航空航天Finite element method有限元法 (FEM) 是对工程和数学建模中出现的微分方程进行数值求解的常用方法。感兴趣的典型问题领域包括结构分析、传热、流体流动、质量传输和电磁势等传统领域。计算机通常用于执行所需的计算。借助高速超级计算机，可以实现更好的解决方案，并且通常需要解决最大、最复杂的问题。 FEM 是一种用于求解二空间或三空间变量中的偏微分方程（即某些边值问题）的通用数值方法。也有关于使用有限元法解决高维问题的研究。为了解决问题，FEM 将大型系统细分为更小、更简单的部分，称为有限元。
Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. Computers are usually used to perform the calculations required. With high-speed supercomputers, better solutions can be achieved and are often required to solve the largest and most complex problems. FEM is a general numerical method for solving partial differential equations in two- or three-space variables (i.e., some boundary value problems). There are also studies about using FEM to solve high-dimensional problems. To solve a problem, FEM subdivides a large system into smaller, simpler parts called finite elements.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。 本条中文为英文百科简介的机器辅助翻译，请结合英文原文核对专业术语。
查看内容许可 ↗在固体力学中，应力集中（也称为应力集中点或应力集中点或缺口敏感度）是物体中应力显着大于周围区域的位置。当结构部件的几何形状或材料不规则导致应力流中断时，就会出现应力集中。这是由孔、凹槽、凹口和圆角等细节产生的。意外损坏（例如刻痕和划痕）也可能导致应力集中。在典型的拉伸载荷下，不连续性的集中程度可以表示为无量纲应力集中因子 K t {\displaystyle K_{t}} ，它是最高应力与标称远场应力的比率。对于无限板中的圆孔，K t = 3 {\displaystyle K_{t}=3} 。
In solid mechanics, a stress concentration (also called a stress raiser or a stress riser or notch sensitivity) is a location in an object where the stress is significantly greater than the surrounding region. Stress concentrations occur when there are irregularities in the geometry or material of a structural component that cause an interruption to the flow of stress. This arises from such details as holes, grooves, notches and fillets. Stress concentrations may also occur from accidental damage such as nicks and scratches. The degree of concentration of a discontinuity under typically tensile loads can be expressed as a non-dimensional stress concentration factor K t {\displaystyle K_{t}} , which is the ratio of the highest stress to the nominal far field stress. For a circular hole in an infinite plate, K t = 3 {\displaystyle K_{t}=3} .
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。 本条中文为英文百科简介的机器辅助翻译，请结合英文原文核对专业术语。
查看内容许可 ↗在材料科学中，断裂韧性是尖锐裂纹的临界应力强度因子，其中裂纹的扩展突然变得快速且无限。它是一种材料特性，可量化其在施加应力下抵抗裂纹扩展和失效的能力。部件的厚度会影响裂纹尖端的约束条件，薄部件具有平面应力条件，导致延性行为，厚部件具有平面应变条件，其中约束增加，导致脆性破坏。平面应变条件给出最低的断裂韧性值，这是一种材料特性。在平面应变条件下测得的 I 型加载应力强度因子的临界值称为平面应变断裂韧性，记为 K Ic {\displaystyle K_{\text{Ic}}} 。
In materials science, fracture toughness is the critical stress intensity factor of a sharp crack where propagation of the crack suddenly becomes rapid and unlimited. It is a material property that quantifies its ability to resist crack propagation and failure under applied stress. A component's thickness affects the constraint conditions at the tip of a crack with thin components having plane stress conditions, leading to ductile behavior and thick components having plane strain conditions, where the constraint increases, leading to brittle failure. Plane strain conditions give the lowest fracture toughness value which is a material property. The critical value of stress intensity factor in mode I loading measured under plane strain conditions is known as the plane strain fracture toughness, denoted K Ic {\displaystyle K_{\text{Ic}}} .
