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相关概念视频

Uncertainty: Overview00:59

Uncertainty: Overview

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In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
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Uncertainty in Measurement: Reading Instruments02:46

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Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such measurements result in exact numbers. By counting the eggs in a carton, for instance, one can determine exactly how many eggs are there in the carton. Similarly, the numbers of defined quantities are also exact. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Quantities...
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Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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Propagation of Uncertainty from Systematic Error01:10

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The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
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The Uncertainty Principle04:08

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Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
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Uncertainty: Confidence Intervals00:54

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The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
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相关实验视频

Updated: Jul 15, 2025

Analyzing Mixing Inhomogeneity in a Microfluidic Device by Microscale Schlieren Technique
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在面向背景的Schlieren中量化数字不确定性.

Pranjal Anand1, Jiacheng Zhang1, Lalit K Rajendran2

  • 1School of Mechanical Engineering, Purdue University, West Lafayette, IN, USA.

Research square
|October 4, 2023
PubMed
概括
此摘要是机器生成的。

这项研究引入了一种新的方法,用于计算背景导向施莱伦 (BOS) 成像中的数值不确定性. 通过整合数值和随机不确定性,该技术显著提高了密度场不确定性预测在流体动力学研究的准确性.

关键词:
以背景为导向的施莱伦 (BOS)理查德森推算法 理查德森推算法 理查德森推算法不确定性估计估计的不确定性

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Last Updated: Jul 15, 2025

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Visualization of Ambient Mass Spectrometry with the Use of Schlieren Photography
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科学领域:

  • 流体动力学 流体动力学
  • 光学测量技术的使用
  • 计算物理 计算物理

背景情况:

  • 面向背景的Schleeren (BOS) 是可视化流体流动的有价值的光学技术.
  • 准确的不确定性量化对于可靠的BOS测量至关重要.
  • 现有的方法往往不能完全解释图像处理中固有的数值不确定性.

研究的目的:

  • 开发和评估一种方法来计算BOS中的数值不确定性.
  • 为了将数值不确定性与随机不确定性整合到一个全面的密度场不确定性.
  • 评估流场特征对不确定性预测的影响.

主要方法:

  • 利用理查德森推断来估计密度梯度的数值积分的不确定性.
  • 评估不确定性基于两个不同电网级别的余量.
  • 结合预测的数值不确定性与现有的随机不确定性.
  • 使用合成数据集与受控噪声和实验BOS图像验证了该方法.

主要成果:

  • 密度梯度的度显著影响偏差误差和数值不确定性预测.
  • 数字不确定性预测与在噪声水平和流场波长变化下偏差误差变化相关.
  • 拟议的方法在预测总不确定性与总错误的平方根平均值相比,达到高达91%的准确性.
  • 对实验性BOS数据的成功应用.

结论:

  • 开发的方法可以更准确地估计BOS测量的总不确定性.
  • 对数值不确定性的计算提高了密度场结果的可靠性.
  • 这种方法对提高未来使用BOS的实验流体动力学研究的严格性有重大影响.