and (b) the effects of correlations on the accuracy of delay estimates. Field data from one intersection approach in Hawaii and nine intersection approaches in Illinois were used. All input variables in the delay model except for the analysis period were considered uncertain; the analysis period remained fixed at 15 min for consistency with HCM. The simulation results showed that the confidence intervals of delay can be large even if the variability of each input parameter is small. The degree of saturation (X) has a significant effect on the uncertainty of delay estimates for X values 0.9. The standard deviation of input parameters is the main factor affecting the uncertainty of delay estimates. The probability distributions have a slight effect. Correlations among input parameters are often overlooked, but they have a significant effect on the confidence intervals of delay estimates, especially when the variability of the input parameters is large and the input parameters are highly correlated. The frequency distribution of delay estimates is not normal; the shifted lognormal distribution provides a better statistical fit.

Characterization of soybeans and calibration of their DEM input parameters

2020 ◽  
pp. 1-19 ◽  
Author(s):  
Thiet Xuan Nguyen ◽  
Lu Minh Le ◽  
Thong Chung Nguyen ◽  
Nguyen Thi Hanh Nguyen ◽  
Tien-Thinh Le ◽  
...  
Keyword(s):  
Input Parameters

Uncertainty analysis of time resolved transmittance characterization of solid tissue phantoms

2010 ◽  
Author(s):  
Jean-Pierre Bouchard ◽  
Israël Veilleux ◽  
Isabelle Noiseux ◽  
Sébastien Leclair ◽  
Rym Jedidi ◽  
...  
Keyword(s):  
Uncertainty Analysis ◽  
Time Resolved ◽  
Solid Tissue ◽  
Tissue Phantoms

scholarly journals CONCEPT OF ECONOMICAL‐MATHEMATICAL MODEL OF LAND MARKET

2007 ◽  
Vol 13 (4) ◽  
pp. 333-340
Author(s):  
Gintautas Šatkauskas
Keyword(s):  
Mathematical Model ◽  
Input Parameter ◽  
Market Price ◽  
Research Process ◽  
Land Market ◽  
Market Prices ◽  
Noise Background ◽  
Input Parameters ◽  
Main Components ◽  
Sufficient Precision

Input parameters, ie factors defining the market price of agricultural‐purpose land, are interrelated very often by means of non‐linear ties. Strength of these ties is rather different and this limits usefulness of information in the research process of land market prices. Influence of input parameter changes to the input parameters in case when there are rather substantial changes may be determined in someone direction with a sufficient precision, whereas in other directions with comparatively small changes of input parameters this influence is difficult to be separated from the “noise” background. Taking into account the above‐listed circumstances, the concept of economical‐mathematical model of land market should be as follows: there is carried out re‐parameterisation of the process by means of introduction of new parameters in such a way that the new parameters are not interrelated, and the full process is evaluated at the minimal number of these parameters. These requirements are met by the main components of the input parameters. Then normalisation of the main components is carried out and dependencies on new parameters are determined. It is easier to interpret the dependencies obtained having reduced the number of input parameters and the higher the non‐linearity of interrelations of primary land market data, the greater effect of normalisation of input-parameter components. The results are compared with the valuations of experts.

Rapid Reflective Facet Characterization Using Fringe Reflection Techniques

2009 ◽  
Author(s):  
Charles E. Andraka ◽  
Scott Sadlon ◽  
Brian Myer ◽  
Kirill Trapeznikov ◽  
Christina Liebner
Keyword(s):  
Data Reduction ◽  
Target Location ◽  
Focal Length ◽  
Complete Analysis ◽  
Small Scale ◽  
Shape Error ◽  
Fringe Analysis ◽  
Forming Process ◽  
Impact Performance ◽  
Slope Error

