Should I use all collected measurements when estimating modal parameters?

Let's discuss this.

估计模态参数时，要用上全部的测量数据吗？

那我们来讨论一下这个问题。

 

This is a very good question. There is no reason to not include all the data collected providing that the data is well measured and consistently related. Providing that there is good dynamic range, with accurate sensitive transducers and all modes are well excited from all reference points and at all the response locations, then, of course, all the data can be used for estimating modal parameters.

这个问题问得很好。如果数据测的质量好并且一致相关的话，没有理由不包含全部的数据。假设在所有的响应位置，有良好的动态范围、准确而灵敏的传感器以及从所有参考点位置都很好地激起了所有阶模态的话，那么当然应该用全部的测量数据来估计模态参数。

 

But as I said that mouthful of requirements, I could tell from the expression on your face that it is highly unlikely that all your measurements meet that requirement. In the past quarter century, I know that I have never had that happen in any test I have conducted or been associated with - so join the club! What I just described is a measurement situation that will likely only occur with an analytical model with infinite dynamic range and infinite frequency resolution. The real fact is that from a practical standpoint, this will probably never happen. So let's discuss the reality of the situation and discuss some practical approaches to minimize some of the measurement shortcomings.

但是当我提到如此众多要求的时候，我从你脸上的表情就能看得出来，你全部测量数据都满足这些要求是极其不可能的。我知道在过去的25年中，在我所进行的或者跟我有关系的任何一次测试中，从来没有遇到那种情况发生 — 我也一样！我刚才所描述的测量情形只在具有无限大动态范围和无限小频率分辨率的理论模型中才可有可能发生。从实际的角度来看，事实是这种情况可能永远也不会发生。所以我们还是讨论实际情况以及某些实用方法来减少测量的不足之处吧。

As an example of a common measurement problem, I will use a test that was run many years ago on an aerospace structure that had very directional modes as well as numerous local modes. The structure is shown in Figure 1 along with some typical FRFs. Notice that the lower FRF only shows a few modes but the upper FRF shows all the modes of the structure. Actually, the problem isn't just an aerospace problem but a general problem that can be seen in many structures we test. In fact, the measurements shown are typical of those that could be from almost any structure subjected to modal testing.

我拿很多年前在航天结构上进行的试验作为常见测量问题的一个例子，这个结构具有非常方向性的模态，同时也有很多阶局部模态。结构、某些典型频响函数如图1所示。注意，下部的频响仅仅显示出了某些模态，但上部的频响显示出了结构的所有阶模态。实际上，这不仅仅是一个航天问题，而是在我们所测试的很多结构上都可以观察到的一个普遍问题。事实上，所示的测量结果是几乎所有模态测试结构上都会有的典型结果。

 

The particular structure shown had several bending and torsional lower order modes followed by many local modes with bending, torsion, in-phase, out-of-phase types of modes for the panels and peripheral equipment on the structure. The actual structure was tested using 5 independent shaker excitations (three vertical and two separate horizontal directions).

所示的这个特定结构具有多阶弯曲和扭转的低阶模态，后面紧接着的是结构上的板结构及垂直设备的许多阶局部模态，它们具有弯曲、扭转、同相位、反相位的形式。用了5个独立的激振器对这个实际结构进行试验（三个垂直方向和两个独立的水平方向）。

 

The first mode of the structure consisted of bending in the x direction with almost no response in the y-direction. Obviously, the shaker in the x-direction can do a very good job of exciting the x-direction modes but the shaker in the y-direction does not excite the structure in the x-direction very well at all. So the measurements obtained from the y shaker are obviously going to be very poor due to the lack of participation of the first mode in the y-direction.

结构的第1阶模态在x方向上具有弯曲变形，而在y方向上几乎没有响应。显然，在x方向上的激振器可以很好地激起x方向上的模态，但y方向的激振器根本不可能很好地对结构进行x方向的激励。所以从y激振器得到的测量结果显然会很差，因为第1阶模态在y方向上没有参与。

 

On the other hand, the second mode of the structure consisted of bending in the y-direction with almost no response in the x-direction. Here the opposite is true from that just discussed. The y shaker can do a very good job of exciting the structure in the y-direction but the shaker in the x-direction cannot excite the structure in the y-direction. But both shakers can do a very good job of exciting the torsional mode from both shaker locations. This directly implies that all of the measurements will not be measured with the same degree of accuracy for each mode.

另一方面，结构的第2阶模态在y方向上具有弯曲变形，而在x方向上几乎没有响应。于是跟刚才所讨论的相对的情形也是正确的。y激振器可以在y向很好地激起结构，但是x向激振器不能在y方向上激起结构。但是从两个激振器位置上，这两个激振器都可以很好地激起扭转模态。这直接表明对于每阶模态，所有的测量结果并非相同程度的准确。

 

During the MIMO excitation with 5 shakers, all of the FRFs are collected simultaneously but clearly not all of the modes are excited equally from each of the shaker locations. This is a physical reality of most test structures that is typically impossible to overcome. So how can all of this data be efficiently and accurately processed?

