Why is mass loading and data consistency important for modal parameter estimation?

Let me explain

为什么质量载荷和数据一致性对于模态参数估计是如此之重要？

那我来解释吧。

 

This is other good example where people can get confused when performing modal parameter estimation. All too often when the curvefitting results are confusing or appear distorted, the effects will be blamed on noise or nonlinearities. This is often a blanket statement that many people use when they don't understand or can't explain something easily. Let's look at why data consistency is important and what effects mass loading will have.

这又是一个很好的问题，是人们进行模态参数估计时会感到困惑的地方。当曲线拟合结果令人迷惑或者看上去不正常的时候，太多的时候是把这些效果归咎于噪声或非线性。这常常是一句空洞的话，当不理解或者不能轻易解释某些事物的时候，很多人使用这句话。那我们看一看为什么数据一致性很重要，质量载荷会有什么影响。

 

The first thing to recall is that the model we use to fit data comes from a linear, symmetric set of equations where the poles (frequency and damping) are defined in terms of global quantities and reciprocity is assumed to be inherent in the formulation of the equations. Now as long as our data fits that model then everything is OK. But how does my testing and data acquisition have an effect.

首先要记起的事情是，我们用以拟合数据的模型是根据一个线性、对称方程组，其中极点（频率和阻尼）定义为全局物理量，而且在方程的推导过程中假定互易性是本质固有的。现在只要我们的数据跟那个模型吻合，则万事大吉。但是，试验和数据采集有影响怎么办？

Let's consider a simple plate test setup that is driven by two shakers for a MIMO test with an 8 channel data acquisition system. Now I'll acquire FRFs using good measurement techniques to assure the best possible measurements are obtained for the 6 accelerometers mounted on the plate shown in Figure 1 (the solid fill points are for the first test and the other points are associated with the second test and are obtained by roving the accelerometers on the structure).

我们来考虑一个简单平板的试验设置，采用一套8通道的数据采集系统，通过两个激振器激励进行MIMO试验。现在，如图1所示，对安装于平板之上的6个加速度计，我将利用高水准的测试技术来采集FRFs，以保证得到尽可能最优的测量结果（第1次试验时测量实心点，第2次试验时测量其他点，并且通过在结构上移动加速度计来得到这些测点）。

 

The mode indicator function is shown in Figure 2 and the stability diagram is shown in Figure 3. The poles are extracted for the first two modes only (for illustration purposes). The stability diagram shows these two poles very clearly. Notice that as the order of the model increases, the poles are clearly identified (overlaid on the summation function). Once the poles are extracted, then the residues or mode shapes are obtained to provide modal data associated with these 6 measurement points; a typical curvefit is shown in Figure 4.

图2显示的是模态指示函数，图3是稳态图。仅仅提取前2阶模态的极点（为示意目的）。稳态图非常清晰地指出了这两个极点。注意，随着模型阶数的增加，很清晰地确定了极点（跟求和函数重叠在一起）。一旦提取出极点，就可以得到留数或振型，这样就得到了与这6个测点相关的模态数据。图4显示了一个典型的曲线拟合。

 

However, this first set of data only consists of 6 measurement points. In order to better define the mode shapes, more measurement points are needed.

可是，第1组数据仅仅包含6个测点。为了更好地确定模态振型，需要更多的测点。

 

 

For the additional points, the accelerometers are relocated to the measurement points shown (non-filled points) and a second set of MIMO measurements were collected. Again, poles are extracted using just this second set of measurement points and a stability diagram obtained. Again the poles are clearly identified and mode shapes associated with these 6 points identified. (These results are not shown here but are similar to the first case.) But the two sets of data were evaluated separately to estimate the poles and residues.

对于其余的测点，加速度计重新布置到图示的测点上（空心点），这样采集到了第2组MIMO测量结果。这一次也是仅仅利用第2组测点来提取极点，并得到稳态图。这一次也清晰地确定了了极点，以及与这6个测点相关的模态振型。（此处，没有显示这些测量结果，但其与第1次情况类似。）但是这两组数据是分别求值来估计极点和留数的。

 

Now let's combine the two data sets together and evaluate the data. The mode indicator function and  stability diagram are computed again. Now instead of 2 distinct peaks as we saw earlier in the MIF, there are now 4 distinct peaks over the same band (Figure 5). The estimation of the poles for the same frequency band (Figure 6) used earlier now shows 4 modes instead of 2!!! How could this possibly be? The plate didn't change - did it?

现在，我们将这两组数据合在一起求值。重新计算模态指示函数和稳态图。现在在相同的频带内，我们在模态指示函数上看到的不是之前观察到的2个明显的峰，反而是4个明显的峰（图5）。之前用过的相同频带现在指示出了4阶模态，而不是2阶模态！！！这怎么可能？平板没有变 — 不是吗？

 

Well, the plate didn't change - but the test setup sure did! The roving accelerometers have a mass effect that caused the modes to shift slightly. So when all the data is processed simultaneously, some of the measurements indicate the poles at a certain frequency and the other measurements indicate the poles at a different frequency.

嗯，平板是没有变 — 但试验设置却真真确确地改变了！移动的加速度计具有质量影响，引起了模态的些许迁移。所以当同时处理所有数据时，有些测量结果指示出极点在某一个频率上，而其他测量结果却指示出极点在另外一个频率上。

 

So which is correct? It is likely that neither is correct. That's because the test setup had an effect on the measured modes of the system. The question is which poles are the correct ones to be used for the modal parameter estimation process. Well, you really can't identify a global set of poles for all the measurements since they are not "global" for all the measurements. Actually, the correct way to extract parameters in this case is to collect a "consistent" set of data by eliminating the mass loading effect by mounting all the instrumentation on the structure (or adding dummy masses) for the duration of the test.  This will provide more "consistent" data which conforms to the model being used to fit the data. Of course, it is very important to point out that we have modified the structure due to the addition of all of the masses. But at least all the data will be consistent and will not distort the modal parameter estimation process due to mass loading effects.

那么哪一个是对的？好像两个都不对。这是因为试验设置对系统的模态产生了影响。问题是哪些极点是正确的，可以用于模态参数估计过程。嗯，对于所有的测量结果，你确实不能确定一组全局的极点，因为它们对于所有测量结果而言并不是“全局的”。实际上，在这种情况下，正确提取参数的办法是，试验过程中在结构上安装上所有的测点（或者加上质量哑元），消除质量荷载的影响，来采集一组“一致”的数据。当然，有一个非常重要的点要指出，由于加上了所有的质量，我们已经改变了结构。但是，至少所有的数据将是一致的，不会因为质量荷载影响造成模态参数估计过程失真。

 

Of course, real world structures have all kinds of measurement problems with respect to noise, linearity, time variability, etc. The modal parameter estimation process is complicated enough. Don't complicate the process further by letting simple items such as mass loading distort your data. I hope this helps to answer your question as to why mass loading and data consistency is so important. If you have any other questions about modal analysis, just ask me.

当然，真实结构具有关于噪声、线性、时变等等方面的各种测量问题。模态参数估计过程已经够复杂的了。不要让一些简单问题将这个过程进一步复杂化了，诸如质量荷载引起数据失真的问题。我希望这个讨论帮你解答了你的关于质量荷载和数据一致性为什么是如此重要的问题。如果你有关于模态分析的任何其他问题，尽管问我好了。