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。 本条中文为英文百科简介的机器辅助翻译，请结合英文原文核对专业术语。
查看内容许可 ↗极限拉伸强度（也称为 UTS、拉伸强度、TS、极限强度或 F tu {\displaystyle F_{\text{tu}}} 符号）是材料在断裂前被拉伸或拉动时可以承受的最大应力。在脆性材料中，极限抗拉强度接近屈服点，而在延性材料中，极限抗拉强度可能更高。极限拉伸强度通常是通过进行拉伸测试并记录工程应力与应变的关系来确定的。应力-应变曲线的最高点是极限拉伸强度，并具有应力单位。压缩而不是拉伸情况下的等效点称为抗压强度。拉伸强度在延性构件的设计中很少有任何影响，但对于脆性构件却很重要。
Ultimate tensile strength (also called UTS, tensile strength, TS, ultimate strength or F tu {\displaystyle F_{\text{tu}}} in notation) is the maximum stress that a material can withstand while being stretched or pulled before breaking. In brittle materials, the ultimate tensile strength is close to the yield point, whereas in ductile materials, the ultimate tensile strength can be higher. The ultimate tensile strength is usually found by performing a tensile test and recording the engineering stress versus strain. The highest point of the stress–strain curve is the ultimate tensile strength and has units of stress. The equivalent point for the case of compression, instead of tension, is called the compressive strength. Tensile strengths are rarely of any consequence in the design of ductile members, but they are important with brittle members.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。 本条中文为英文百科简介的机器辅助翻译，请结合英文原文核对专业术语。
查看内容许可 ↗在连续介质力学中，最大变形能准则（也称为冯·米塞斯屈服准则）指出，当偏应力的第二个不变量 J 2 {\displaystyle J_{2}} 达到临界值时，延性材料开始屈服。它是塑性理论的一部分，主要适用于延性材料，例如某些金属。在屈服之前，材料响应可以假设为线性弹性、非线性弹性或粘弹性行为。在材料科学与工程中，冯·米塞斯屈服准则也根据冯·米塞斯应力或等效拉伸应力 σ v {\displaystyle \sigma _{\text{v}}} 来制定。这是可以根据柯西应力张量计算出的应力标量值。
In continuum mechanics, the maximum distortion energy criterion (also von Mises yield criterion) states that yielding of a ductile material begins when the second invariant of deviatoric stress J 2 {\displaystyle J_{2}} reaches a critical value. It is a part of plasticity theory that mostly applies to ductile materials, such as some metals. Prior to yield, material response can be assumed to be of a linear elastic, nonlinear elastic, or viscoelastic behavior. In materials science and engineering, the von Mises yield criterion is also formulated in terms of the von Mises stress or equivalent tensile stress, σ v {\displaystyle \sigma _{\text{v}}} . This is a scalar value of stress that can be computed from the Cauchy stress tensor.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。 本条中文为英文百科简介的机器辅助翻译，请结合英文原文核对专业术语。
查看内容许可 ↗莫尔圆是柯西应力张量变换定律的二维图形表示。莫尔圆经常用于与机械工程的材料强度、岩土工程的土壤强度以及结构工程的建筑结构强度相关的计算。它还用于通过将许多平面中的应力简化为垂直和水平分量来计算应力。这些称为主平面，在其中计算主应力；莫尔圆还可用于在图形表示中查找主平面和主应力，并且是最简单的方法之一。对假设为连续体的材料体进行应力分析后，特定材料点处的柯西应力张量相对于坐标系的分量是已知的。
Mohr's circle is a two-dimensional graphical representation of the transformation law for the Cauchy stress tensor. Mohr's circle is often used in calculations relating to mechanical engineering for materials' strength, geotechnical engineering for strength of soils, and structural engineering for strength of built structures. It is also used for calculating stresses in many planes by reducing them to vertical and horizontal components. These are called principal planes in which principal stresses are calculated; Mohr's circle can also be used to find the principal planes and the principal stresses in a graphical representation, and is one of the easiest ways to do so. After performing a stress analysis on a material body assumed as a continuum, the components of the Cauchy stress tensor at a particular material point are known with respect to a coordinate system.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。 本条中文为英文百科简介的机器辅助翻译，请结合英文原文核对专业术语。
