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The purpose of this paper is to employ analytical and numerical techniques to generate modal displacement data of damaged beams containing very small crack-like surface flaws or slots and to use the data in the development of damage detection methodology. The detection method involves the use of double differentiation of the modal data for identification of the flaw location and magnitude.

The modal displacements of damaged beams are simulated analytically using the Bernoulli-Euler theory and numerically using the finite element method. The principle used in the analytical approach is based on changes in the transverse displacement due to the localized reduction of the flexural rigidity of the beam. Curvature analysis is employed to identify and locate the structural flaws from the modal data. The curvature mode shapes are calculated using a central difference approximation. The effects of random noise on the detectability of the structural flaws are also computed.

The analytical approach is much more robust in simulating modal displacement data for beams with crack-like surface flaws or slots than the finite element analysis (FEA) approach especially for crack-like surface flaws or slots of very small depths. The structural flaws are detectable in the presence of random noise of up to 5 per cent.

Simulating the effects of small crack-like surface flaws is important because it is essential to develop techniques to detect cracks at an early stage of their development. The FEA approach can only simulate the effects of crack-like surface flaws or slots with depth ratio greater than 10 per cent. On the other hand, the analytical approach using the Bernoulli-Euler theory can simulate the effects of crack-like surface flaws or slots with depth ratio as small as 2 per cent.

The purpose of this paper is to employ the acoustic wave propagation method for leakage detection in pipes. The first objective is to use acoustic finite element analysis (AFEA) method to simulate acoustic wave propagation and acoustic wave reflectometry in an intact pipe and in pipes with leaks of various sizes. This is followed by the second objective which is to validate the effectiveness and the practicability of the acoustic wave method via experimental testing. The third objective involves the decomposition and de-noising of the measured acoustic waves using stationary wavelet transform (SWT). It is shown that this approach, which is used for the first time on leakage detection in pipes, can be used to identify, locate and estimate the size of a leakage defect in a pipe.

The research work was designed inline with best practices and acceptable standards. The research methodology focusses on five basic areas: literature review; experimental measurements; simulations; data analysis and writing-up of the study with clear-cut communication of the findings. The approach used was acoustic wave propagation-based method in conjunction with SWT for leakage detection in fluid-filled pipe.

First, the simulation of acoustic wave propagation and acoustic wave reflectometry in fluid-filled pipes with and without leakage have great potential in leakage detection in pipeline systems and can detect very small leaks of 1 mm diameter. Second, the measured noise-contaminated acoustic wave propagation in a fluid-filled pipe can be successfully de-noised using the SWT method in order to clearly identify and locate leakage as little as 5 mm diameter in a pipe. Third, AFEA of a fluid-filled pipe can be achieved with the simulation of only the fluid content of the pipe and without the inclusion of the pipe in the model. This eliminates contact interaction of the solid pipe walls and the fluid, and as a consequence reduces computational time and resources. Fourth, the relationship of the ratio of the leakage diameter to the ratio of the first and second secondary wave amplitudes caused by the leakage can be represented by a second-order polynomial function. Fifth, the identification of leakage in a pipe is intuitive from mere comparison of the acoustic waveforms of an intact pipe with that of a pipe with a leakage.

The research work is a novelty and was developed from the scratch. The AFEA of acoustic wave propagation and acoustic wave reflectometry in a static fluid-filled pipe, and the SWT method have been used for the first time to detect, locate and estimate the size of a leakage in a fluid-filled pipe.