现在有一种流行的方法，将数学模型分为机理模型和数据模型。我一直认为，对于工业应用来说，这种分类是不合适的。因为现实机械模型往往是两者结合在一起的，只是程度的不同。

Now there is a popular method to divide mathematical model into mechanism model and data model. I always think that this classification is inappropriate for industrial applications. Because the real mechanical model is often combined with the two, but the degree is different.

所谓机理模型，本质上是理想模型(或抽象模型)。当模型能够准确描述真实对象时(或误差足够小时)，模型的计算结果能够与实际结果高度一致，使用起来非常方便。如果模型主要从事纯算数或逻辑计算、几何对象转换等。，计算结果确实可以与现实高度融合。因此，在离散制造业中，3D设计模型可以大大提高R&D效率。

The so-called mechanism model is essentially an ideal model (or abstract model). When the model can accurately describe the real object (or the error is small enough), the calculated results of the model can be highly consistent with the actual results, so it is very convenient to use. If the model is mainly engaged in pure arithmetic or logical calculation, geometric object transformation, etc., The calculation results can be highly integrated with the reality. Therefore, 3D design model can greatly improve R & D efficiency in discrete manufacturing.

但是抽象模型总归不等于现实对象。例如，欧几里得几何学中的线是没有宽度的，而现实中的线是有宽度的。牛顿力学中的质点是没有体积的，而现实世界中的优良物质是有体积的。

But the abstract model is not equal to the real object. For example, lines in Euclidean geometry have no width, while lines in reality have width. The particle in Newtonian mechanics has no volume, while the good material in the real world has volume.

实际工业对象是具体的。

The actual industrial object is concrete.

当理论模型应用于特定对象(如特定设备和工厂)时，问题就会出现：机理模型忽视的干扰，现实可能不容忽视；机理模型需要测量的参数，现实可能无法测量或无法测量。还有一个问题：当这些误差太大而无法忽略时，该怎么办？

When the theoretical model is applied to specific objects (such as specific equipment and factory), problems will arise: the interference ignored by the mechanism model may not be ignored in reality; The parameters of mechanism model need to be measured, which may not be measured or measured in reality. There is another question: what to do when these errors are too big to ignore?

方案大致有三种:1。充分考虑各种干扰。但这样做，模型的复杂性会大大提高，不一定实用；2.准确测量相关参数。但是，这往往需要大量的成本，甚影响实施效率，实用性差。3.更现实的方法是用实际数据纠正。因此，机制与数据模型相结合。事实上，第三种方法是平时常用的。

There are three solutions: 1. All kinds of interference should be fully considered. But in this way, the complexity of the model will be greatly improved, and it is not necessarily practical; 2. Accurate measurement of relevant parameters. However, this often requires a lot of cost, even affects the implementation efficiency, and the practicability is poor. 3. A more realistic method is to correct with actual data. Therefore, mechanism is combined with data model. In fact, the third method is usually used.

众所周知，非线性物体通常可以局部简化为线性模型。这是自然界中常见的现象。但是在工业场景中，除了局部使用的线性回归模型之外，很少有纯数据模型。因为用纯数据模型建立非线性和时变模型时，往往难以保证可靠性，不适合工业应用。

It is well known that nonlinear objects can be reduced to linear models locally. This is a common phenomenon in nature. However, in industrial scenarios, there are few pure data models except for the local linear regression model. Because it is difficult to guarantee the reliability when using pure data model to build nonlinear and time-varying model, it is not suitable for industrial application.

因此，工业模型上实用的数学模型，往往是机制和数据的结合。

Therefore, the practical mathematical model of industrial model is often the combination of mechanism and data.

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