Mirror facets for Concentrating Solar Power (CSP) systems have stringent requirements on slope accuracy in order to provide adequate system performance. This paper presents a newly developed tool that can characterize facets quickly enough for 100% inspection on a production line. A facet for a CSP system, specifically a dish concentrator, has a parabolic design shape. This shape will concentrate near-parallel rays from the sun to a point (or a line for trough systems). Deviations of surface slope from the design shape impact the performance of the system, either losing power that misses the target, or increasing peak fluxes to undesirable levels. Three types of facet slope errors can impact performance. The first is a focal length error, typically caused by springback in the facet forming process. In this case, the wavelength of the error exceeds the size of the facet, resulting in a parabola, but with the wrong focal length. The results in a slope error that is largely systematic across the facet when the measured slope is compared to the design slope. A second shape error, in which the period of the error is on the order of the length of the facet, manifests also as a systematic slope error. In this case, the facet deviates from a parabolic shape, but can be modeled with a higher order curve. Finally, the residual errors after a model is proposed are usually lumped through a Root Mean Square (RMS) process and characterized as the 1-sigma variation of a normal distribution. This usually characterizes the small-scale imperfections in the facet, and is usually called “slope error”. However, all of these deviations from design are in facet errors in the slope of the manufactured facet. The reported characterization system, named SOFAST (Sandia Optical Fringe Analysis Slope Tool) has a computer-connected camera that images the reflective surface, which is positioned so that it views the reflection of an active target, such as an LCD screen. A series of fringe patterns are displayed on the screen while images are captured. Using the captured information, the reflected target location of each pixel of mirror viewed can be determined, and thus through a mathematical transformation, the surface normal map can be developed. This is then fitted to the selected model equation, and the errors from design are characterized. The reported system currently characterizes point focus mirrors (for dish systems), but extensions to line focus facets are planned. While similar approaches have been explored, several key developments are presented here. The combination of the display, capture, and data reduction in one system allows rapid capture and data reduction. An “electronic boresight” approach is developed accommodating physical equipment positioning errors, making the system insensitive to setup errors. A very large number of points are determined on each facet, providing significant detail as to the location and character of the errors. The system is developed in MatLab, providing intimate interactions with the data as techniques and applications are developed. Finally, while commercial systems typically resolve the data to shape determination, this system concentrates on slope characterization and reporting, which is tailored to the solar applications. This system can be used for facet analysis during development. However, the real payoff is in production, where complete analysis is performed in about 10 seconds. With optimized coding, this could be further reduced.

Mechanical Testing and Reliability Analysis for 3D Printed Cubic Lattices

2020 ◽  
Author(s):  
Nitin Nagesh Kulkarni ◽  
Stephen Ekwaro-Osire ◽  
Paul F. Egan
Keyword(s):  
3D Printing ◽  
Average Length ◽  
Input Parameter ◽  
Chi Square ◽  
Reliability Method ◽  
Input Parameters ◽  
Chi Square Test ◽  
Length Width ◽  
3D Printed

Abstract 3D printing has enabled new avenues to design and fabricate diverse structures for engineering applications, such as mechanically efficient lattices. Lattices are useful as implants for biological applications for supporting in vivo loads. However, inconsistencies in 3D printing motivates a need to quantify uncertainties contributing to mechanical failure using probabilistic analysis. Here, 50 cubic unit cell lattice samples were printed and tested with designs of 50% porosity, 500-micron beam diameters, and 3.5mm length, width, and height dimensions. The average length, width, and height measurements ranged from 3.47mm to 3.48mm. The precision in printing with a 95% confidence level was greater than 99.8%. Lattice elastic moduli ranged from about 270 MPa to 345 MPa, with a mean of 305 MPa. Probabilistic analyses were conducted with NESSUS software. The distributions of input parameters were determined using a chi-square test. The first-order reliability method was used to calculate the probability of failure and sensitivity of each input parameter. The elastic modulus was the most sensitive among all input parameters, with 57% of the total sensitivity. The study quantified printing inconsistencies and sensitives using empirical evidence and is a significant step forward for designing 3D printed parts for mechanical applications.

Optimizing Dressing Conditions for Minimum Flatness Tolerance when Grinding SKD11 Tool Steel

2021 ◽  
Vol 1020 ◽  
pp. 83-90
Author(s):  
Thi Hong Tran ◽  
Tran Ngoc Giang ◽  
Ngoc Vu Ngo ◽  
Thanh Danh Bui ◽  
Thanh Tu Nguyen ◽  
...  
Keyword(s):  
Tool Steel ◽  
Feed Rate ◽  
Input Parameter ◽  
Experimental Results ◽  
Grinding Wheel ◽  
Input Parameters

This study is to determine effects of the dressing parameters to the flatness tolerance (Fl) when grinding SKD11 steel using HaiDuong grinding wheel and also propose the suitable dressing parameters to obtain the smallest flatness tolerance. In this paper, the effects of the six input parameters including feed rate (S), depth of rough dressing cut (ar), rough dressing times (nr), depth of finish dressing cut (af), finish dressing times (nf) and non-feeding dressing (nnon) to the flatness tolerance were investigated. To find out the influence of each input parameter on output results, the S/N ratio was analysized. Evaluated experimental results show that, the average flatness tolerance was 4.05μm and deviation of this value was 11.38% compared with the predicted value.

