High resolution imaging of pressurized water supply lines using high frequency acoustic waves

A method for detecting one or more defects on a surface of an interior region of a pipeline, the method comprising:

• installing a plurality of transducers in the interior region, each of the transducers being capable of converting an electrical signal into an acoustic signal and vice versa;
• acoustically imaging the surface of the interior region to thereby generate an imaging function of the interior region, the imaging function being an estimated geometrical model of the interior region;
• and
• comparing the imaging function with an original geometrical model of the interior region to thereby identify the one or more defects on the surface of the interior region;
• wherein the acoustic imaging of the surface of the interior region comprises:
• sensing, by each transducer in the plurality of transducers, a transient response of the interior region due to an excitation caused by an acoustic source signal generated by a transducer selected from the plurality of transducers;
• repeating the sensing of the transient response until all transducers in the plurality of transducers are selected to excite the interior region, whereby respective transient responses generated by the plurality of transducers form multi-input multi-output (MIMO) imaging data resulted from sensing the interior region;
• and
• computing the imaging function according to the MIMO imaging data;
• wherein the MIMO imaging data are expressed as a three-dimensional (3D) transfer matrix of the interior region, wherein the 3D transfer matrix is given by [Pn/,i\j]i=j, . . . , Mij=1, . . . , N where Pn,i\j is an acoustic pressure sensed by an ith transducer at an nth sampling instant due to the excitation generated by a ith transducer, M is a number of transducers in the plurality of transducers, and N is a number of samples in the transient response;
• and
• wherein the computing of the imaging function according to the MIMO imaging data comprises the steps of:
• (a) applying a moving Hanning window (MHW) in time to the 3D transfer matrix to yield a plurality of 3D local matrices;
• (b) applying a Fourier transform to an individual 3D local matrix to yield a frequency-transformed 3D local matrix;
• (c) evaluating the frequency-transformed 3D local matrix at a selected frequency determined according to the acoustic source signal to yield a frequency-domain two-dimensional (2D) local matrix;
• (d) applying a singular value decomposition (SVD) to the frequency-domain 2D local matrix to yield a plurality of left singular vectors, a plurality of right singular vectors, and a plurality of singular values;
• (e) selecting, from the plurality of left singular vectors, a selected plurality of left singular vectors belonging to a noise subspace identified from the plurality of singular values;
• (f) forming a local imaging function associated with the frequency-domain 2D local matrix according to a green function vector and the selected plurality of left singular vectors, wherein the green function vector is a theoretical singular vector from a signal subspace associated with an arbitrary scatterer, the theoretical singular vector being derived according to at least the original geometrical model of the interior region;
• (g) repeating the steps (d)-(f) for respective frequency-domain 2D local matrices generated for the plurality of 3D local matrices, whereby respective local imaging functions are obtained;
• and
• (h) computing the imaging function as a sum of the respective local imaging functions.