查看内容许可 ↗在力学和热力学中，热应力是由材料温度的任何变化产生的机械应力。这些应力可能导致破裂或塑性变形，具体取决于加热的其他变量，包括材料类型和约束。温度梯度、热膨胀或收缩以及热冲击都会导致热应力。这种类型的应力高度依赖于不同材料的热膨胀系数。一般来说，温度变化越大，可能发生的应力水平就越高。温度的快速变化可能会导致热冲击，从而导致破裂或破碎。
In mechanics and thermodynamics, thermal stress is mechanical stress created by any change in temperature of a material. These stresses can lead to fracturing or plastic deformation depending on the other variables of heating, which include material types and constraints. Temperature gradients, thermal expansion or contraction and thermal shocks are things that can lead to thermal stress. This type of stress is highly dependent on the thermal expansion coefficient which varies from material to material. In general, the greater the temperature change, the higher the level of stress that can occur. Thermal shock can result from a rapid change in temperature, resulting in cracking or shattering.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。 本条中文为英文百科简介的机器辅助翻译，请结合英文原文核对专业术语。
查看内容许可 ↗热膨胀是物质尺寸随着温度升高而增大的趋势。随着温度的升高（通常不包括相变），物质的长度、面积和体积通常会增加，从而改变其尺寸和密度。物质通常随着温度降低而收缩，这称为热收缩。热膨胀的 SI 单位是开尔文倒数 (K−1)。温度是体内分子平均动能的量度。分子运动得越快，身体的温度就越高。具体来说，它是物质平均分子动能的单调函数。随着粒子能量的增加，它们开始移动得越来越快，削弱了它们之间的分子间力，从而使物质膨胀。
Thermal expansion is the tendency of matter to increase in size with increasing temperature. Matter generally increases in length, area, and volume, changing its size and density, in response to an increase in temperature (usually excluding phase transitions). Substances usually contract with decreasing temperature which is called thermal contraction. The SI unit of thermal expansion is the inverse kelvin (K−1). Temperature is a measure of the average kinetic energy of the molecules in a body. The faster the molecules are moving, the higher that body's temperature is. Specifically, it is a monotonic function of the average molecular kinetic energy of a substance. As the energy in the particles increases, they start moving faster and faster, weakening the intermolecular forces between them and therefore expanding the substance.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。 本条中文为英文百科简介的机器辅助翻译，请结合英文原文核对专业术语。
查看内容许可 ↗物质的体积模量（ K {\displaystyle K} 或 B {\displaystyle B} 或 k {\displaystyle k} ）是物质抵抗体积压缩的能力的量度。它被定义为无限小的压力增加与由此产生的相对体积减少的比率。其他模量描述材料对其他类型应力的响应（应变）：剪切模量描述对剪切应力的响应，杨氏模量描述对法向（纵向拉伸）应力的响应。对于流体来说，只有体积模量才有意义。对于复杂的各向异性固体（例如木材或纸张），这三个模量不包含足够的信息来描述其行为，必须使用完整的广义胡克定律。固定温度下体积模量的倒数称为等温压缩率。
The bulk modulus ( K {\displaystyle K} or B {\displaystyle B} or k {\displaystyle k} ) of a substance is a measure of the resistance of a substance to bulk compression. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume. Other moduli describe the material's response (strain) to other kinds of stress: the shear modulus describes the response to shear stress and Young's modulus describes the response to normal (lengthwise stretching) stress. For a fluid, only the bulk modulus is meaningful. For a complex anisotropic solid such as wood or paper, these three moduli do not contain enough information to describe its behaviour, and one must use the full generalized Hooke's law. The reciprocal of the bulk modulus at fixed temperature is called the isothermal compressibility.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。 本条中文为英文百科简介的机器辅助翻译，请结合英文原文核对专业术语。
查看内容许可 ↗在固体力学中，剪切模量或刚性模量，用 G（有时用 S 或 μ）表示，是材料弹性剪切刚度的量度，定义为剪切应力与剪切应变之比： G := τ x y γ x y = F A Δ x l...
In solid mechanics, the shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to shear strain: G := τ x y γ x y = F A Δ x l...