在用5个激振器进行MIMO激励过程中，所有的频响函数FRFs是同时采集的，但是显然，并非从每个激振器位置都相同程度地激起了所有阶模态。这是大多数测试结构通常无法克服的客观事实。那么怎么可能将所有的这些测量数据都有效而准确地进行处理呢？

 

Most modal parameter estimation performed today, generally utilizes a two step process. First, the poles are estimated and then the residues or mode shapes are computed (once global poles have been extracted). With this in mind, the poles of the system do not need to be estimated using all the measurements collected. The poles can be estimated using only a subset of measured functions that best describe the poles of interest. Once the global poles have been estimated, then the residues or mode shapes can be extracted using all the measurement DOFs (It is also not necessary to estimated residues for all references especially if the references do not sufficiently excite all the modes). The selection of particular FRFs for the extraction of poles is schematically shown in Figure 2.

今天几乎所有的模态参数估计通常使用两步法。首先估计极点，接下来计算留数或者振型（当全局极点提取出来之后）。记住这一点，不需要利用所有采集到的测量结果来估计系统极点。可以仅仅利用测量函数的一个子集来估计极点，这个子集最佳地描述了感兴趣的极点。一旦全部极点估计出来后，接着就可以利用全部的测量结果D0Fs来提取留数或者模态振型（没有必要对所有的参考点来估计留数，特别是如果参考点不能充分激起所有阶模态，更是这样。）用来提取极点的特定频响函数FRFs的选择如图2所示。

In the example discussed, the first x-bending mode was estimated using only the x-response location from the x-excitation location. Only the y-response locations were used for the y-excitation location for the y bending modes. But both x and y excitations with the x and y responses were used for the torsional mode. Notice that the z-direction excitation and response were not used for the estimation of any of these poles. This is because the z-excitation locations have a very hard time exciting either the x or y direction modes efficiently. While these references/excitations are necessary for the excitation of some of the higher frequency modes, these vertical excitations are not very good for the excitation of the lower order x and y direction modes. But, of course, once the poles are estimated, then the residues or mode shapes are estimated using all the measurements in the x, y and z directions - but only using the x and y shaker excitations for the x and y lower order modes.

在这个讨论的例子中，仅仅利用从x-激励位置得到的x-响应位置来估计第1阶x-弯曲模态。对于y-激励位置，y弯曲模态来讲，仅仅利用到了y-响应位置。但是对于扭转模态来讲，x和y这两者的激励和响应都用上了。注意，都没有用到z-向的激励和响应来估计任何极点。这是因为z-激励位置很难有效地激起x向或者y向的模态。尽管这些参考点/激励对于激起某些更高频率的模态是必要的，但这些垂直激励不能很好地激起低阶的x和y向模态。但是当然，当极点估计出来以后，就可以利用所有的x，y和z向的测量结果来估计留数或者模态振型了– 但是对于x和y的低阶模态，仅仅利用了x和y激振器的激励数据。

 

During the modal parameter estimation process, extreme care needs to be exercised to extract the best possible poles to describe the system characteristics. However, many of the measurements and often times all of the references are not optimum for all the modes of the system. As an example, a large telescope structure was recently tested with 4 reference excitation locations. Clearly, the references were not all optimum for all the lower order directional modes of the structure. As a first pass on evaluating the data, all the FRFs from all the reference locations were used to extract poles and residues for the structure. Once parameters were selected, a synthesized FRF was generated and compared to the actual acquired measurement as part of the validation process. The synthesized and measured FRF are shown in Figure 3a. Please carefully note that this is not a good comparison of the measured and synthesized FRFs. However, after a very careful evaluation of the data and careful selection of measurements to extract the poles of the system (followed by residue extraction), a far better model was obtained. This is confirmed by the comparison of the synthesized and measured FRF shown in Figure 3b. Of course, this approach requires significant effort but the modal parameters are generally greatly improved.

在模态参数估计过程中，需要极其小心地来提取最优的可能极点来描述系统特性。但是，对于系统的所有阶模态，测量结果以及很多时候所有的参考点并不是最优的。举个例子，近期用4个参考点激励位置测量了一个大型望远镜结构。显然对于结构的所有低阶方向性的模态，参考点并非都是最优的。作为第一次评判测量数据，所有参考点位置得到的全部频响都用于提取结构的极点和留数。当参数选定后，作为验证过程的一部分，可以生成一个综合频响用来跟实际采集到的测量结果进行对比。综合频响和测量频响如图3a所示。请仔细观察，测量频响和综合频响的对比结果并不好。但是，经过仔细评估数据、仔细选择测量结果来提取系统极点（接下来提取留数），可以得到一个更好的模型。这点由图3b所示的综合频响和测量频响的对比得以证实。当然，这种方法需要付出极大的努力，但是模态参数通常大为改善。

I hope this explanation helps you to understand why it may not be necessary (or actually detrimental) to use all of the measured FRFs when extracting modal parameters. A careful selection of the best measured FRFs will generally produce much better global poles of the system for the modal parameter estimation process. If you have any other questions about modal analysis, just ask me.

我希望这个解释有助于你理解在提取模态参数时，为什么没有必要（或者说实际上是不利的）用上所有的测量频响。在模态参数估计过程中，仔细选择最好的测量频响通常会得到更好的系统全局极点。如果你有关于模态分析的任何其他问题，尽管问我好了。