Does it make any sense to use the actual operating loads

as the excitation force for a modal test

if the force is a random signal ?

利用实际工作载荷作为模态试验的激振力，有意义吗？

如果这个力是随机信号的话？

 

The answer to this question is not an easy one. There are many aspects related to this question that we need to discuss in order to fully understand the answer.

这个问题不容易回答。它牵涉到的方面有很多，为了充分理解其解答，我们需要进行讨论。

 

The use of a random operating excitation may seem to be an excellent idea, but the bottom line is that the modal parameters that are extracted are not likely to be nearly as good as those obtained from a  modal test where the excitation is one of the more traditional excitation techniques. Let's discuss this to see where some of the pitfalls exist. In order to understand all of the implications, there have been some other modal questions that have been asked and answered that will help shed light on this question (SEM ET V23 No1, V23 No4, V23 No6 ).

利用随机工作激励似乎是一个很好的主意，但结果是，提取出来的模态参数不可能跟模态试验中得到的参数那样几乎一样好，其中模态试验利用更为传统意义的某种激励技术。我们讨论一下这个问题，来看一看容易犯的一些错误在哪里。为了理解全部真谛（所有的含义），之前另外一些已经问过并其已经作答的模态问题将有助于阐明这个问题(SEM ET V23 No1, V23 No4, V23 No6 )。

 

Let's recall that an experimental modal test is typically performed to extract the underlying modal parameters of the structure - that is, the frequency, damping and mode shapes. Accurate measured frequency response functions are needed in order to extract these parameters. Typically, we go to extreme lengths to excite the structure with very specialized excitations to minimize, and ultimately eliminate, leakage and other signal processing errors that can possibly result. Remember that any signal processing errors that do result, distort the measured frequency response and manifest themselves as less accurate modal parameters.

让我们回想一下，通常情况下进行试验模态测试来提取结构的固有的模态参数 — 即，频率、阻尼和模态振型。为了提取这些参数，需要测得精确的频响函数。通常，我们竭尽全力地激励结构，利用非常专门的激励技术来减少，或者尽大可能地消除可能存在的泄漏和其他信号处理误差。记住，任何存在的信号处理误差都会使测得的频响畸变，并且它们自身表现为不准确的模态参数。

 

As a general rule, random signals do not provide the best excitation for the development of accurate frequency response functions. Random excitation techniques are notorious for causing leakage in the measured spectra. Even with the use of windows, the measured frequency response functions are distorted when compared to other leakage-free measurement techniques (i.e., burst random, sine chirp, digital stepped sine). A comparison of a frequency response function from a random excitation and a burst random excitation is shown in Figure 1. It is very clear in the measurement that the burst random, leakage free measurement is far superior to the random measurement. (While not shown, the coherence is also far superior.)

一般说来，随机信号不能提供最优的激励来得到精确的频响函数。随机激励技术以在测得的频谱中引起泄漏而不受人待见。跟其他没有泄漏的测量技术（如猝发随机、正弦扫频、数字步进正弦）相比，即使加窗，所测得的频响函数也会失真。利用随机激励和猝发随机激励得到的频响函数之间的比较如图1所示。很清楚，在测量结果中没有泄漏的猝发随机的测量结果远远优于随机测量结果。（尽管没有显示，相干也是同样更优。）

 

To go one step further, the extracted modal parameters from the random excitation will also be distorted, and in many cases, there actually appears to be two peaks as seen in the measurement. This is a typical effect seen in frequency response functions measured using random excitation. Leakage is a serious concern and windows are necessary to minimize leakage. The whole purpose for the development of specialized functions for modal testing is to provide highly accurate frequency response functions which do not require the use of any windows and provide leakage free measurements for the accurate extraction of modal parameters.

更进一步讲，从随机激励中提取出来的模态参数同样会有畸变，并且在很多情况下，在测量结果中实际上看起来好像是有两个峰。这是利用随机激励进行测量的频响函数中可以看到的典型影响。泄漏是一个需要认真关注的问题，需要加窗来减少泄漏。开发用于模态试验的专门函数的全部意义所在就是为了得到高精度的频响函数，这样就不需要加任何窗函数，可以得到免受泄漏影响的测量结果，这样可以精确提取模态参数。

So what would ever posses anyone to perform a modal test using an operating random excitation.  Well, if the actual force was used to excite the structure, then the response will be similar to the actual response in service. This response will be an accurate depiction of the actual in-service deformations that will be seen in the structure. But then the response that is measured is more appropriate for use in an operating deflection analysis - but not an experimental modal survey!

那么是什么让人想到要用工作随机激励来进行模态试验？嗯，如果真要用实际激励来激振结构，那么响应将会与运行中的实际响应一样。这个响应将是实际运行变形的准确描述，这可以在结构中看出来。但另一方面，测量到的响应用于工作变形分析更为恰当 — 而不是试验模态研究！

 

Figure 2 shows a schematic of the response of a structure due to an arbitrary input excitation. There are several aspects of this figure that will give greater insight into the question at hand. The forcing function is broadband, but has a very distinct profile which is not flat, thereby exciting all of the modes with different excitation levels.