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。 本条中文为英文百科简介的机器辅助翻译，请结合英文原文核对专业术语。
查看内容许可 ↗挫屈（buckling）力学称屈曲 ，土木工程称为挫屈；是指细长杆件受到压力时，发生弯曲变形的一种现象。由不稳定造成的结构失效称为屈曲失效。理想压杆丧失稳定后，由原来的直线平衡状态变为弯曲平衡状态。理论上，挫曲是因为力学平衡方程式的解出现分岔（解的本质发生改变）所造成的。在受力增加到一定程度之后，物体会出现二种平衡状态，一种是纯压缩力，另一个是有侧向偏移变形的平衡状态。 挫屈的特点是在结构件中，边缘承受压缩应力的元件突然断裂，而元件失效时的压应力小于材料可以承受的终极抗压应力。挫曲的数学分析一般会设法加入方向也是轴向，但和轴有一段位移（偏心）的压应力，以产生原来理想施力时不会受现的二次弯矩。 当在一元件（例如杆件）上的压缩负荷增加，多半最后负荷会大到使元件变形不稳定。若负荷继续加大，会造成明显，甚至无法预测的变形，可能让元件完全无法承受负荷。若变形还不是灾难性的，元件仍会继续承受负载。若挫曲的元件是结构件（例如大楼）中的一部分，会由其他的元件来分担已挫曲元件原来要承受的负载。
In structural engineering, buckling is the sudden change in shape (deformation) of a structural component under load, such as the bowing of a column under compression or the wrinkling of a plate under shear. If a structure is subjected to a gradually increasing load, when the load reaches a critical level, a member may suddenly change shape and the structure and component is said to have buckled. Euler's critical load and Johnson's parabolic formula are used to determine the buckling stress of a column. Buckling may occur even though the stresses that develop in the structure are well below those needed to cause failure in the material of which the structure is composed. Further loading may cause significant and somewhat unpredictable deformations, possibly leading to complete loss of the member's load-carrying capacity. However, if the deformations that occur after buckling do not cause the complete collapse of that member, the member will continue to support the load that caused it to buckle.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗裂纹扩展方程用于计算循环载荷产生的疲劳裂纹的尺寸。疲劳裂纹的增长可能导致灾难性故障，特别是对于飞机而言。当许多不断增长的疲劳裂纹相互作用时，就被称为广泛的疲劳损伤。通过预测裂纹的大小，裂纹扩展方程可用于确保设计阶段和运行期间的安全。在关键结构中，可以记录载荷并用于预测裂缝的大小，以确保在任何裂缝失效之前进行维护或报废。由于疲劳寿命对裂纹萌生缺陷的尺寸和形状以及部件所承受的假定载荷和实际载荷之间的可变性的敏感性，安全系数用于将预测疲劳寿命缩短为使用寿命。
A crack growth equation is used for calculating the size of a fatigue crack growing from cyclic loads. The growth of a fatigue crack can result in catastrophic failure, particularly in the case of aircraft. When many growing fatigue cracks interact with one another it is known as widespread fatigue damage. A crack growth equation can be used to ensure safety, both in the design phase and during operation, by predicting the size of cracks. In critical structure, loads can be recorded and used to predict the size of cracks to ensure maintenance or retirement occurs prior to any of the cracks failing. Safety factors are used to reduce the predicted fatigue life to a service fatigue life because of the sensitivity of the fatigue life to the size and shape of crack initiating defects and the variability between assumed loading and actual loading experienced by a component.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。 本条中文为英文百科简介的机器辅助翻译，请结合英文原文核对专业术语。
查看内容许可 ↗辐射冷却是指物件透过辐射散去热能的过程。 在气象学上，地球表面所吸收的太阳热能，到了夜晚会向天空发射出长波辐射，如果夜间天气晴朗、微风及干燥的情况下，地表的温度会快速冷却，产生突然降到低温的情形，就是所谓的“辐射冷却效应”。在日间时，地面吸收来自太阳热能的速度比散发的快，因此气温就会上升；到了夜晚，地面吸收来自太阳热能的速度比散发的慢，气温就会下降。另外，云层会阻隔辐射冷却，空气中的水分会阻挡地面的热能向外散发，因此部分天气晴朗以及干燥的地方，夜间温度下降的速度会特别快。
In the study of heat transfer, radiative cooling is the process by which a body loses heat by thermal radiation. As Planck's law describes, every physical body spontaneously and continuously emits electromagnetic radiation. Radiative cooling has been applied in various contexts throughout human history, including ice making in India and Iran, heat shields for spacecraft, and in architecture. In 2014, a scientific breakthrough in the use of photonic metamaterials made daytime radiative cooling possible. It has since been proposed as a strategy to mitigate local and global warming caused by greenhouse gas emissions known as passive daytime radiative cooling.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗黑体辐射指处于热力学平衡态的黑体发出的电磁辐射。黑体辐射的电磁波谱只取决于黑体的温度。另一方面，所谓黑体辐射是光和物质达到平衡所表现出的现象。物质达到平衡，所以可以用一个温度来描述物质的状态，而光和物质的交互作用很强，如此光和光之间也可以用一个温度来描述（光和光之间本身不会有交互作用，但光和物质的交互作用很强），而描述这关系的便是普朗克分布（Planck distribution）。黑体辐射能量按波长的分布仅与温度有关。 黑体不仅仅能全部吸收外来的电磁辐射，且散射电磁辐射的能力比同温度下的任何其它物体强。对于黑体的研究，使自然现象中的量子效应被发现。而黑体作为一个理想化的物体，在现实中是不存在的，因此现实中物体的辐射也与理论上的黑体辐射有所出入。但是，可以观察一些非常类似黑体的物质发出的辐射，例如一颗恒星或一个只有单一开口的空腔所发出的辐射。举个例来说，人们观测到宇宙背景辐射，对应到一个约3K的黑体辐射，这暗示宇宙早期光是和物质达到平衡的。而随着时间演化，温度慢慢降了下来，但方程式依然存在。（频率和温度的效应抵销）
