模型的定義及其分類
Definition and classification of models
模型是對現實世界的事物、現象、過程或系統的簡化描述，或其部分屬性的模仿。在一般的意義下是指模仿實物或設計中的構造物的形狀制成的雛型，其大小可以分為縮小型、實物型和放大型。有些模型甚連細節(jié)都跟實物一模一樣，有些則只是模仿實物的主要特征。模型的意義在于可通過視覺了解實物的形象，除了具有藝術欣賞價值外，在教育、科學研究、工業(yè)建設、土木建筑和軍事等方面也有極大的效用。隨著科學技術的進步，人們將研究的對象看成是一個系統，從整體的行為上對它進行研究。這種系統研究不在于列舉所有的事實和細節(jié)，而在于識別出有顯著影響的因素和相互關系，以便掌握本質的規(guī)律。對于所研究的系統可以通過類比、抽象等手段建立起各種模型。這稱為建模。模型可以取各種不同的形式，不存在統一的分類原則。按照模型的表現形式可以分為物理模型、數學模型和結構模型。
A model is a simplified description of things, phenomena, processes, or systems in the real world, or an imitation of some of their properties. In a general sense, it refers to a prototype made by imitating the shape of physical objects or structures in design, and its size can be divided into miniaturization, physical type, and enlargement. Some models even have the same details as the real object, while others only imitate the main features of the real object. The significance of models lies in their ability to visually understand the image of physical objects. In addition to having artistic appreciation value, they also have great utility in education, scientific research, industrial construction, civil engineering, and military affairs. With the advancement of science and technology, people view the research object as a system and study it from a holistic perspective. This type of systematic research is not about listing all facts and details, but about identifying significant influencing factors and interrelationships in order to grasp the essential laws. Various models can be established for the studied system through analogy, abstraction, and other means. This is called modeling. The model can take various forms and there is no unified classification principle. According to the representation of models, they can be divided into physical models, mathematical models, and structural models.
物理模型
physical model
也稱實體模型，又可分為實物模型和類比模型。①實物模型：根據相似性理論制造的按原系統比例縮小（也可以是放大或與原系統尺寸一樣）的實物，例如風洞實驗中的飛機模型，水力系統實驗模型，建筑模型，船舶模型等。②類比模型：在不同的物理學領域（力學的、電學的、熱學的、流體力學的等）的系統中各自的變量有時服從相同的規(guī)律，根據這個共同規(guī)律可以制出物理意義完全不同的比擬和類推的模型。例如在一定條件下由節(jié)流閥和氣容構成的氣動系統的壓力響應與一個由電阻和電容所構成的電路的輸出電壓特性具有相似的規(guī)律，因此可以用比較容易進行實驗的電路來模擬氣動系統。
Also known as physical models, they can be divided into physical models and analog models Physical model: A physical model manufactured according to the theory of similarity, which is scaled down (or can be enlarged or the same size as the original system) according to the original system, such as an aircraft model in wind tunnel experiments, a hydraulic system experimental model, a building model, a ship model, etc Analogy model: In different fields of physics (mechanics, electricity, thermodynamics, fluid mechanics, etc.), the variables of each system sometimes follow the same law. Based on this common law, models with completely different physical meanings can be created for analogy and analogy. For example, under certain conditions, the pressure response of a pneumatic system composed of a throttle valve and a gas volume has a similar pattern to the output voltage characteristics of a circuit composed of resistance and capacitance. Therefore, a circuit that is relatively easy to experiment with can be used to simulate pneumatic systems.
數學模型
mathematical model
用數學 語言描述的一類模型。數學模型可以是一個或一組代數方程、微分方程、差分方程、積分方程或統計學方程，也可以是它們的某種適當的組合，通過這些方程定量地或定性地描述系統各變量之間的相互關系或因果關系。除了用方程描述的數學模型外，還有用其他數學工具，如代數、幾何、拓撲、數理邏輯等描述的模型。需要指出的是，數學模型描述的是系統的行為和特征而不是系統的實際結構。
A type of model described in mathematical language. A mathematical model can be an algebraic equation, differential equation, difference equation, integral equation, or statistical equation, or an appropriate combination of them, which quantitatively or qualitatively describes the interrelationships or causal relationships between variables in the system. In addition to mathematical models described by equations, there are also models described by other mathematical tools such as algebra, geometry, topology, mathematical logic, etc. It should be pointed out that mathematical models describe the behavior and characteristics of a system rather than its actual structure.
結構模型
Structural model
主要反映系統的結構特點和因果關系的模型。結構模型中的一類重要模型是圖模型。此外生物系統分析中常用的房室模型等也屬于結構模型。結構模型是研究復雜系統的有效手段。
A model that mainly reflects the structural characteristics and causal relationships of the system. An important type of model in structural models is graph models. In addition, commonly used room models in biological system analysis also belong to structural models. Structural modeling is an effective means of studying complex systems.
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