MODAL SPACE - IN OUR OWN LITTLE WORLD

模态空间–在我们自己的小世界中   

Pete Avitabile 著  KINGSCI INSTRUMENTS-KSI科尚仪器 组织 westrongmc 译

Curvefitting is so confusing to me!

What do all the different techniques mean?

There's a lot to it all ...

曲线拟合搞得我一头雾水！

所有这些不同的技术是什么意思？

说来话长了…

Curvefitting is probably the most difficult part of the whole experimental modal analysis process for most people. Actually, it’s better to refer to it as modal parameter estimation. But that's a mouthful - so we usually just call it curvefitting. But we are actually trying to extract modal parameters (frequency, damping and mode shapes) from measured data. Let's discuss a few general items first.

对大多数人来讲，曲线拟合可能是整个试验模态分析过程中最难的部分。实际上，最好称它为模态参数估计。但那有点绕口 — 所以我们一般就称它为曲线拟合。但实际上我们是试图从测试数据中提取模态参数（频率，阻尼和模态振型）。让我们首先讨论一些一般性的内容。

Basically, we need to describe the system in terms of its modes of vibration. For example, the three mode system shown in Fig 1 can be described by the following frequency domain representation of the system as

从根本上讲，我们需要根据系统的振动模态来描述系统。例如，图1所示的三阶模态系统可以根据下面的系统频响函数表达式来描述，

or broken down into the contribution of each of the modes as

或者分解为各阶模态的贡献，

Now as you start to look at this measurement, some quick thoughts come to mind. How many data points should I use? What should the order of the model be? Are there any effects from modes outside the band of the curvefitter? Does the same technique need to be applied to all the modes? When do I use a SDOF vs. a MDOF technique? Should I use a time or frequency domain curvefitter? (And the most important thing that should come to mind is - Oh how I wished I listened in modal class that day instead of going out to party!)

现在当你开始观察这个测量结果时，很快会想到几个问题。我应该用多少数据点？模型阶数该是多少？曲线拟合算子的带外模态有什么影响吗？需要应用相同的技术于所有阶模态吗？我什么时候用单自由度，什么时候用多自由技术？我该用时域还是频域曲线拟合算子？（而最应该想起来的是 — 哎呀，我多么希望那天我是去听模态课了，而不是跑出去开派对了！）

First let's consider the some simple force gage calibration data in Fig 2. Now if the force gage should read zero at zero load, then Fig 2a represents the best straight line fit of the data – but that fit doesn't look very good. But what if the force gage had a preload. Then it may be necessary to allow for some compensation as shown in Fig 2b. And what if some of the measured data was outside the useful range of the force transducer. Possibly only a portion of the data should be used as shown in Fig 2c. And who said that the force gage was linear with a first order approximation of y=mx+b? I could possibly envision a cubic function that would better describe the measured data. For some reason everyone understands this force gage example but have a hard time realizing that my measured FRF has the same characteristics. Basically the analyst must decide on the order of the model, the amount of data to use and the need for residual compensation as shown in Fig 3. The basic equation to address this measurement is

首先，让我们考虑某个简单的测力计校准数据，图2所示。现在，如果在不受载荷情况下，测力计应该读到零值，则图2a代表了数据的最优直线拟合 — 但是，那个拟合看起来不是很好。另一方面，测力计要是有预载荷，情况又是怎样呢？那么，可能需要允许来点补偿，如图2b所示。另外，要是有些测量数据超出力传感器的有效范围，情况又是如何呢？很可能仅仅应该使用一部分数据，如图2c所示。另外，谁说力传感器是线性的，可以用y=mx+b来一阶近似了？我有可能设想用一个三次函数来更好地描述测量数据。出于某些原因，人人都理解这个测力计的例子，但却很难认识到我测量的FRF也有相同的特性。从根本上讲，分析人员必须确定模型阶数，用多少数据量，以及是否需要进行残余项补偿，如图3所示。表示这个测量结果的基本方程如下

Basically, I select a band of modes to fit, specify the order of the model and decide on inclusion of residual terms.