Black-body radiation is the thermal electromagnetic radiation emitted from a body in thermodynamic equilibrium with its environment. A black body is an idealized opaque and non-reflective body. The radiation emitted is a continuous spectrum over all possible radiation wavelengths that depends only on the body's temperature. A perfectly-insulated enclosure which is in thermal equilibrium internally contains black-body radiation and will emit it through a hole made in its wall, provided the hole is small enough to have a negligible effect upon the equilibrium. The thermal radiation spontaneously emitted by many ordinary objects can be approximated as black-body radiation. Of particular importance, although planets and stars (including the Earth and Sun) are neither in thermal equilibrium with their surroundings nor perfect black bodies, black-body radiation is still a good first approximation for the energy they emit.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗PID控制器（比例-积分-微分控制器），由比例单元（Proportional）、积分单元（Integral）和微分单元（Derivative）组成。可以透过调整这三个单元的增益 K p {\displaystyle K_{p}} ， K i {\displaystyle K_{i}} 和 K d {\displaystyle K_{d}} 来调定其特性。PID控制器主要适用于基本上线性，且动态特性不随时间变化的系统。 PID控制器是一个在工业控制应用中常见的回授回路部件。这个控制器把收集到的数据和一个参考值进行比较，然后把这个差别用于计算新的输入值，这个新的输入值的目的是可以让系统的数据达到或者保持在参考值。PID控制器可以根据历史数据和差别的出现率来调整输入值，使系统更加准确而稳定。 PID控制器的比例单元（P）、积分单元（I）和微分单元（D）分别对应目前误差、过去累计误差及未来误差。若是不知道受控系统的特性，一般认为PID控制器是最适用的控制器。借由调整PID控制器的三个参数，可以调整控制系统，设法满足设计需求。控制器的响应可以用控制器对误差的反应快慢、控制器过冲的程度及系统震荡的程度来表示。不过使用PID控制器不一定保证可达到系统的最佳控制，也不保证系统稳定性。 有些应用只需要PID控制器的部分单元，可以将不需要单元的参数设为零即可。因此PID控制器可以变成PI控制器、PD控制器、P控制器或I控制器。其中又以PI控制器比较常用，因为D控制器对回授噪声十分敏感，而若没有I控制器的话，系统不会回到参考值，会存在一个误差量。
A proportional–integral–derivative (PID) controller, or three-term controller, is a feedback-based control loop mechanism commonly used to manage machines and processes that require continuous control and automatic adjustment. It is typically used in industrial control systems and various other applications where constant control through modulation is necessary without human intervention. The PID controller automatically compares the desired target value (setpoint or SP) with the actual value of the system (process variable or PV). The difference between these two values is called the error value, denoted as e ( t ) {\displaystyle e(t)} . It then applies corrective actions automatically to bring the PV to the same value as the SP using three methods: The proportional (P) component responds to the current error value by producing an output that is directly proportional to the magnitude of the error. This provides immediate correction based on how far the system is from the desired setpoint.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗在工程中，传递函数（英语：transfer function，也称系统函数、转移函数或网络函数，画出的曲线叫做传递曲线）是用来拟合或描述黑箱模型（系统）的输入与输出之间关系的数学表示。在二维图像的应用中，输入和输出的位图间的关系函数称作转移曲线、转换曲线（transfer curve）或特征曲线（characteristic curve）。 通常它是零初始条件和零平衡点下，以空间或时间频率为变量表示的线性时不变系统（LTI）的输入与输出之间的关系。然而一些资料来源中用“传递函数”直接表示某些物理量输入输出的特性，（例如二端口网络中的输出电压作为输入电压的一个函数）而不使用变换到S平面上的结果。