受到随机输入激励引起的结果响应的示意图如图2所示。这个图形上有多个方面的内容会有助于搞清楚我们手头的这个问题。激励函数是宽带的，但具有非常清楚的轮廓，轮廓并不平坦，于是按照不同的激振水平激起了所有阶模态。

 

First, and foremost, notice that the frequency response function is nothing more than a bandpass filter which amplifies and attenuates the input force excitation as a function of frequency. What would happen if the estimation of this frequency response was tainted or distorted by the digital signal processing procedure (i.e., digitization, quantization, leakage, windows, FRF method, etc.) ???  Well, of course, there would be an effect on the computed response! The goal of a modal test is to extract the accurate dynamic system characteristics.

首先最重要的一点是，注意到频响函数无非是一个带通滤波器，作为一个频域函数，对输入强迫激励进行放大和衰减。如果频响函数的估计受到数字信号处理过程（如，数字化、量化、泄漏、加窗、频响估计方法，等等）的损害或者扭曲，情况又会如何呢？？？嗯，当然，这会影响到计算得到的响应！模态试验的目的是要提取准确的系统动力学特性。

Second, the level of the force spectrum over the frequency band has a direct effect on the response of the system. Figure 3 very clearly shows that the response has significant variation over the frequency band. Since the ADC maximum setting is determined by the total spectrum, there will be a wide variation in the accuracy of the measured function. In fact, the lower response spectral components will have a much larger effect due to quantization errors associated with the analog to digital conversion process. This is particularly true when looking at the response of mode 1 and mode 3.  Notice that mode 1 shows very little response due to the extremely low input excitation; mode 1 response will be very small and may be affected by noise.

第二点，在频带范围内的激励频谱的水平对系统的响应有直接的影响。图3非常清楚地表明了在频带范围内响应具有明显的变化。因为ADC模数转换器的最大量程设置是由总体频谱决定的，在测得的函数的准确度上将会有很大的差异。实际上，响应谱分量的量级越小，与模数转换过程相关的量化误差的影响就越大，当观察1、3阶模态的响应时，这个情况就特别明显。注意到因为输入激励的量级极小所致，1阶模态表现出非常微弱的响应；1阶模态的响应非常小，可能会受到噪声的影响。

 

Third, remember that if a random signal is used, then a Hanning window must be applied otherwise the measured signals will contain significant leakage. In any event, the measured frequency response function will be affected by the window and leakage that does result. The measured function will not be of the best quality and the extracted modal parameters will suffer from these signal processing effects.

第三点，记住如果利用随机信号，那么必须施加汉宁窗，否则测量到的信号中将含有明显的泄漏。无论如何，测得的频响函数必将受到窗函数和泄漏的影响。测得的函数不是最好的，提取出来的模态参数将会受到这些信号处理的不良影响。

 

Fourth, the measured frequency response function will have errors associated with poor excitation signal strength over some frequency regions, leakage and window errors due to the random nature of the signal type, frequency response function errors as seen in the coherence associated with leakage especially at the resonant peaks, and modal parameter estimation errors due to poor estimated frequency response functions used for the modal parameter estimation process.

第四点，在某些频率区间内激励信号的能量不足、信号类型的随机特性导致的泄漏和窗函数误差，与之相关，测得的频响函数会有误差。在相干中可以看到与泄漏相关的频响函数误差，在共振峰附近尤甚，模态参数估计值会有误差，这是因为用于模态参数估计过程的频响函数估计值比较差。

 

So in the big picture of the development of a modal model from measured functions, the best excitation techniques will provide the best representation of the modal parameters of the structure. This will not necessarily occur using an operating random spectrum. Once a modal model is developed, then the actual response of the structure can be determined, if necessary, using the measured frequency response function as pictorially shown in Figure 2. But in order for accurate response to be computed, an accurate modal model from accurate frequency response functions is of paramount importance.

那么，在从测得的函数中求取模态模型的重点事项中，激励技术越好，得到的结构模态参数也就越好。利用工作随机频谱，就不一定会发生这种情况了。一旦得到模态模型，如有必要，利用测得的频响函数就可以确定结构的实际响应，如图2所示。但是为了求得准确的响应，最重要的是要从准确的频响函数中得到准确的模态模型。

 

Now, there is tremendous merit in performing an operating test using operating excitations. However, this is not necessarily the best way to estimate frequency response functions for use in the development of a modal model. Now I hope you understand the problems associated with running an experimental modal test with an operating excitation. If you have any other questions about modal analysis, just ask me.

嗯，利用工作条件下的激励进行工作条件下的测试有着极大的价值。但未必是用于求取模态模型的估计频响函数的最优方法。我希望现在你理解了用工作激励进行试验模态测试相关的这个问题。如果你有关于模态分析的任何其他问题，尽管问我好了。