Seismic hazard sensitivity analysis: A multi-parameter approach

1991 ◽  
Vol 81 (3) ◽  
pp. 796-817
Author(s):  
Nitzan Rabinowitz ◽  
David M. Steinberg
Keyword(s):  
Sensitivity Analysis ◽  
Seismic Hazard ◽  
Subjective Probability ◽  
Probability Distributions ◽  
Input Parameter ◽  
The Other ◽  
Probabilistic Assessment ◽  
Input Parameters ◽  
Parameter Approach

Abstract We propose a novel multi-parameter approach for conducting seismic hazard sensitivity analysis. This approach allows one to assess the importance of each input parameter at a variety of settings of the other input parameters and thus provides a much richer picture than standard analyses, which assess each input parameter only at the default settings of the other parameters. We illustrate our method with a sensitivity analysis of seismic hazard for Jerusalem. In this example, we find several input parameters whose importance depends critically on the settings of other input parameters. This phenomenon, which cannot be detected by a standard sensitivity analysis, is easily diagnosed by our method. The multi-parameter approach can also be used in the context of a probabilistic assessment of seismic hazard that incorporates subjective probability distributions for the input parameters.

On the thinning variations in hydrostatic forming of sheet metal

2021 ◽  
Vol 15 (1) ◽  
pp. 7824-7836
Author(s):  
Thu Thi Nguyen ◽  
N.D. Trung
Keyword(s):  
Sheet Metal ◽  
Thickness Distribution ◽  
Input Parameter ◽  
Relative Depth ◽  
Technological Parameters ◽  
Forming Technology ◽  
Input Parameters ◽  
Forming Characteristics ◽  
Cylindrical Cup ◽  
Forming Methods

In sheet metal forming, thinning phenomenon is one of the most concerned topics to ameliorate the final quality of the manufactured parts. The thinning variations depend on many input parameters, such as technological parameters, geometric shape of die, workpiece’s materials, and forming methods. Hydrostatic forming technology is particularly suitable for forming thin-shell products with complex shapes. However, due to the forming characteristics, the thinning variations in this technology are much more intense than in other forming methods. Therefore, in this paper, an empirical study is developed to determine the thinning variations in hydrostatic forming for cylindrical cup. Measurement of thickness at various locations of deformed products are conducted to investigate the thickness distribution and determine the dependence of the largest thinning ratio on the input parameters (including the blank holder pressure, the relative depth of the die and the relative thickness of the workpiece). The results are expressed in charts and equation which allow determining the effect of each input parameter on the largest thinning ratio.

scholarly journals Sensitivity and Uncertainty Analysis of One-Dimensional Tanaka and Liang-Rogers Shape Memory Alloy Constitutive Models

Materials ◽  
2019 ◽  
Vol 12 (10) ◽  
pp. 1687 ◽  
Author(s):  
A. B. M. Rezaul Islam ◽  
Ernur Karadoğan
Keyword(s):  
Shape Memory Alloy ◽  
Uncertainty Analysis ◽  
Shape Memory ◽  
Shape Memory Effect ◽  
Memory Effect ◽  
Constitutive Models ◽  
Loading Conditions ◽  
Input Parameters ◽  
Stress Dependent ◽  
Sensitivity And Uncertainty Analysis

A shape memory alloy (SMA) can remember its original shape and recover from strain due to loading once it is exposed to heat (shape memory effect). SMAs also exhibit elastic response to applied stress above the characteristic temperature at which transformation to austenite is completed (pseudoelasticity or superelasticity). Shape memory effect and pseudoelasticity of SMAs have been addressed by several microscopic thermodynamic and macroscopic phenomenological models using different modeling approaches. The Tanaka and Liang-Rogers models are two of the most widely used macroscopic phenomenological constitutive models for describing SMA behavior. In this paper, we performed sensitivity and uncertainty analysis using Sobol and extended Fourier Amplitude Sensitivity Testing (eFAST) methods for the Tanaka and Liang-Rogers models at different operating temperatures and loading conditions. The stress-dependent and average sensitivity indices have been analyzed and are presented for determining the most influential parameters for these models. The results show that variability is primarily caused by a change in operating temperature and loading conditions. Both models appear to be influenced by the uncertainty in elastic modulus of the material significantly. The analyses presented in this paper aim to provide a better insight for designing applications using SMAs by increasing the understanding of these models’ sensitivity to the input parameters and the cause of output variability due to uncertainty in the same input parameters.

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