In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a mathematical function that models the system's output for each possible input. It is widely used in electronic engineering tools like circuit simulators and control systems and in chemical reaction engineering for the study and modeling of the residence time distribution and stability of a reactor. In simple cases, this function can be represented as a two-dimensional graph of an independent scalar input versus the dependent scalar output (known as a transfer curve or characteristic curve). Transfer functions for components are used to design and analyze systems assembled from components, particularly using the block diagram technique, in electronics and control theory. Dimensions and units of the transfer function model the output response of the device for a range of possible inputs.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗反馈（英语：feedback，台湾作回馈），又称回授，是控制论的基本概念，指将系统的输出返回到输入端并以某种方式改变输入，它们之间存在因果关系的回路，进而影响系统功能的过程。在这种情况下，我们可以说系统“反馈到它自身”。在讨论反馈系统时，因果关系的概念应当特别仔细对待： “对于反馈系统，很难作出简单的推理归因，因为当系统A反馈到系统B，系统B又反馈到系统A，形成了循环。这使得基于因果关系的分析特别困难，需要将系统作为一个整体来看待。” 反馈可分为负反馈和正反馈。前者使输出发挥与输入相反的作用，使系统输出与系统目标的误差减少，系统趋于稳定；后者使输出发挥与输入相似的作用，使系统偏差不断增加，使系统振荡，可以放大控制作用。对负反馈的研究是控制论的核心问题。
Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause and effect that forms a circuit or loop. The system can then be said to feed back into itself. The notion of cause-and-effect has to be handled carefully when applied to feedback systems: Simple causal reasoning about a feedback system is difficult because the first system influences the second and second system influences the first, leading to a circular argument. This makes reasoning based upon cause and effect tricky, and it is necessary to analyze the system as a whole. As provided by Webster, feedback in business is the transmission of evaluative or corrective information about an action, event, or process to the original or controlling source.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗传感器（英语：Sensor）是一种检测环境中的事件或变化，并将此信息传送至其他电子设备（如中央处理器）的设备，通常由敏感器件和转换器件组成。传感器如被动式红外传感器和触摸传感器已广泛应用于日常物品，如触摸感应的电梯按钮和调光灯，以及温度、压力和流量测量等传统领域之外的无数应用中。随着微机电系统（MEMS）技术的进步，传感器可在微观尺度上批量制造，达到更快的测量速度和更高的灵敏度。一次性传感器的需求也在增长，用于短期监测或单次测量，无需重新校准且避免交叉污染。
A sensor is often defined as a device that receives and responds to a signal or stimulus. The stimulus is the quantity, property, or condition that is sensed and converted into electrical signal. In the broadest definition, a sensor is a device, module, machine, or subsystem that detects events or changes in its environment and sends the information to other electronics, frequently a computer processor. Sensors like PIR sensor or touch sensor are used in everyday objects such as touch-sensitive elevator buttons (tactile sensor) and lamps which dim or brighten by touching the base, and in innumerable applications of which most people are never aware. With advances in micromachinery and easy-to-use microcontroller platforms, the uses of sensors have expanded beyond the traditional fields of temperature, pressure and flow measurement, for example into MARG sensors. Analog sensors such as potentiometers and force-sensing resistors are still widely used.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗标定（英语：Calibration），即为科学上之校准行为，意指“对某仪器、药物或须有精确单位之物品，其只知的体积、浓度......等刻度或单位之准确度，进行检测是否合乎标准，若否则修正。”
In measurement technology and metrology, calibration is the comparison of measurement values delivered by a device under test with those of a calibration standard of known accuracy. Such a standard could be another measurement device of known accuracy, a device generating the quantity to be measured such as a voltage, a sound tone, or a physical artifact, such as a meter ruler. The outcome of the comparison can result in one of the following: no significant error being noted on the device under test a significant error being noted but no adjustment made an adjustment made to correct the error to an acceptable level Strictly speaking, the term "calibration" means just the act of comparison and does not include any subsequent adjustment. The calibration standard is normally traceable to a national or international standard held by a metrology body.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗不确定性量化（UQ）是对计算和现实世界应用中的不确定性进行定量表征和估计的科学。它试图确定如果系统的某些方面不完全已知的话某些结果的可能性有多大。一个例子是预测人体与另一辆车正面相撞时的加速度：即使速度是准确已知的，个别汽车制造过程中的微小差异、每个螺栓的拧紧程度等都会导致不同的结果，而这些结果只能在统计意义上进行预测。自然科学和工程学中的许多问题也充满了不确定性。计算机模拟的计算机实验是研究不确定性量化问题的最常见方法。
