When impact testing, can the use of the exponential window cause any problems?

Let's discuss this

锤击试验时，加指数窗会带来什么问题吗？

那我们就讨论一下这个问题吧。

The exponential window can cause some problems if not used properly. If an excessive amount of damping is needed to minimize the effects of leakage, then you run the risk of missing closely spaced modes. There are a few examples to show the relative to the use of the window and what can happen if care is not exercised in using the exponential window.

如果指数窗使用不当，会带来某些问题。如果需要过大的阻尼来减少泄漏的影响，那么你要承担丢掉密集模态的风险。用多个例子来说明关于窗函数的使用以及如果没有合理使用指数窗，会发生什么情况。

 

First of all, let me clearly state that in many impact testing situations the use of an exponential window is necessary. However, before any window is applied, it is advisable to try alternate approaches to minimize the leakage in the measurement. Increasing the number of spectral lines or halving the bandwidth are two things that should always be investigated prior to using a damping window. Both of these items will essentially increase the total time for the collected data. This can often help by allowing the response of the system to naturally decay before the end of the sample period. If this can be accomplished, then the use of the exponential window may not be necessary.

首先，我要清晰地表明我的观点：在很多冲击试验情况下，有必要使用指数窗。但是，在施加任何窗函数之前，还是要尝试其他办法来减少测量结果中的泄漏为好。在施加阻尼窗之前，增加谱线条数或者带宽减半是两件总要研究的事情。这两种情况实质上将增加采集数据的总时间。这通常有助于允许系统的响应在采样周期结束之前自然衰减到零。如果这样，就没有必要用指数窗了。

However, if the response still does not decay by the end of the sample period, then an exponential window may be necessary. The use of the window should not be employed until these first two items (mentioned above) are checked as possible ways to minimize the leakage problem. The arbitrary use of the exponential window without first looking at the time response is not recommended as the first step in the measurement process. Let's look at this through the use of a simple example.

但是，如果在采样周期结束的时候，响应仍然没有衰减到零，那么指数窗是有必要的。采取前面两项措施（上面提到过的）作为可能的方法来减少泄漏问题以后才可以施加指数窗。不先观察时域响应就随意使用指数窗作为测量过程的第一个步骤是不推荐的。让我们通过简单例子来考察这个问题。

 

A very simple, lightly damped structure was subjected to an impact test. The signal processing parameters were selected for a 400 Hz bandwidth which resulted in a 1.0 second time window. Since the structure was expected to have a response that would not decay by the end of the sample interval, an exponential window was applied such that the windowed response would decay to a reasonably small value by the end of the sample interval thereby minimizing the effects of leakage. The impact excitation, windowed exponential response and the FRF are shown in Figure 1. On the surface, this measurement looks acceptable. [Note that the input spectrum (not shown) was reasonably flat over the entire frequency range thereby allowing sufficient excitation of the structure. Also note that the coherence (not shown) was also considered very acceptable.]

对一个非常简单的，小阻尼结构进行锤击测试。400Hz带宽选作信号处理参数，最后得到1.0秒的时间窗。由于这个结构预计在采样时段结束的时候还有响应没有衰减到零，施加指数窗，这样加窗后的响应在采样时段结束的时候应该衰减到一个非常小的数值，这样就减少了泄漏的影响。锤击激励、加窗后的指数衰减响应以及频响函数如图1所示。这个测量结果表面上看起来可以接受。[注意输入谱（没有显示出来）在整个频率范围内相当平坦，这样可以充分激励起这个结构。另外也注意到相干（没有显示出来）也认为是非常可以接受的。]

 

From all aspects, this measurement appears very acceptable. But we need to look at this measurement in more depth. First, let's consider the same measurement but add significantly more damping to the response signal. Figure 2 shows the same data but with a significantly larger value of damping used for the exponential window. The FRF that results from the impact measurement of this signal clearly has significantly more damping than that shown in the FRF of Figure 1. The peaks of the FRF show this effect; notice that the peaks are much wider due to the excessive use of the damping window.

从各方面来看，这个测量结果看上去很让人接受。但我们需要从更深的层次上来观察这个测量结果。首先，我们考虑相同的测量结果但是添加更大的阻尼到响应信号中去。图2显示了相同的数据，但是指数窗的阻尼值更大。与图1中所示的频响相比，这个信号的锤击测量结果得到的频响很明显地具有更大的阻尼。频响的峰值表明了这种影响；注意因为阻尼窗的过度使用，峰更宽了。

Now let's look yet a little deeper into this measurement and try some alternate signal processing parameters. In order to minimize the use of the damping window, either the bandwidth can be shortened or the number of spectral/time lines of resolution can be increased. Both of these changes result in an increase in the total time necessary to collect the sample of data. If the total time is increased, then there is less need for a significant amount of damping window to be applied to the collected time data.

现在，我们更深入地探究一下这个测量结果，并且尝试一些可能的信号处理参数。为了不用阻尼窗，要么减少带宽要么增加谱线条数。这二者的改变最终都增加了采集样本数据所需的总时间。如果总时间增加了，那么就不那么需要对采集的时域数据施加大的阻尼窗了。

 

Figure 3 shows a doubling of the number of spectral/time lines of resolution. The time sample was increased from 1.0 second to 2.0 seconds. While an exponential window was still necessary to minimize leakage, the overall damping effect that was added to the measurement is far less than that used for the measurements shown in Figure 1 and Figure 2 above.

图3显示了谱线/时间条数增加一倍的情况。时域样本点从1.0秒增加到2.0秒。尽管仍然需要一个指数窗来减少泄漏，但是加到测量结果上的总体阻尼影响远小于前面图1和图2中所示的测量结果。

The most important item to notice in Figure 3 is that what appeared to be one mode at the first peak in the FRF actually turns out to be two very closely spaced modes of the structure. The use of the damping window in Figure 1 and 2 resulted in an FRF that appeared to have only one mode at the first peak in the FRF. The use of the damping window caused these two distinct modes to appear as only one peak in the FRF.

图3中最需要注意的一点是频响函数中在第一个峰附近看上去像是一阶模态实际上是结构的两阶紧邻模态。图1和图2中加指数窗的结果是在频响函数第一个峰附近看上去像是只有一阶模态。阻尼窗的使用导致了完全不同的两阶模态在频响函数中看起来像是只有一个峰。

 

While the damping window was necessary to minimize the leakage, the window distorted the actual FRF in Figure 1 and 2 such that it was difficult to observe that two peaks existed at this frequency.  The use of the exponential window, while necessary for digital signal processing considerations, can cause some significant difficulties when evaluating structures with light damping and closely spaced modes as seem in this example.

尽管需要阻尼窗来减少泄漏，但是窗函数使得图1和图2 中的实际频响函数发生了失真，以至于难以观察在这个频率附近存在的两个峰。尽管从信号处理的考虑来看，是需要使用指数窗的，但是当评价如本例所示的小阻尼结构以及密集模态的时候，它也带来一些很大的麻烦。

 

Now, I hope you can see some of the effects of the exponential window in this example. While an exponential window may be necessary to minimize the effects of leakage, the use of the window may also hide or distort the modes in the measurement. It is extremely important to be very careful when using the exponential window when performing an impact test. If you have any other questions about modal analysis, just ask me.

好了，我希望你能理解本例中指数窗的某些影响。尽管或许需要指数窗来减少泄漏的影响，但是窗函数的使用也可能导致测量结果中的模态丢失或者失真。进行锤击试验使用窗函数时，非常小心是极其重要的。如果你有关于模态分析的任何其他问题，尽管问我好了。