Data Acquisition Protocol for Determining Embedded Sensitivity Functions

Test fixtures should be designed to replicate realistic boundary conditions so that results will be applicable under operating conditions. The selection of the number of impact points used for testing is a trade-off between having sufficient spatial resolution and the testing time. Select the hammer based on the size of the test specimen and the frequency range of interest. In general, the smaller the hammer, the broader the frequency range excited. However, smaller hammers typically produce lower amplitude forces. Impact hammers are instrumented with a force gauge to measure the time history of the impact. The type of hammer tip also affects the frequency range of excitation. The harder the tip, the broader the frequency band of excitation. Super glue is chosen over wax, for example, to minimize the attenuation of the response by the mounting material.

In the data acquisition software, enable double hit detection in order to automatically indicate when a double impact has occurred. Single impacts are desired because they produce a broader, more repeatable force spectrum. When the amplitude of the force rises above the selected trigger level, the data acquisition is started. Time data is acquired by the data acquisition software. During acquisition data should be monitored to ensure data quality. Channel clipping, which occurs when the response measured by the sensor exceeds the allowable voltage range, should be avoided. Coherence is an excellent metric to use to judge data quality. In general, coherence should be near one for all frequencies within the frequency range excited by the impact. Dips in coherence are expected near anti-resonance frequencies of the test specimen because the signal to noise ratio is low and the noise is uncorrelated with the input. Once quality data is acquired, the time histories are converted into the frequency domain via the Fast Fourier Transform (FFT), and the average FRF is estimated using the H1 estimator ¹⁰.

To determine the ESF from the FRFs measured during testing, equation 1 can be used in one of two ways. First, the direct approach can be used, which requires measurements for Hjm, Hjn, Hkm, and Hkn. These FRFs would be determined by placing a sensor at location k and roving a sensor to each potential sensor location j. Impacts would be applied at the two locations that span the damage location. To make data collection more efficient, the principal of reciprocity can be used to reverse the input and measurement locations. Using this approach, Hmj, Hnj, Hmk, and Hnk are determined. Now, instead of having to move the sensors for each different measurement, the sensors stay stationary and the impact location is roved. Once the ESFs are calculated for each location, their amplitudes are compared to determine which location j is most sensitive to damage between locations m and n. Note that a single damage location is assumed in this work.

The results of the ESF analysis can now be used in an FRF-based structural health monitoring scheme. In ¹¹, it was demonstrated that the sensor locations identified by ESFs as being most sensitive to damage were more effective in identifying the presence of damage to a wind turbine blade.

Other methods to predict locations at which a structure's FRF will be sensitive to damage typically rely on analytical modeling of the structure^{3, 6, 12}. FRF data is simulated using different combinations of input and measurement locations. However, the results of these methods rely on the development of a reliable and accurate model, which requires detailed knowledge of material properties and the geometry of the structure. Because ESFs can be calculated from experimentally measured data on the healthy structure, the identification of material properties is not required and the geometry of the structure does not need to be determined.

One potential limitation of the technique is that it requires a priori knowledge of where the damage is going to occur. In many applications, this requirement is not limiting because due to stress analyses and prior experience, the damage location can be foreseen. In applications where the damage location is unknown, multiple data sets can be acquired, each time assuming a different damage location. Within the data acquisition protocol, many best practices were identified that not only apply to data acquisition for ESFs, but also apply generally to modal impact testing. Being able to judge the quality of the data being acquired improves with experience, but knowing fundamentals including determining force roll-off and evaluating coherence will enable even those new to modal impact testing to acquire high-quality data.