error propagation

简明释义

误差传播

英英释义

例句

1.In physics experiments, understanding error propagation 误差传播 is crucial for accurate results.

在物理实验中，理解误差传播 error propagation 对于获得准确结果至关重要。

2.The formula for error propagation 误差传播 helps determine the uncertainty in calculated values.

用于误差传播 error propagation 的公式有助于确定计算值中的不确定性。

3.In statistics, error propagation 误差传播 is important when combining multiple measurements.

在统计学中，当组合多个测量时，误差传播 error propagation 是重要的。

4.When measuring the length and width of a rectangle, error propagation 误差传播 can affect the area calculation.

在测量矩形的长度和宽度时，误差传播 error propagation 可能会影响面积计算。

5.Engineers must consider error propagation 误差传播 when designing precise instruments.

工程师在设计精密仪器时必须考虑误差传播 error propagation。

作文

In the field of science and engineering, precision is paramount. When conducting experiments or calculations, it is crucial to understand how errors can affect the final results. This is where the concept of error propagation comes into play. 误差传播 refers to the way in which uncertainties in measurements or calculations can influence the overall uncertainty of a result. It is essential for researchers and engineers to account for these uncertainties to ensure that their findings are reliable and valid.Consider a simple example: measuring the length and width of a rectangle to calculate its area. If the length is measured as 5.0 cm with a possible error of ±0.1 cm, and the width is measured as 3.0 cm with a possible error of ±0.1 cm, we must consider how these errors propagate when calculating the area. The area of the rectangle can be calculated using the formula A = length × width. Here, the area would be A = 5.0 cm × 3.0 cm = 15.0 cm².However, to determine the uncertainty in the area, we need to apply error propagation. The formula for propagating errors in multiplication is given by:ΔA/A = (ΔL/L) + (ΔW/W)where ΔA is the uncertainty in the area, ΔL is the uncertainty in length, L is the length, ΔW is the uncertainty in width, and W is the width. Plugging in our values:ΔA/15.0 cm² = (0.1 cm/5.0 cm) + (0.1 cm/3.0 cm)Calculating this gives us:ΔA/15.0 cm² = 0.02 + 0.0333 ≈ 0.0533Thus, ΔA = 15.0 cm² × 0.0533 ≈ 0.8 cm². Therefore, the area of the rectangle is reported as 15.0 ± 0.8 cm².This example illustrates the importance of error propagation in ensuring that the uncertainties in our measurements are accurately reflected in our results. Without considering error propagation, one might mistakenly report a more precise value than what is justified by the data, leading to potentially misleading conclusions.In more complex scenarios, such as those involving multiple variables and operations, error propagation becomes even more critical. For instance, in physics, when calculating quantities like velocity or acceleration, one often has to deal with multiple measurements, each with its own uncertainty. In such cases, understanding how these uncertainties combine through error propagation is vital for accurate reporting.Moreover, in fields such as statistics, the concept of error propagation plays a significant role in determining the reliability of statistical estimates. When analyzing data, the uncertainties associated with sample measurements can affect the confidence intervals and hypothesis testing outcomes. By properly applying error propagation, researchers can provide a clearer picture of the reliability and significance of their results.In conclusion, error propagation is a fundamental concept that underlies much of scientific inquiry and engineering practice. It serves as a reminder that precision in measurement is not just about obtaining a number, but also about understanding the uncertainty that accompanies it. By mastering the principles of error propagation, scientists and engineers can enhance the credibility of their work and contribute to the advancement of knowledge in their respective fields.

在科学和工程领域，精确性至关重要。在进行实验或计算时，理解误差如何影响最终结果至关重要。这就是误差传播这一概念的作用。误差传播指的是测量或计算中的不确定性如何影响结果的整体不确定性。研究人员和工程师必须考虑这些不确定性，以确保他们的发现是可靠和有效的。考虑一个简单的例子：测量矩形的长度和宽度以计算其面积。如果长度测量为5.0厘米，可能存在±0.1厘米的误差，而宽度测量为3.0厘米，可能存在±0.1厘米的误差，我们必须考虑在计算面积时这些误差是如何传播的。矩形的面积可以使用公式A = 长度 × 宽度来计算。在这里，面积为A = 5.0厘米 × 3.0厘米 = 15.0厘米²。然而，要确定面积的不确定性，我们需要应用误差传播。乘法中传播误差的公式为：ΔA/A = (ΔL/L) + (ΔW/W)其中ΔA是面积的不确定性，ΔL是长度的不确定性，L是长度，ΔW是宽度的不确定性，W是宽度。将我们的值代入：ΔA/15.0厘米² = (0.1厘米/5.0厘米) + (0.1厘米/3.0厘米)计算得出：ΔA/15.0厘米² = 0.02 + 0.0333 ≈ 0.0533因此，ΔA = 15.0厘米² × 0.0533 ≈ 0.8厘米²。因此，矩形的面积报告为15.0 ± 0.8厘米²。这个例子说明了误差传播的重要性，确保我们测量中的不确定性准确地反映在我们的结果中。如果不考虑误差传播，人们可能会错误地报告一个比数据所能支持的更精确的值，从而导致潜在的误导性结论。在更复杂的情况下，例如涉及多个变量和操作的情况，误差传播变得更加重要。例如，在物理学中，当计算速度或加速度等量时，通常需要处理多个测量，每个测量都有其不确定性。在这种情况下，理解这些不确定性如何通过误差传播结合起来，对于准确报告至关重要。此外，在统计学等领域，误差传播的概念在确定统计估计的可靠性方面发挥着重要作用。在分析数据时，与样本测量相关的不确定性可能会影响置信区间和假设检验的结果。通过正确应用误差传播，研究人员可以提供更清晰的结果可靠性和显著性的图景。总之，误差传播是科学探究和工程实践中一个基本的概念。它提醒我们，测量的精确性不仅仅是获取一个数字，而是理解伴随而来的不确定性。通过掌握误差传播的原理，科学家和工程师可以增强其工作的可信度，并为各自领域知识的进步做出贡献。