linearization

简明释义

英[ˌlɪnɪəraɪˈzeɪʃən]美[lɪnɪəraɪˈzeɪʃən]

n. 线性化；直线化

英英释义

单词用法

同义词

反义词

例句

1.For the input state linearization method, the states are related linearly to the inputs, so the system can operate well over a wide region.

对于输入-状态线性化方法由于输入状态为线性关系，因此系统可以在较大的范围内正常的工作。

2.This paper proposes a linearization conception of the statistical quantization characteristic of roundoff quantizer.

本文提出了一种舍入量化器统计量化特性线性化的概念。

3.Linearization of power amplifiers has become an important issue, with the advent of linear modulation methods in mobile communication.

随着移动通信中线性调制方式的出现，功率放大器的线性化已成为一个重要的研究课题。

4.The linearization problem of general nonlinear control systems is discussed.

讨论了一般非线性控制系统的线性化问题。

5.The article firstly introduces the linearization techniques: predistortion technique and technique feedforward.

文章首先介绍了功放中的线性化技术——预失真技术和前馈技术。

6.Based on the gas flowing equation, each unit dynamic mathematical model was established using linearization and Laplace transform.

根据气体流动方程，通过线性化和拉氏变换，建立各单元的动态数学模型。

7.In this paper, the optimization and global linearization of nonlinear mechanical systems are studied.

本文研究了非线性力学系统的优化与全局线性化问题。

8.The process of linearization allows us to simplify complex equations for easier analysis.

进行线性化的过程使我们能够简化复杂方程以便于分析。

9.The linearization of the function helps in finding the slope at a given point.

该函数的线性化有助于找到给定点的斜率。

10.Engineers often rely on linearization techniques when designing systems that must respond predictably.

工程师在设计必须可预测响应的系统时，通常依赖于线性化技术。

11.In control theory, linearization is used to approximate nonlinear systems near an equilibrium point.

在控制理论中，线性化用于在平衡点附近近似非线性系统。

12.The linearization of the model made it easier to compute the expected outcomes.

模型的线性化使得计算预期结果变得更加容易。

作文

In the realm of mathematics and engineering, the concept of linearization plays a crucial role in simplifying complex systems. Essentially, linearization refers to the process of approximating a nonlinear function by a linear function around a specific point. This technique is invaluable when dealing with real-world problems where nonlinear dynamics can complicate analysis and solutions. By using linearization, we can make calculations more manageable and gain insights into the behavior of systems that would otherwise be difficult to analyze.For instance, consider a scenario where an engineer is tasked with designing a bridge. The forces acting on the bridge can be described by nonlinear equations due to the complexities of materials and loads. However, by applying linearization, the engineer can approximate these nonlinear relationships with linear ones, making it easier to predict how the bridge will respond to various stresses. This approximation allows for quicker calculations and a clearer understanding of the system's behavior under different conditions.Moreover, linearization is not limited to engineering; it is also widely used in economics, biology, and physics. In economics, for example, demand and supply curves are often nonlinear. However, economists frequently use linearization to simplify the analysis of market behaviors, allowing them to derive useful insights about equilibrium prices and quantities. By examining small changes around a point of interest, they can apply linear models to forecast market trends effectively.In the field of control theory, linearization is essential for designing control systems. Many dynamic systems exhibit nonlinear behavior, but control engineers often need to design controllers based on linear models. By linearizing the system around an operating point, they can apply classical control techniques, such as PID (Proportional-Integral-Derivative) control, which are easier to implement and understand than their nonlinear counterparts.However, it is important to note that linearization has its limitations. The accuracy of the linear approximation depends heavily on the point around which the function is linearized and the range of input values considered. If the system experiences significant changes outside the linear region, the predictions made from the linear model may become unreliable. Therefore, while linearization is a powerful tool, it is crucial for practitioners to recognize its boundaries and apply it judiciously.In conclusion, linearization is a fundamental technique that aids in the simplification of complex systems across various fields. By transforming nonlinear functions into linear approximations, it allows for easier analysis and problem-solving. Whether in engineering, economics, or control theory, the ability to apply linearization can lead to more efficient designs, better predictions, and a deeper understanding of underlying principles. As we continue to encounter increasingly complex systems in our world, mastering the art of linearization will remain an essential skill for professionals in many disciplines.

在数学和工程领域，线性化的概念在简化复杂系统中起着至关重要的作用。基本上，线性化是指围绕特定点用线性函数近似非线性函数的过程。这种技术在处理现实世界问题时非常宝贵，因为非线性动态可能会使分析和解决方案变得复杂。通过使用线性化，我们可以使计算更易于管理，并深入了解否则难以分析的系统的行为。例如，考虑一个工程师被委派设计一座桥的场景。作用于桥上的力可以通过非线性方程来描述，这些方程由于材料和负载的复杂性而变得复杂。然而，通过应用线性化，工程师可以用线性关系来近似这些非线性关系，从而更容易预测桥在各种压力下的反应。这种近似允许更快的计算和对系统在不同条件下行为的更清晰理解。此外，线性化不仅限于工程；它在经济学、生物学和物理学中也被广泛使用。例如，在经济学中，需求和供给曲线通常是非线性的。然而，经济学家经常使用线性化来简化市场行为的分析，从而使他们能够有效地推导出均衡价格和数量的有用见解。通过检查围绕感兴趣点的小变化，他们可以应用线性模型来有效预测市场趋势。在控制理论领域，线性化对于设计控制系统至关重要。许多动态系统表现出非线性行为，但控制工程师通常需要基于线性模型设计控制器。通过在操作点周围对系统进行线性化，他们可以应用经典控制技术，如PID（比例-积分-微分）控制，这些技术比其非线性对应物更易于实现和理解。但是，需要注意的是，线性化有其局限性。线性近似的准确性在很大程度上依赖于线性化的点以及考虑的输入值范围。如果系统在超出线性区域的情况下经历显著变化，则从线性模型得出的预测可能变得不可靠。因此，虽然线性化是一个强大的工具，但从业者必须认识到其边界并谨慎使用。总之，线性化是一种基本技术，有助于简化各个领域的复杂系统。通过将非线性函数转化为线性近似，它使分析和问题解决变得更加容易。无论是在工程、经济学还是控制理论中，应用线性化的能力都可以导致更高效的设计、更好的预测和对基本原理的更深刻理解。随着我们继续在世界上遇到越来越复杂的系统，掌握线性化的艺术将仍然是许多学科专业人士的重要技能。