Damage Dosimeter Third Octave and Time History Rms Values

The Air Force sponsored flight tests using damage dosimeters, fabricated by The Boeing Company, to measure temperature and structural dynamic strains on B-52, F-15 and C-130 aircraft. The dosimeter measurements help diagnose difficultto-analyze structural conditions, such as acoustics and high cycle fatigue, and support the durability patch design process to repair secondary structure cracks. The dosimeter is a rugged, small, lightweight data acquisition unit that runs autonomously off of battery power. It measures 3 channels of strain at a rate up to 15 kilo-samples per second and 1 channel of temperature at a rate of 1.3 samples per second. The dosimeter acquires data above a programmer defined root mean square (rms) strain threshold. It is currently programmed to store 42 time history records (0.3 seconds each) and compute and store 29,544 third octave spectra (18 bands each) in its 4megabyte memory. LabVIEWTM virtual instruments (VIs) provide a quick look at the time history and third octave data and stores mean, rms and standard deviation values into a spreadsheet. This paper compares rms values computed from third octave data with rms values from time history data. 1. Background and Theory Aircraft damage resulting from a high cycle fatigue (HCF) environment of greater than 10 cycles is often referred to as nuisance cracks. Typical cracking of secondary aircraft structure is shown in figure 1. This damage results in costly inspection and repair. Design of a durability repair patch requires information characterizing temperature, resonant response frequency and strain levels. The durability patch and damage dosimeter program is an Air Force effort to resolve these problems by measuring the operating environment with a compact, stand-alone, electronics called a damage dosimeter and then applying a specifically-designed damped bonded repair patch. A composite bonded patch used by Roach (1998) is shown in figure 2. Hardware and software details for the damage dosimeter can be found in Ikegami, Rogers, Haugse and Trego (2001) and Haugse, Johnson, Smith, Rogers and Ryan (1999). A dosimeter photo and block diagram is shown in figures 3 and 4 respectfully. The dosimeter implements the Anderson Current Loop (ACL) signal conditioning technique described by Anderson (1995). Two types of data records are stored in the non-volatile memory of a dosimeter. A Strain Time History (TH) record consists of 2048 points of strain data sampled at 7600 samples per second for each of 3 channels. If the root mean square (rms) value of the data is above a predefined threshold, the dosimeter computes a Fast Fourier Transform (FFT) of each of the three strain time histories to generate a Power Spectral Density (PSD). The PSD is then integrated over 18 discrete third octave frequency bands to compress the strain data into contiguous third octave bands as described by Banaszak, Brown and Trego (2002). The 2048 points for the first 42 TH records above threshold are stored in the dosimeter’s non-volatile flash memory. The third octave data are stored until memory is filled in Standard Data Records (SDRs). Table I from Ikegami, Rogers, Haugse and Trego (2001) shows the format of SDR and TH records in the 4megabyte (MB) flash memory for the current dosimeter configuration. As noted by Bain and Englebert (1992), basic statistical property for any probability distribution of a random variable X (strain) is that E (X)= rms = μ + σ (1) where, E (X) = rms = Expectation (X), μ is the mean square of X and σ is the variance of X or σ is the standard deviation of X. For the dosimeter, let X = one of the 2048 sample points of a stored TH record, then E (X)=rms, μ and σ are easy to compute. For a time history, μ is the steady (DC) portion of the time history and σ is alternating (AC) portion of the time history and E (X) = rms is the total of the DC plus the AC portion of the time history. For the dosimeter, equation (1) is easily verified by using a spreadsheet for any dosimeter TH record by computing E (X), μ and σ. By design, the dosimeter’s DC static component of the strain is μ = 0 so that E (X)= RMS = 0 + σ = σ. One-third octave bands are stored in up to 29,455 SDR records. The starting point of the third octave band distribution is programmable. Practical limits on the starting point are between 15 Hz and 75 Hz. Below 15 Hz, the width of the third octave band is less than the frequency increment of 3.71 Hz (= Joint Statistical Meetings Section on Physical & Engineering Sciences (SPES)