3 Real-Time State Detection in Highly Dynamic Systems 29 new to the SHM community [13] and has also been defined as damage before [14]. What is different is the idea that changes in boundary conditions, or any other changes detected in the system, are not necessarily indications of structural damage, but can provide critical information about the system. The stepped sine wave measurement method utilized by impedance analyzers is simply not capable of measuring fast enough to be of use for real-time state detection. A faster excitation signal is necessary, therefore a chirp signal will be utilized. A chirp signal allows for the excitation of a very large frequency band in a relatively short amount of time which is exactly what is needed in order to make fast measurements. Chirp signals have been used successfully in SHM measurements and have been shown to give results similar to impedance analyzers [4, 5, 15]. In place of the impedance analyzer a field-programmable gate array (FPGA) will be used for both data acquisition and signal processing. An FPGA is a reprogrammable integrated circuit that offers two advantages over conventional data acquisition methods. First, an FPGA allows for high sample rates, in the realm of 100 MS/s or higher, which are necessary for microsecond data acquisition. Second, FPGAs are inherently well suited for use in real-time computing systems. Here it becomes necessary to define what “real-time” means in terms of a computer systems because it has a separate and distinct meaning compared to how the term real-time was used previously in this paper. When discussing computer systems, real-time refers to both hardware and software that runs with very precise timing and high reliability. Two additional terms are used when discussing real-time computer systems. The first is jitter, which is a measure in the amount of variation in completion time that occurs through multiple iterations of a process. The second is determinism, which refers to the guarantee that a process will be completed within a certain time frame. Standard personal computers use x86 processor architectures and are paired with conventional operating systems (OS) such as Windows and because of this have a relatively high amount of jitter and are not deterministic. This can be minimized by using a real-time OS, which helps reduce jitter and increase determinism by not allowing system interrupts such as user input, not running background programs, etc. Furthermore, the use of FPGAs and other integrated circuits allow for significantly lower jitter and higher determinism. Real-time computer systems help to ensure consistent and accurate data, which make them ideal for use in a real-time data acquisition and processing system. 3.4 Preliminary Timing Study The following section is a “back-of-the-napkin” style analysis which gives an estimated completion time for the entire process of real-time state detection using impedance analysis. The process begins with the generation of the chirp excitation signal at the output pins of the FPGA DAQ card via digital-to-analog convertors (DAC). Then the signal travels across the PZT and is changed due to the PZT impedance. This response signal is then sampled at the input pins of the DAQ with analog-to-digital convertors (ADCs) simultaneously to the signal generation. The generation of the chirp signal [5] is given by xŒn DA sin 2 FS n f2 f1 2N nCf1 (3.1) where Nis the number of samples, n D0;1; : : : ; N 1, f1 is the initial frequency, f2 is the final frequency, FS is the sampling rate, andAis the amplitude. The next step is the processing of the acquired data in order to calculate the electrical impedance of the PZT. The first, and by far most time consuming, stage is the calculation of the fast Fourier transform (FFT). The FFT is then used to calculate the frequency response function (FRF) which can then be used to solve for the impedance of the PZT [4, 5]. This step is unique to the method of impedance analysis that utilizes data acquisition devices because the impedance analyzers normally used by the SHM community step through and record the impedance at each frequency one at a time and therefore don’t require the use of an FFT. In order to improve the statistical certainty of the measurement averages can be taken, which would result in repeating the previous two steps. Once the impedance of the measurement is calculated to the desired statistical certainty the root-mean-squared deviation is calculated by comparing the measurement to a known stored state and if this value exceeds a certain predefined value it is concluded that a change in state has occurred. The time calculations are made by using just three input variables. The desired spectral resolution df which is given by Fs/N, the highest frequency to be generated in the excitation signal f2, and the number of averages desired. These input values dictate the essential characteristics of the measurement system, Fs and N, which determine the timing of the various processes. Fs is calculated by using the relationship Fs D4f2 which was chosen because it limits Fs from becoming unnecessarily high, which can have a negative impact on timing, while ensuring that the sampling frequency is well above the Nyquist frequency. Nis given by manipulating the previously mentioned relationship for the desired spectral resolution giving N D Fs=df . An important note is that most FFT architectures require the number of samples taken to be a power of 2 [16] because they are based off of the radix-2 implementation of the Cooley-Tuckey FFT algorithm [17]. This works by
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