This paper portrays work for the development of a Lamb wave scanning method for the detection of defects in thin plates. The approach requires the generation of an ultrasonic Ao and So-Mode Lamb Wave using an incident transmitter excited with a tone burst centered at a near non-dispersive frequency. With a fixed relative separation both transmitter and receiving transducer, remotely scan a specific line section of the plate. The arrival time information coming from incident and reflected waves contain information associated with the location of reflection surfaces or potential flaws. The Hilbert-Huang transform is applied to the intrinsic mode functions which permit the computation of the signal energy as a function of time, proportional to the square of the amplitude of the analytical signal. The arrival times and amplitudes of the notch-reflected energy are used to calculate by means of two geometric methods, the coordinates of the source of the reflections. The resulting coordinates outline the extent and relative direction of notches in two different scenarios. One is having notches in a 0 to 22.5 degree orientation in respect to the far edge of the plate and two with notches of various sizes at a single rivet hole. Results of experiments conducted on 1.6mm-thick Aluminum square plates, with an arrangement of notches as described compare favorably with the actual notches.
This paper describes a Lamb-wave scanning method for the detection of notches simulating cracks at rivet holes in thin plates. The approach requires the generation of an ultrasonic So-Mode Lamb wave using an incident transmitter excited with a tone burst centered at a near non-dispersive frequency. Area scans are performed on a plate with a hole with a notch to generate times series information which is used to create animations illustrating the wave propagation characteristics. The time series are subject to a sifting process to obtain intrinsic mode functions which contain narrow frequency banded information of the signals. The Hilbert-Huang transform is applied to the intrinsic mode functions which permit the computation of the signal energy as a function of time, proportional to the square of the amplitude of the analytical signal. Animations of the propagation of the Lamb-wave energy illustrate that a potential scanning approach is to acquire time series along a line between the transmitter and the hole, capturing wave scattering from the hole and reflections from the notches. The times of flight and amplitudes of the notch-reflected energy are used to calculate coordinates of the source of the reflections by a geometric approach. The identified coordinates of the reflections outline the extent of the notch at the rivet hole. Results of experiments conducted on thin square plates with a single hole with notches of various sizes compare favorably with the actual notches.
Several techniques are known for non-destructive testing of aerospace structures, such as pulse echo, Eddy current, magnetic resonance, etc. Each of these techniques detects some faults but misses others, so it is desirable to combine (fuse) the results of these techniques. Several methods of data fusion are known. To improve the quality of fault detection, we modified the straightforward statistical method as follows: (1) we computed mean and variance iteratively: detected faults are excluded form the computation on the next iteration; (2) we treated the plate's edge and the inside separately; (3) we dismissed measurements in which only one technique detects a fault as possibly erroneous. The resulting method indeed leads to a much better
fault detection.
The inverse problem is usually difficult because the signal that we want to reconstruct is weak. Since it is weak, we can usually neglect quadratic and higher order terms, and consider the problem to be linear. Since the problem is linear, methods of solving this problem are also, mainly, linear. In most real-life problems, this linear description works pretty well. However, at some point, when we start looking for a better accuracy, we must take into consideration non-linear terms. This may be a minor improvement for normal image processing, but these non- linear terms may lead to a major improvement and a great enhancement if we are interested in outliers such as faults in non-destructive evaluation or bumps in mammography. Non- linear terms give a great relative push to large outliers, and thus, in these non-linear terms, the effect of irregularities dominate. The presence of the non-linear terms can serve, therefore, as a good indication of the presence of irregularities.
In many real-life situations, it is very difficult or even impossible to directly measure the quantity y in which we are interested: e.g., we cannot directly measure a distance to a distant galaxy or the amount of oil in a given well. Since we cannot measure such quantities directly, we can measure them indirectly: by first measuring some relating quantities x1,...,xn, and then by using the known relation between xi and y to reconstruct the value of the desired quantity y. In practice, it is often very important to estimate the error of the resulting indirect measurement. In this paper, we show that in a natural statistical setting, the problem of estimating the error of indirect measurement can be formulated as a simplified version of a tomography problem. In this paper, we use the ideas of invariance to find the optimal algorithm for solving this simplified tomography problem, and thus, for solving the statistical problem or error estimation for indirect measurements.
Satellite imaging is nowadays one of the main sources of geophysical and environmental information. It is, therefore, extremely important to be able to solve the corresponding inverse problem,: reconstruct the actual geophysics- or environmental-related image from the observed noisy data. Traditional image reconstruction techniques have been developed for the case when we have a single observed image. This case corresponds to a single satellite photo. Existing satellites take photos in several wavelengths. To press this multiple-spectral information, we can use known reasonable multi-image modifications of the existing single-image reconstructing techniques. These modifications, basically, handle each image separately, and try to merge the resulting information. Currently, a new generation of image satellites is being launched, that will enable us to collect visual images for about 500 different wavelengths. This two order of magnitude increase in data amount should lead to a similar increase in the processing time, but surprisingly, it does not. An analysis and explanation of this paradoxical simplicity is given in the paper.
Most practical applications of statistical methods are based on the implicit assumption that if an event has a very small probability, then it cannot occur. For example, the probability that a kettle placed on a cold stove would start boiling by itself is not 0, it is positive, but it is so small, that physicists conclude that such an event is simply impossible. This assumption is difficult to formalize in traditional probability theory, because this theory only describes measures on sets and does not allow us to divide functions into 'random' and non-random ones. This distinction was made possible by the idea of algorithmic randomness, introduce by Kolmogorov and his student Martin- Loef in the 1960s. We show that this idea can also be used for inverse problems. In particular, we prove that for every probability measure, the corresponding set of random functions is compact, and, therefore, the corresponding restricted inverse problem is well-defined. The resulting techniques turns out to be interestingly related with the qualitative esthetic measure introduced by G. Birkhoff as order/complexity.
Optimum binary phase codes of length L are characterized by an autocorrelation function R((tau) ) with uniform sidelobes of level 1/L with respect to the main lobe. These optimum binary codes are called Barker codes. Binary phase codes that exhibit minimum peak sidelobes above 1/L are called suboptimum. A genetic algorithm is implemented to conduct the search for optimum and suboptimum binary codes of a given length L. In this approach, several different fitness functions are considered. These fitness functions are based on sidelobe level (SLL) and generalized entropy measures. To verify that these are reasonable fitness functions, they are first applied to sequence lengths for which optimum codes are known to exist. It is shown that if L is such that a Barker code exists, and S is a generalized entropy measure, then the Barker codes are the only ones that give the minimum value for S. It is also shown that the proposed binary phase code search is efficient for large values of L.
Motion compensation of range-Doppler target signatures results in focused target imagery. Recently, an iterative approach based on a logarithmic entropy measure has been proposed for the motion compensation of signatures collected in the frequency domain. The effectiveness of this approach can be significantly improved by using an entropy-like function which is maximally resistant to noise and consistent with statistical boundaries. For purposes of analysis, the entropy-like function is written in terms of an information gain function (Delta) I. Several expressions for (Delta) I are tested to verify the accuracy of radial-motion parameter estimation. The effectiveness of these expressions is determined by the number of iterations required to find the minimum entropy measure, within an acceptable tolerance level for a given signal-to-noise ratio. Results show that the exponential information gain (Delta) I equals exp(1-I) yields an optimally convex entropy measure surface over a prescribed motion- parameter solution space. The surface minimum in this solution space has coordinates which are interpreted as the optimum motion-parameter estimates that can be obtained for the purpose of image focusing.
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