Uncertainty Quantification (UQ) is the science of quantitative characterization and estimation of uncertainties in both computational and real world applications. It tries to determine how likely certain outcomes are if some aspects of the system are not exactly known. An example would be to predict the acceleration of a human body in a head-on crash with another car: even if the speed was exactly known, small differences in the manufacturing of individual cars, how tightly every bolt has been tightened, etc., will lead to different results that can only be predicted in a statistical sense. Many problems in the natural sciences and engineering are also rife with sources of uncertainty. Computer experiments on computer simulations are the most common approach to study problems in uncertainty quantification.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。 本条中文为英文百科简介的机器辅助翻译，请结合英文原文核对专业术语。
查看内容许可 ↗在数值分析中，数值方法是一种旨在解决数值问题的数学工具。用编程语言实现具有适当收敛性检查的数值方法称为数值算法。
In numerical analysis, a numerical method is a mathematical tool designed to solve numerical problems. The implementation of a numerical method with an appropriate convergence check in a programming language is called a numerical algorithm.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。 本条中文为英文百科简介的机器辅助翻译，请结合英文原文核对专业术语。
查看内容许可 ↗微分方程（英语：Differential equation，DE）是一种数学方程，用来描述某一类函数与其导数之间的关系。微分方程的解是一个满足方程的函数，通常微分方程的解并不唯一，经常要给定恰当的初始条件或边界条件才能确定。而在初等数学的代数方程里，其解是常数。 微分方程的应用十分广泛，可以解决许多与导数有关的问题。物理学中许多涉及变力的运动学、动力学问题，如空气阻力为速度函数的自由落体运动等问题，很多可以用微分方程求解。此外，微分方程在化学、工程学、经济学和数理生物学等领域都有应用。 数学领域对微分方程的研究着重在几个不同的面向，但大多数都是关心微分方程的解。只有少数简单的微分方程可以求得解析解。不过即使没有找到其解析解，仍然可以确认其解的部分性质。在无法求得解析解时，可以利用数值分析的方式，利用电脑来找到其数值解。 动力系统理论强调对于微分方程系统的量化分析，而许多数值方法可以计算微分方程的数值解，且有一定的准确度。
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common in mathematical models and scientific laws; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. The study of differential equations consists mainly of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly.
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
查看内容许可 ↗傅里叶变换 （法语：Transformation de Fourier，英语：Fourier transform，缩写：FT）是一种线性变换，通常定义为一种积分变换。其基本思想是一个函数可以用（可数或不可数，可数的情况对应于傅里叶级数）无穷多个周期函数的线性组合来逼近，从而这些组合系数在保有原函数的几乎全部信息的同时，还直接地反映了该函数的“频域特征”。因其基本思想首先由法国学者约瑟夫·傅里叶系统地提出，所以以其名字来命名以示纪念。在现代数学理论中，傅里叶积分变换可以得到各种推广，并在分析学中有广泛应用，构成了调和分析这一数学领域。 经过傅里叶变换生成的函数 f ^ {\displaystyle {\hat {f}}} 称作原函数 f {\displaystyle f} 的傅里叶变换，应用意义上称作频谱。在特定情况下，傅里叶变换是可逆的，即将 f ^ {\displaystyle {\hat {f}}} 通过逆变换可以得到其原函数 f {\displaystyle f} 。通常情况下， f {\displaystyle f} 是一个实函数，而 f ^ {\displaystyle {\hat {f}}} 则是一个复数值函数，其函数值作为复数可同时表示振幅和相位。
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex valued function of frequency. The term Fourier transform refers to both the mathematical operation and to this complex-valued function. When a distinction needs to be made, the output of the operation is sometimes called the frequency domain representation of the original function. The Fourier transform is analogous to decomposing the sound of a musical chord into the intensities of its constituent pitches. Functions that are localized in the time domain have Fourier transforms that are spread out across the frequency domain and vice versa, a phenomenon known as the uncertainty principle. The critical case for this principle is the Gaussian function, of substantial importance in probability theory and statistics as well as in the study of physical phenomena exhibiting normal distribution (e.g., diffusion).
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维基百科条目作者 · 获取于 2026-10-04 · CC BY-SA 4.0。简介经过纯文本提取与截取；两个语言版本的内容侧重可能不同。用于概念速查，不替代标准原文。
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