現(xiàn)在有一種流行的方法，將數(shù)學(xué)模型分為機(jī)理模型和數(shù)據(jù)模型。我一直認(rèn)為，對(duì)于工業(yè)應(yīng)用來說，這種分類是不合適的。因?yàn)楝F(xiàn)實(shí)機(jī)械模型往往是兩者結(jié)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.

所謂機(jī)理模型，本質(zhì)上是理想模型(或抽象模型)。當(dāng)模型能夠準(zhǔn)確描述真實(shí)對(duì)象時(shí)(或誤差足夠小時(shí))，模型的計(jì)算結(jié)果能夠與實(shí)際結(jié)果高度一致，使用起來非常方便。如果模型主要從事純算數(shù)或邏輯計(jì)算、幾何對(duì)象轉(zhuǎn)換等。，計(jì)算結(jié)果確實(shí)可以與現(xiàn)實(shí)高度融合。因此，在離散制造業(yè)中，3D設(shè)計(jì)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.

但是抽象模型總歸不等于現(xiàn)實(shí)對(duì)象。例如，歐幾里得幾何學(xué)中的線是沒有寬度的，而現(xiàn)實(shí)中的線是有寬度的。牛頓力學(xué)中的質(zhì)點(diǎn)是沒有體積的，而現(xiàn)實(shí)世界中的優(yōu)良物質(zhì)是有體積的。

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.

實(shí)際工業(yè)對(duì)象是具體的。

The actual industrial object is concrete.

當(dāng)理論模型應(yīng)用于特定對(duì)象(如特定設(shè)備和工廠)時(shí)，問題就會(huì)出現(xiàn)：機(jī)理模型忽視的干擾，現(xiàn)實(shí)可能不容忽視；機(jī)理模型需要測(cè)量的參數(shù)，現(xiàn)實(shí)可能無法測(cè)量或無法測(cè)量。還有一個(gè)問題：當(dāng)這些誤差太大而無法忽略時(shí)，該怎么辦？

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?

方案大致有三種:1。充分考慮各種干擾。但這樣做，模型的復(fù)雜性會(huì)大大提高，不一定實(shí)用；2.準(zhǔn)確測(cè)量相關(guān)參數(shù)。但是，這往往需要大量的成本，甚影響實(shí)施效率，實(shí)用性差。3.更現(xiàn)實(shí)的方法是用實(shí)際數(shù)據(jù)糾正。因此，機(jī)制與數(shù)據(jù)模型相結(jié)合。事實(shí)上，第三種方法是平時(shí)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.

眾所周知，非線性物體通常可以局部簡化為線性模型。這是自然界中常見的現(xiàn)象。但是在工業(yè)場(chǎng)景中，除了局部使用的線性回歸模型之外，很少有純數(shù)據(jù)模型。因?yàn)橛眉償?shù)據(jù)模型建立非線性和時(shí)變模型時(shí)，往往難以保證可靠性，不適合工業(yè)應(yīng)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，工業(yè)模型上實(shí)用的數(shù)學(xué)模型，往往是機(jī)制和數(shù)據(jù)的結(jié)合。

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

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