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相关概念视频

Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
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Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
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Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
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Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

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The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
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Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

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In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
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Calibration Curves: Linear Least Squares01:20

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A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
For data that follow a straight line, the standard method for fitting is the linear...
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相关实验视频

Updated: Jun 22, 2025

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
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通过使用受约束最小平方的最小计算成本,为最小计算成本提供最优的零碎多项式近似.

Jieun Song1, Bumjoo Lee1

  • 1Department of Electronic Engineering, Myongji University, Yongin 17058, Republic of Korea.

Sensors (Basel, Switzerland)
|June 27, 2024
PubMed
概括
此摘要是机器生成的。

本研究介绍了一种最佳近似算法 (OPP),可以有效地将复杂的函数简化为片式多项式. 它尽量减少计算成本,同时保持准确性,这对于实时系统至关重要.

关键词:
有约束的最小平方.函数的近似函数的近似函数.一块块的多项式.这是一个回归回归的回归.

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科学领域:

  • 数字分析 数字分析
  • 计算机科学 计算机科学
  • 应用数学 应用数学 应用数学

背景情况:

  • 简化非线性函数和离散数据对于计算效率至关重要.
  • 现有的方法通常需要手动选择多项式顺序和间隔数,影响运行时间.
  • 时间敏感的应用程序和嵌入式系统需要高精度和低计算成本的近似.

研究的目的:

  • 提出一种最佳近似算法 (OPP) 用于将函数简化为片式多项式.
  • 为了最大限度地降低计算成本,同时确保近似误差低于指定的值.
  • 为了自动确定最佳多项式的顺序和间隔数.

主要方法:

  • 使用受约束的最小平方来近似数据,用光滑的片式多项式.
  • 开发一个算法,通过考虑计算成本和错误来搜索最佳的片式多项式 (OPP).
  • 在目标CPU上对所有可能的多项式组合进行离线计算和计算成本的表格化.
  • 采用随机选择方法来优化与给定的样本点的组合.

主要成果:

  • OPP算法成功地确定了最佳的多项式顺序和间隔数.
  • 通过选择符合误差容忍度的最低成本的OPP来最大限度地降低计算成本.
  • 该算法在简化代表函数方面表现出有效的性能.

结论:

  • 拟议的OPP算法为资源有限的环境中函数近似提供了一种有效的方法.
  • 它自动选择最佳参数,减少手工劳动和提高性能.
  • 这种方法对于准确性和运行时间效率都至关重要的应用非常有价值.