大致说来，我选择一段模态进行拟合，指定模型阶数，以及确定包含残余项。

Now I need to know when to use a SDOF or MDOF technique. What I need to know is how much modal overlap exists from one mode to the next. Fig 4 shows a variety of different situations for a two DOF system. Fig 4a shows modes that are well separate with very light damping. These types of modes can be approximated with a SDOF fit. Fig 4b shows modes that are closely spaced with very light damping.

现在，我需要知道何时使用单自由度或多自由度技术。我所需要知道的是，一阶模态与相邻的下一阶模态在多大程度上有模态重叠。图4显示了对于两自由度系统的各种不同情况。图4a表示各阶模态分离的很开，并且具有很小的阻尼。此类多阶模态可以用单自由度拟合来近似。图4b表示各阶模态相邻的很近，并且带有很小的阻尼。

There is some overlap from one mode to the next which may not be correctly compensated with a SDOF fit. It is likely that a MDOF fit may need to be employed for these two modes. Fig 4c shows well separated modes but damping causes some overlap which may also require a MDOF fit. But for both of these last two cases, you may try a SDOF fit for comparison with the MDOF fit. Fig 4d shows modes that are closely spaced with heavy damping. A MDOF fit would be needed for this case.

一阶模态与相邻的下一阶模态有些重叠，这或许不能用单自由度拟合来正确地补偿。对于这两阶模态，有可能需要用多自由度拟合。图4c表示分得很开的模态，但阻尼引起一定程度的重叠，这可能需要用多自由度拟合。但是，对于后面这两种情况，你或许可以试试单自由度拟合，来与多自由度拟合进行对比。图4d表示各阶模态相邻的很近，并且具有大阻尼。对此情形，这就需要用多自由度拟合。

The last thing to consider is whether to use a time or frequency domain technique. The mathematical relationship is basically the same - it just looks different. Many times we write a relationship in a given form because there is some mathematical gimmick that makes the equation easier to solve or more efficient from a computational standpoint. But, in essence, both domains are equivalent. However, many times we tend to use the time domain techniques for lightly damped systems and the frequency domain techniques for heavily damped systems.

最后一件要考虑的事情是，是要用时域技术还是要用频域技术？从本质上讲，数学关系式是相同的 — 只是看起来不一样。很多情况下，我们按某种形式写出关系式，是因为有些数学技巧在其中，这样使得方程更易于求解，或者从计算的角度来看，更高效。但是，从本质上讲，这两个域是等价的。无论如何，很多时候对于小阻尼系统，我们倾向于用时域技术；而对于大阻尼系统，我们倾向于用频域技术。

If I now look at Fig 5, what would I think would be appropriate for estimating parameters for this measurement? Well it is probably alright to use a SDOF for that first peak. But modes 2 and 3 are too closely spaced to use a SDOF, so most likely a MDOF technique would be used for these modes.  Another thing to realize is that the cursors don't need to overlap or cover the whole frequency band.  Remember that we are trying to extract parameters that identify the frequency, damping and residue for the system for each of the modes.

如果现在观察图5，对于这个测量结果来讲，要估计模态参数，我该怎样去想才是恰当的呢？嗯，对第一个峰，利用单自由度有可能是正确的。但是模态2和模态3相邻的太近，不能用单自由度。这样，对这些模态，很有能要用多自由度技术。要意识到的另外一件事情是，光标间不需要重叠或者覆盖整个频率区间。记住，我们是要试图提取参数，对系统辨识出每一阶模态的频率、阻尼和留数信息。

We really need to spend a lot more time discussing all the details of each of the techniques but there isn't enough time right now to cover everything. But this quick overview should give you an idea of some of the concepts involved. Think about what we have discussed and maybe another time we can discuss each of the techniques in more detail. If you have any more questions on modal analysis, just ask me.

我们真的需要花更多的时间来讨论每种技术的全部细节，但是当下没有足够的时间来面面俱到。但是这个概述应该可以让你对所涉的某些概念有个初步认识。好好思考一下我们讨论过的内容，或许在下一次，我们可以更详尽地讨论每种技术。如果你有模态分析的任何其他问题，问我好了。